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ORIGINAL PAPER
Hypericin and pseudohypericin concentrations of a valuable
medicinal plant Hypericum perforatum L. are enhanced
by arbuscular mycorrhizal fungi
Szymon Zubek &Sebastian Mielcarek &
Katarzyna Turnau
Received: 10 March 2011 /Accepted: 15 May 2011 /Published online: 28 May 2011
#The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract Hypericum perforatum L. (St. John ’s-wort,
Hypericaceae) is a valuable medicinal plant species cultivatedfor pharmaceutical purposes. Although the chemical compo-
sition and pharmacological activities of H. perforatum have
been well studied, no data are available concerning theinfluence of arbuscular mycorrhizal fungi (AMF) on this
important herb. A laboratory experiment was therefore
conducted in order to test three AMF inocula on H. perforatum
with a view to show whether AMF could influence plant
vitality (biomass and photosynthetic activity) and the produc-
tion of the most valuable secondary metabolites, namelyanthraquinone derivatives (hypericin and pseudohypericin) as
well as the prenylated phloroglucinol —hyperforin. The
following treatments were prepared: (1) control —sterile soil
without AMF inoculation, (2) Rhizophagus intraradices (syn.
Glomus intraradices ), (3) Funneliformis mosseae (syn.
Glomus mosseae ), and (4) an AMF Mix which contained:
Funneliformis constrictum (syn. Glomus constrictum ),Fun-
neliformis geosporum (syn. Glomus geosporum ),F. mos seae ,
and R. intraradices . The application of R. intraradicesinoculum resulted in the highest mycorrhizal colonization,
whereas the lowest values of mycorrhizal parameters weredetected in the AMF Mix. There were no statistically
significant differences in H. perforatum shoot mass in any
of the treatments. However, we found AMF species specific-
ity in the stimulation of H. perforatum photosynthetic activity
and the production of secondary metabolites. Inoculation with
the AMF Mix resulted in higher photosynthetic performanceindex (PI
total) values in comparison to all the other treatments.
The plants inoculated with R. intraradices and the AMF Mix
were characterized by a higher concentration of hypericin andpseudohypericin in the shoots. However, no differences in the
content of these metabolites were detected after the applica-
tion of F. m o s s e a e . In the case of hyperforin, no significant
differences were found between the control plants and those
inoculated with any of the AMF applied. The enhanced
content of anthraquinone derivatives and, at the same time,better plant vitality suggest that the improved production of
these metabolites was a result of the positive effect of the
applied AMF strains on H. perforatum . This could be due to
improved mineral nutrition or to AMF-induced changes in the
phytohormonal balance. Our results are promising from the
biotechnological point of view, i.e. the future inoculation ofH. perforatum with AMF in order to improve the quality of
medicinal plant raw material obtained from cultivation.
Keywords AMF species specificity .Anthraquinone
derivatives .Arbuscular mycorrhiza .Hyperforin .
Photosynthetic performance index .St. John ’s-wort
Introduction
Hypericum perforatum L. (St. John ’s-wort; Hypericaceae) is
a common perennial plant with a reputed medicinal value.S. Zubek ( *)
Laboratory of Mycology, Institute of Botany,Jagiellonian University,
Lubicz 46,
31-512 Kraków, Polande-mail: [email protected]
S. Mielcarek
Institute of Natural Fibres and Medicinal Plants,Wojska Polskiego 71b,
60-630 Pozna ń, Poland
K. Turnau
Institute of Environmental Sciences, Jagiellonian University,
Gronostajowa 7,
30-387 Kraków, PolandMycorrhiza (2012) 22:149 –156
DOI 10.1007/s00572-011-0391-1 | e34541027b4913acc7deed56804118a527f18f9e | page_0000 |
This species is included in the European Pharmacopoeia
(2008 ) and American Herbal Pharmacopoeia ( 1997 –2005 )
as well as many other pharmaceutical monographs (Barneset al. 2007 ). The aerial parts of H. perforatum contain
anthraquinone derivatives (h ypericin and pseudohyperi-
cin), flavonoids, prenylated phl oroglucinols (hyperforin),
tannins, phenolic acids, a nd volatile oil as major
constituents (Barnes et al. 2007 ).H. perforatum is held
to possess sedative and astringent properties. It has beenutilized for excitability, neur algia, anxiety and depression
and as a nerve tonic. St. John ’s-wort has a long history of
traditional use in topical prep arations for wound healing.
H. perforatum is presently utilized extensively in homeo-
pathic as well as in herbal products (Barnes et al. 2007 ;
van Wyk and Wink 2008 ). At one time, the plant was
collected only in the wild; however, due to the demand for
high plant material quality for use in the herbal industry, as
well as the need to standardize medicinal plant rawmaterials for pharmaceuti cal purposes, the species has
been cultivated by introducin g it into agriculture (van Wyk
and Wink 2008 ).
To meet the increasing demand for plants utilized in the
herbal industry, the emphasis in recent research has been on
the development of new techniques to improve the yield
and quality of plant material. One of the techniques for
enhancing the biomass and standard of medicinal plants isthe application of arbuscular mycorrhizal fungi (AMF)
during their cultivation. AMF have been found to stimulate
growth and improve pathogen, heavy metal, and salinityresistance, as well as to influence the level of secondary
metabolites in plants (reviewed in Smith and Read 2008 ).
Therefore, the practical use of these symbiotic soil micro-organisms is proposed for agricultural (Hamel 1996 ;
Feldmann et al. 2008 ; Gianinazzi et al. 2010 ), endangered
(Gemma et al. 2002 ; Zubek et al. 2008 ,2009 ; Bothe et al.
2010 ), and medicinal plant species (Kapoor et al. 2002a ,b,
2007 ; Copetta et al. 2006 ; Khaosaad et al. 2006 ; Toussaint
2007 ; Toussaint et al. 2007 ; Zubek and B łaszkowski 2009 ;
Ceccarelli et al. 2010 ; Zubek et al. 2010 ,2011 ).
Although the chemical composition and pharmaco-
logical activities of H. perforatum have been well studied
(Barnes et al. 2007 ;v a nW y ka n dW i n k 2008 ), and earlier
observations indicate that H. perforatum is colonized by
AMF (Wang and Qiu 2006 ;Z u b e ka n dB łaszkowski 2009 ),
no data are available on the influence of AMF on this
important medicinal plant species. The aim of our present
laboratory experiment was therefore to test three AMFinocula on H. perforatum grown in sterile soil in order to
show whether inoculation could influence plant vitality and
the production of the most valuable secondary metabolites,namely anthraquinone derivatives (hypericin and pseudo-
hypericin), as well as the prenylated phloroglucinol —
hyperforin. The effects of AMF inoculation on H.perforatum were evaluated by physiological and phyto-
chemical methods, namely by shoot mass, mycorrhizal
colonization assessment, a nd HPLC measurements of the
aforementioned secondary met abolite contents, as well as
by biophysical methods, known as the JIP-test. This test
translates the polyphasic chlorophyll afluorescence
transient OJIP exhibited by pl ants upon illumination into
the biophysical parameters of the photosynthetic machin-
ery, evaluating plants ’vitality. It has been successfully
utilized for the evaluation of the role of AMF inoculation
on plants, including those of medicinal importance
(Tsimilli-Michael et al. 2000 ; Pinior et al. 2005 ;B i r óe t
al.2006 ;S t r a s s e re ta l . 2007 ; Tsimilli-Michael and
Strasser 2008 ; Zubek et al. 2009 ; Jurkiewicz et al. 2010 ;
Zubek et al. 2010 ).
Materials and methods
AMF inocula
The inocula applied in the experiment were: (1) Rhizo-
phagus intraradices (syn. Glomus intraradices N.C.
Schenck & G.S. Smith) C. Walker & A. Schüßler(BEG140), (2) Funneliformis mosseae (syn. Glomus
mosseae T.H. Nicolson & Gerd.) C. Walker & A. Schüßler
(BEG12), and (3) an AMF Mix inoculum which contained
the following isolates: Funneliformis constrictum (syn.
Glomus constrictum Trappe) C. Walker & A. Schüßler
(262-5 C. Walker), Funneliformis geosporum (syn. Glo-
mus geosporum T.H. Nicolson & Gerd.) C. Walker & A.
Schüßler (UNIJ AG.PL.12-2), F. m o s s ea e (BEG12), and R.
intraradices
(BEG 140). The fungal species names are
after Schüßler and Walker ( 2010 ). The fungi were
multiplied on a sterile substratum of sand: expandedvolcanic clay, and rock phosphate —3:1, v/v;5 0gL
−1,
using Plantago lanceolata L. as the host plant. Dried
inocula containing P . lanceolata roots colonized to over
than 80% of the root length with no other fungal
endophytes present, extraradical mycelium, and spores
were used in the experiment.
Plant material
The seeds of H. perforatum L. var. Topaz were obtained
from the Institute of Natural Fibres and Medicinal Plants,
Pozna ń. They were germinated on wet filter paper in Petri
dishes at room temperature and daylight.
Experiment set-upOne-week-old H. perforatum seedlings were transferred
into 1-L pots. There were two pots for each treatment, with150 Mycorrhiza (2012) 22:149 –156 | e34541027b4913acc7deed56804118a527f18f9e | page_0001 |
seven individual plants per pot. Each pot contained 900 ml
of substratum, i.e. sterile commercially available soil
which was expanded using volcanic clay (5:1, v/v;
respectively). The soil was sterilized twice at 90°C for
1 h at 24-h intervals, and it was then sprayed with distilled
water for 2 weeks before using in the experiment. Thechemical properties of th es o i lw e r ep H5 . 9 ,N1 . 6 % ,C
39.9%, P 1,506.7 mg kg
−1, K 663.3 mg kg−1,a n dC a
2,436.7 mg kg−1. The following treatments were prepared:
(1) control —sterile soil without AMF inoculation, (2) R.
intraradices BEG140, (3) F. m o s s ea e BEG12, and (4) the
AMF Mix. Dried inocula were mixed with the soil, using30 g per pot. The pots were kept under greenhouse
conditions at 22±2°C and the following light regime:
100–110μmol PAR photons×m
−2×s−1. The pots were
kept in sealed Sigma-Aldrich Sunbags for the first month,
after which the bags were o pened. The cultures were
watered one time per week.
After 4 months of H. perforatum growth, chlorophyll
(Chl) afluorescence measurements were conducted, and
the plants were then harvested. The roots were stained tovisualize AMF mycelium for the mycorrhizal colonization
assessment, and the shoots were dried at room temperature
and used for the evaluation of plant biomass and secondary
metabolite contents. The shoots were weighed using a
Radwag WPA 60/c/1 electronic analytical balance with theprecision of 0.0001 g. The aforementioned analyses and
assessments were performed on each of the individual
plants —in total, 14 per treatment. Additional data were
obtained in the case of Chl afluorescence measurement
(see below).
Evaluation of the plants ’vitality
Measurement of Chl a fluorescence transient OJIPChl afluorescence transients OJIP were measured with a
HandyPEA-fluorimeter (Hansatech Instruments Ltd.,King’s Lynn Norfolk, PE30 4NE, UK). The transients were
induced by a red light (peak at 650 nm) of 3,000 μmol
photons m
−2s−1provided by an array of three light-
emitting diodes and recorded for 1 s with 12 bit resolution.
The data acquisition was conducted every 10 μs, in the
interval from 10 μs to 0.3 ms, every 0.1 ms (0.3 –3 ms),
every 1 ms (3 –30 ms), every 10 ms (30 –300 ms) and every
100 ms (300 ms to 1 s). The measurements were conducted
on fully expanded leaves, still attached to the plants, whichwere dark-adapted for 30 min prior to measuring. Measure-
ments were performed on one leaf of each individual plant.
Where it was possible, i.e. when the leaves were at thesame developmental stage, additional measurement on a
single plant was performed, giving a total of 20 replicates
for each treatment.The JIP-test
For each treatment, the average OJIP fluorescence transient
was analysed according to the JIP-test (Strasser et al. 2004 ),
using the “Biolyzer ”software produced by the Laboratory
of Bioenergetics at the University of Geneva, Switzerland.The parameter chosen for presentation was the performance
index (PI
total), which evaluates the overall photosynthetic
performance; for the analytical description, see Tsimilli-Michael and Strasser ( 2008 ). PI represents an index
combining functional and structural criteria of the photo-
system (PS) II functioning and is based on severalindependent parameters used to characterize the responses
of PSII to diverse environmental factors (Tsimilli-Michael
and Strasser 2008 ).
Determination of AMF colonization
The roots were stained in accordance with the Phillips and
Hayman ( 1970 ) protocol, with minor modifications as
incorporated by Zubek et al. ( 2010 ). After staining, the
roots were cut into ca. 1-cm fragments, then mounted on
slides in glycerol:lactic acid (4:1, v:v), and analysed using a
Nikon Eclipse 80i light microscope with Nomarski inter-
ference contrast optics. The mycorrhizal colonization
assessment was carried out in line with the Trouvelotmethod (Trouvelot et al. 1986 ). The parameters analysed
were mycorrhizal frequency (F), relative mycorrhizal root
length (M), and relative arbuscular richness (A).
Estimation of secondary metabolite contents
The dried shoots were stored in the dark at room temperature
until required for analysis. The sample preparation and
quantification of anthraquinone derivatives and the prenylatedphloroglucinol —hyperforin —were carried out using high-
performance liquid chromatography —HPLC FLD and HPLC
DAD techniques for hypericin and pseudohypericin and forhyperforin, respectively (de los Reyes and Koda 2002 ). The
identification of the compounds under analysis was based on
the comparison of their retention times and spectralparameters with hypericin, pseudohypericin and hyperforin
standards obtained from PhytoLab GmbH & Co. KG.
Statistical analysis
The data obtained from mycorrhizal colonization assess-
ments were analysed by means of the nonparametric
Kruskal –Wallis test ( p<0.05). The analysis of biomass,
secondary metabolite contents and photosynthetic perfor-mance index values were conducted using a one-way
analysis of variance. The significance of differences
between treatments was tested following Tukey ( p<0.05).Mycorrhiza (2012) 22:149 –156 151 | e34541027b4913acc7deed56804118a527f18f9e | page_0002 |
The analyses were carried out using Statsoft ’s STATIS-
TICA version 9.
Results
AMF colonization
The roots of the plants from all AMF treatments were
colonized by AMF mycelium with arbuscules. Other root
endophytes were not detected in the material under
investigation. The roots of H. perforatum from the control
treatments were devoid of fungi. In the case of mycorrhizal
frequency (F), no statistically significant differences were
found between the treatments. The application of R.
intraradices inoculum resulted in the highest mean mycor-
rhizal colonization rate (M) and arbuscule richness (A). The
lowest values of mycorrhizal parameters (M, A) weredetected after the AMF Mix ap plication. Statistically
significant differences were only found between these two
extreme mean values (Fig. 1).
Shoot mass
There were no statistically significant differences in H.
perforatum shoot mass in any of the treatments (Fig. 2).
Only a slight tendency towards higher biomass production
was observed after the AMF inoculation in comparison to
the control treatment.
Photosynthetic performance index
The application of R. intraradices andF . mosseae had no
significant impact on the photosynthetic performance
(expressed in PI
total)o f H. perforatum comparing to thecontrol plants, whereas inoculation with the AMF Mix
resulted in significantly higher PI totalvalues in comparison
to all the other treatments (Fig. 3).
Anthraquinone derivative and hyperforin shoot contents
The plants inoculated with R. intraradices and the AMF
Mix were characterized by a higher concentration of the
two studied anthraquinone derivatives in the shoots in
comparison to the control plants. However, no differences
were detected in hypericin and pseudohypericin concen-
trations after the application of F. mosseae (Fig. 4). In the
case of hyperforin, no statistically significant differences
were found between the control plants and those inoculated
with any of the AMF applied (Fig. 5).
Discussion
Mycorrhizal colonization may induce quantitative and/or
qualitative changes in plant secondary metabolite contentssuch as alkaloids (Abu-Zeyad et al. 1999 ; Rojas-Andrade et
al.2003 ); terpenoids (Maier et al. 1997 ,1999 ; Fester et al.
1999 ; Akiyama and Hayashi 2002 ; Kapoor et al. 2002a ,b,
2007 ; Copetta et al. 2006 ; Jurkiewicz et al. 2010 ), including
carotenoids (Fester et al. 2002 ) and thymol derivatives
(Zubek et al. 2010 ); glucosinolates (Vierheilig et al. 2000 );mycorrhizal parameters [%]
020406080100
F M a a a a
ab
b R.intra. F.moss. Mix
A a
ab b
Fig. 1 Mycorrhizal colonization (percentages; mean±SD) of H.
perforatum roots; AMF treatments: R.intra. R. intraradices (BEG140),
F. mo ss . F. m os se ae (BEG12), Mixinoculum containing F . constrictum
(262-5 C. Walker), F . geosporum (UNIJAG.PL.12-2), F . mosseae
(BEG12), and R. intraradices (BEG 140); mycorrhizal parameters: F
mycorrhizal frequency, Mrelative mycorrhizal root length, Arelative
arbuscular richness. The different letters above the bars indicate
statistically significant differences ( p<0.05)0,00,10,20,30,40,50,6shoot mass [g]a
a a a
Control R.intra. F.moss. Mix
Fig. 2 H. perforatum shoot dry mass (grams; mean±SD) of the
control and AMF treatments presented in Fig. 1; no statistically
significant differences were found between treatments ( p>0.05)
0102030PItotal a a a b
Control R.intra. F.moss. Mix
Fig. 3 The performance index (PI; mean±SD) of H. perforatum for
the treatments presented in Fig. 2. The different letters above the bars
indicate statistically significant differences ( p<0.05)152 Mycorrhiza (2012) 22:149 –156 | e34541027b4913acc7deed56804118a527f18f9e | page_0003 |
phenolic compounds such as flavonoids (Morandi et al.
1984 ; Larose et al. 2002 ) and phenolic acids (Toussaint et
al.2007 ,2008 ; Ceccarelli et al. 2010 ; Jurkiewicz et al.
2010 ). The mechanism of AMF-induced alterations in the
phytochemical concentration in roots and/or shoots can be
multidirectional (Toussaint 2007 ). Firstly, the modification
of compound concentrations such as flavonoids andalkaloids in roots may be the consequence of signalling
mechanisms between the host plant and fungi (Larose et al.
2002 ; Rojas-Andrade et al. 2003 ). Secondly, the alterations
in the secondary metabolite balance can also result from
plant response to AMF colonization. In general, theproduction of phenolic compounds and terpenoids, the
components of essential oils, is considered as a defensive
response to fungal colonization/infection. Given the fungi-cide properties of several constituents of essential oils, and
the increased production of these metabolites in mycorrhi-
zal plants, it has been suggested that they could besynthesized as a defensive response to AMF presence
(Copetta et al. 2006 ). Thirdly, the enhanced synthesis of
secondary metabolites in mycorrhizal plants, namelyterpenoids and phenolic acids, may reside in better
phosphorus and/or nitrogen nutrition owing to AMF
(Kapoor et al. 2002a ,b; Toussaint et al. 2007 ). Finally, an
association between the alterations in secondary metabolite
contents, namely terpenoids, and the changes in phytohor-
mone levels in plants induced by AMF has been posited(Copetta et al. 2006 ; Kapoor et al. 2007 ; Toussaint 2007 ;
Toussaint et al. 2007 ).
In the present study, we report, to the best of our
knowledge for the first time, the AMF influence on the
content of anthraquinone derivatives and hyperforin in
plants. The enhanced hypericin and pseudohypericin shootconcentrations of the R. intraradices and AMF Mix
treatments, as well as the parallel stimulation of H.
perforatum photosynthetic performance after the AMF
Mix inoculation, may suggest positive plant response to
the inocula applied. This could be the result of improvedplant phosphorus and/or nitrogen nutrition due to symbio-
sis. A similar tendency was found in the studies conducted
by Zubek et al. ( 2010 ) concerning the response of Inula
ensifolia L. to AMF. An increase in the quantity of thymol
derivatives in roots was found after Rhizophagus clarus
(Glomus clarum ) inoculation, and at the same time, good
plant vitality indicated by the high values of photosynthetic
performance index was observed. Moreover, the decreased
production of these metabolites and the lowest PI wereobserved in R. intraradices (G. intraradices ) treatments
(Zubek et al. 2010 ). In addition, a second possible
interpretation of our results could be that the AMF appliedinfluenced phytohormone contents differently, and changes
thus occurred in the physiology of H. perforatum . Howev-
er, in order to fully support both of the mechanisms positedhere, further studies are planned involving the parallel
analysis of AMF influence on anthraquinone derivatives,
phytohormones, and P and N contents in both the roots andshoots of H. perforatum . In this investigation, our focus
was on the therapeutic compound contents in the aerial
parts, which is important for the medicinal value of H.
perforatum and the possible future application of AMF in
the cultivation of this species for pharmaceutical purposes.
In our experiment, commercially available soil with a
relatively high phosphorus content was used. This could
have decreased mycorrhizal colonization levels, and as a
consequence, the effects of AMF on the plants might have01234concentration of hyperforin
[% d.w.]a a a a
Control R.intra. F.moss. Mix
Fig. 5 Hyperforin concentrations (percentages of dry weight; mean±
SD) in the H. perforatum aerial parts from the treatments presented in
Fig. 2; no statistically significant differences were found between
treatments ( p>0.05)00,020,040,060,080,10,120,1400,020,040,060,08concentration of hypericin
[% d.w.]
a b
a a b
a ab b
Control R.intra. F.moss. Mix concentration of pseudohypericin
[% d.w.]a)
b)
Fig. 4 Anthraquinone derivative concentrations: hypericin ( a) and
pseudohypericin ( b) (percentages of dry weight; mean±SD) in the H.
perforatum aerial parts from the treatments presented in Fig. 2. The
different letters above the bars indicate statistically significant differ-
ences ( p<0.05)Mycorrhiza (2012) 22:149 –156 153 | e34541027b4913acc7deed56804118a527f18f9e | page_0004 |
been less pronounced. High soil P content usually results in
low AMF colonization (Smith and Read 2008 ). For
instance, Duan et al. ( 2010 ) found low colonization levels
in maize, soybean, and wheat grown on fertilized soils.
However, high levels of colonization in soils high in P and
the apparent insensitivity of AMF colonization to increasedP content have also been reported (Vosátka 1995 ; Ryan and
Ash 1999 ). Furthermore, the plants were grown in a soil
relatively high in P, and these conditions might have led toa reduction in the role of AMF in enhancing P acquisition.
In view of this fact, the aforementioned mechanism
whereby AMF influence the secondary metabolism of H.
perforatum by improving plant nutritional status seems to
be less possible.
The inoculation of H. perforatum with R. intraradices
and the AMF Mix enhanced the concentration of anthra-
quinone derivatives, with no differences being noted in the
F . mosseae treatment. This is in accordance with recent
investigations which have revealed that various fungal
strains induced different changes in the production of
several groups of secondary metabolites in the same plantspecies (Kapoor et al. 2002a ,b; Copetta et al. 2006 ;
Khaosaad et al. 2006 ; Kapoor et al. 2007 ; Toussaint et al.
2007 ; Ceccarelli et al. 2010 ; Jurkiewicz et al. 2010 ; Zubek
et al. 2010 ). For example, Jurkiewicz et al. ( 2010 ) found
that total phenolic acid accumulation was enhanced in theroots and leaves of Arnica montana L. after application of
AMF isolates originating from one of the plant ’s natural
stands with no significant influence of other inoculants.Similarly, Ceccarelli et al. ( 2010 ) proved that R. intra-
radices was more effective in the stimulation of total
phenolic content in the leaves of Cynara cardunculus L.
var.scolymus than in those of F . mosseae (G. mosseae ).
In our studies, the lowest mycorrhizal colonization rates
ofH. perforatum roots were observed after the application
of the AMF Mix. At the same time, the enhanced content of
anthraquinone derivatives in shoots and the highest photo-
synthetic performance index values were found in the caseof plants inoculated with the AMF Mix. As earlier studies
have shown, the extent of mycorrhizal colonization is not
necessarily correlated with the effects of AMF on plants(Kapoor et al. 2002a ; Toussaint et al. 2007 ; Smith and Read
2008 ). Experimental and field data acquired by Feldmann
et al. ( 2009 ) showed that AMF symbiosis was the most
effective when root colonization ranged between 20%
and 30%. In the studies conducted by Toussaint et al.
(2007 ), even a relatively low level of colonization by F.
mosseae had a considerable effect on Ocimum basilicum
physiology, with increased caffeic acid content in shoots.
However, a positive correlation was found between fungalcolonization rate and the content of castanospermine, an
alkaloid of the indolizidine type, in Castanospermum
australe seeds (Abu-Zeyad et al. 1999 ).The enhanced H. perforatum performance and the
improved production of anthraquinone derivatives after
the AMF Mix inoculation in comparison to the single AMFtreatments could result from AMF species complementarity.
Direct evidence for such a mechanism among AMF species
was provided by Jansa et al. ( 2008 ). The authors found that
leek colonized by a mixture of Claroideoglomus claroi-
deum (Glomus claroideum ) and R. intraradices acquired
more phosphorus than with either of the two AMFseparately. However, Janou šková et al. ( 2009 ) found that
inoculation with a mixture of C. claroideum and R.
intraradices brought no additional benefit to the host plants
under study in comparison to single treatments. In addition,
the plant growth depression observed after inoculation with
C. claroideum persisted in the AMF Mix treatment. In our
experimental approach, the better stimulation of H. perfo-
ratum performance in the case of the AMF Mix application
could result not only from the potential complementarity ofF . mosseae andR. intraradices but also from the additional
presence of F . constrictum and/or F.geosporum in this
treatment. The presence of these two strains and theirsymbiotic potential might have reinforced the positive
response of the plant to inoculation. Furthermore, both
plants and fungal strains can differ in their responsiveness
and in the input of nutrients that influence the final effect of
the symbiosis. For instance, in the studies conducted byGrace et al. ( 2009 ),F . geosporum (G. geosporum ) has been
shown to be a much less effective root colonizer and P
contributor to the plant symbiont than R. intraradices . The
presence of such a fungus could result in the reinforced
production of the secondary metabolites that maintain the
fungal colonization at the low level, while simultaneouslyallowing the increased performance of H. perforatum that
might be due to the presence of R. intraradices . The
evidence that plants colonized by AMF regulate furthercolonization by AMF through altered secondary metabolite
production, namely root exudates, was provided by Pinior
et al. ( 1999 ). The interactions between different AMF
species and host plants are little understood at present, but
the data available to date seem to support the view that the
manipulation of rhizosphere communities may be ofimportance in developing more sustainable agriculture and
more effective production of medicinal plant materials.
The inoculation of H. perforatum with Mix inoculum
seems to be the best solution for improving both plant
performance and the quality of medicinal plant raw material
obtained from cultivation for pharmaceutical purposes.However, large-scale field experiments are required in
order to support our laboratory investigations before an
attempt can be made to utilize AMF in H. perforatum
agricultural systems. Nevertheless, there is a need for the
cultivation process to be carried out in accordance with the
ecological approach, i.e. with low chemical inputs, such as154 Mycorrhiza (2012) 22:149 –156 | e34541027b4913acc7deed56804118a527f18f9e | page_0005 |
fertilizers and pesticides, in order to both produce medicinal
plant raw materials devoid of contaminants and avoid soil
pollution. Therefore, the exploitation and possible applica-tion of soil microorganisms such as AMF could greatly
benefit the herbal industry (Copetta et al. 2006 ; Toussaint
2007 ; Zubek and B łaszkowski 2009 ; Ceccarelli et al. 2010 ;
Zubek et al. 2010 ,2011 ).
Acknowledgements The present research was financially supported
by the Polish Ministry of Science and Higher Education, project no. NN304 381939 (2010 –2013). Dr. hab. K. Seidler- Łożykowska (Institute of
Natural Fibres and Medicinal Plants, Pozna ń)i sa c k n o w l e d g e df o r
providing us with the seeds of H. perforatum .
Open Access This article is distributed under the terms of the Creative
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noncommercial use, distribution, and reproduction in any medium,
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fpls-07-01621 October 24, 2016 Time: 16:15 # 1
REVIEW
published: 26 October 2016
doi: 10.3389/fpls.2016.01621
Edited by:
Hanjo A. Hellmann,
Washington State University, USA
Reviewed by:
Karl-Josef Dietz,
Bielefeld University, Germany
Sutton Mooney,
Washington State University, USA
*Correspondence:
Zhong-Guang Li
[email protected]
Specialty section:
This article was submitted to
Plant Physiology,
a section of the journal
Frontiers in Plant Science
Received: 07 May 2016
Accepted: 13 October 2016
Published: 26 October 2016
Citation:
Li Z -G, Min X and Zhou Z -H (2016)
Hydrogen Sulfide: A Signal Molecule
in Plant Cross-Adaptation.
Front. Plant Sci. 7:1621.
doi: 10.3389/fpls.2016.01621
Hydrogen Sulfide: A Signal Molecule
in Plant Cross-Adaptation
Zhong-Guang Li1,2,3*, Xiong Min1,2,3and Zhi-Hao Zhou1,2,3
1School of Life Sciences, Yunnan Normal University, Kunming, China,2Engineering Research Center of Sustainable
Development and Utilization of Biomass Energy, Ministry of Education, Kunming, China,3Key Laboratory of Biomass Energy
and Environmental Biotechnology, Yunnan Normal University, Kunming, China
For a long time, hydrogen sulfide (H 2S) has been considered as merely a toxic by
product of cell metabolism, but nowadays is emerging as a novel gaseous signal
molecule, which participates in seed germination, plant growth and development, as
well as the acquisition of stress tolerance including cross-adaptation in plants. Cross-
adaptation, widely existing in nature, is the phenomenon in which plants expose to
a moderate stress can induce the resistance to other stresses. The mechanism of
cross-adaptation is involved in a complex signal network consisting of many second
messengers such as Ca2C, abscisic acid, hydrogen peroxide and nitric oxide, as well
as their crosstalk. The cross-adaptation signaling is commonly triggered by moderate
environmental stress or exogenous application of signal molecules or their donors, which
in turn induces cross-adaptation by enhancing antioxidant system activity, accumulating
osmolytes, synthesizing heat shock proteins, as well as maintaining ion and nutrient
balance. In this review, based on the current knowledge on H 2S and cross-adaptation
in plant biology, H 2S homeostasis in plant cells under normal growth conditions; H 2S
signaling triggered by abiotic stress; and H 2S-induced cross-adaptation to heavy metal,
salt, drought, cold, heat, and flooding stress were summarized, and concluded that
H2S might be a candidate signal molecule in plant cross-adaptation. In addition, future
research direction also has been proposed.
Keywords: cross-adaptation, hydrogen sulfide, signal crosstalk, stress tolerance
INTRODUCTION
Cross-adaptation, widely existing in nature, is the phenomenon in which plants expose to a
moderate stress can induce the resistance to other stresses ( Li and Gong , 2011 ;Foyer et al. , 2016 ;
Hossain et al., 2016 ). For example, cold pretreatment can improve the heat tolerance of winter
rye, salt shock can rapidly induce the cold tolerance in spinach and potato, ultraviolet radiation
(UV-B) can enhance the heat tolerance in cucumber and the cold tolerance in Rhododendron ,
and mechanical stimulation can improve the heat tolerance and the chilling tolerance in tobacco
cells ( Knight , 2000 ;Li and Gong, 2011 , 2013 ). Interestingly, Foyer et al. ( 2016) found that cross-
adaptation also can be induced between abiotic and biotic stresses. Infection by mycorrhizal fungi
can improve the resistance of tomato, sunflower, pea, and rice to drought, chilling, salinity, metal
toxicity, and high temperature stress ( Grover et al., 2011 ), while drought stress can reduce aphid
fecundity in Arabidopsis (Pineda et al. , 2016 ). Our previous work also showed that heat shock could
improve the resistance of maize seedlings to heat, chilling, salt, and drought stress ( Gong et al.,
2001 ). Numerous studies found that the acquisition of stress tolerance including cross-adaptation
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Li et al. H2S: A Cross-Adaptation Signal
was involved in a complex signal network consisting of many
second messengers such as Ca2C, abscisic acid (ABA), hydrogen
peroxide (H 2O2) and nitric oxide (NO), as well as their crosstalk
(Knight, 2000; Pandey, 2015; Li and Gu, 2016; Li and Jin, 2016;
Niu and Liao, 2016; Wang et al., 2016). In tobacco, mechanical
stimulation can successively trigger H 2O2and NO signaling (Li
and Gong, 2011, 2013), heat shock can induce Ca2Cand ABA
signaling one after the other (Gong et al., 1998a,b), which in
turn induce cross-adaptation to heat and chilling stress, similar
results were reported by Gong et al. (2001) in maize seedlings.
These results indicate that the acquisition of cross-adaptation is
involved in signal crosstalk among Ca2C, H 2O2, NO, and ABA
in plants. Recently, hydrogen sulfide (H 2S) was also found to
be a member of this signal network in plants (Calderwood and
Kopriva, 2014; Hancock and Whiteman, 2014; Fotopoulos et al.,
2015; Guo et al., 2016), indicating that H 2S might be a signal
molecule in plant cross-adaptation.
For a long time, H 2S has been considered as merely a toxic
intermediate of cell metabolism due to its strong affinity to Fe2C-
containing proteins such as cytochrome oxidase, hemoglobin
and myoglobin, which may have been primary cause of the
mass extinction of species in the Permian (Li, 2013; Lisjak
et al., 2013; Calderwood and Kopriva, 2014; Hancock and
Whiteman, 2014; Fotopoulos et al., 2015; Guo et al., 2016;
Y amasaki and Cohen, 2016). H 2S can inhibit oxygen release
from young seedlings of six rice cultivars (Bluebelle, Dawn,
Norin 22, Saturn, Yubae, and Zenith) and nutrient uptake
such as phosphorus (Li, 2013; Calderwood and Kopriva, 2014;
Hancock and Whiteman, 2014). But nowadays, H 2S is found to
function as gaseous signal molecule at low concentration similar
to carbon monoxide (CO) and NO in plants, and it has been
shown that plants can actively synthesize endogenous H 2S under
normal, especially biotic or abiotic stress conditions (Li, 2013;
Calderwood and Kopriva, 2014; Hancock and Whiteman, 2014;
Y amasaki and Cohen, 2016). The accumulation of endogenous
H2S has become a common response of plants to environmental
stress, including salt, heavy metal (HM), drought, heat and
cold stress, as well as pathogen infection, which may be
closely associated with the acquisition of stress tolerance in
plants (Li, 2013; Calderwood and Kopriva, 2014; Hancock and
Whiteman, 2014). More interestingly, exogenously applied H 2S,
releasing from its donors such as NaHS and morpholin-4-ium
4-methoxyphenyl(morpholino) phosphinodithioate (GYY4137),
shows significant positive effects on seed germination (Li et al.,
2012a; Li and He, 2015; Wojtyla et al., 2016), organogenesis and
growth (Lin et al., 2012; Fang T. et al., 2014), the regulation
of senescence (Zhang et al., 2011), as well as the acquisition
of stress tolerance such as salt (Christou et al., 2013), HM
(Chen et al., 2013), drought (Christou et al., 2013), heat
(Li et al., 2013a,b; Li, 2015c) and cold tolerance (Fu et al.,
2013). These results indicate that H 2S may be a candidate
signal molecule in plant cross-adaptation. In addition, NaHS
and GYY4137 are commonly used as H 2S donors because
they can release H 2S when dissolved in water, but NaHS
giving a relatively short burst of H 2S, while GYY4137 giving a
longer more prolonged exposure to H 2S (Wang, 2012; Lisjak
et al., 2013). However, whether H 2S concentration in plantcells or tissues is consistent with that of NaHS and GYY4137
applied as well as actual H 2S concentration triggering cross-
adaptation need to be further investigated. In addition, H 2S
usually exist in the forms of H 2S (approximately 20%) and
HS (approximately 80%) in water solution, exact physiological
concentration of H 2S in plant cells or subcellular organelles is not
clear.
Though, there are a lot of excellent reviews which expound
potential physiological function of H 2S in seed germination, plant
growth and development, as well as the acquisition of stress
tolerance (Li, 2013; Calderwood and Kopriva, 2014; Hancock
and Whiteman, 2014, 2016; Jin and Pei, 2015; Guo et al., 2016;
Scuffi et al., 2016; Y amasaki and Cohen, 2016), the role of
H2S as a candidate signal molecule in plant cross-adaptation
was not summarized in depth. Therefore, in this review, H 2S
homeostasis in plant cells under normal growth conditions, H 2S
signaling triggered by adverse environment and H 2S-induced
cross-adaptation to various abiotic stresses are summarized,
which further uncovers that H 2S may be a candidate signal
molecule in plant cross-adaptation.
H2S HOMEOSTASIS IN PLANT CELLS
As mentioned above, due to the dual role of H 2S, that is,
as cytotoxin at high concentration and as cell signal molecule
at low concentration, H 2S homeostasis in plant cells is very
important to exert its physiological functions including cross-
adaptation induction. In plant cells, there are many metabolic
pathways to regulate H 2S homeostasis, similar to other signal
molecules like H 2O2, NO. H 2S homeostasis is closely regulated
by L-cysteine desulfhydrase (LCD, EC 4.4.1.1), D-cysteine
desulfhydrase (DCD, EC 4.4.1.15), sulfite reductase (SiR, EC
1.8.7.1), cyanoalanine synthase (CAS, EC 4.4.1.9), and cysteine
synthase (CS, EC 4.2.99.8; Li, 2013, 2015a; Figure 1 ). LCD/DCD
catalyzes the degradation of L-/D-cysteine to produce H 2S,
amine and pyruvate; SiR reduces sulfite to H 2S using ferredoxin
as electron donor; H 2S can be released from cysteine in the
present of hydrogen cyanide by CAS; CS, namely O-acetyl-
(thiol)-serinelyase (OAS-TL), can incorporate H 2S into O-acetyl-
L-serine to form cysteine, and its reverse reaction can release H 2S
(Li, 2013, 2015a; Figure 1 ). Generally, plants synthesize H 2S via
LCD or DCD, which respond to environment stress and induce
the acquisition of stress tolerance. In addition, excess H 2S can be
released to air (Li, 2013; Calderwood and Kopriva, 2014; Hancock
and Whiteman, 2014).
H2S SIGNALING TRIGGERED BY
ABIOTIC STRESS
Similar to other second messengers such as Ca2C, H 2O2, ABA
and NO, the rapid production of endogenous H 2S in many
species of plant can be triggered by numerous stresses ( Table 1 ;
Figure 2 ), this is a common response of plants to various abiotic
stresses, which is closely associated with the acquisition of cross-
adaptation in plants.
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fpls-07-01621 October 24, 2016 Time: 16:15 # 3
Li et al. H2S: A Cross-Adaptation Signal
FIGURE 1 | Hydrogen sulfide (H 2S) homeostasis in plant cells. H2S
homeostasis can be regulated by L-cysteine desulfhydrase (LCD), D-cysteine
desulfhydrase (DCD), sulfite reductase (SiR), cyanoalanine synthase (CAS),
and cysteine synthase (CS) pathways in plant cells (adapted from Li, 2015a).
H2S Signaling Triggered by Heavy Metal
Stress
The rapid production of H 2S has become a common response
of plants to various HM stress, among HMs, Cd is the most
severe stress due to its toxicity and stability (Ahmad, 2016). In
rice seedlings, 0.5 mM Cd stress resulted in an increment of
H2S content from approximately 5 mmol g 1fresh weight (FW)
to approximately 6 mmol g 1FW. The addition of 0.1 mM
NaHS caused an even further increase in the level of H 2S
(approximately 8 mmol g 1FW) as compared with Cd treatment
alone. Exposure to 0.2 mM hypotaurine (HT, H 2S scavenger) with
NaHS decreased H 2S level compared with NaHS alone, indicating
that this elevated level of H 2S is correlated with the enhanced Cd
tolerance (Mostofa et al., 2015). Zhang et al. (2015) found that the
endogenous H 2S emission was stimulated by Cd stress in Chinese
cabbage. The relative expression of DCD1 and DES1 (cysteinedesulfhydrase, OAS-TL homogenous family) genes (responsible
for H 2S synthesis) was up-regulated after treatment with Cd
with a range of concentrations (0, 5, 10, and 20 mM) for 24 h.
Expression of DES1 at 5 mM Cd already showed a significant
increase, and at 20 mM Cd was 4.7 times of the control.
Following a similar pattern, the endogenous H 2S concentrations
also significantly rose from 0.38 to 0.58 nmol mg 1protein
min 1at 20 mM. Chromium (Cr), existing in the form of Cr3C
and Cr6C, is regarded as the second most common HM, both
forms have become major environmental pollution sources. In
foxtail millet seedlings, Fang H. et al. (2014) also reported that
the expressions of H 2S-emission related genes LCD, DCD2, and
DES markedly increased during the first 12 h of Cr6Cexposure
following decline at 24 h, while the expression of DCD1 was
consistently increased from 0 to 24 h under 10 mM Cr6Cstress.
Additionally, the H 2S production rate is induced by Cr6Cstress
in dose- and time-dependent manner, and this induction was
the most significant with 24 h of 10 mM Cr6Ctreatment (from
0.6 to 1.6 nmol mg 1protein min 1). These results imply
that endogenous H 2S synthesis was activated by Cr6Cstress by
activating its emission system in foxtail millet. Inconceivably,
in compared with to other plant species, the both species
Chinese cabbage and foxtail millet show a remarkable tolerance
to HM (Cd and Cr6C). At 20 mM Cd for Chinese cabbage and
10 mM Cr6Cfor foxtail millet, these treatment concentrations
are far beyond the physiological level (generally micromolar
concentrations) for many plant species, the precise physiological,
biochemical, and molecular mechanisms are waiting for being
uncovered.
H2S Signaling Triggered by Salt Stress
Salt stress commonly leads to an osmotic stress response,
similar to drought stress, which triggers rapid generation of
second messengers like H 2S. In alfalfa seedlings, the increasing
concentration of NaCl (from 50 to 300 mM) progressively
caused the induction of total LCD activity and the increase of
TABLE 1 | Different abiotic stresses trigger endogenous H 2S production in plants.
Species Stress H 2S content Reference
Normal conditions Stress conditions
Rice Cd 5 mmol g 1FW 6 mmol g 1FW Mostofa et al., 2015
Chinese cabbage Cd 0.38 nmol mg 1Pr min 10.58 nmol mg 1Pr min 1Zhang et al., 2015
Foxtail millet Cr6C0.6 nmol mg 1Pr min 11.6 nmol mg 1Pr min 1Fang H. et al., 2014
Alfalfa NaCl 30 nmol g 1FW 70 nmol g 1FW Lai et al., 2014
Strawberry PEG-6000, NaCl 25 nmol g 1FW 35 nmol g 1FW Christou et al., 2013
Arabidopsis Drought 6 nmol mg 1Pr min 114 nmol mg 1Pr min 1Jin et al., 2011
Arabidopsis Cold 3 nmol g 1FW 5 nmol g 1FW Shi et al., 2015
Grape Cold 7 mmol g 1FW 15 mmol g 1FW Fu et al., 2013
Bermudagrass Cold 5 nmol g 1FW 14 nmol g 1FW Shi et al., 2013
Lamiophlomis rotata Cold 12 nmol g 1FW 24 nmol g 1FW Ma et al., 2015
Tobacco Heat 2 nmol g 1FW 8 nmol g 1FW Chen et al., 2016
Barley UV-B 125 nmol g 1FW 230 nmol g 1FW Li et al., 2016
Pea Hypoxia 0.8 mmol g 1FW 1.5 mmol g 1FW Cheng et al., 2013
The FW and Pr in the table represent fresh weight and protein respectively.
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FIGURE 2 | Mutiple environmental stress can induce endogenous H 2S
production in plants. Abiotic stress (heavy metal, drought, salt, cold, heat,
flooding, and UV-B radiation) and biotic stress (fungal infection) induce the
generation of endogenous H 2S by mainly activating LCD.
endogenous H 2S production (from 30 to 70 nmol g 1FW)
(Lai et al., 2014). Exposure of strawberry seedlings to salinity
(100 mM NaCl) and non-ionic osmotic stress (10% PEG-6000)
greatly enhanced H 2S concentration (48 and 50 nmol g 1FW)
in leaves, while 0.1 mM NaHS-pretreated plants subsequently
exposed for 7 days to both stress factors were found to accumulate
significantly higher amounts of H 2S (55 nmol g 1FW) in their
leaves compared with NaCl-stressed plants (Christou et al., 2013).
H2S Signaling Triggered by Drought
Stress
One of the most severe abiotic stresses being experienced world-
wide is drought. In Arabidopsis seedlings, the results of Shen
et al. (2013) showed that treating wild type with polyethylene
glycol (PEG) 8000, to simulate drought stress, caused an increase
in production rate of endogenous H 2S (0.8 nmol mg 1protein
min 1). At early stage of osmotic exposure (PEG 6000 for 2 days),
the endogenous H 2S in wheat seeds rapidly increased from 1.5 to
3.5mmol g 1dry weight (DW) (Zhang et al., 2010a).
H2S Signaling Triggered by Low
Temperature Stress
Low temperature is a major environmental stress factors that
limit plant growth, development and distribution. In grape
(Vitis vinifera L.) seedlings, chilling stress at 4C induced the
expression of L/DCD genes and increased the activities of
L/DCD, which in turn enhanced endogenous H 2S accumulation
(from 7 to 15 mmol g 1FW) (Fu et al., 2013). Similarly,
Shi et al. (2013) also found that cold stress treatment at
4C could induce the accumulation of endogenous H 2S level
(14 nmol g 1FW) in bermudagrass [ Cynodon dactylon (L).
Pers.] seedlings. To uncover the adaptive strategies of alpine
plants to the extremely cold conditions prevailing at high
altitudes, Ma et al. (2015), using a comparative proteomics,
investigated the dynamic patterns of protein expression in
Lamiophlomis rotata plants grown at three different altitudes
(4350, 4,800, and 5,200 m), and the results showed that the
levels and enzyme activities of proteins (OAS-TL, CAS, L/DCD)involved in H 2S biosynthesis markedly increased at higher
altitudes (4,800 and 5,200 m), and that H 2S accumulation
increased to 12, 22, and 24 nmol g 1FW, respectively,
demonstrating that H 2S plays a central role during the
adaptation of L. rotata to environmental stress at higher
altitudes.
H2S Signaling Triggered by High
Temperature Stress
Similar to other stresses, high temperature also can induce
endogenous H 2S generation in many species of plant. In
3-week-old seedlings of tobacco, Chen et al. (2016) found
that treatment with high temperature at 35C increased the
activity of LCD, which in turn induced the production of
endogenous H 2S (8 nmol g 1FW) in tobacco seedlings, and
that H 2S production remained elevated level after 3 days of high
temperature exposure. More interestingly, H 2S production by
high temperature can induce the accumulation of jasmonic acid,
followed by promoting nicotine synthesis. These data suggest
that H 2S and nicotine biosynthesis is linked in tobacco plants
subjected to high temperature stress. Additionally, heat stress
caused a marked modulation in H 2S content in strawberry
seedlings, as indicated in a significant increase after 1, 4,
and 8 h of exposure to 42C compared with control plants.
A significant increase in H 2S content was also observed in
0.1 mM NaHS-pretreated plants after 1 h exposure to heat stress,
gradually lowering to control levels thereafter (Christou et al.,
2014).
H2S Signaling Triggered by UV-B
Radiation
Recently, Li et al. (2016) found that UV-B radiation could induce
H2S production in leaves of barley seedlings, reaching a peak of
approximately 230 nmol g 1FW after 12 h of exposure, which
in turn promoted the accumulation of UV-absorbing compounds
flavonoids and anthocyanins. H 2S began to decline with time,
but it is overall significantly higher than that of the control
(approximately 125 nmol g 1FW) at 48 h of exposure. A similar
trend was observed for LCD activity, which was corroborated
by the application of DL-propargylglycine (PAG, an inhibitor of
LCD) that resulted in complete inhibition of the H 2S production
and the accumulation of UV-absorbing compounds induced by
UV-B radiation (Li et al., 2016).
H2S Signaling Triggered by Hypoxia and
Fungal Infection
Flooding often leads to hypoxia in plant roots, which significantly
limits agriculture production. In pea ( Pisum sativum L.)
seedlings, Cheng et al. (2013) found that hypoxia could activate
H2S biosynthesis system (LCD, DCD, OAS-TL, and CS), which
in turn induced the accumulation of endogenous H 2S from
approximately 0.9 (control) to 5.1 mmol g 1FW (hypoxia for
24 h), indicating that H 2S might be a hypoxia signaling that
triggers the tolerance of the pea seedlings to hypoxic stress, this
hypothesis was further supported by exogenously applied NaHS.
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Li et al. H2S: A Cross-Adaptation Signal
Pathogen infection is a common biotic stress in plants. In
oilseed rape ( Brassica napus L.) seedlings, fungal infection with
Sclerotinia sclerotiorum led to an even stronger increase in H 2S,
reaching a maximum of 3.25 nmol g 1DW min 12 days after
infection, suggesting that the release of H 2S seems to be part of
the response to fungal infection (Bloem et al., 2012).
H2S Signaling Triggered by Exogenously
Applied NaHS or Up-regulating the
Expression of L/DCD
In addition to above-described abiotic and biotic stressors, H 2S
signaling in plant cells also can be triggered by exogenously
applying NaHS (H 2S donor) or up-regulating the expression of
genes involved in H 2S biosynthesis like L/DCD under normal
growth conditions. In strawberry seedlings, treatment of root
with 0.1 mM NaHS resulted in significantly elevated H 2S
concentration (35 nmol g 1FW) in leaves compared with control
plants (25 nmol g 1FW) (Christou et al., 2013). In wheat seeds,
the endogenous H 2S level [4.5 mmol g 1dry weight (DW)]
in NaHS-treated seed was slightly higher than that of control
(1.7 mol g 1DW) (Zhang et al., 2010a). These results indicated
that H 2S is easy to enter into plant cells and follow on being
transported to other tissues or organs due to its highly lipophilic
property, which in turn exert its physiological role in plants.
Additionally, Jin et al. (2011) found that the Arabidopsis
seedlings expressing L/DCD showed higher endogenous H 2S
content under both normal (6 nmol mg 1protein min 1)
and drought stress conditions (14 nmol mg 1protein min 1)
compared with the control (3 nmol mg 1protein min 1), and
the expression pattern of L/DCD was similar to the drought
associated genes dehydration-responsive element-binding
proteins ( DREB2A, DREB2B, CBF4, and RD29A ) induced by
dehydration, while exogenous application of H 2S (80 mM)
was also found to stimulate further the expression of drought
associated genes. In addition, drought stress significantly induced
endogenous H 2S production in both transgenetic plant and wild
type, a process that was reversed by re-watering (Jin et al.,
2011). Interestingly, Arabidopsis seedlings overexpressing LCD
or pre-treated with NaHS exhibited higher endogenous H 2S
level (from 2 to 10 nmol g 1FW), followed by improving
abiotic stress (drought, salt, and chilling) tolerance and biotic
stress (bacteria) resistance, while LCD knockdown plants
or HT (H 2S scavenger) pre-treated plants displayed lower
endogenous H 2S level and decreased stress resistance (Shi et al.,
2015).
In conclusion, above-mentioned researches in this section
display that: (1) under normal growth conditions, the content of
endogenous H 2S or production rate in various plant species are
different, ranging from 2 nmol g 1FW to 7 mmol g 1FW or
0.38 to 6 nmol mg 1protein min 1. These differences may be
relative to measurement methods, plant species and development
stage, and experiment system. (2) Under abiotic stress conditions,
the level of endogenous H 2S in various plant species is averagely
increased by 22.5-fold, indicating that different environment
stresses can trigger the H 2S signaling, which may be a trigger that
induces the acquisition of cross-adaptation in plants.H2S-INDUCED CROSS-ADAPTATION
As described above, not only there are a broad range of
environmental stressors can trigger H 2S signaling in plants, but
pretreating plants with exogenously applied H 2S can provide
additional resistance to subsequent stress exposure. The next
section explores the role of H 2S as an important signaling
molecule for cross-adaptation to HM, salt, drought, cold, heat
and flooding stress by enhancing antioxidant system activity,
accumulating osmolyte, synthesizing heat shock proteins (HSPs),
as well as maintaining ion and nutrient balance ( Table 2 ;
Figure 3 ), which may be common mechanism of cross-
adaptation induced by H 2S.
H2S-Induced Metal and Metalloid
Tolerance
Heavy metals refer to a group of metal elements with a density
greater than 6 g/cm3, including Cr, Cu, Zn, and so forth (Gupta
et al., 2013; Ahmad, 2016). Due to their toxicity and stablility, HM
has become the major abiotic stress in plants, and even threatens
human health by way of the food chain. HM stress commonly
results in oxidative stress, that is, the excessive accumulation
of ROS, which leads to lipid peroxidation, protein oxidation,
enzyme inactivation, and DNA damage (Y adav, 2010; Gupta et al.,
2013; Ahmad, 2016). However, higher plants have evolved a
sophisticated antioxidant defense system to scavenge excessive
ROS and maintain its homeostasis in plants (Foyer and Noctor,
2009, 2011).
Arsenic (As) is a highly toxic metalloid, it is major
pollutant in the soil. In pea seedlings, As treatment increased
the accumulation of ROS, which in turn damage to lipids,
proteins and biomembranes. Meanwhile, higher cysteine level
was observed in As-stress seedlings in comparison to all other
treatments (As-free; NaHS; As CNaHS), while these effects
were alleviated by the addition of NaHS (Singh et al., 2015).
Further experiments showed that As treatment inhibited the
activity of the enzymes involved in the ascorbic acid (AsA)–
glutathione (GSH) cycle, whereas their activities were enhanced
by application of NaHS (Singh et al., 2015). In addition, the
redox status of AsA and GSH was disturbed, as indicated
by a steep decline in their reduced/oxidized ratios. However,
exogenously applied NaHS restored the redox status of the
AsA and GSH pools under As stress (Singh et al., 2015).
Furthermore, NaHS treatment ameliorated As toxicity, which was
coincided with the increased accumulation of H 2S. The results
demonstrated that H 2S might counterbalance ROS-mediated
damage to macromolecules by reducing the accumulation
of As and triggering up-regulation of the AsA–GSH cycle,
further suggesting that H 2S plays a crucial role in plant
priming, and in particular for pea seedlings in mitigating As
stress.
Under Cr stress, exogenous application of NaHS could
improve the germination rate of wheat seeds in a dose-
dependent manner and the activities of amylase, esterase as well
as antioxidant enzymes superoxide dismutase (SOD), catalase
(CAT), ascorbate peroxidase (APX) and glutathione peroxidase
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TABLE 2 | NaHS (H 2S donor)-induced cross-adaptation in plants.
Species Tolerance NaHS
(mM)Responsible factors Reference
Pea As 0.1 AsA–GSH cycle, reducing As accumulation Singh et al., 2015
Wheat Cr 1.2 Activating antioxidant enzymes Zhang et al., 2010b
Wheat Cu 1.4 Promoting amylase and esterase activities, maintain plasma membrane integrity Zhang et al., 2008
Wheat Al 0.6 Decreasing Al accumulation, alleviating citrate secretion, and oxidative stress Zhang et al., 2010c
Barley Al 0.2 Decreasing Al accumulation, alleviating citrate secretion, and oxidative stress Chen et al., 2013
Solanum nigrum Zn 0.2 Enhancing the metallothioneins, alleviating oxidative stress, reducing Zn uptake Liu et al., 2016
Wheat Salt 0.05 Promoting amylase and esterase activities Bao et al., 2011
Alfalfa Salt 0.1 Activating antioxidant enzyme Wang et al., 2012
Arabidopsis Salt 0.2 Maintaining a lower NaC/KCratio, promoting the genes expression and the
phosphorylation of HC-ATPase and NaC/HCantiporterLi J. et al., 2014
Wheat PEG-6000 0.6 Increasing CAT and APX activities, reducing lipoxygenase activity Zhang et al., 2010d
Wheat PEG-6000 1.0 Increased antioxidant enzymes activities and gamma-glutamylcysteine
synthetaseShan et al., 2011
Arabidopsis Drought 0.08 Stimulating the expression of drought associated genes Jin et al., 2011
Vicia faba Drought 0.1 Increasing relative water content García-Mata and
Lamattina, 2010
Bermudagrass Cold 0.5 Modulating antioxidant enzymes and non-enzymatic antioxidant Shi et al., 2013
Grape Cold 0.1 Enhancing SOD activity and the expression of VvICE1 and VvCBF3 genes Fu et al., 2013
Arabidopsis Cold 0.1 Up-regulating the transcripts of multiple abiotic and biotic stress-related genes Shi et al., 2015
Lamiophlomis rotata Cold 0.05 Increasing antioxidant enzyme activity, proline and sugar accumulation Ma et al., 2015
Banana Cold 0.5 Increasing the phenylalanine ammonia lyase activity, total phenolics content and
antioxidant capacityLuo et al., 2015
Strawberry Heat 0.1 Maintaining ascorbate/glutathione homeostasis, inducting gene expression of
enzymatic antioxidants, HSPs and aquaporinsChristou et al., 2014
Maize Heat 0.7 Increasing antioxidant activity Li Z.G. et al., 2014
Maize Heat 0.5 Inducing proline accumulation Li and Gong, 2013; Li
et al., 2013a
Tobacco Heat 0.05 Increasing antioxidant activity Li et al., 2012b, 2015
Pea Hypoxia 0.1 Protecting ROS damage, inhibiting ethylene production Cheng et al., 2013
(GPX), whereas reduced the activity of lipoxygenase and over-
production of malondialdehyde (MDA) as well as H 2O2induced
by Cr, and sustained higher endogenous H 2S level (Zhang
et al., 2010b). Additionally, NaHS pretreatment increased the
activities of SOD and CAT, but decreased that of lipoxygenase
in wheat under Cu stress (Zhang et al., 2008), these results were
consisted with the response of wheat to Cr stress (Zhang et al.,
2010b).
Also, NaHS could alleviate the inhibitory effect of Cu stress
in wheat in a dose-dependent manner, and H 2S or HS derived
from NaHS rather than other sulfur-containing components
(S2 , SO 42 , SO32 , HSO 4 , and HSO 3 ) attribute to the
potential role in promoting seed germination under Cu stress
(Zhang et al., 2008). Further experiments showed that NaHS
could increase amylase and esterase activities, reduced the
disturbance of plasma membrane integrity induced by Cu in
the radicle tips, and sustain lower MDA and H 2O2levels in
germinating seeds (Zhang et al., 2008), similar to the reports by
(Zhang et al., 2010b).
Aluminium (Al), a non-essential element for plants, adversely
affects plant growth, development and survival, especially
in acid soil. In barley ( Hordeum vulgare L.) seedlings, Al
stress inhibited the elongation of roots, while pretreatmentwith NaHS partially rescued the inhibition of root elongation
induced by Al, and this rescue was closely correlated with
the decrease of Al accumulation in seedlings (Chen et al.,
2013). Additionally, application of NaHS significantly alleviated
citrate secretion and oxidative stress (as indicated in lipid
peroxidation as well as ROS burst) induced by Al by activating
the antioxidant system (Chen et al., 2013). Similar results
were reported by Zhang et al. (2010c) in wheat ( Triticum
aestivum L.).
Though zinc (Zn) is an essential element for plants, its
toxic effects can be observed when being excessive accumulation
in plants. In Solanum nigrum L. seedlings, H 2S ameliorated
the inhibition of growth by excess Zn, especially in roots,
and an increase in free cytosolic Zn2Ccontent in roots,
which was correlated well with the down-regulation of Zn
uptake and homeostasis related genes expression like zinc-
regulated transporter (ZRT), iron-regulated transporter (IRT)-
like protein (ZIP) and natural resistance associated macrophage
protein (NRAMP) (Liu et al., 2016). In addition, H 2S further
enhanced the expression of the metallothioneins to chelate
excessive Zn and alleviated Zn-oxidative stress by regulating
the genes expression of antioxidant enzymes (Liu et al.,
2016).
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Li et al. H2S: A Cross-Adaptation Signal
FIGURE 3 | Mechanisms underlining H 2S-induced abiotic tolerance in plants. Abiotic stress causes oxidative stress, membrane injury, osmotic stress, protein
denaturation, as well as ion and nutrient imbalance, while exogenously applied or endogenously synthesized H 2S can alleviate these damages by enhancing the
activity of antioxidant system, synthesizing osmolytes and heat shock proteins (HSPs) and regulating ion and nutrient balance (adapted from Min et al., 2016).
H2S-Induced Salt Tolerance
Salts stress is negative effects of excessive salt on seed
germination, plant growth and development, and even survival,
which is a major abiotic stress in agriculture production world-
wide. Salt stress commonly leads to direct and indirect injury,
namely ion toxicity, osmotic stress, nutrient imbalance, and
oxidative stress (Ahmad et al., 2013a,b). To combat with
salt injury, plants have evolved many protective strategies,
including osmotic adjustment by synthesizing osmolytes such as
proline (Pro), glycine betaine (GB), trehalose (Tre), and total
soluble sugar (TSS); ion and nutrient balance by regulating
transporter; and enhancement of antioxidant capacity by
activating the activity of antioxidant enzymes SOD, CAT, APX,
GPX and glutathione reductase (GR), as well as by synthesizing
antioxidants like AsA and GSH (Ahmad et al., 2013a,b). In salt-
sensitive wheat cultivar LM15, the results of Bao et al. (2011)
showed that wheat seed priming with different concentrations
of NaHS (0.01, 0.05, 0.09, 0.13 mM) for 12 h could significantly
alleviate the inhibition of seed germination and seedling growth
induced by 100 mM NaCl in a concentration-dependent manner,
as indicated in germination rate, germination index, vigor index
and growth of seedlings of wheat. In alfalfa ( Medicago sativa ),
NaHS pretreatment differentially activate total and isoenzymatic
activities as well as corresponding transcripts of antioxidant
enzymes (SOD, CAT, POD, and APX) under 100 mM NaCl stress,
thus resulting in the alleviation of oxidative damage induced
by NaCl (Wang et al., 2012). In addition, NaCl stress inhibited
seed germination and seedling growth, but pretreatment with
NaHS could significantly attenuate this inhibitive effect and
increase the ratio of potassium (K) to sodium (Na) in the
root parts (Wang et al., 2012). Also, under 100 mM NaCl
stress, Arabidopsis roots displayed a great increase in electrolyte
leakage and NaC/KCratio, indicating that Arabidopsis was
sensitive to salt stress, while treatment with NaHS enhanced
the salt tolerance by maintaining a higher KC/NaCratio (LiJ. et al., 2014). In addition, the level of gene expression and
the phosphorylation of plasma membrane HC-ATPase and
NaC/HCantiporter protein was promoted by H 2S, while the
effect of H 2S on the plasma membrane NaC/HCantiporter
system was removed by diphenylene iodonium (DPI, a PM
NADPH oxidase inhibitor) or dimethylthiourea (DMTU, an ROS
scavenger) (Li J. et al., 2014), suggesting that H 2S can maintain
ion homeostasis in salt-stress Arabidopsis root in the H 2O2-
dependent manner.
H2S-Induced Drought Tolerance
Similar to other stressors, drought stress, namely water
deficiency, usually leads to osmotic stress and oxidative
stress, which adversely affects plant growth, development and
production (Iqbal et al., 2016). Plants can maintain water
balance and ROS homeostasis by osmotic adjustment and
antioxidant system (Foyer and Noctor, 2009, 2011; Iqbal et al.,
2016). Zhang et al. (2010d) found that the germination rate
reduced gradually with the increasing concentrations of PEG-
6000, which mimicked osmotic stress, while NaHS treatment
could promote wheat seed germination under osmotic stress
in a dose-dependent manner, NaCand other sulfur-containing
components (S2 , SO 42 , SO32 , HSO 4 , and HSO 3 ) were
not able to replace NaHS, confirming H 2S or HS derived from
NaHS contribute to the protective roles (Zhang et al., 2010d).
Further experiments showed that NaHS treatment significantly
increased CAT and APX activities, reduced that of lipoxygenase
as well as the accumulation of MDA and H 2O2in seeds (Zhang
et al., 2010d). Additionally, exogenously applied NaHS increased
the activities of APX, GR, dehydroascorbate reductase (DHAR)
and gamma-glutamylcysteine synthetase in wheat seedlings, as
well as the contents of AsA, GSH, total ascorbate and total
glutathione under water stress compared to the control without
NaHS treatment, which in turn decreased the MDA content
and electrolyte leakage induced by water deficiency in wheat
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seedlings (Shan et al., 2011). In Arabidopsis seedlings, under
drought stress, the expression pattern of L/DCD was similar
to the drought associated genes, whose express was stimulated
further by H 2S (Jin et al., 2011). Also, seedlings treated with NaHS
exhibited a higher survival rate and a significant reduction in
the size of the stomatal aperture compared to the control (Jin
et al., 2011). In addition to these, García-Mata and Lamattina
(2010) also found that, in Vicia faba (L.) var. major and
Impatiens walleriana Hook. f., H 2S treatment could increase
relative water content (RWC) and protect plants against drought
stress.
H2S-Induced Cold Tolerance
Low temperature stress includes chilling stress ( >0C) and
freezing stress ( <0C). Low temperature usually leads to osmotic
stress and oxidative stress, plants can reduce the low temperature
injury by osmotic adjustment and activating antioxidant system
(Foyer and Noctor, 2009, 2011; Iqbal et al., 2016). Shi et al. (2013)
found that exogenous application of NaHS conferred multiple
stress tolerance including freezing tolerances in bermudagrass, in
reflected in decreased electrolyte leakage and increased survival
rate under freezing conditions. Additionally, NaHS treatment
mitigated the ROS burst and cell damage induced by freezing
stress via modulating the activities of antioxidant enzymes CAT,
GPX and GR, as well as non-enzymatic GSH pool and redox
state (Shi et al., 2013). In grape ( Vitis vinifera L) seedlings,
Fu et al. (2013) reported that treatment with NaHS showed
the high activity of SOD and gene expression of VvICE1 and
VvCBF3, lowed superoxide radical and MDA levels as well as
cell membrane permeability under chilling stress at 4C, while
HT treatment displayed contrary effect under the chilling stress.
Also, Arabidopsis seedlings overexpressing LCD or pretreating
with NaHS exhibited higher endogenous H 2S level and stronger
chilling stress tolerance, while LCD knockdown or HT pre-
treated plants displayed lower endogenous H 2S level and weaker
stress resistance. Moreover, H 2S could up-regulate the expression
of genes involved in multiple abiotic and biotic stress and
inhibited ROS accumulation (Shi et al., 2015). Ma et al. (2015)
found that the levels and enzyme activities of proteins involved
in H 2S biosynthesis (L/DCD, CAS, OAS-TL) markedly increased
at higher altitudes at 4800 and 5200 m, which in turn maintained
higher H 2S level. Exogenous H 2S application reduced ROS and
RNS (reactive nitrogen species) damage by increasing antioxidant
enzyme and GSNOR ( S-nitrosoglutathione reductase) activities,
activated the downstream defense response, resulting in protein
degradation as well as Pro and SS accumulation. However,
such defense responses could be reversed by HT and PAG,
respectively. These results illustrated that H 2S plays a central
role in L. rotata uses multiple strategies to adapt to the alpine
stress environment. Also, H 2S fumigation maintained higher
values of lightness and peel firmness of banana fruit and reduced
the accumulation of MDA under chilling stress (Luo et al.,
2015). In addition, H 2S could increase the activities of GPX,
SOD, CAT, APX, GR and the phenylalanine ammonia lyase and
total phenolics content, which in turn improved antioxidant
capacity of banana fruits, reducing H 2O2and superoxide anion
accumulation (Luo et al., 2015). Further experiments also foundthat H 2S fumigation elevated Pro content by activating P5CS
activity and decreasing that of ProDH, which might be related to
chilling injury tolerance improvement (Luo et al., 2015), similar
to the report by Li and Gong (2013). These data indicate that
H2S alleviated the chilling injury may be achieved through the
enhancement of antioxidant system and Pro accumulation in
banana fruit.
H2S-Induced Heat Tolerance
Along with global warming, high temperature has already
become a noticeable abiotic stress worldwide, and the
mechanisms of high temperature injury and heat tolerance
have attracted much attention (Wahid et al., 2007; Asthir,
2015; Hemmati et al., 2015). Christou et al. (2011) found that
pre-treatment of roots with NaHS effectively alleviated the
decrease in leaf chlorophyll fluorescence, stomatal conductance
and relative leaf water content in strawberry ( Fragaria x ananassa
cv. Camarosa) under heat stress at 42C, as well as an increase in
ion leakage and MDA accumulation in comparison with plants
directly subjected to heat stress. In addition, NaHS pretreatment
preserved AsA/GSH homeostasis, as evidenced by lower AsA
and GSH pool redox disturbances and enhanced transcription
of AsA and GSH biosynthetic enzymes, 8 h after heat stress
exposure. Furthermore, NaHS root pretreatment increased
the gene expression of antioxidant enzymes (cAPX, CAT,
MnSOD, GR), heat shock proteins (HSP70, HSP80, HSP90), and
aquaporins (PIP) (Christou et al., 2014). These results suggest
that H 2S root pretreatment activates a coordinated network of
heat shock defense-related pathways at a transcriptional level and
systemically protects strawberry plants from heat stress-induced
damage. Our previous study also showed that 0.7 mM NaHS
treatment increased the activities of CAT, GPX, SOD and GR,
and the contents of GSH and AsA, as well as the ratio of reduced
antioxidants to total antioxidants [AsA/(AsA CDHA) and
GSH/(GSHCGSSG)] in maize seedlings under normal culture
conditions compared with the control (Li Z.G. et al., 2014).
Under heat stress, antioxidant enzymes activities, antioxidants
contents and the ratio of the reduced antioxidants to total
antioxidants in control and treated seedlings all decreased,
but NaHS-treated seedlings maintained higher antioxidant
enzymes activities and antioxidants levels as well as reduced
antioxidants/total antioxidants ratio (Li Z.G. et al., 2014), similar
results also were found in tobacco cells (Li et al., 2015). In
addition, NaHS pretreatment significantly increased the survival
percentage of tobacco cells under heat stress and regrowth ability
after heat stress, alleviated a decrease in vitality of cells and an
increase in electrolyte leakage and MDA accumulation (Li et al.,
2012b). Meanwhile, the heat tolerance induced by NaHS was
markedly enhanced by exogenous application of Ca2Cand its
ionophore A23187, respectively, while was weakened by addition
of Ca2Cchelator ethylene glycol-bis( b-aminoethylether)-
N,N,N0,N0-tetraacetic acid, plasma membrane channel blocker
La3C, as well as calmodulin antagonists chlorpromazine and
trifluoperazine, respectively (Li et al., 2012b). Similarly, in maize,
pretreatment with NaHS markedly improved the germination
percentage of seeds and the survival percentage of seedlings
under heat stress, alleviated an increase in electrolyte leakage
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Li et al. H2S: A Cross-Adaptation Signal
of roots and a decrease in tissue vitality and accumulation
of MDA in coleoptiles of maize seedlings (Li et al., 2013a).
Furthermore, NaHS pretreatment could improve the activity
of11-pyrroline-5-carboxylate synthetase (P5CS) and lowered
that of Pro dehydrogenase (ProDH), which in turn induced the
accumulation of endogenous Pro in maize seedlings (Li et al.,
2013a). Also, exogenously applied Pro could increase endogenous
Pro content, followed by increase in the survival percentage of
maize seedlings under heat stress (Li et al., 2013a). These results
suggest that NaHS pretreatment can improve the heat tolerance
in plants and the acquisition of heat tolerance induced by NaHS
may require the synergistic effect of antioxidant system, calcium
messenger system, HSPs and Pro.
H2S-Induced Flooding Tolerance and
Pathogen Resistance
Flooding stress usually causes hypoxia, and even anoxia in
plant roots, plants can improve hypoxia tolerance by reducing
oxidative damage (van Dongen and Licausi, 2014). Cheng et al.
(2013) found that hypoxia could induce root tip death of pea
seedlings, while pretreatment with exogenous H 2S dramatically
alleviated cell death by protecting root tip cell membranes from
ROS damage induced by hypoxia and by inhibiting ethylene
production. Conversely, root tip death induced by hypoxia was
strongly enhanced by inhibiting the key enzymes responsible for
endogenous H 2S biosynthesis (adding hydroxylamine to inhibit
LCD activity). These results demonstrated that H 2S can enhance
the tolerance of the plant to hypoxic stress by alleviating hypoxia-
induced root tip death in pea seedlings.
More interestingly, H 2S also could transcriptionally regulate
MIR393-mediate auxin signaling, including MIR393a/b and their
target genes (TIR1, AFB1, AFB2, and AFB3), and this regulation
was related with H 2S-induced antibacterial resistance (Shi et al.,
2015).
All of the above studies in this section show exogenous
application of NaHS (a H 2S donor) can induce cross-adaptation
to HM, salt, osmosis, drought, cold, heat and hypoxia stresses
in different plant species, and the optimal NaHS concentration
range from 0.05 to 1.5 mM ( Table 2 ), while higher NaHS
concentration ( >1.5 mM) exhibits negative effect on plant
growth, development, survival, and even the acquisition of stress
tolerance. Therefore, the optimal concentration of NaHS should
be carefully selected according to plant species and experimental
system.
CONCLUSION AND FUTURE
PROSPECTIVE
In general, after undergoing a moderate stress, plants not only
can improve the resistance to this stress, but also can increase
the tolerance to subsequent other stresses, which known as cross-
adaptation. Many studies found that signaling triggered by a
moderate stress, such as Ca2C, ABA, H 2O2, and NO signaling,
is a common response of plants to abiotic and biotic stress, whichin turn induces the acquisition of cross-adaptation. In addition,
exogenously applied these signal molecules also can trigger
corresponding signaling, followed by improving stress tolerance
of plants, thus Ca2C, ABA, H 2O2, and NO are considered to be
candidate signal molecules in cross-adaptation in plants (Knight,
2000; Gong et al., 2001; Li and Gong, 2011; Li et al., 2012b; Fang
H. et al., 2014; Qiao et al., 2015; Chen et al., 2016). More recently,
many research groups found that a number of abiotic stresses
also can trigger H 2S signaling, while exogenously applied H 2S
can induce cross-adaptation to multiple stresses, indicating that
H2S represents a potential candidate signal molecule in cross-
adaptation in plants (Li, 2013; Lisjak et al., 2013; Calderwood
and Kopriva, 2014; Hancock and Whiteman, 2014; Fotopoulos
et al., 2015; Guo et al., 2016). However, H 2S acts as a signal
molecule in plants cross-adaptation, the following questions need
to be further answered: (1) Receptor or target of H 2S. Due to
H2S is easy to penetrate the cell membrane, maybe there is no
H2S receptor in plant cells, but Li et al. (2011) and Aroca et al.
(2015) found that H 2S could modify the activity of some proteins
with sulfhydryl (-SH) by sulfhydrylation (-SSH), whether these
proteins are the receptors of H 2S needs to be further research. (2)
Physiological concentration of H 2S. Many assay methods for H 2S
including colorimetric, fluorescence-based, gas chromatographic
and electrochemical methods give highly contrasting results
(Table 2 ; Peng et al., 2012; Li, 2015b), so accurate physiological
concentration of H 2S in plant cells or organelles is waiting for
uncovering. It will be important to design the stress treatments
closer to physiologically relevant stress intensities, thus low
micromolar rather than millimolar HM concentration should
be investigated in order to strengthen the conclusions. (3)
Crosstalk between H 2S and other signal molecules in cross-
adaptation. The acquisition of abiotic tolerance is involved in
a signal network consisting of many signal molecules including
H2S, interaction among signal molecules needs to be updated
and perfected. (4) Physiological, biochemical and molecular
mechanisms of H 2S-induced cross-adaptation. The study on
H2S-induced abiotic tolerance including cross-adaptation has
just started, many physiological, biochemical and molecular
mechanisms require being expounded using transcriptome,
proteome and metabolome approaches.
AUTHOR CONTRIBUTIONS
Z-GL wrote and revised the paper, XM and Z-HZ provided the
idea.
ACKNOWLEDGMENTS
This research is supported by National Natural Science
Foundation of China (31360057) and Doctor Startup Foundation
of Yunnan Normal University China (01200205020503099). We
appreciate the reviewers and editors for their exceptionally
helpful comments about the manuscript.
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fpls-07-01621 October 24, 2016 Time: 16:15 # 10
Li et al. H2S: A Cross-Adaptation Signal
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Conflict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
The reviewer SM and handling Editor declared their shared affiliation, and the
handling Editor states that the process nevertheless met the standards of a fair and
objective review.
Copyright © 2016 Li, Min and Zhou. This is an open-access article distributed
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Frontiers in Plant Science | www.frontiersin.org 12 October 2016 | Volume 7 | Article 1621 | 51752ea9921d9e648af766a9a03936ea31aac98f | page_0011 |
arXiv:cond-mat/0605239v1 [cond-mat.mtrl-sci] 9 May 2006Molecular-Spintronics : the art of driving spin through molecules
S. Sanvito∗and A. R. Rocha
School of Physics, Trinity College, Dublin 2, IRELAND
(Dated: 29th October 2018)
Spintronics is the ability of injecting, manipulating and detecting ele ctron spins into solid state
systems. Molecular-electronics investigates the possibi lity of making electronic devices using organic
molecules. Traditionally these two burgeoning areas have l ived separate lives, but recently a growing
number of experiments have indicated a possible pathway tow ards their integration. This is the
playground for molecular-spintronics , where spin-polarized currents are carried through molecu les,
and in turn they can affect the state of the molecule. We review the most recent advances in
molecular-spintronics. In particular we discuss how a full y quantitative theory for spin-transport in
nanostructures can offer fundamental insights into the main factors affecting spin-transport at the
molecular level, and can help in designing novel concept dev ices.
PACS numbers:
Contents
I. Introduction 1
II. Spin-Electronics 2
A. Transition metals and spin valves 2
B. Spin valves 3
C. Spin polarization of a device 4
III. Molecular-Electronics 4
A. Electrons transport through molecules 4
B. The bonding with the contacts 5
C. Why spins and molecules? 6
IV. Quantitative Transport Theory 7
A. Simple Model 7
B.Ab initio methods 8
V. Molecular Spin-valves 9
A. Metallic and tunneling junctions 9
B. Carbon Nanotubes 13
C. Long molecules and phonons 14
VI. More exotic phenomena 15
A. Molecular Magnets 15
B. d0ferromagnetism and magnetic proximity 16
VII. Conclusions 17
Acknowledgement 17
References 17
I. INTRODUCTION
Very few scientific discoveries have moved from an
academic laboratory to industrial mass production as
quickly as the giant magnetoresistance effect (GMR)1,2,
now exploited in any read-head for standard hard drives.
GMR is the change of the electrical resistance of a mag-
netic device when an external magnetic field is appliedand it is essentially associated to a change in the mag-
netic state of the device itself. The revolutionary sci-
entific message revealed by the GMR effect is that the
electron spin, as well as the electronic charge, can be
used in electronic applications. This somehow has set a
new paradigm.
More recently, the electron spin has made its appear-
ance in semiconductor physics. This new field, usually
called spin-electronics or spintronics3,4,5has the poten-
tial of bringing memory and logic functionalities on the
same chip. The electron spin is the ultimate logic bit. In
semiconductors spin preserves coherence over extremely
long times6and distances7, thus it offers the tantaliz-
ing prospect of being used for quantum logic8. More-
overallelectronicwaysofmanipulatingthespindirection
have been proposed9. These are based on the spin-orbit
interaction10, which interestingly plays a ubiquitous rˆ ole
in semiconductor spintronics.
One the one hand spin-orbit allows us to manipulate
the electron spins by electric only means. It is an in-
trinsic property of the electronic structure, and therefore
it can be engineered by appropriate heterojunction fab-
rication and manipulated by stress or with an external
electric field. Importantly it can be controlled, at least
in principle, at an extremely local level. The spin Hall11
effect, a solid state version of the Stern-Gerlach exper-
iment utilizing spin-orbit interaction instead of a mag-
netic field gradient, is a good example of all-electrical
spin manipulation. On the other hand spin-orbit is the
main source of spin-dephasing through the Dyakonov-
Perel mechanism12, i.e. in semiconductors it is the main
interaction responsible for reducing spin coherence.
Ultimately spin looks like an attractive degree of free-
dom to be used in logic because the energy scale relevant
for its typical dynamics is order of magnitudes smaller
than that involved in manipulating the electron charge
in standard transistors. This can translate in devices
exhibiting ultra-low power consumption and high speed.
Moreover the sole existence of magnetic materials with
high Curie temperature suggests the possibility of pow-
erless non-volatility. | ce750a91139b8da9337138787fb059155774d160 | page_0000 |
2
At the same time and almost in parallel there has
been a growing interest in making electronic devices
using organic molecules. This field, which takes the
suggestive name of molecular-electronics13, aims at re-
placing standard semiconductors with organic materials.
These have the advantages to be manufactured with low-
temperature low-cost chemical methods, instead of ex-
pensive high-temperature solid-state growth (e.g. molec-
ular beam epitaxy) and patterning (lithography) tech-
niques. In addition the endless possibilities of chemi-
cal synthesis and end-groups engineering give good ex-
pectation for new concept devices. Negative differen-
tial resistance14and rectification15have been already
proved at the molecular level and prototypes of molec-
ular transistors17, memories16and logic gates18,19, have
all been demonstrated.
It is only until recently that spin has entered the
realm of molecular electronics. The driving idea be-
hind the first pioneering experiment of Tsukagoshi and
coworkers20, who injected spin polarized electrons into
carbon nanotubes, is that spin-orbit interaction is very
weak in carbon-basedmaterials. This fact, in addition to
the ratherweakhyperfine interaction, suggestsextremely
long spin relaxation times, and therefore the possibil-
ity of coherent spin propagation over large distances. A
rather conservative estimate of the spin diffusion length
from the Tsukagoshi’s experiment indicated 130 nm as
a lower bound of the spin-diffusion in carbon nanotubes.
These findings have stimulated a growing activity in the
areaand severalexperiments dealing with moleculartun-
neling junctions21, spin-transport through polymers22,23
and optical pump/probe experiments through molecular
bridges24have recently appeared.
The molecular world has all the ingredients that spin-
electronics needs. The conductivity of polymers can be
changed by more than ten order of magnitudes25and ele-
mentary molecules can be designed with the desired elec-
tronic structure. Molecules can be anchored to metals in
numerous ways and the bonding angle can be further
engineered by the coverage density. The spin-relaxation
times can be extremely long and furthermore both para-
magnetic and ferromagnetic molecules26are available.
Theory and modeling is a powerful engine for the de-
velopment of this new area. At present accurate quanti-
tativealgorithmsforevaluatingthe I-Vcharacteristicsof
molecular devices are available27,28,29,30,31,32,33, and they
are revolutionarizing the world of nanoscale device simu-
lators, as density functional theory (DFT)34did for elec-
tronic structure methods in the sixties. Some of these al-
gorithms are spin polarized27,28,29,32, and therefore read-
ily applicable to spin-transport phenomena. Certainly
such calculations are not easy. For instance the degree
of accuracy needed for the description of the underling
electronic structure may go beyond what is standard in
solid state physics35. Here in fact one needs to describe
the metallic state of the current/voltage electrodes, the
molecular state of the actual device and magnetism on
the same footing. In addition since a transport prob-lem is essentially a non-equilibrium problem, variational
principles are not valid. One cannot depend on the free
energy for atomic relaxation and the full dynamics must
be considered36. Finally detailed information about the
elementary excitations (phonons, spin waves etc.) and
the exact atomic positions are essential.
The aim of this review is to offer a complete overview
of the fascinating field of molecular-spintronics. In par-
ticular we will demonstrate that a quantitative theory of
quantum transport can offer important insights and can
be an invaluable tool for understanding complicated ex-
periments and for novel device designing. The paper is
organized as follows. In the first two sections we will in-
troduce the two fields of spin- and molecular-electronics.
Then we will introduce the main computational tools,
and we will discuss the latest progresses with molecu-
lar spin-valves. Finally we will overview the most recent
andcontroversialfindings, namely transportin molecular
magnets, d0ferromagnetism and contact induced ferro-
magnetism.
II. SPIN-ELECTRONICS
A. Transition metals and spin valves
Magnetic transition metals and their permalloys oc-
cupy an important place in the field of spin-electronics.
This is essentially due to their generally high Curie tem-
perature (for a commercially useful magnetic materials it
must exceed ∼500oK37), and the possibility of engineer-
ing the various magnetic properties by alloying. The fer-
romagnetism in 3 dtransition metals can be understood
by simply looking at their electronic structure.
The nominal atomic configurations of Ni, Co and Fe
are respectively 4 s23d8, 4s23d7and 4s23d6. Therefore in
forming a solid one expects the Fermi level ( EF) to be
in a region of density of states (DOS) with dominant d
character. Since the dshells arerather localized the DOS
is extremely large around EFand the material becomes
Stoner unstable thus developing a ferromagnetic ground
state. The band energies ǫ/vectorkσfor the two different spin
orientations ( σ=↑,↓) are shifted with respect to each
other by a constant ∆ = ǫ/vectork↓−ǫ/vectork↑, with ∆ approximately
1.4 eV in Fe, 1.3 eV in Co and 1.0 eV in Ni. More so-
phisticated DFT calculations show that such picture is
a good approximation of the real electronic structure of
Ni, Co and Fe.
In addition to the formation of a net magnetic moment
a consequence of the bandstructure spin-splitting is that
the Fermi surface for the two spin directions is rather dif-
ferent. This difference is more pronounced in the case of
strong ferromagnet, where only one of the two spin-split
dmanifolds is fully occupied (majority band) while the
other has some fractional occupation (minority band).
An example of this situation is fcc Co (the high temper-
ature phase), whose electronic structure is presented in
figure 1. | ce750a91139b8da9337138787fb059155774d160 | page_0001 |
3
-10 -8 -6 -4 -2 0 2 4
Energy (eV)DOS (Arb. Units)b1)
b2)
c1) c2)
Figure 1: a) Band structure, b) densityof states, and c) Ferm i
surface for fcc Co. The figures a1), b1) and c1) refers to
the majority spin electrons, while a2), b2) and c2) to the
minority. The pictures a) and b) have been obtained with
density functional theory using the code SIESTA38, and c)
from an spdtight-binding Hamiltonian39.
The main feature of the bandstructure of Co (and in-
deed of the other 3 dmagnetic transition metals) is the
presence of a broad (delocalized) and only weakly spin-
splitsband, and of a narrow(localized) and largely spin-
splitdband. The former has almost free electron-like
character for energies both below (note the parabolic be-
havior of the bands around Γ for E∼-9 eV) and above
EF. In contrast the latter is only about 5 eV wide and
cutsclosetotheFermilevel. Becauseofthespin-splitting
of thedmanifold, ∆, the majority spin band has an al-
most spherical Fermi surface (see figure 1c1), while the
minority one has a rather complicated structure, mostly
arising from the dmanifold (see figure 1c2). The differ-
ent structure of the Fermi surface for majority and mi-
nority spins and the fact that these differences arise from
a different orbital character are the main ingredients for
understanding the transport properties of magnetic tran-
sition metal heterostructures.Importantly the effects of alloying can be understood
in the context of a rigid-band model, by shifting the
Fermi level according to the valence of the dopant40,41.
Finally it is worth mentioning that there are materials
that at the Fermi level present a finite DOS for one spin
specie and a gap for the other. These are known as half-
metals42and are probably among the best candidates as
materials for future magneto-electronics devices.
B. Spin valves
The prototype of all spin devices is the spin-valve.
This is formed by two magnetic layers (normally tran-
sition metals) separated by a non-magnetic spacer (ei-
ther metal or insulator). One of the two magnetic layers
is free to rotate in tiny magnetic fields, while the other
usually is pinned by exchange coupling with a antiferro-
magnet or by strong magnetic anisotropy. The current
passing through a spin-valve depends over the mutual
orientation of the two magnetic layers and it is typically
higher for a parallel alignment (PA) than for an antipar-
allel(AA). Thusaspin-valvebehavesessentiallyasaspin
polarizer/analyzer device. The quantity that defines the
effectiveness of the spin-filtering effect is the GMR ratio
RGMRdefined as (“optimistic definition”)
RGMR=IPA−IAA
IAA. (1)
An alternative definition (“pessimistic definition”) using
IPA+IAAas normalization is sometime used.
An intuitive understanding of the spin-filtering pro-
duced by a spin-valve can be obtained by looking at the
Fermi level lineup of the materials forming the device.
Let us consider for example a Ni/Cu/Ni spin-valve (see
figure2), andassumethatthetwospin-bandsdonotmix.
This is the two spin fluid approximation, which is valid
in the case of weak spin-orbit scattering and collinear
magnetism43.
In the AA a spin electron propagates in the majority
spin band in one layer and in the minority band in the
other. Consequently electrons always travel across the
Fermi surfaces of Cu and of both the spin-bands of Ni.
In contrast in the PA the two spin currents are rather
different. The majority current is made from electrons
that have traveled within the Fermi surfaces of Cu and
that of the majority spin of Ni, while the down spin cur-
rent from electrons that have traveled within the Fermi
surfaces of Cu and that of the minority spin of Ni. This
leads to two different current paths for the AA and the
PA.Since the twospincurrentsaddto formthe totalcur-
rent and since generally the resistances of majority and
minority electrons are different in a magnetic transition
metal, the current passing through the PA and AA con-
figurations are different. Importantly the larger is the
mismatch between the two spin currents, the larger in
the GMR ratio. | ce750a91139b8da9337138787fb059155774d160 | page_0002 |
4
Figure 2: Magnetoresistance mechanism in a Ni/Cu/Ni spin
valve in the two spin fluid approximation. In the parallel cas e
a)theresistance ofthemajority spinchannelislowsinceth ere
is good match of the majority Fermi surfaces across the entir e
device. Incontrastintheantiparallel stateb)thealignme ntof
the Fermi surface is such to have one high resistance interfa ce
for both the spin channels. This is given by the interface
between the minority spin band of Ni and that of Cu. The
formation of high resistance channels for both spins in the A A
is responsible for the GMR effect.
C. Spin polarization of a device
An important question is how to quantify the relative
difference between the two spin currents in a magnetic
device and how to relate this properties to the elemen-
tary electronic structure of the materials forming the de-
vice. We then define the spin-polarization Pof a mate-
rial/device as
P=I↑−I↓
I↑+I↓, (2)
whereIσis thespin- σcontributiontothecurrent. Iσand
Pare not directly observable and must be calculated or
inferred from indirect measurements. Unfortunately the
way to relate the spin-current Iσto the electronic struc-
ture of a material is not uniquely defined and depends on
the particular experiment carried out.
As brilliantly pointed out by Mazin44, the relation be-tween the spin-polarization of a magnetic material and
its electronic structure depends critically on the trans-
port regime that one is considering (ballistic, diffusive,
tunneling ..). As a first approximation the current Iis
simply proportional to NFvn
F, whereNFandvFare the
DOS at the Fermi level and the Fermi velocity respec-
tively. Different transport regimes weight the contribu-
tion of the Fermi velocity differently, and one has n= 2
for diffusive transport, n= 1 for ballistic transport and
n= 0 for tunneling.
Therefore the spin-polarization Pbecomes
Pn=N↑
F(v↑
F)n−N↓
F(v↓
F)n
N↑
F(v↑
F)n+N↓
F(v↓
F)n. (3)
Typical values of Pnfor several magnetic metals are re-
ported in table I.
Pn(%)n=2n=1n=0
Fe 20 30 60
Ni 0 -49 -82
CrO2 100 100 100
La0.67Ca0.33MnO3 92 76 36
Tl2Mn2O7 -71 -5 66
Table I: Spin-polarization of typical magnetic metals acco rd-
ing to the various definitions given in the text. The data
are taken from literature as follows: Ni and Fe44, CrO 245,
La0.67Ca0.33MnO346and Tl 2Mn2O747.
Importantly the spin-polarization of a device can be
different from that of the materials forming it. This
is connected to the fact that the bonding at the inter-
facebetween twodifferent materialscan be stronglyspin-
selective. For instance if the bonding between two ma-
terials has mainly s-character, then one expects strong
scattering for d-like electrons. As a consequence the
spin-polarization of the current will be determined by
the spin-polarization of the almost free s-electrons. This
is usually much smaller than that of the d-electrons and
it may even have the opposite sign. For instance it is
demonstrated that the sign of the magnetoresistance of
a magnetic tunneling junction can be altered by simply
replacing the insulator forming the barrier48.
III. MOLECULAR-ELECTRONICS
A. Electrons transport through molecules
Transport through molecules and in general through
low dimensional objects is somehow different than that
in standard metals or semiconductors. This is substan-
tially due to the collapse of the Fermi surface into a sin-
gle energy level (the highest occupied molecular orbital
- HOMO). The nature and lineup of the HOMO with | ce750a91139b8da9337138787fb059155774d160 | page_0003 |
5
the Fermi energy of the current/voltage probes deter-
mine most of the transport properties. Let us consider
the simple case of a two probe device. Following a sim-
ple model proposed by Datta49the typical energy level
lineup is schematically presented in figure 3.
HOMOa)
−IP−EA
EWF
FEWF
Fb)
LUMO
Figure 3: Energy level lineup between a molecule and two
current voltage probes. In the weak coupling limit a) the
molecule is characterized by the ionization potential (IP) and
the electron affinity (EA), which line up with the metal Fermi
energy (WF is the work function of the contact). In the case
of strong coupling b) between the molecule and the leads the
molecular levels shift and broaden. It is then more appro-
priate to discuss transport in terms of HOMO and LUMO
states.
In absence of any coupling (figure 3a) both the energy
levels of the molecule and the Fermi level of the elec-
trodes will align with a common vacuum level. In this
case the system is characterized by the work function of
the electrodes and both the ionization potential (IP) and
the electron affinity (EA) of the molecule. In this setup
the molecule can exchange electrons with the electrodes
only if the typical temperature is comparable to either
IP-WF or WF-EA, a condition which is normally not
satisfied. This guarantees local charge neutrality of the
whole system and integer occupation of the molecule.
In contrast, the interaction between the molecular lev-
els and the extended wave-functions of the metallic con-
tactshastheeffectofbroadeningandshiftingthemolecu-
larlevels. In the extremelimit of largecoupling extended
states spanning throughthe entire system (electrode plus
molecule) can develop and the molecular device will be-
have as a good metal. In this limit the molecular lev-
els cannot be associated any longer to the elementary
removal energies of the isolated molecule and a descrip-
tion in terms of fractionally occupied HOMO and LUMO
(lowest unoccupied molecular orbital) is more appropri-
ate.
The transition from integer to fractional occupation of
the molecule somehow depends on the typical molecular
charging energy (say the EA) compared to the hopping
integral Γ between the molecule and the contacts (Γ /¯h
is the escape rate from the molecule to the contacts).
One has integer occupation if EA ≫Γ and metallic-like
behaviour when Γ ≫EA. This is essentially the same
physicsleadingtoMottmetal-insulatortransitioninsolid
state. An electronic structure theory capable of explor-
ing on the same footing all the intermediate situations
between the strong and weak coupling limit is still notavailable unless at prohibitive computational costs35.
The effect of an applied bias Vis that of shifting the
chemicalpotentialsofthe twocurrent/voltageprobesrel-
ative to each other by eV, withethe electronic charge.
As a rule of thumbs current will flow whenever a molecu-
lar level (either the HOMO or the LUMO) is positioned
within such a bias window. The appearing of molecu-
lar levels in the bias window when the potential is in-
creased typically leads to changes in the slope of the I-V
characteristics, in steps in the differential conductance
dI/dV(V) and in peaks in its derivative d2I/dV2(V).
This means that fingerprints of the molecular spectrum
can be found in the measurement of its electrical proper-
ties. The same is true for the molecular elementary ex-
citations, and peaks in d2I/dV2(V) can be found in cor-
respondence of the energy of relevant phonon modes50.
B. The bonding with the contacts
One of the fundamental aspects of molecular electron-
ics is that the bonding between a molecule and the cur-
rent/voltageprobescanbe engineeredtoadegreeusually
superior to that achievable in conventionalinorganic het-
erostructures. This can dramatically change the current
flowing through a device. Consider for instance the sim-
ple case of an atomic gold chain, described by sorbitals
only, sandwiching a π-bonded molecule (see figure 4).
a)
s s
pxpxs sb)p
θxpx
Figure 4: Au atomic chain sandwiching a π-bonded molecule
(say an S 2molecule). a) the molecule is aligned with the Au
chain and the transmission is suppressed because the matrix
element /an}bracketle{ts|H|px/an}bracketri}htvanishes. In contrast when the molecule
forms some angle θwith the Au chain b) then a component
of the hopping integral along the bond develops and current
can flow.
Let us assume that the relevant molecular state (the
one close to the Fermi level of the gold chain) is formed
bypxorbitals, i.e. those perpendicular to the chain axis.
When the molecule is positioned along the axis of the
chain the hopping integral between the molecule and the
chain∝angbracketlefts|H|px∝angbracketrightvanishes regardless of the separation be-
tween the two. This is simply the result of the particu-
lar symmetry of the problem since sandpxorbitals do | ce750a91139b8da9337138787fb059155774d160 | page_0004 |
6
not share the same angular momentum about the bond
axis51. As a consequence the current is identically zero.
In contrast if the molecule is not coaxial to the chain
(figure 4b), then there is a component of the pxorbital
along the bond axis and the hopping integral becomes
γspσsinθ, where γspσis thespσhopping integral and
θthe bond angle. This dependence of the bonding on
the bond orientation may have dramatic consequences
on theI-Vcharacteristics. In figure 5 we present the
I-Vcurve for the system of figure 4 calculated with a
self-consistent tight-binding model where it is assumed a
linear dependence of the on-site energies over the orbital
occupation (see reference [35] for details).
0 0.5 1 1.5 2
V (Volts)010203040I (µΑ)θ = 5o
15o
30o
45o
60o
Figure 5: I-Vcharacteristics for a S 2molecule sandwiched
between two semi-infinite gold chains (see figure 4). The
curves are calculated using the tight-binding based non-
equilibrium Green function method of reference35with the
following parameters: ǫAu=-5.9 eV, ǫS=-6.15eV eV, γssσ=-
3.0 eV,γspσ=1.52 eV, γppπ=-0.98 eV, UAu=-6.7 eV and US=-
6.15 eV. ǫis the on-site energy, γhopping integral and Uthe
charging energy.
From figure 5 it is clear that the I-Vcharacteristics
of a molecule can be largely engineered by simply chang-
ing the details of the bonding with the electrodes. This
is considerably more complicated in extended interfaces
(for instance between two metals), since disorder, inter-
diffusion and roughness have the effect of averaging out
the atomistic details of the bonding. It is important to
remarkthat evenwhenmolecularlayersaregrownagood
level of tuning of the bonding properties still exists. For
instance the bonding site and the bond angle usually de-
pend on the layer density (coverage)52, and these can be
further tuned by changing the end groups.
C. Why spins and molecules?
What are the advantages of using molecules instead of
inorganic materials for performing spin-physics? These
are essentially two. On the one hand there are intrin-
sic molecular properties and in particular the weak spin-
orbitandhyperfineinteractions. Ontheotherhandthereare the properties connected to the formation of inter-
faces between magnetic metals and molecules. We will
return to the interfacial properties in the next sections,
here we focus our attention only on the intrinsic aspects.
Spin-orbit interaction is a relativistic effect which cou-
ples the electron spin /vectorSwith its angular momentum /vectorL.
The spin-orbit Hamiltonian in general can be written as
HSO=VSO/vectorS·/vectorL, whereVSO(/vector r) is a term which contains
the gradient of the electrostatic potential. Although it
is rather intuitive to realize that the strength of this in-
teraction grows with the atomic number Z(it is propor-
tional to Z4), its actual value in the solid state depends
on various factors such as the crystal symmetry and the
material composition. Importantly the spin-orbit effect
is responsible for spin-precession and the loss of spin-
coherence. In organic materials usually the spin-orbit in-
teraction is rather small. This is mostly due to the small
atomic number of carbon. In table II we compare the
spin-orbit splitting ∆ SOof the valence band of several
semiconductors53with that of carbon diamond54. The
∆SO(meV)
Si 44
Ge 290
GaAs 340
AlAs 280
InAs 380
GaP 80
InP 111
GaSb 750
AlSb 670
InSb 980
C 13
Table II: Valence band spin-orbit splitting for various sem i-
conductors.
table shows that in carbon the spin-split of the valence
band is approximately one order of magnitude smaller
than in ordinary III-V or group IV semiconductors and
one should expect a considerably longer spin-lifetime6,7.
Another important interaction, which generally leads
to spin-decoherence, is the hyperfine interaction between
electron and nuclear spins. This has the form
Hhyp=Ahyp/vector s·/vectorSN, (4)
where/vector sand/vectorSNare respectively the electronic and nu-
clear spin, and Ahypis the hyperfine coupling strength.
Similarly to the case of spin-orbit, also hyperfine interac-
tion is a source of spin de-coherence55, since the random
flipping of a nuclear spin can cause that of an electron
spin. However, in III-V semiconductors hyperfine inter-
action was also proved to be a tool for controllingnuclear
spins via optically polarized electron spins56. In organic
materials usually the hyperfine interaction is weak. The
main reason for this is that most of the molecules used | ce750a91139b8da9337138787fb059155774d160 | page_0005 |
7
for spin-transport are π-conjugate molecules where the
transport is mostly through molecular states localized
over the carbon atoms. Carbon, in its most abundant
isotopic form,12C, has nuclear spin SN=0, and therefore
is not hyperfine active. Moreoverthe π-states are usually
delocalized and Hhypcan be anyway rather small. In ta-
ble III we report the value of the nuclear spin for various
atomic species with their relative isotopic abundance.
Isotope IA (%) SN
1H 99.98 1/2
2H 0.02 1
12C 98.93 0
13C 1.1 1/2
14N 99.632 2
15N 0.368 1/2
16O 99.757 0
18O 0.205 0
19F 100 1/2
69Ga 60.108 3/2
71Ga 39.892 3/2
75As 100 3/2
28Si 92.2297 0
29Si 4.6832 1/2
30Si 3.0872 0
Table III: Nuclear spin for elements present in typical orga nic
molecules and in both Si and GaAs. Here we report the nu-
clear spin for the most abundant isotopes, together with the ir
relative isotopic abundance (IA).
Estimatesofthe spin-lifetime oforganicmaterialsfrom
transport experiments are at the moment only a few.
Moreover in most cases these are extracted from spin-
valves measurements by fitting to the Jullier’s formula57.
This procedures does not distinguish the source of spin-
flip, which may not be located inside the molecule, but
at the interface with the magnetic electrodes. Therefore
these measurements are likely to offer a conservativeesti-
mate of the spin-lifetime. Nevertheless the values of the
spin diffusion length reported in the literature are rather
encouraging for carbon nanotubes (130nm)20, polymers
(200nm)23, or Alq 3molecules (5nm)58.
Finally a conclusive note needs to be made on con-
ducting polymers. These are extremely attractive ma-
terials since their electrical conductivity can be changed
by over twelve orders of magnitude with the chemical
or electrochemical introduction of various counterions59.
Spin-dynamics in polymers has been extensively stud-
ies with EPS spectroscopy60and it is largely dominated
by the presence of paramagnetic centers in the form of
free radicals, ion-radicals, molecules in triplet states and
transition metal complexes. Even more interesting is the
fact that the elementary excitations leading to electron
transport are not band-like but usually involve lattice
vibrations, and most importantly some of them are spin-polarized.
Forinstanceinthe trans-isomerofpolycetylenethe Su-
Schrieffer-Heeger theory59predicts a soliton-like trans-
port mechanism. This has a peculiar spin-charge rela-
tionship, since a neutral soliton corresponds to a radi-
cal with spin 1/2, while both negatively and positively
charge solitons are spinless and diamagnetic. The study
of spin-transport in devices made by transition metals in
contact with such polymers is potentially extremely in-
teresting. This is because of the proximity of two funda-
mentally different ground states, one electronicallycorre-
lated (the magnetic material), and one with strong corre-
lation between electronic and vibrational degrees of free-
dom (the polymer). The investigation, both experimen-
tally and theoretically, of these combined systems is in
its infancy61.
IV. QUANTITATIVE TRANSPORT THEORY
A. Simple Model
Modern theory of quantum transport is based on scat-
tering theory in conjunction with accurate electronic
structure methods. Although this approach has recently
come to question, in particular in the case of electrons
interacting beyond the mean-field level62, it still remains
the most versatile and scalable available. In addition its
foundations are extremely intuitive and simple. Let us
start our discussion by presenting a simple model, first
introduced by Datta49, which already contains all the el-
ements of a more formal and accurate theory.
Consider a given molecule attach to two cur-
rent/voltage probes kept at two different chemical po-
tentials µα, withα=L (left), R (right). The leads
are assumed featureless, which is with a constant DOS.
The molecule is described by an energy level ǫ(say the
HOMO), coupled to the current/voltage probes by the
hopping integrals tα(α=L, R). The density of states as-
sociated to such a state is
Dǫ(E) =t/2π
(E−ǫ)2+(t/2)2, (5)
where the level lifetime ¯ h/tis determined by the coupling
withtheleadsonly t=tL+tR. Boththecurrent Iflowing
through the molecular state and state occupation Ncan
be determined by balancing the in-going and out-going
fluxes and read
I=e
¯h/integraldisplay+∞
−∞dE Dǫ(E)tLtR
t[fL(E)−fR(E)],(6)
and
N=/integraldisplay+∞
−∞dE Dǫ(E)tLfL(E)+tRfR(E)
t,(7)
wherefα(E) =1
1+e(ǫ−µα)/kBTis the Fermi distribution of
the contact α. From the equations above it is clear that | ce750a91139b8da9337138787fb059155774d160 | page_0006 |
8
current will flow only (at least for small broadening and
low temperature) if the energy level is in between the
chemical potentials of the two leads. With no external
biasthese areidentical, but when apotential Visapplied
thenµL−µR=eVand current will flow.
In general ǫdepends on the details of the electronic
structure of the system. As a simple approximation we
may assume it is a function of the level occupation only
ǫ=ǫ(N). This suggests a simple self-consistent proce-
dure where ǫ(N) and the equation (7) are solved itera-
tively before the current is evaluated with the (6).
Spin can be easily introduced in this simple model in
the two spin fluid approximation. Since the two spin
channels do not mix the equations (6) and (7) can be
replaced by two pairs of equations for the spin-resolved
molecular level occupation Nσand the spin-current Iσ.
In a similar way the molecular level can also be spin-
polarized ǫ→ǫσand it may depend of the spin den-
sity instead of the density only ǫσ(N↑,N↓). Importantly
in the case where the current/voltage probes are ferro-
magnetic spin-degeneracy is lifted by introducing spin-
dependent hopping integrals tσ
αbetween the leads and
the molecule. These however capture the fact that ma-
jority and minority electrons couple to the molecule in
a different way, but not that the DOS for the different
spin directions in a ferromagnet is different. For this
last feature a more detailed description of the electronic
structure of the leads is needed.
B.Ab initio methods
Thenon-equilibriumGreen’sfunction(NEGF)method
is by far the most used among all the quantum transport
schemes. Although it is based on very rigorous ground63
it can be understood as the natural extension of the toy-
model discussedin the previoussection. The generalidea
is to divide a two probe device into three regions: two
current/voltage probes and a scattering region. The cri-
terion for this fragmentation is that the scattering region
is the portion of the device where the potential drops. Its
boundaries are defined by the condition that the charge
densitymatchesexactlythatofthebulkmaterialforming
theleads(seereference27foramoredetaileddescription).
Let usassumethat theproblemcan beformulatedover
some sort of localized basis set, and therefore the Hamil-
tonian for the whole system (scatteringregionplus leads)
is simply an infinite hermitian matrix. The central quan-
tity, which replaces the simple density of states Dǫ(E), is
the non-equilibrium Green’s function for the scattering
regionG(E)
G(E) = lim
η→0[(E+iη)−HS−ΣL−ΣR]−1.(8)
This is the Green’s function associated to the Hamilto-
nianHS+ΣL+ΣR,whichiscomposedbytheHamiltonian
of the scattering region HSand the self-energies Σ Land
ΣR.Note that if one assumes that HS, ΣLand Σ Rare just
C-numbers, then i[G(E)−G∗(E)] isDǫ(E) forǫ→HS
(real) and tα/2→Σα(purely imaginary). Thus the self-
energies can be associated with the interaction between
the scattering region and the current/voltage probes. In
practice they can be written as Σ L=H†
LSgLHLSand
ΣR=HRSgRH†
RS, withHαSthecouplingmatrixbetween
the leads αand the scattering region. gαare the surface
Green’s functions for the leads, i.e. the Green’s func-
tion for a semi-infinite lead evaluated at the termination
plane64. Thus the self-energies contain information on
both the coupling between the scattering region and the
electrodes and on the electronic structure of the leads
themselves.
The crucial point is that both the two-probe current I
andthedensitymatrixassociatedtothescatteringregion
ρcan be obtained from the Green’s function G(E)
I=e
h/integraldisplay+∞
−∞dETr[GΓLG†ΓR][fL(E)−fR(E)],(9)
and
ρ=1
2π/integraldisplay
dE G[ΓLfL+ΓRfR(E)]G†,(10)
whereG=G(E), Γ = Γ( E) we have now introduced the
broadening matrices
Γα=i[Σα−Σ†
α]. (11)
Equations (8) and (9) allow us to calculate the cur-
rent once the Hamiltonian for the scattering region and
the self-energies are given. Unfortunately these are not
knowna priori, since they require the evaluation of the
electronic structure of an infinite non-periodic system.
However their calculation do not require the actual solu-
tion of this open system and the notion of locality (the
same that allows us to separate the leads from the scat-
tering region) can be efficiently used. The self-energies in
factinvolveonlybulkquantities,i.e. quantitieswhichcan
be evaluated from a bulk calculation for a periodic sys-
tem. In addition a self-consistent schemecan be designed
for evaluating HS. The crucial point here is to assume
that the whole electronic structure can be described by
a single-particle theory, in such a way that HSdepends
only on the density matrix HS=HS[ρ]. This is for in-
stance the case of DFT or Hartree-Foch methods. Hence
HS[ρ] and the equations (8) and (10) can be iterated self-
consistently until convergence, and then the current can
be evaluated with equation (9). This scheme, with differ-
ences concerning the specific numerical implementation,
is used by most of the DFT-based NEGF packages avail-
able at present27,28,29,30,31,32,33.
Also in this case the addition of spin polarization does
not bring any fundamental changes in the formalism. In
the simple case of collinear-spins, then all the quantities
introduced (Green’s functions, charge density, Hamilto-
nian, self-energies ...) becomes block diagonal matrices | ce750a91139b8da9337138787fb059155774d160 | page_0007 |
9
in spin space. The Hamiltonian now depends on both
the charge density and the magnetization as in standard
spin-polarized mean field electronic structure methods.
Importantly the current is still carried in parallel by the
two spin species. In the more complicated case of non-
collinear spin (or if spin-orbit is present) then the off-
diagonal blocks to not vanish and the current cannot be
broken down into the majority and minority contribu-
tions.
Note that computationally the introduction of mag-
netism usually makes the calculation more complicated.
First one needs to consider matrices larger than the
unpolarized case. Secondly and most importantly the
Hamiltonian matrix becomes considerably more sparse.
In a ferromagnet in fact, for instance in a transition
metal, the delocalized s-electrons responsible for most
of the electron transport coexist with the tightly bound
d-electrons, which provide the local magnetic moment.
This means that most of the matrix elements between
dorbitals located on atoms far from each other vanish,
making the Hamiltonian more sparse than that of stan-
dard free-electron like metals (for instance Au). In the
case of sparse matrices standard recursive methods for
evaluating the self-energies become numerically unstable
if not prohibitive, and more sophisticated schemes are
needed27,28.
V. MOLECULAR SPIN-VALVES
As pointed out in the introduction spin-valves are the
prototypicalspin-devicesandthereforearethemoststud-
ied architectures for spin-transport through molecules.
The first prediction of a GMR-like effect in molecules
is from Emberly and Kirczenow, who investigated the
transport through a 1,4-benzenedithiolate molecule at-
tached to Ni electrodes. Because of the problems of deal-
ing with magnetic current/voltage probes mentioned in
the previous section, this work and most of the early
calculations65were limited to empirical models for the
electronic structure.
A first step in the direction of using ab initio elec-
tronic structure methods was suggested by Pati and co-
workers66,67,68, who considered a setup in which a given
molecule is sandwiched between two magnetic ions, or
clusters, which then are attached to non-magnetic elec-
trodes (see figure 6).
This setup removes the problems connected with con-
structing the self-energies for magnetic materials and a
GMR-like effect is produced by the magnetic ions, which
in turn are exchanged coupled through the molecule.
Clearly the scheme is highly idealized. It essentially
describes the transport through a magnetic molecule
(molecule plus magnetic ions) from non-magnetic leads,
and not that of a magnetic spin-valve. Importantly it
does not account for both the spin-polarized DOS of the
contacts and the accurate orbital character of the bond-
ing between the molecule and the magnetic surfaces.
Figure 6: Setup for early molecular spin-valve calculation s.
A molecule (black circles) is sandwiched between two mag-
netic ions (blue circles), which are then contacted by two no n-
magnetic current/voltage electrodes. The red arrows indic ate
the local magnetic moments.
An interesting alternative, that still avoids the con-
struction of magnetic leads, was proposed by Wei and
co-workers69, who used Al leads locally immersed in a
magnetic field. In this case the spin-polarization of the
leadsisachievedthroughsimpleZeemansplittingandthe
direction of the local magnetic fields at the two contacts
replaces that of the magnetic moments of a ferromag-
net. In this case the DOS of the leads is spin-polarized,
however the orbital nature of the bonding is identical for
both majority and minority spins. Importantly most of
these early calculations were ahead of experiments and
largely inspired them.
A. Metallic and tunneling junctions
The study of molecular transport with ferromagnetic
contacts from first principles has a young history since
only recently algorithms stable enough to deal with ex-
tremely sparse matrices and thus with magnetic leads
were made available27,28. Here we describe the results
obtained with the code Smeagol27,28for both insulating
and tunneling molecules.
As an example of different transport regimes, we
consider spin-valves made from Ni leads and a
molecular spacer which is either [8]-alkane-dithiolate
(octane-dithiolate) or 1,4-[3]-phenyl-dithiolate (tricene-
dithiolate). A schematic DOS and the charge density
isosurfaces of the HOMO and LUMO states for the iso-
lated molecules are presented in figures 7 and 8.
The two molecules present rather different characteris-
tics. TheHOMO-LUMOgap70isabout2.5eVfortricene
and almost double (5 eV) for octance. In addition while
in tricene the charge density of the first two HOMO lev-
els and the LUMO is extended over the whole molecule,
in octane this is predominantly localized around the S
atoms of the thiol groups. We then expect that the
octane and the tricene will form respectively TMR and
GMR devices, as actually found in our calculations27.
Let us consider octane first. The zero-bias transmis-
sion coefficient of the Ni/octane/Ni junction presents
a sharp peak at EFthat scales exponentially with the | ce750a91139b8da9337138787fb059155774d160 | page_0008 |
10
-8 -6 -4 -2 0
Energy [ eV ]010203040DOS [ a. u. ]EF
Figure 7: [8]-alkane (octane) molecule: DOS and charge den-
sity isosurface plots for the relevant molecular states of t he
isolated molecule. EFdenotes the position of the Fermi level
for the isolated molecule.
Figure 8: 1,4-[3]-phenyl (tricene) molecule: DOS and charg e
density isosurface plots for the relevant molecular states of
the isolated molecule. EFdenotes the position of the Fermi
level for the isolated molecule.
number of alkane groups T∝e−βn(β∼0.88). This
is demonstrated in figure 9 for the parallel configura-
tion and confirms that device is in a tunneling regime.
Note that the method is accurate down to a conduc-
tance of ∼50pS. Interestingly the exponent is similar
to that found for the same molecule attached to gold
(111) surfaces71. The coupling between the thiol groups
and the electrodes is strong and it gives rise to a small
spin-polarizationofthe two S atoms. Howeversince both
the HOMO and LUMO states are strongly localized at
the thiol groups, at the Fermi level there is no molecular
state extending through the entire structure. Hence the
Ni/octane/Ni junction presents the features of a TMR
spin-valve.
Thecaseof1,4-[n]-phenyl-dithiolateisdifferent, inpar-
ticular we find that the current does not scale sensibly
with the number ofphenyl groupsin the molecule. In fig-4 5 6 7 8 9 10
Number of Carbons-6-5-4-3-2-10ln( T[E] )ln( T[E] )
y = 3.158 - 0.88029 x
Figure 9: ln[ T(EF)] as a function of the number of C atom
for [n]-alkane-dithiolate attached to Ni leads. The black c ir-
cles correspond to our calculated values, and the solid line
is our best linear fit. Here the spin-valve is in the parallel
configuration.
ure 10 we present the transmission coefficient as a func-
tion of energy of 1,4-[n]-phenyl-dithiolate for 1, 3 and 4
phenyl rings when the magnetization vectors of the leads
are parallel to each other. It is clear that, although there
-2 -1 0 1 2
E-EF (eV)00.511.5T(E)00.511.5T(E)
Majority
Minority00.511.5T(E)n=1
n=3
n=4
Figure 10: Transmission coefficient as a function of energy
for 1,4-[n]-phenyl-dithiolate molecules with n=1, 3, and 4 .
Here the spin-valve is in the parallel configuration. A simil ar
scaling of the transmission coefficient as a function of n is
found for the antiparallel configuration.
is a reduction of the transmission coefficient as a func-
tionofthenumber ofrings, this remainsclosetounity for
mostoftheenergyrange,andcertainlythereisnotanex-
ponential decay. Therefore in this class of molecules the
transport seems to be appropriately described by a co-
herent resonant tunneling mechanism through extended
molecular states.
This picture is enforced by the fact that the zero-
bias transmission coefficient approaches unity for ener-
gies close to the leads Fermi level. In addition, from | ce750a91139b8da9337138787fb059155774d160 | page_0009 |
11
the study of the evolution of the orbital resolved density
of states as a function of the distance between the thiol
group and the electrodes27we identify such a resonant
state as the HOMO state of tricene. However it is worth
mentioning that this appearsrather broad and spin-split,
because of the strong coupling with the dorbitals of the
leads. In conclusionallthis suggeststhat aNi/tricene/Ni
spin-valve behaves as metallic spin-valve.
TheI-Vcharacteristics of both the molecules are
strongly non-linear with the bias and consequently also
the GMR ratio suffers this non-linearity. In figures 11
and12we presentthe I-Vcurves, the GMR ratioandthe
zero-bias transmission coefficient for the two molecules.
00.1T(E)
Majority
Minority
-2 -1 0 1 2
(E-EF) [ eV ]00.1T(E)-2 -1 0 1 2
V (Volt)-0.4-0.20.00.20.4I (µA)
P configuration
AP Configuration-2 -1 0 1 2050100R(%)
a)
b)
c)
Figure 11: a) I-Vcharacteristic, and zero bias transmission
coefficients for the b) parallel and c) antiparallel configura -
tion of an octane-based Ni spin-valve. In the antiparallel c ase
the transmission coefficient is identical for both the spin di -
rections. In the inset we present the corresponding MR ratio .
EFis the position of the Fermi level of the Ni leads. From
reference28.
Again consider octane first. Here the transmission co-
efficient at zero bias is dominated by a number of sharp
peaks in the parallel configuration, which get consider-
ably suppressed in the antiparallel one. In particular a
minority peak appears at the Fermi level and it is mostly
responsible for the low-bias conductivity. Such sharp
peaks in the transmission coefficient are usually a signa-
ture of resonant states at the interface between the leads
and the insulating media. At resonance they can carry
a considerable current, however small bias and disorder
are usually rather effective in suppressing their contribu-
tion to the current. Evidence for these surface states has
been already provided for conventional magnetic tunnel-
ing junctions both experimentally72and theoretically73.
TheI-Vcharacteristic is rather linear for the antipar-
allel configuration but presents a non-trivial slope for the
parallel case. This gives rise to a non-monotonic depen-
dance of the GMR ratio over the bias. Importantly both
the layer resistance and the TMR ratio are in the same
range as in recent experiments on octane-based Ni spin-
valves21. However, a direct comparisonwith experiments00.511.5T(E)
Majority
Minority
-2 -1 0 1 2
(E-EF) [ eV ]00.51T(E)-2 -1 0 1 2
V (Volt)-40.0 -20.0 0.0 20.0 40.0 I (µA)
P configuration
AP Configuration-2 -1 0 1 20200400600R(%)
a)
b)
c)
Figure 12: a) I-Vcharacteristic, and zero bias transmission
coefficients for the b) parallel and c) antiparallel configura -
tion of a tricene-based Ni spin-valve. In the antiparallel c ase
the transmission coefficient is identical for both the spin di -
rections. In the inset we present the corresponding MR ratio .
EFis the position of the Fermi level of the Ni leads. From
reference28.
is difficult since the actual number of molecules bridging
the two electrodes is not known with precision. Moreover
a degradation of the GMR signal due to spin-flip and
electron-phonon scattering, misalignment of the magne-
tization of the contacts and current shortcut through
highlyconductivepin-holes, candrasticallyreduce RGMR
in actual samples.
In contrast in the case of metallic (tricene) junctions
the transmission coefficient at zero bias presents a much
higher transmission and is a rather smooth function of
the energy. In the parallel case most of the transmission
atEFis due to the majority spin, while the contribution
of the minority is significant only for energies at about
200meVabove EF. Intheantiparallelconfigurationsuch
transmissionattheFermilevelisstronglysuppressedand
theresultingcurrentisconsiderablylower. Thisproduces
an extremely large GMR ratio for small bias, exceeding
600%.
An interesting feature is that, in first approximation,
the transmission coefficient at zero bias for the antipar-
allel state appears to be a convolution of those for the
majorityandminorityspinintheparallelcase. Thisfind-
ing can be qualitatively understood in terms of transport
throughasinglemolecularstate(seefigure13). Let t↑(E)
be the majority spin hopping integral from one of the
leads to the molecular state, and t↓(E) the same quan-
tity for the minority spins. Then, neglecting multiple
scattering (i.e. all interference effects), the total trans-
mission coefficients of the entire spin-valve in the parallel
state can be written T↑↑(E) = (t↑)2andT↓↓(E) = (t↓)2
respectively for the majority and minority spins. Simi-
larly the transmission in the anti-parallel configuration
isT↑↓(E) =T↓↑(E) =t↑t↓. ThusT↑↓(E) is a convolu- | ce750a91139b8da9337138787fb059155774d160 | page_0010 |
12
tion of the transmission coefficients for the parallel case
T↑↓∝√
T↑↑T↓↓.
Figure 13: Scheme of the spin-transport mechanism through
a single molecular state. t↑(E) (t↓(E)) is the majority (mi-
nority) spin hopping integral from one of the leads to the
molecular state. Neglecting quantum interference, in the
parallel case (a) the total transmission coefficient is simpl y
T= (t↑)2+ (t↓)2, while in the antiparallel (b) T= 2t↑t↓.
Note that if either t↑ort↓vanishes, the current in the an-
tiparallel configuration will also vanish (infinite GMR).
An extreme case is when only one spin couples to the
molecular state. Then the total transmission in the an-
tiparallel case is identically zero since either t↑ort↓van-
ishes. This is the most desirable situation in real devices
since, in principle, an infinite RGMRcan be obtained.
Note that in this situation the system leads+molecule
behaves as a half-metal although the two materials form-
ing the device are not half-metals themselves. An even
more extreme situation is when for a particular energy
window the transport is through two distinct molecular
states,whicharerespectivelycoupledtothemajorityand
minority spin only. This may happen for instance due a
particular symmetry of the molecular anchoring groups.
Then in this energy window one will find T↑↑(E)∝negationslash= 0,
T↓↓(E)∝negationslash= 0 butT↑↓(E) = 0 (see figure 14).
The fact that in good approximation T↑↓∝√
T↑↑T↓↓
can be used for enhancing the GMR ratio. Consider
for instance the case when T↑↑≫T↓↓. Then we have
TP≈T↑↑andTAP≈√
T↑↑T↓↓for the total transmission
coefficients respectively of the parallel and antiparallel
configurations. Clearly a reduction of T↓↓will produce
a considerable reduction in the transmission of the an-
tiparallel alignment, leaving almost unchanged that of
the parallel one. We have explored this avenue27by re-
placing the thiol group with either a Se or a Te atoms.
These provide a rather strong bond, although generally
the bond length is increased due to the larger atomic ra-
dius of the anchoring atom. The transmission, I-Vchar-
acteristics and GMR for 1,4-benzene anchored to Ni via
S, Se or Te are presented in figures 15, 16 and 17. Clearly
the pictures show a rather dramatic increase of the GMR
Figure 14: Scheme of the spin-transport mechanism through
two energetically closely spaced molecular states. The firs t
state (red) couples only to the majority spin band, while the
minority spin couple only to the purple state. In the paralle l
case one finds T↑↑(E)/ne}ationslash= 0 and T↓↓(E)/ne}ationslash= 0 but in the antipar-
allelT↑↓(E) = 0. We then expect an infinite GMR for such
an energy window.
demonstrating that the GMR signal can be tuned by an
appropriate choice of the anchoring chemistry.
00.511.5T(E)
Majority
Minority
-2 -1 0 1 2
E-EF (eV)00.51T(E)-2 -1 0 1 2
V (Volt)-60-40-200204060I (µA)
P configuration
AP Configuration-2 -1 0 1 20150300450600R(%)
Figure 15: Transport properties for a 1,4-phenyl molecule
attached to Ni (100) surfaces through a S group. The top
panel shows the I-Vcharacteristics for both the parallel and
antiparallel alignment of the leads and the inset the corre-
sponding GMR ratio. The lower panel is the transmission
coefficient at zero bias as a function of energy. Because of
spin-symmetry, in the antiparallel case we plot only the ma-
jority spin. Reprinted with permission from27A.R. Rocha et
al., Phys. Rev. B 73, 085414 (2006). Copyright American
Physical Society 2006.
Finally it is worth mentioning that a severe bias de-
pendance of the GMR ratio, with also the possibility of
negative values, has been recently predicted with either
semi-empirical74andab initio75methods. | ce750a91139b8da9337138787fb059155774d160 | page_0011 |
13
00.511.5T(E)
Majority
Minority
-2 -1 0 1 2
E-EF (eV)00.51T(E)-2 -1 0 1 2
V (Volt)-40-200 2040I (µA)
P configuration
AP Configuration-2 -1 0 1 20150300450600R(%)
Figure 16: Transport properties for a 1,4-phenyl molecule a t-
tached to Ni (100) surfaces through a Se group. The top
panel shows the I-Vcharacteristics for both the parallel and
antiparallel alignment of the leads and the inset the corre-
sponding GMR ratio. The lower panel is the transmission
coefficient at zero bias as a function of energy. Because of
spin-symmetry, in the antiparallel case we plot only the ma-
jority spin. Reprinted with permission from27A.R. Rocha et
al., Phys. Rev. B 73, 085414 (2006). Copyright American
Physical Society 2006.
B. Carbon Nanotubes
Carbon nanotubes are almost defect-free graphene
sheets rolled up to form one-dimensional molecules with
enormousaspectratios76. Theirconductingstate(metal-
icity) depends on their chirality, however in the metallic
configuration they are ideal conductors with a remark-
ably long phase-coherence length77,78. An important as-
pect is that the relevant physics at the Fermi level is
entirely dominated by the pzorbitals, which are radi-
ally aligned with respect to the tube axis. These in-
clude the bonding properties with other materials and
betweentubes. Thereforecarbonnanotubesappearasan
ideal playground for investigating both GMR and TMR
through molecules. In fact one can expect that two tubes
with different chirality will bond to a magnetic surface in
a similar way, allowing us to isolate the effects of the
molecule from that of the contacts. Indeed TMR-like
transport through carbon nanotubes has been experi-
mentally reported by several groups20,79,80,81,82,83,84,85.
Why would one expect a large GMR from a carbon
nanotube? To answer this question we use an argument
derived by Tersoff86and then subsequently refined87for
explaining the contact resistance between a C-nanotube
and an ordinary metal. Consider for simplicity an arm-
chair nanotube (metallic). The Fermi surface of such
tube consists only of two points, symmetric with respect
to Γ in the 1D Brillouin zone (see figure 18). The Fermi
wave-vector is then kF= 2π/3z0withz0=d0√
3/2 and
d0the C-C bond distance ( d0=1.42˚A).00.511.5T(E)
Majority
Minority
-2 -1 0 1 2
E-EF (eV)00.51T(E)-2 -1 0 1 2
V (Volt)-30 -20 -1001020 30 I (µA)
P configuration
AP Configuration-2 -1 0 1 20150300450600R(%)
Figure 17: Transport properties for a 1,4-phenyl molecule a t-
tached to Ni (100) surfaces through a Te group. The top
panel shows the I-Vcharacteristics for both the parallel and
antiparallel alignment of the leads and the inset the corre-
sponding GMR ratio. The lower panel is the transmission
coefficient at zero bias as a function of energy. Because of
spin-symmetry, in the antiparallel case we plot only the ma-
jority spin. Reprinted with permission from27A.R. Rocha et
al., Phys. Rev. B 73, 085414 (2006). Copyright American
Physical Society 2006.
qkk
kk
kk(a) (b) (c)
q q
Figure 18: Fermi surfaces of an armchair carbon nanotube
and of a magnetic transition metal. The Fermi surface of
the nanotube consists in two points kN
F=q, symmetric with
respect to the Γ point. The Fermi surface of a transition
magnetic metal consists of two spheres (for ↑and↓spins)
whose different diameters depend on the exchange field. The
three possible scenarios discussed in the text: (a) q < k↓
F<
k↑
F, (b)k↓
F< k↑
F< q, (c)k↓
F< q < k↑
F.
Assume now for simplicity that our magnetic metal is
an exchange-split free-electron gas, whose band-energy is
Eσ
k=¯h2k2
2m+σ∆/2, (12)
withσ=−1 (σ= +1) for majority (minority) spins and
∆ the exchange energy. The spin-dependent Fermi wave-
vectors are then respectively k↑
F=/radicalbig
2m(EF+∆/2)/¯h
andk↓
F=/radicalbig
2m(EF−∆/2)/¯h.
The transport through an interface between such a
magnetic metal and the nanotube is determined by the
overlapbetween the correspondingFermisurfaces. Three
scenariosare possible. First the Fermi-wave vector of the
carbon nanotube is smaller than both k↑
Fandk↓
F(see fig- | ce750a91139b8da9337138787fb059155774d160 | page_0012 |
14
ure 18a). In this case in the magnetic metal there is
always a k-vector that matches the Fermi-wave vector of
the nanotube for both spins. Therefore both spins can
be injected into the tube and the total resistance will be
small and spin-independent.
Secondly the Fermi-wave vector of the carbon nan-
otube is larger than both k↑
Fandk↓
F(see figure 18b).
Nownostatesareavailableinthemetalliccontactswhose
wave-vectors match the Fermi wave-vector of the carbon
nanotube. For zero-bias and zero-temperature the re-
sistance is extremely large. Nevertheless upon increasing
thetemperature, phononassistedtransportbecomespos-
sible. Spin electrons can be scattered out of the Fermi
surface into states with large longitudinal momentum.
At temperature Tthe fraction of electrons with energy
aboveEFissimplyproportionaltotheFermidistribution
function. However, because of the exchange energy, spin-
up electrons will possess higher momentum than spin-
down. Therefore one can find more spin-up states with
a longitudinal momentum matching the one of the nan-
otube than spin-down states. This potentially gives a
temperature-induced spin-dependent resistance.
Finally if the Fermi wave-vector of the carbon nan-
otube is larger than k↓
Fbut smaller than k↑
F(see figure
18c), only the majority electrons can enter the nanotube.
The system becomes fully spin-polarized and the Fermi
surfacematchingreplacesthebondingspin-selectivityen-
counteredintheprevioussection. Alsointhiscaseaspin-
valve structure made by magnetic contacts and carbon
nanotube as spacer is predicted to show infinite GMR at
zero temperature. An increase of the temperature will
produce a degradation of the polarization since minor-
ity spins can be thermally scattered outside their Fermi
surface, and therefore contribute to the transport.
Two important aspects must be pointed out. First all
these considerations are based on the assumption of per-
fectly crystallinesystems. This maynot be truein reality
and the effects of breaking the translational invariance
must be considered. From a qualitative point of view
disorder smears the Fermi surface and eventually may
produce some states with large longitudinal momentum.
Thiswillimprovetheconductancethroughthenanotube,
even if its spin-polarization will be in general dependent
on the nature of disorder.
Secondly, our heuristic argument does not necessar-
ily apply to the case of transition metal contacts, where
the spin-selectivity arising from the different bonding
nature of the two spin-subands can play an important
rˆ ole. Clearly more realistic bandstructure calculations
are needed. These however are rather problematic. In
addition to the need of simulating transition metal leads
one has to consider ratherlargesupercell for a reasonable
description of the nanotube/metal interface.
For this reason most of the calculations to date have
used simple tight-binding models without self-consistent
procedures88,89,90. These roughlyagreeon the possibility
of large GMR ratios in transition metals contacted nan-
otubes, although the actual values predicted are some-how affected by the different methods and the contact
geometry.
C. Long molecules and phonons
As mentioned previously electronic transport in poly-
mers and long molecules offer a considerable higher
level of complexity when compared to small ballistic
molecules. The first consideration is that the trans-
port is often driven by strong electron-phonon interac-
tion, therefore the relevant current carriers are some cor-
related electronic-vibronic states (polarons, bi-polarons,
etc.). Moreover in the case of spin-transport one has
to take into account the likely presence of paramagnetic
centers60. They usually appear in low concentrations,
but they become relevant to the spin-dynamics in long
molecules. These two features add to the large scale of
the system and make the problem of spin-transport in
large organic molecules intractable with ab initio meth-
ods. This is the main reason why to date only simple
Hamiltonian models have been used.
When the electron-phonon interaction is weak, or al-
ternativelythe moleculeisrathershortinsuchawaythat
polaronic-typeoftransportisnotdominant, then phonon
absorption/emission has only the effect of smearing the
transmissioncoefficient. In spin-valvesmade from transi-
tion metals such a smearing is likely to result in a reduc-
tion of the spin-polarization of the device and therefore
of the GMR91. However quantitative predictions are dif-
ficult, since also in this case a detailed description of the
electronic structure of the electrodes and of the bond-
ing with the molecule is essential. For instance calcula-
tionsofspin-injectionintoshortstrandsofDNAobtained
with simple single-orbital tight-binding models and some
parameterization of the metal/molecule bonding, report
both an enhancement92and a reduction93of the GMR
with the bias.
When the electron-phonon interaction is strong and
the molecules are rather long, then the ground state of
the molecule is some correlated electronic-vibronic state.
In this case the situation is more complex and to the best
ofourknowledgenotransportcalculationshavebeen car-
ried out to date. Some interesting insights come from the
investigation of the ground state of polymers in contact
with magnetic metals. Xie and co-workers61investigated
a non-degenerate polymer in contact with a model metal
reproducing either a magnetic transition metal or man-
ganite. Interestingly they found that when no charge is
transferred from the metal to the polymer, this remains
metallic with a rather uniform distribution of the charge
acrossthe interface. In contrastchargetransferpromotes
the formation of spinless bipolarons in the polymers. An
analysis of the DOS of the whole structure further sug-
gest that the bipolaron formation drastically reduces the
spin polarization of the whole system. | ce750a91139b8da9337138787fb059155774d160 | page_0013 |
15
VI. MORE EXOTIC PHENOMENA
A. Molecular Magnets
Extremely interesting features appear in quantum
transport through molecules when the conducting elec-
trons interact with some internal molecular degrees of
freedom. This is for instance the case of vibrational
levels, where electron-phonon interaction manifests itself
with sharp changes in the slope of the I-Vcurve, steps in
dI/dVand in peaks in d2I/dV2. It is therefore natural
to speculate about similar effects associated to internal
magnetic degrees of freedom, i.e. the molecular spin94.
Until recently the experimental activity was focussed on
reproducingat the molecular level effects alreadydemon-
strated in quantum dots, such as the Zeeman splitting of
the Coulomb-blockade as well as the Kondo effect95,96.
More recently, advances in the chemical functionaliza-
tion of magnetic molecules have allowed the formation
of stable bonding between the molecules and metallic
surfaces97,98, thus the construction of two and three ter-
minal devices99,100.
Magnetic molecules101are molecules comprising a
number of transition metal ions magnetically coupled to
each other in such a way to give rise to a global net
spinS. They are usually described by the following spin
Hamiltonian H0
H0=DS2
z+gµBHzSz, (13)
whereD(D <0) is the zero field splitting constant and
Hzis thezcomponent of an external magnetic field ( µB
is the Bohr magneton). The term proportional to S2
z
lift the degeneracy of the spin-multiplet and the energy
levels can be labeled by the magnetic quantum number
MS, with−S≤MS≤S.
If the dynamics is solely determined by the Hamilto-
nianH0then a molecule prepared in a given MSstate
will remain in such state. However a perturbation H1,
which does not commute with H0will create mixing be-
tween the MSstates, thus transition between levels with
different MSwill be possible. Selection rules for these
transitions are given by the particular symmetry of the
perturbation, and for instance transverse anisotropy
H1=E(S2
x−S2
y), (14)
allows transitions MS→MS±2nwithnan integer.
Evidence of quantum tunneling of the magnetization for
magnetic molecules are now numerous101.
Let us now consider the case of electronic transport
through such a molecule and in particular the case
of weak coupling between the molecule and the cur-
rent/voltage electrodes, which is the most likely situa-
tion in actual experiments99,100. In general the ground
state for a charged molecule will be different from that
of its neutral state, and so will be the excitation spec-
trum. This means that sequential tunneling can poten-
tiallyleavethe moleculein someexcitedstatenotallowedto relax by the selection rules. Importantly also the op-
posite is true, namely that a charged exited molecule can
relax to a state which does not allow electron transfer to
the electrodes because of the selection rules. This may
lead to a complete suppression of the current99.
Two experimental works have been published so
far on transport through magnetic molecules99,100.
They both consist in a transistor geometry
where a single Mn 12molecule is trapped. Mn 12,
[Mn12O12(CH3COO) 16(H2O)4], is perhaps the proto-
type of all molecular magnets. The 12 Mn ions occupy
three inequivalent atomic sites, namely two Mn3+and
one Mn4+. The Mn ions with different valence couple
antiferromagnetically to each other resulting in a total
S= 10 ground state. In one case the molecule has been
functionalized (see figure 19) with thiol groups in order
to form stable contacts with the gold surfaces of the
electrodes. The crucial aspect of both these experiments
is the discovery of fingerprints of the molecular state
into the I-Vcharacteristics of the device. In particular
negative differential conductance, complete current
suppression99and non-trivial dependence of the peaks
in the differential conductance over an applied magnetic
field100, can all be interpreted as a result of the internal
spin-dynamics of the molecule.
Figure 19: Top and side views of a ball-and-stick model
for a Mn 12magnetic molecule. In this case we con-
sider [Mn 12O12(O2C-R-SAc) 16(H2O)4] where R= {C6H4,
C15H30}. Colour code: green=carbon, yellow=sulphur,
blue=hydrogen, red=oxygen and violet=manganese.
Several model calculations have been performed for
explaining the various features of these experiments102
and proposing a new setup where one of the electrodes
is a ferromagnet103,104. These are based on the spin-
Hamiltonian of equations (13) and (14) and an addi-
tional term that takes into account the coupling with the
electrodes. Then the transport calculation is performed
within the standard master equation formalism familiar
to transport through interacting quantum dots105. Al-
though these calculations are certainly important since
they demonstrate the mechanisms behind the various ef-
fects, they depend heavily on the specific choice of the
parameters used. For this reason ab initio simulations
would be very important. For instance questions about
the actual charging state of the molecule under bias, the
strength of the interaction between the conducting elec- | ce750a91139b8da9337138787fb059155774d160 | page_0014 |
16
trons and the Mn ions, and the electrical response of the
whole system are likely to find an answer with DFT cal-
culations. The problem is indeed complicated and even
the simple evaluation of the ground state of magnetic
molecules from DFT is not trivial106,107. For this reason
no first principle calculations of transport through mag-
neticmoleculeshavebeenperformedtodate. Howeverwe
believe that this is an extremely challenging field where
order-N capability, strong correlation and scalable quan-
tum transport schemes can find a common playground.
Finally we want to discuss the possibility of construct-
ing all-molecular spin-valves, i.e. spin-valves where both
the spin-injector and spin-detector are molecules or part
of the same molecule and the metallic current/voltage
electrodes have the only function of electron reservoirs.
Also in this case the expectation is to detect electrically
themagneticstateofthemolecule,howeverforspin-valve
operation we also demand the possibility of switching re-
versibly between two spin-configurations by applying a
magnetic field. An interesting proposal is that of using
dicobaltocene molecules108. These belong to the metal-
locene family and are characterized by two Co ions sep-
arated by a spacer that can be chemically engineered.
DFT calculations108show that dicobaltocene attached
to gold electrodes in its ground state is stabilized by su-
perexchange in an antiferromagnetic configuration, i.e.
the local moments of the two Co ions are antiparallel to
each other. As in a conventional spin-valve a parallel
alignment can be obtained by applying a large magnetic
field (around 20 T for a C 2H4spacer), and the calcula-
tion shows a rather large GMR ratio. This is suggestive
of the possibility of all-molecular spin-valves and future
experiments in this area are certainly welcome.
B. d0ferromagnetism and magnetic proximity
We wish to close this review with a brief discussion of
two recently discovered intriguing phenomena, that chal-
lenge our current understanding of ferromagnetism and
mayofferanewplaygroundforspin-transport. Theseare
d0ferromagnetism and magnetic proximity effect. The
measurement of long-range ferromagnetic order in ma-
terials not containing ions with either dorfelectrons,
thereforewithout anobviouswayto producealocalmag-
netic moment, is the common factor of these two aspects
of magnetism.
Let us consider first the case of d0ferromagnetism109.
This is the intrinsic ferromagnetism of usually highly de-
fectivematerials,whichdonotcontainanypartiallyfilled
dorfshells. Among the several examples we wish to
mention irradiated graphite and fullerenes110, nonstoi-
chiometric CaB 6111, and HfO 2thin films112. A com-
mon explanation for the magnetism in all these mate-
rials is not available at present. Note that one has to
explain both the formation of a magnetic moment and
the long-rangecouplingbetween moments. Generallythe
moments are associated to intrinsic defects. Paramag-netic defects in organic materials are not uncommon60
and strongly correlated molecular orbitals associated to
vacancies have been suggested for magnetic oxides113,114.
However the demonstration of long range coupling re-
mains elusive. For instance recent DFT calculations115
demonstrate, at least for CaO, that the defect concentra-
tion needed for long range ferromagnetismis three orders
of magnitude larger than that obtainable at equilibrium.
Finally we wish to mention that ferromagnetism origi-
nating from p-shells has been suggested for oxygenmixed
valence compounds such as Rb 4O6116.
In contrast to d0ferromagnetism magnetic proximity
is not an intrinsic material property and it does require
the presence of a magnetic material. The basic idea is
quite simple: there is always some charge transfer at the
contact between a conducting molecule and a metal as-
sociated with the alignment of their respective chemical
potentials. In a ferromagnet some degree of spin trans-
fer accompanies the charge transfer giving rise to an in-
duced magnetic moment. Note that the magnetic prox-
imity effect does not imply intrinsic ferromagnetism and
no spin aligning potential exists in the non-magnetic ma-
terial. This means that a magnetic moment is detected
only when a secondferromagneticmaterialis presentand
when good contact is made.
A first indirect evidence of this effect was found in
explaining the unaccounted magnetization in a carbon
meteorite rich of magnetic inclusions117. Then Ferreira
and Sanvito derived a close system of equations for the
induced magnetic moment and for the energetic of a car-
bon nanotube deposited on a magnetic surface118. The
calculation, based on a simple tight-binding model, re-
vealed that induced magnetic moments of the order of
0.1µBper carbon atom in contact can be achieved at
room temperature. This paved the way for a more con-
trolled set of experiments.
Experimentally the problem is to detect the small in-
duced moment over a huge background coming from the
ferromagnetic substrate. One possible strategy is that of
measuring the stray field around the nanotube once this
is placed on a smooth thin film. A uniformly magnetized
thin film creates no stray field whatever its direction of
magnetization. In contrast a magnetized nanotube will
produce a stray field, which will be directly detectable.
ThisideawasexploitedintheexperimentsfromC´ espedes
etal.119, whomeasuredinducedmagneticmomentsinex-
cess of 0.1 µBper carbon atom in contact, in good agree-
ment with the theoretical prediction. The experiment
consists in taking AFM and MFM images of nanotubes
on various surfaces. The difference between the topo-
graphic (AFM) and the magnetic images (MFM) is a di-
rect measure of the stray field coming from the nanotube
and therefore provides evidence for the induced magnetic
moment (see figures 20 and 21).
In the another experiment, Mertins et al.120produced
a multilayer of thin, alternating iron and carbon layers,
of thickness 2.55 and 0.55 nm, respectively. Then, they
probed locally the magnetic moment of the carbon by X- | ce750a91139b8da9337138787fb059155774d160 | page_0015 |
17
Figure 20: AFM images of a carbon nanotube on copper a)
and silicon c) substrate and their corresponding MFM scans
b) and d). The MFM images do not show any magnetic con-
trast indicating no induced magnetic moment.
ray magneto-optical reflectivity of polarized synchrotron
radiation. In this type of measurement the Fe and C
absorption edges differ by about 500 eV enabling one
of establishing with precision whether the magnetic mo-
ment comes from C or not. With this method magnetic
moments of the order of 0.05 µBwere found.
Figure 21: AFM images of a carbon nanotube on cobalt sub-
strate (left) and the corresponding MFM scans (right). The
MFM image shows magnetic contrast indicating an induced
magnetic moment.
Finally we wish to mention a few experiments whereferromagnetism is claimed in heterostructures in which
none of the components is ferromagnetic. This is for in-
stance the case of gold surfaces and nanoparticles coated
with different organic molecules121,122,123. Common fea-
tures to these heterostructures are the extreme magnetic
anisotropy and the fact that the magnetization is almost
independent from the temperature. A possible explana-
tion is that the charge transfer between the molecule and
the substrate and the peculiar 2D properties of the or-
ganic layers result in the formation of triplet states with
consequent boson condensation124. In addition a crucial
rˆ ole of spin-orbit interaction has been suggested125. To
our knowledge, no first principles calculations of these
systems have been performed.
VII. CONCLUSIONS
We have reviewed the most recent advances in spin-
transport through organic molecules. This is a new chal-
lenging field where disciplines such as physics, chemistry,
biologyandelectronicengineeringarerapidlyconverging.
In particular we have discussed the main advantages and
prospectives of spin-phenomena at the molecular level.
From a theoretical side ab initio methods for quan-
tum transport are rapidly approaching the limit where
quantitative predictions of molecular transport can be
made. Spin-transport however brings additional com-
plexity since magnetism and strong electron correlation
must be considered. These call for even more sophis-
ticated algorithms capable of high accuracy and of un-
demanding scaling with the system size, an enormous
challenge for the future. Finally more and more experi-
ments are appearing where the interaction between con-
ducting electrons and internal molecular degrees of free-
dom are important. Such systems go way beyond our
present computational capabilities in terms of ab initio
theories and open a completely unexplored way.
Acknowledgement
We wish to thank Cormac Toher, Ivan Rungger, Chai-
tanya Das Pemmaraju and Miguel Afonso Oliveira for
useful discussions and Hang Guo for giving us access to
unpublished material. Figures 20 and 21 are courtesy
of J.M.D. Coey and O. C´ espedes. This work is spon-
sored by Science Foundation of Ireland under the grants
SFI02/IN1/I175 and SFI05/RFP/PHY0062.
∗Electronic address: [email protected]
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Precision aging. Human lifespan has intrinsic limits but
measurable outcomes
Warren Ladigesa,*
aDepartment of Comparative Medicine, School of Medicine, University of Washington, Seattle,
WA 98195, USA.
A recent article by Pyrkov et al. [1] suggests that progressive loss of physical resilience
to aging coincides with an absolute limit of human lifespan in the range of 120 to 150
years. Furthermore, the authors conclude that end of life is an intrinsic biological property
independent of internal or external stress factors. Their analysis is based on a log-linear
mortality estimate of complete blood count variables, such as neutrophil lymphocyte ratio,
as single quantitive measures of the aging process correlated with physical activity data
from individual tracking devices. These statistical projections are intriguing and potentially
impactful but need to be validated in such a way as to provide practical approaches to
defining physical resilience. Once this is established, more accurate predictions can be made
for the degree of individual resilience with increasing age, and the power to align with
appropriate aging intervention strategies.
One area of current biological research on resilience and aging is focused on developing
physical stress tests that actually predict resilience to aging in animal models. For example,
in older naïve mice, a non-lethal dose of the drug cyclophosphamide triggers a response
in the white blood cell population such that the neutrophil lymphocyte ratio predicts
more youthful cognition and physical activity in a subset of mice with increasing age
[2]. Another example is immune response to a vaccine. Adult mice vaccinated with the
clinically-used vaccine Prevenar13 could be stratified into high antibody responders and
low antibody responders and when followed to older ages, showed high performance and
low performance, respectively, in cognition and physical assessment activities [ 3]. Similar
observations were made in a wound healing model where adult mice were administered a
small skin punch biopsy and measured for how fast the biopsy closed over several weeks.
With increasing age, the rate of closure correlated with physical performance [ 4].
These preclinical observations speak for the inclusion of physical stress test variables
into the organismal projections described by Pyrkov et al. [1]. This would allow for
the development of in vitro assessments that would align with physical resilience and
the response patterns associated with the administration of specific physical stress. This
*Corresponding author: Warren Ladiges, Mailing address: Department of Comparative Medicine, School of Medicine, University of
Washington, Seattle, WA 98195, USA, [email protected].
Declarations
Conflict of interest: Warren Ladiges is a member of the Editorial Board of Aging Pathobiology and Therapeutics. The author declares
no conflict of interest and is not involved in the journal’s review or desicions related to this manuscript.
HHS Public Access
Author manuscript
Aging Pathobiol Ther . Author manuscript; available in PMC 2022 January 25.
Published in final edited form as:
Aging Pathobiol Ther . 2021 June 29; 3(2): 39–40. doi:10.31491/apt.2021.06.061.
Author Manuscript Author Manuscript Author Manuscript Author Manuscript | d5e91ba005ad6d5ae25a4fc597efdb1bdf4696b1 | page_0000 |
approach does not contradict the premise of stress as a non-causal element in aging,
but merely provides a means of better defining trajectories of physical resilience with
lifespan. By definition, it also implies that individuals with continued robust resilience with
increasing age would be in relatively good health and maintain functional independence.
On the other hand, the ability to predict a lack of robustness of physical resilience to
aging provides a platform for the possibility of extending healthy aging and lifespan up
to the lifespan limits defined by Pyrkov et al. [1]. Aging intervention strategies are being
developed that target multiple aging pathways and enhance resilience [ 5], and could be
designed on an individual basis depending on the predictive power of one or several in vitro
stress test response patterns. This concept then allows precision medicine to enter into the
biology of the aging arena as precision aging (Figure 1), where the objective is not to search
for immortality but for ways each individual can maintain a more youthful level of resilience
for a healthy and functional life with increasing age but still within an intrinsic lifespan
domain.
Financial support and sponsorship:
Supported by NIH grants R01 AG057381 (PI, Ladiges).
References
1. Pyrkov TV , Avchaciov K, Tarkhov AE, et al. Longitudinal analysis of blood markers reveals
progressive loss of resilience and predicts human lifespan limit. Nature Communications, 2021,
12(1): 1–10.
2. Zhu L, Dou Y , Bjorner M, et al. Development of a cyclophosphamide stress test to predict resilience
to aging in mice. GeroScience, 2020, 42(6): 1675–1683. [PubMed: 32613492]
3. Oveson R, Jiang Z, Izhak M, et al. An immune stress test for resilience to aging: Pneumococcal
vaccine response. Aging Pathobiology and Therapeutics, 2020, 2(3): 171–172. [PubMed:
35083447]
4. Jiang Z, Chen J, Wang J, et al. A model for studying cutaneous wound healing and resilience to
aging: Ear punch biopsy in old mice. Aging Pathobiology and Therapeutics, 2020, 2(3): 173–175.
[PubMed: 35083448]
5. Ellis M, Ladiges W, Jiang Z. Physical performance is enhanced in old mice fed a short term diet
medicated with rapamycin, acarbose, and phenylbutyrate. Aging Pathobiology and Therapeutics,
2021, 3(1): 12–13. [PubMed: 35083452] Ladiges Page 2
Aging Pathobiol Ther . Author manuscript; available in PMC 2022 January 25.
Author Manuscript Author Manuscript Author Manuscript Author Manuscript | d5e91ba005ad6d5ae25a4fc597efdb1bdf4696b1 | page_0001 |
Figure 1. Precision aging and resilience.
Precision aging can be used to interrogate resilience trajectories for in vitro stress response
patterns on an individual basis. These patterns can then serve as a basis to develop
intervention strategies to move resilience in individuals with low resilience trajectories
towards a more optimal and projected organismal lifespan endpoint.Ladiges Page 3
Aging Pathobiol Ther . Author manuscript; available in PMC 2022 January 25.
Author Manuscript Author Manuscript Author Manuscript Author Manuscript | d5e91ba005ad6d5ae25a4fc597efdb1bdf4696b1 | page_0002 |
Statistics and Related Topics in Single-Molecule Biophysics
Hong Qian and
Department of Applied Mathematics, University of Washington Seattle, WA 98195
S. C. Kou
Department of Statistics, Harvard University, MA 02138
Abstract
Since the universal acceptance of atoms and molecules as the fundamental constituents of matter
in the early twentieth century, molecular physics, chemistry and molecular biology have all
experienced major theoretical breakthroughs. To be able to actually “see” biological
macromolecules, one at a time in action, one has to wait until the 1970s. Since then the field of
single-molecule biophysics has witnessed extensive growth both in experiments and theory. A
distinct feature of single-molecule biophysics is that the motions and interactions of molecules and
the transformation of molecular species are necessarily described in the language of stochastic
processes, whether one investigates equilibrium or nonequilibrium living behavior. For laboratory
measurements following a biological process, if it is sampled over time on individual participating
molecules, then the analysis of experimental data naturally calls for the inference of stochastic
processes. The theoretical and experimental developments of single-molecule biophysics thus
present interesting questions and unique opportunity for applied statisticians and probabilists. In
this article, we review some important statistical developments in connection to single-molecule
biophysics, emphasizing the application of stochastic-process theory and the statistical questions
arising from modeling and analyzing experimental data.
1 Introduction
Although the concept of atoms and molecules can be traced back to ancient Greece, the
corpuscular nature of atoms was firmly established only in the beginning of the 20th
century. The stochastic movement of molecules and colloidal particles in aqueous solutions,
known as the Brownian motion, explained by the diffusion theory of A. Einstein (1905) and
M. von Smoluchowski (1906), and the stochastic differential equation of P. Langevin (1908)
– confirmed experimentally through the statistical measurements of J.-B. Perrin (1912), T.
Svedberg and A.F. Westgren (1915) – played a decisive role in its acceptance [1]. The
literature on this subject is enormous. We refer the readers to the excellent edited volume
[2], which included now classical papers by Chandrasekhar, Uhlenbeck-Ornstein, Wang-
Uhlenbeck, Rice, Kac and Doob, and [3], a collection of lectures by Kac, one of the
founding members of the modern probability theory [4].
While physicists, ever since Isaac Newton, have been interested in the position and velocity
of particle movements, chemists have always perceived molecular reactions as discrete
events, even though no one had seen it until the 1970s. Two landmark papers that marked
the beginning of statistical theories in chemistry (at least in the U.S.) appeared in the 1940s
NIH Public Access
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Annu Rev Stat Appl . 2014 January 1; 1: 465–492. doi:10.1146/annurev-statistics-022513-115535.
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[5, 6]. Kramers' paper [5] elucidated the emergence of a discrete chemical transition in terms
of a continuous “Brownian motion in a molecular force field” with two stable equilibria
separated by an energy saddle and derived an asymptotic formula for the reaction rate.
Probabilistically speaking, this is the rate of an elementary chemical reaction as a rare event
[7]. Delbrück's paper [6] assumed discrete transitions with exponential waiting time for each
and every chemical reaction and outlined a stochastic multi-dimensional birth-and-death
process for a chemical reaction system with multiple reacting chemical species. Together,
these two mathematical theories have established a path from physics to cell biology by ( i)
bridging the atomic physics with individual chemical reactions in aqueous solutions, and ( ii)
connecting coupled chemical reactions with dynamic chemical/biochemical systems. In
1977, Gillespie independently discovered Delbrück's chemical master equation approach [8]
in terms of its Markovian trajectories based on a computational sampling algorithm now
bears his name in the biochemistry community [9]. The simulation method actually can be
traced back to Doob [10].
Experimental techniques have experienced major breakthroughs along with these theoretical
developments. J.-B. Perrin's investigations on Brownian motion gave perhaps the first set of
single-particle measurements with stochastic trajectory. The spatial and temporal resolutions
back in 1910s were on the order of micrometer and tens of second. By the late 1980s, they
became nanometer and tens of millisecond. The observation of discrete stochastic transitions
between different states of a single molecule was first achieved in the 1970s on ion
channels, proteins imbedded in the biological cell membrane. This was made possible by the
invention of the patch-clamp technique, together with the exquisite electronics, for
measuring small electrical current [11]. To measure the stochastic dynamics of a “tumbling”
single molecule in an aqueous solution, one needs to be able to “see” the molecule under a
microscope for a sufficiently long time. For this purpose, one needs an experimental
technique to immobilize a molecule and a highly sensitive optical microscopy. This was first
accomplished for enzyme molecules at room temperature in 1998 [12].
To statisticians and probabilists, this is abundantly clear that biophysical dynamics at the
molecular level are stochastic processes. To characterize such dynamics, called fluctuations
in chemical physics literature, one thus needs stochastic models. In an experiment, if such
processes are sampled over time, one molecule at a time, then the analysis of experimental
data naturally calls for the inference of stochastic processes. Therefore, the theoretical and
experimental developments of single-molecule biophysics constitute one great opportunity
for applied statistics and probabilities.
The aim of this article is to review some important statistical developments in single-
molecule biophysics from the construction of theoretical models to advances in the
experiments, mostly drawing from our own limited research experience. The discussion is
far from complete, as the field of single-molecule biophysics, with a substantial background,
is advancing too rapidly to be captured by a short review. Still, we hope to convey a certain
amount of historical continuity, as well as current excitement at the research interface
between statistics and molecular biophysics. Special attention is paid to the application of
stochastic-process theory and the statistical questions arising from analyzing experimental
data.Qian and Kou Page 2
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In the presentation we discuss the underlying theory, the experiments as well as the analysis
of experimental data. The discussion of theory focuses more on the application of stochastic
processes in modeling various problems in single-molecule biophysics, whereas the
discussion of experiments and data focuses more on the statistical analysis of data. However,
we want to emphasize that, as one observes in the advance of modern sciences, theory and
experiment/data really go hand in hand: the development in one stimulates and inspires the
other.
2 Brownian motion and diffusion of biological macromolecules
Before we discuss Brownian motion and its profound implications in biophysics, we want to
first clarify the terminology, because the term “Brownian motion” used by physicists and
chemists and the term “Brownian motion” used in probability and statistics refer to different
things: physicists and chemists' Brownian motion corresponds to the integral of the
Ornstein-Uhlenbeck process (as we shall see shortly), whereas statisticians and probabilists'
Brownian motion refers to the Wiener process, although both share the characteristic of
E[x2(t)]∝ t for large t. Likewise, “diffusion” has different meaning in statistics and
biophysics. In statistics and probability, the term “diffusion processes” typically refers to
continuous-time and continuous-space Markov processes, such as Itō's diffusions. In
biophysics, the term “diffusion” typically refers to physical motion of a particle without an
external potential; when there is a drift, it is often called biased diffusion.
To facilitate our discussion, let us first review the derivation of the law of physical
Brownian motion [7]. Suppose we have a particle with mass m suspended in a fluid. Then
according to Newton's equation of motion formulated by Langevin, the velocity v(t) of the
particle satisfies
(1)
where ζ is the damping coefficient and F(t) is a white noise – formally the “derivative” of
the Wiener process. To correctly represent an inert particle in thermal equilibrium with the
fluid, the Langevin equation has an important physical constraint that links the damping
coefficient ζ with the noise level, because both the movement of the particle and the friction
originate from one source – the collision between the particle and surrounding fluid
molecules:
(2)
where δ(·) is Dirac's delta function, kB is the Boltzmann constant, and T is the underlying
temperature. Equation (2) is a consequence of the fluctuation-dissipation theorem in
statistical mechanics [13]. Probabilistically speaking, a Markov-process model for an inert
system that tends to thermal equilibrium is necessarily reversible [14, 15].
In the more rigorous probability notation, equations (1) and (2) translate toQian and Kou Page 3
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(3)
where B(t) is the Wiener process, and the formal association of “
”
is recognized. The stationary solution of equation (3) is the Ornstein-Uhlenbeck process [2],
which is Gaussian with mean function E[v(t)] = 0 and covariance function
. It follows that for the displacement,
,
which can be recorded in single-particle tracking, its mean squared is
Therefore,
(4a)
(4b)
Equation (4b) gives the famous Einstein-Smoluchowski relation, which links the diffusion
constant D with the “mobility” ζ of the particle D = kBT/ζ. This equation is historically
highly significant in that by combining it with Stokes' law, ζ = 6πηr, and the definition of
the Boltzmann constant ( kB = R/N), one obtains
(5)
where η is the viscosity, r is the radius of the spherical particle, R is the gas constant, and N
is the Avogadro constant.
An immediate experimental consequence of (5) is that by measuring the diffusion constant
of a spherical particle, one can estimate the Avogadro constant! The experiments on
Brownian motions in fact had a rather shinning history in both physics and chemist. In 1926,
Jean-Baptiste Perrin and Theodor Svedberg won the Nobel Prizes in physics and chemistry
respectively. Perrin had studied trajectories of Brownian motions, verifying Einstein's
description of Brownian motion and providing one of the first modern estimates of the
Avogadro constant, while Svedberg developed the method of analytical ultracentrifugation
using which he studied the counts of Brownian particles in a well-defined volume and how
this counting process evolves over time. This counting process is referred to as the
Smoluchowski process (first by M. Kac in [3]). Both Perrin and Svedberg's observations
were performed on large colloids; it has to wait for nearly a half century for suchQian and Kou Page 4
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measurements to be performed on biological macromolecules. A version of the Svedberg
experiment appeared in the 1970s under the name of Fluorescence Correlation Spectroscopy
(FCS, see Sec. 4), and the measurement of single trajectory was developed in the 1980s,
known as Single-Particle Tracking (SPT), using the principle of “spatial high-resolution by
centroid localization”. This principle is responsible for driving much of the recent advance
in single-molecule biophysics and super-resolution imaging.
For experimental data from a true Brownian motion, a natural statistical question is to obtain
estimates of the diffusion constant. If the data consist of the trajectories of individual
particles as in SPT, the diffusion constant can be estimated by either a least-square
regression or an MLE. Sec. 2.1 will discuss it in some detail. If the data consist of particle
counting over time, the statistical estimation becomes more involved. We will discuss it in
Sec. 3, starting with the Smoluchowski process, which is non-Markovian [16, 17].
In addition to estimating the diffusion constant, often the experimental objective is to
investigate the motion that deviates from a simple Brownian motion. This has yielded a
great deal of development in statistical treatments of these data: What if there is a drift, if the
space is not homogeneous, if the Brownian particles can reversibly attach to other stationary
or moving objects, or if the particles are interacting (e.g., not independent)? With the
emerging of super-resolution imaging, these questions are still constantly being asked in
laboratories; a systematic statistical treatment of the problem is yet to be developed [18].
2.1 Single-particle tracking of biological molecules
Since the late 1980s, camera-based single-particle tracking (SPT) has become a popular tool
for studying the microscopic behavior of individual molecules [19]. The trajectory of an
individual particle is typically recorded through a microscope by a digital camera in such
experiments; the speed of the camera can be as fast as a few milliseconds per frame. The
superb spatial resolution owes to the idea of centroid localization.
One of the most common statistical questions is to determine the diffusion constant D of the
underlying particle from the experimental trajectory. If we denote ( x(t1), …, x(tn)) the true
positions of the particle at times t1, …, tn, where Δ t ≡ ti – ti−1 is the time interval between
successive positions, then the experimental observations ( y1, y2, …, yn) are yi = x(ti) + εi,
where
are the localization (measurement) error. If the particle's motion is
really Brownian, then, as we have seen in equation (4b) the process x(t) can be well
approximated by
, where B(t) is the standard Wiener process, provided t ≫ m/ζ.
This leads to
(6)
An intuitive estimate of D used by many experimentalists utilizes the mean square
displacement (MSD) [20], such asQian and Kou Page 5
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which are averages of correlated (square) increments, or
which are averages of nonoverlapping (square) increments. One can also try to combine
them, for example, by weighting or a regression (against k) [21].
Given the parametric specification (6), another natural estimate of D is the maximum
likelihood estimate (MLE) [22]. It is interesting to note that ( i) MLE and the optimal
estimate based on MSD have comparable accuracy [23], and ( ii) the estimation error in D
decreases with n, the sample size (the number of camera frames), at the rather slow rate of
O(n−1/4), which contrasts with the familiar rate of O(n−1/2) as in the central limit theorem
[24, 25, 26].
The determination of the diffusion constant D serves many purposes, ranging from (Perrin's
original) estimation of the Avogadro constant to the test of whether the underlying motion is
Brownian to the elucidation of detailed molecular mechanism. For example, Blainey et al.
[27] studied how DNA-binding proteins move along DNA segments. Does a DNA-binding
protein simply slide along the DNA, in which a protein executes simple one-dimensional
translational move parallel to the DNA without rotation, or does a DNA-binding protein
move along the DNA through a helical path, in which it retains a specific orientation with
respect to the DNA helix and rotates with the helix (in a spiral fashion) [28, 29]? If we
measure a protein's position along the DNA over time, then the two motions are subject to
different expressions of the diffusion constant: in the parallel motion, the diffusion constant
is
as we have seen in equation (5), where η is the viscosity and r is the size of the protein; in
the helical motion, the diffusion constant is
(7)
where roc is the distance between the protein's center of mass and the axis of the DNA, and b
is the distance along the DNA traveled by the protein per helical turn. Equation (7) isQian and Kou Page 6
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derived from hydrodynamic considerations [30, 31]. The parallel motion and helical motion
can thus be told apart from the experimentally estimated diffusion constant. By tracking
DNA-binding proteins with various sizes from different functional groups and estimating
their diffusion constants from single-molecule experimental data, Blainey et al. [27] found
that the helical motion is the general mechanism.
2.2 Subdiffusion
As we have seen in (4b), a key characteristic of Brownian motion is that the mean squared
displacement E[x2(t)] ∝ t for moderate and large t. In some physical and biological systems
[32, 33] the motion is observed to follow E[x2(t)] ∝ tα with 0 < α < 1. These motions are
referred to as subdiffusion because of α < 1. One theoretical approach to model subdiffusion
is to employ fractional calculus (such as the use of fractional derivatives). This approach is
reviewed in [34]. We review an alternative approach here: generalized Langevin equation
with fractional Gaussian noise as postulated in [91].
We start with a generalized Langevin equation (GLE) [13]
(8)
where, in comparison with the Langevin equation (1), ( i) a noise G(t) having memory
replaces the white noise, and ( ii) the memory kernel K convoluted with the velocity makes
the process non-Markovian. Owing to the fluctuation-dissipation theorem, the memory
kernel K(t) and the noise are linked by [35]
Note that the GLE reduces to the Langevin equation when K is the delta function.
Within the GLE framework, we are looking for a kernel function that can give subdiffusion.
As the white noise is the formal “derivative” of a Wiener process, which is the unique
process that satisfies ( a) being Gaussian, ( b) having independent increment, ( c) having
stationary increment, and ( d) being self-similar, to generalize the white noise, a good
candidate is a process with the properties of ( a) Gaussian, ( b) stationary increment and ( c)
self-similar. The only class of processes that embodies all three properties is the fractional
Brownian motion (fBm) BH(t) [36, 37], which has mean E[BH(t)] = 0, and covariance
. H ∈ [0, 1] is called the Hurst parameter.
BH(t) reduces to the Wiener process when H = 1/2.
Taking G(t) in (8) to be the (formal) derivative of fBm,
, we
reach the model
, where the kernel KH(t) is
given byQian and Kou Page 7
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(9)
FH(t) is known as the fractional Gaussian noise (fGn).
In the more rigorous probability notation, the model can be written as
(10)
This equation is non-Markovian. Nevertheless, it can be solved in closed form via a Fourier
analysis [38]. The solution v(t) is a stationary Gaussian process, and the displacement
satisfies
for large t. Therefore, the model with H > 1/2 leads to subdiffusion.
If there exists an external potential U(x), a term − U′(x(t)) will be added to the right hand side
of (8), yielding
(11)
For a harmonic potential
, the model can be solved by the Fourier transform
method [38].
The subdiffusive motion is observed in single-molecule experiments on protein
conformational fluctuation [39, 40]. The experiments studied the conformation fluctuation
through the fluorescence lifetime of the protein. The fluorescence lifetime is a sensitive
indicator, as it depends on the 3D atomic arrangements of the protein in an exponential way.
The stochastic fluctuation of the fluorescence lifetime, recorded in the experiments, reveals
the stochastic fluctuation in the protein's conformation. Detailed analysis of the
autocorrelation, three-step and four-step correlation of the experimental fluorescence
lifetime data shows that ( i) the conformation fluctuation of the two protein systems undergo
subdiffusion; ( ii) the memory kernel is well described by equation (9), ( iii) the conformation
fluctuation is reversible in time, and ( iv) a harmonic potential captures the fluctuation quite
well. These subdiffusive observations, therefore, directly support the notation of fluctuating
enzymes, also known as dynamic disorder – as an enzyme molecule spontaneously changes
its conformation, its catalytic rate does not hold constant. The different conformations of an
enzyme molecule and their intertransitions thus could have direct implications in the
enzyme's catalytic behavior [41]. We will discuss some of those implications in Sec. 5.5.Qian and Kou Page 8
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From a pure statistics standpoint, inference and testing the subdiffusive models beyond the
autocorrelation function and three-step, four-step correlations are an open question.
3 Particle counting
The idea of counting the number of particles in a fixed region and using the temporal
correlation of the resulting counting process to extract the kinetic parameters of the
underlying experimental system has a long history, dating back to Smoluchowski's
investigation of Brownian motion in the early twentieth century. Suppose we have
indistinguishable particles, each undergoing independent Brownian motion. Let n(t) be the
number of particles at time t in a region Ω (such as an area illuminated under a microscope).
This counting process { n(t), t ≥ 0} is referred to as the Smoluchowski process. Under the
assumption that the initial positions of the particles are uniformly distributed in a volume S
(which is typically much larger than Ω), it can be shown that E(n(t)) = | Ω | / |S| and that for t
≫ m/ζ,
(12)
where | Ω| and | S| are the volumes of Ω and S, respectively, and D is the diffusion constant [3,
42, 43, 17, 44]. Note that under t ≫ m/ζ, the Brownian diffusion is well approximated by
the Wiener process, which is the basis for equation (12). Historically, this result allowed the
Brownian diffusion theory to be tested by particle counting – this was done notably by
Svedberg and Westgren in the 1910s. It also allowed Smoluchowski to successfully account
for the apparent “paradox” of microscopic reversibility of the motion of molecules and the
macroscopic irreversibility as in the Second Law of Thermodynamics [45]. Finally, it offers
an experimental way to determine the diffusion constant.
Estimating D from the experimentally observations ( n(t1), …, n(tM)), where Δ t ≡ ti − ti−1, is
a statistical question. An intuitive method is to match the theoretical covariance function
with the empirical one [42]:
(13)
where C(Δt, D) is the right hand side of (12), which is a function of Δ t and D. The solution
D̂ of the generalized difference equation (13) is the estimate of D. Alternatively, one can
also match lag- k square difference
or use the nonlinear least squareQian and Kou Page 9
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or its (weighted) variation to estimate D [43].
The approach of using MLE to estimate D encounters the difficulty that the Smolochowski
process is non-Markovian and that it does not have analytically tractable joint probability
function. Approximating the Smolochowski process by an emigration-immigration (birth-
death) process, which is Markovian, has been proposed [16, 17], where the birth rate and
death rates can be set by making sure that the emigration-immigration and Smolochowski
processes share the same mean and covariance (for small Δ t). Systematic comparison
between the two different estimation methods – the one based on empirical autocovariance
function versus the quasi-likelihood estimate based on the emigration-immigration
approximation – is an open question.
The scheme of counting particles and utilizing the temporal correlation to extract kinetic
parameters was further developed into fluorescence correlation spectroscopy (FCS) in the
1970s, as we shall discuss in the next section, where, instead of the exact counts, the
fluorescence level of the underlying system, which depends on the molecules' concentration,
is recorded. The autocorrelation of the stochastic fluorescence reading can be used to
estimate the parameters such as the diffusion constant and the reaction rate.
4 Fluorescence correlation spectroscopy and concentration fluctuations
With the development of laser-based microscope, one can now measure the number of
molecules in a very small region within an aqueous solution and “count” the number of
molecules: The counting is based on the fluorescent light emitted from the molecules.
Assuming molecules are continuously giving out fluorescence, then the measurement of
stationary fluorescence fluctuation from a small region provides information on
concentration fluctuation. Since fluorescent emission requires excitation of an incoming
light, the small region is naturally defined by the laser intensity function I(r), where r = (x,
y, z) is the three-dimensional (3D) location of the particle [46]; I(r) can often be nicely
represented by a Gaussian function
.
For a collection of free-moving, identical, independent fluorescence-emitting particles, the
theory is built upon the function of a single Brownian motion: I(Xt), where Xt is a 3D
Brownian motion, with diffusion coefficient D, confined in a large finite volume Ω. To
compare with a real experiment, we consider N i.i.d. Brownian motions and let N, Ω → ∞
such that N / |Ω| = c corresponds to the concentration of the particles in the real experiment
[47], with | Ω| denoting the volume of Ω. Then one can derive the autocovariance function of
I(Xt) [46]:Qian and Kou Page 10
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which can be used to obtain the diffusion constant D. This result and the corresponding
experiments were developed in the 1970s. If the number of fluorescent particles are very
large, then the measured stationary intensity I(t) is essentially a Gaussian process with the
mean and variance given by
(14)
which can be derived by assuming that the particles are distributed in space according to a
homogeneous Poisson point process. In the Gaussian limit, one can thus measure the
concentration
and the “brightness” of a particle from the Fano factor
Var[I]/E[I].
FCS can also be used to obtain the reaction rate of a chemical process. Suppose we have a
two-state reversible chemical reaction A ⇌ B, where A and B are the two states of the
reaction. Let
be the rate of A changing to B and
be the rate of B changing to A. This
two-state reaction is typically described by a two-state continuous-time Markov chain with
and
being the (infinitesimal) transition rate. Suppose the two states A and B have
different fluorescence intensity IA and IB. If we use Xt to denote the two-state process, then
This equation can be used to estimate the relaxation time
of the reaction.
In the late 1980s, researchers started to measure non-Gaussian intensity distributions and
obtain information about the heterogeneity of brightness in a mixture of particles. Various
methods emerged: fluorescence distribution spectroscopy (FDS), high-moment analysis
(HMA), photon-counting histogram (PCH), and fluorescence intensity distribution analysis
(FIDA), to name a few. Non-Gaussian behavior means that higher-order temporal statistics
such as E[I(t1 + t2)I(t1)I(0)] also contains useful information.
If ΔI(t) = I(t)−E[I] is a Markov process and is linear, i.e., the conditional expectation
(15)
then the autocovariance functionQian and Kou Page 11
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(16)
Therefore, we see that the functional form of the autocorrelation function (16) and the
relaxation function after perturbation (15) are the same. This is the mathematical basis of the
traditional, phenomenological approach of Einstein, Onsager, Lax, and Keizer to
fluctuations. In a similar spirit, the higher-order temporal correlation functions are
mathematically related to relaxations with multiple perturbations, known as multi-
dimensional spectroscopy [48, 49].
The experimentally determined fluorescence autocorrelation function ĝ(nδ), with n = 1, 2,
⋯ and δ being the time step for successive measurements, often has a curious feature: The
measured ĝ(0) is always much greater than the extrapolated value from ĝ(n) based on n ≥ 1.
In fact, the difference is about E(I). This is known as “shot noise”; its origin is the Poisson
nature of the random emissions of fluorescent photons, which are completely uncorrelated
on the time scale of δ. Instead of treating the experimental fluorescence reading as a
deterministic function of the underlying Xt, one needs to consider the quantum nature of
photon emission – the photon counts are Poisson with the intensity function as the mean.
Taking this into consideration, the photon count from a single diffusing particle is an integer
random variable with distribution [50]
in which fX(r, t) is the probability density function of Xt Therefore, we see that, under the
assumption that Brownian particles are uniformly distributed in space
Now again consider total N i.i.d. particles, and let N, Ω → ∞ and N / |Ω| = c. Assuming that
the particles are distributed in space according to a homogeneous Poisson point process, we
have
Comparing this with equation (14), we see the extra shot noise term E[I]. This is a good
example of the textbook problem of the sum of a random number of independent random
variables. In a laser illuminated region, there are random number of fluorescent particles,
and each particle emit a Poisson number of photons; the total photon count is, thus, a sum of
a random number of terms.Qian and Kou Page 12
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Recently, the optical setup for FCS has been expanded to have two different colored
fluorescence, or to have two laser beams at different locations of the system [51, 52]. These
measurements generate multivariate stationary fluorescence fluctuations. There are good
opportunities for in-depth statistical studies of the new data; for example, the assessment of
time-reversibility of a Gaussian process [14, 99].
5 Discrete Markov description of single-molecule kinetics
While the diffusion theory describes a continuous-state, continuous-time Markov process [2,
7], intense studies of discrete-state continuous-time Markov processes (also called Q-process
by Doob [10] and Reuter [53]) as models for internal stochastic dynamics of individual
biomacromolecules started in the 1970s, mainly driven by the novel experimental data from
single-channel recording of membrane protein conductance. For their contributions, E.
Neher and B. Sakmann received Nobel prize in 1976. The book by Sakmann and Neher [11]
provides a thorough review of single-channel recording. We also refer the readers to earlier
accounts in the pre-single-channel era of the development of discrete-state Markov approach
in biochemistry [54, 8] and an exhaustive summary of the literature on ion-channel
modeling and statistical analysis [55].
Enzymes and proteins are large molecules consisting of tens of thousands of atoms. (They
are sometimes called biopolymers ; see also Section 6.) One of the central concepts
established since the 1960s is that a protein can have several discrete conformational states :
These states have different atomic arrangements within the molecule, and they can be
“observed” through various molecular characteristics, including absorption and emission
optical spectra, physical sizes, or biochemical functional activities. These different “probes”
can have different temporal resolutions and sensitivities. If one has an access to a highly
sensitive probe with reasonably high temporal resolution, then one can measure dynamic
fluctuations of a single protein as a stationary, discrete-state stochastic process. Markov, or
hidden Markov models, therefore, are natural tools to describe the conformational dynamics
of a protein and such measurements.
5.1 Single-channel recording of membrane proteins
The earliest “single-molecule” experiments were carried out in the 1970s on ion channels;
the patch-clamp technique pioneered by Neher and Sakmann enables reliable recording of
membrane protein conductance on a single channel. Since the close and open of an ion
channel control the passage of ions across a cell membrane, the conductance recorded in the
experiments essentially consists of step functions, such as (stochastically) alternating high
and low current levels. The simplest model to describe such on-off signal is the two-state
continuous-time Markov chain model
(17)
Due to experimental noise and data filtering, the sequence of real observations { y(ti), i = 1,
2, …} are better described by hidden Markov models. Under specific models, such as y(ti)|Qian and Kou Page 13
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X(ti) ∼ N(X(ti), σ2), where X(t) is the underlying state of the Ion channel, maximum
likelihood estimation can be (straightforwardly) obtained for the transition rates.
The conductance of real ion channels, however, is typically much more complicated than the
simple two-state model. For example, in addition to the open and closed states of the ion
channel, there might exist “blocked” states, in which a blocking molecule's binding to the
ion channel stops the ion flow; alternatively, the channel's opening might be triggered by an
agonist molecule's binding. An ion channel, thus, could have multiple closed and open
states. The complication for modeling and inference is that these open states (and closed
states) are not distinguishable from the experimental data: typically the open states (and
closed states) have the same conductance. We are, therefore, dealing with aggregated
Markov processes: although the underlying mechanism is Markovian, we only observe in
which aggregate (i.e., a collection of states) the process is [56]. A natural question is the
identifiability of different models given that we can only observe the aggregates. Note that it
is possible that two distinct models give the same data structure/likelihood.
Statistical questions include estimating the number of (open and closed) states, postulating a
model and inferring the parameters of the model. Ball and Rice [55] overviews the statistical
analysis and modeling of ion channel data. Chapter 3 and Part III of the encyclopedic book
by Sakmann and Neher [11] provide an introduction and review of ion channel data analysis,
from initial data processing to the inference complications, such as the time interval
omission problem.
Parallel to constructing, testing and estimating Markov models, an alternatively statistical
approach is to treat the inference as an change-point detection problem: given the on-off
signal, determine from the data the change points (i.e., the transition times) and then infer
the sojourn times and their correlation, which provide clues for the eventual model building.
The change-point approach can be viewed as non-parametric as it does not explicitly rely on
a (Markov) model specification. The problem of change-point estimation has a long history
in statistics dating back to the 1960s. More recent approaches, particularly relevant for
single-channel data, include the use of BIC (Bayesian information criterion) penalty [57],
quasi-likelihood method [58], L1 penalty method [59], the multi-resolution method [60], and
the marginal likelihood method [61]. Compared to the parametric inference methods based
on continuous-time Markov chains, many of these change-point methods are flexible and
can be made automatic. Thus, they are suitable for fast initial analysis of a large amount of
single-channel data, such as thousands of data traces commonly generated in a modern
single-channel recording experiment.
5.2 Two-state and three-state single-molecule kinetics
The two-state Markov chain, such as in (17), is widely used in biochemical kinetics. They
are typically diagrammed as
(18)Qian and Kou Page 14
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where A and B are the two states, and
and
are the (infinitesimal) transition rates.
One of the simplest biochemical reactions, the reversible binding of a single protein E to its
substrate molecule S, E+S ⇌ ES, can often be described by such two-state Markov model
with rate parameters
and
, where cS denotes the concentration of the substrate
molecules. Note that the expression
assumes that the protein concentration is
sufficiently dilute, while there are a large number of substrate molecules S per E so that the
concentration cS remains essentially constant. Writing out
also highlights the fact
that the concentration cS of the substrate can be controlled in the experiments. Thus, one can
study the effect of the concentration cS on the overall reaction.
and
are called second-
order and pseudo-first-order rate constants in chemical kinetics, respectively: A second-
order rate constant has a dimension [time]−1×[concentration]−1 while a first-order rate
constant has a dimension [time]−1. The states E and ES of a single protein can be monitored
through a change in the fluorescence intensity of the molecule; for example, either through
the intrinsic fluorescence of the protein or Föster resonance energy transfer (FRET) between
the protein and the substrate.
A three-state Markov chain is often used to describe an enzyme's cycling through three
states E, ES, EP:
(19)
An enzyme catalytic cycle is completed every time it helps convert a substrate molecule S to
a product P, while the state of the enzyme molecule returns to the E so that it can start the
cycle to convert the next substrate molecule, as shown in Fig. 1. The enzyme E serves as a
catalyst to the chemical transformations S ⇌ P. Again, using the idea of pseudo-first order
rate constants, we have the (infinitesimal) transition rates
and
, where cP
is the concentration of the product P.
A three-state Markov process is reversible if
, which is a special case
of the Kolmogorov criterion of reversibility [62]. This mathematical concept precisely
matches the important notion of a chemical equilibrium between S and P when
In fact, it is widely known in biochemistry that in the absence of the enzyme, reaction S ⇌ P
will have very small forward and backward first-order rate constants α+ and α−.
Nevertheless, the fundamental law of chemical equilibrium dictates that
[64].Qian and Kou Page 15
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In a living cell, however, the substrate and the product of an enzyme are usually not at their
chemical equilibrium, and their concentrations cS and cP do not satisfy the equality in Eq.
5.2. This means
In this case, the corresponding Markov chain is no longer reversible. This motivated the
mathematical theory of nonequilibrium steady state (NESS) [65, 66, 67]. For strongly
irreversible, three-state Markov process, its Q-matrix (i.e., the infinitesimal generator) is
possible to have a pair of complex eigenvalues, giving rise to non-monotonic, oscillatory
autocorrelation function [68]. For example, if
and
, then the
two non-zero eigenvalues are
. Such oscillatory behavior has been observed in
single-molecule experiments.
5.3 Entropy production and nonequilibrium steady state
The chemical NESS also motivated the mathematical concept of entropy production rate
[69, 65]:
(20)
For a continuous-time Markov process X(t), ℙt in equation (20) is the likelihood of a
stationary trajectory, and
is the likelihood of the time-reversed trajectory. For example, if
ℙt is the likelihood of a particular trajectory 2 → 3 → 1, where the transitions occur at t1 and
t2 with 0 < t1 < t2 < t, then
is the likelihood of the trajectory 1 → 3 → 2, where the
transitions occur at t − t2 and t − t1.
For a three-state system, it is easy to show that
(21)
with NESS probability circulation
We see that ep is never negative; and it is zero if and only if the Markov process is
reversible. In fact, in the energy unit of kBT, the logarithmic term in equation (21) is theQian and Kou Page 16
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chemical potential different between S and P:
; Jness is the number
of reactions per unit time, and ep is the amount of heat dissipated into environment per unit
time. The chemical potential equaling heat dissipation is the First Law of Thermodynamics;
ep ≥ 0 is interpreted as the Second Law of Thermodynamics. The Second Law has always
been taught as an inequality; equation (20) provides it a more quantitative formulation in
terms of a Markov process.
For finite t, the ep in equation (20) is stochastic and it has a negative tail. Characterizing this
negative tail under a proper choice of the initial probability for a finite trajectory is the
central theme of the recently developed fluctuation theorems [70, 71].
5.4 Michaelis-Menten single-enzyme kinetics
In single-molecule enzyme kinetics [12], one can measure the arrival times of successive
product P, following the simple Michaelis-Menten enzyme kinetic scheme [72, 73]:
(22)
This is a simpler model than that in equation (19): It is assumed that reactions associated
with
and
are so fast that they can be neglected. Since each arriving P is immediately
processed,
. The arrivals of P's are now a renewal process with mean waiting
time E[T] easily computed [72, 68, 74] from
Solving E[T] and noting
, one obtains
(23)
This is the celebrated Michaelis-Menten (MM) equation for steady-state enzyme catalytic
velocity, first discovered in 1913 based on a non-statistical theory. One of the immediate
insights from the probabilistic derivation of MM equation is that if an enzyme has only a
single unbound state E, then irrespective of how many and how complex the bounding states
(ES)1, ⋯, (ES)n might be, the MM equation is always valid. The expressions for the Vmax
and KM can be very complex [73, 75]. We will discuss in some detail the single-molecule
experiments on enzymes and models beyond the Michaelis-Menten mechanism in the next
subection.
If cP ≠ 0, then the NESS probability circulation in the enzyme cycle is [74]:Qian and Kou Page 17
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This equation is known as Briggs-Haldane equation (1925) for reversible enzyme.
5.5 Single-molecule enzymology in aqueous solution
We have seen how schemes (19) and (22) describe enzyme kinetics. Traditionally, they are
used to set up (coupled) differential equations, which specify how the concentrations of the
enzyme, the substrate and the product change over time. These theoretical descriptions then
can be compared with the experimental results carried out in balk solution, which involve a
large ensemble of enzyme molecules.
In contrast to these traditional ensemble experiments, to be able to see the action of a single
enzyme molecule in aqueous solution, one needs to develop methods to immobilize an
enzyme molecule, to make the experimental system fluorescent, and one also needs high
sensitivity optical microscopy. This was first accomplished in 1998 [12] on cholesterol
oxidase, where the active site of the enzyme, E + S and ES in equation (22), is fluorescent,
yielding an on-off system. The experimental data of [12] have similar appearance as the on-
off data from ion channels (Section 5.1). Thus, many data analysis tools developed for
single-channel recording can be applied. The experimental fluorescence techniques, such as
the design and utilization of fluorescent substrate, fluorescent active site and fluorescent
product, and the experimental techniques to immobilize an enzyme molecule were reviewed
in [76, 77], which also discussed the relationship between single-molecule enzymology and
the traditional ensemble approach.
As the experimental methods develop and mature, we are finally able to directly study and
test the Michaelis-Menten mechanism (22) on the single-molecule scale. English et al.
(2006) [73] conducted single-molecule experiments on the enzyme β-galactosidase, using
fluorescent product. The sharp fluorescence spikes from the product enables the
experimental resolution of β-galactosidase's individual turnovers (i.e., the successive cycles
of the enzyme). It was found from the experimental data that ( a) the distribution of the
enzyme's turnover times is much heavier than an exponential distribution, contradicting the
Michaelis-Menten mechanism's prediction; ( b) there is a strong serial correlation in a single
enzyme's successive turnover times, also contradicting the Michaelis-Menten mechanism;
and ( c) the hyperbolic Michaelis-Menten relationship of E−1(T) ∝ cS/(cS + KM), as given in
(23), still holds. To explain the experimental results, in particular, their contradiction with
the Michaelis-Menten mechanism, Kou et al. (2005) [72] introduced the following model, as
diagrammed in Fig. 2:
In Fig. 2 E1, E2, … represent the different conformations of the enzyme, and SEi are the
different conformations of the enzyme-substrate complex. The model is based on the insight
that a protein molecule can have multiple conformational states: these states have different
atomic arrangements and can have different biochemical functional activities. DetailedQian and Kou Page 18
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calculation in [72, 73, 78, 79] shows that the model is capable of explaining the
experimental data.
The data from experiments like [73] have different pattern from the on-off data of [12].
Since fluorescent product is used, which, once formed, quickly diffuses away from the focus
of the microscope, the experimental data consist of fluorescent spikes, with each spike
corresponding to the formation of one product molecule, amid fluorescence from the
background. In principle, the time lag between two successive spikes is the (individual)
turnover time of the enzyme. In practice, since the level of the fluorescent spike is random
(as a product molecule spends a random time in the focal area of the microscope before
diffusing away), one needs to threshold the data to locate the spikes. Finding statistically
efficient thresholding level (to minimize false positive) for such data is an open problem.
5.6 Motor protein with mechanical movements against external force
One particular type of enzymes, called motor proteins, can move along their designated
linear, periodic tracks inside a living cell, even against a resistant force. The energy of the
motor is derived from the chemical potential in the S → P reaction, given in equation (21)
[80, 81, 82, 83, 84].
An external mechanical force Fext enters the rate constants for a conformational transition of
a motor protein as follows: If the transition from conformational state A to state B moves a
distance dAB along the track against the force, then according to Boltzmann's law
Substituting such a relation into equation (21), and let d be the total motor step length for
one enzyme cycle (from S to P), then
In this case, part of the chemical energy from transformation S → P is converted to
mechanical energy. The part that becomes heat is the entropy production.
The motor protein carries out a biased random walk with velocity vmotor = Jnessd. With
increasing force Fext, vmotor decreases. When Fext = ΔμS→P/d, the random walk is no longer
biased; this is known as a stalling force . One can also compute the dispersion of the motor,
i.e., a “diffusion coefficient”:
Qian and Kou Page 19
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In fact, as a semi-Markov process (also known as Markov renewal process or continuous-
time random walk), the mean cycle time is E[Tc] and the ratio of probabilities of forward
and backward cycles is
.
5.7 Advanced topics
5.7.1 Empirical measure with finite time— Even for the simplest two-state Markov
process, some of the statistics can be complex. For example, [85] studies analytically the
statistical quantity
in which ξB(t) is the indicator function for state B in Eq. (18). They showed that the pdf
(probability density function) of Xτ can be obtained in terms of its Fourier transform γ(y):
in which
, and
We see for large τ,
5.7.2 Non-Markovian two-state systems— Some enzymes exhibit clear two-state
stochastic behavior, but the process is not Markovian. For example, the consecutive dwell
times in state B could have non-zero correlation [12]. This is a strong violation of the
Markovian property. To explain this observation, the theory of dynamic disorder , or
fluctuating enzyme, assumes that
and
in equation (18) are themselves stochastic
processes in the form
in which Xt is an Ornstein-Uhlenbeck process (see Eq.
(3)) [86, 87, 88]. In this case, even though ξB(t) is no longer a Markov process, ( ξB, X)
together is now a coupled diffusion process [89]. A more complex model on Xt (describing it
as fractional Gaussian noise) is considered in [90]. One can also model Xt by the generalized
Langevin equation [91] of Sec. 2.2.Qian and Kou Page 20
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5.7.3 Dwell time distribution peaking— As we have discussed above, a continuous-
time Markov chain in a NESS can have complex eigenvalues, thus the power spectrum of its
stationary data can exhibit off-zero peak representing intrinsic frequency [92]. However, a
surprising result is that one can also observe an off-zero peak in the pdf of the dwell time
within a group of states, and this is impossible for a reversible process. This has been
discovered independently in [93, 94, 95].
5.7.4 Detailed balance violation and event ordering— The fundamental insight that
an sustained chemical energy input is necessary for observing an irreversible Markov
process in molecular systems has opened several lines of inquiry on stationary data. On the
one hand, for stationary molecular fluctuations in chemico-thermodynamic equilibrium, one
wants to test the preservation of detailed balance [96, 97, 98]. On the other hand, for a
molecular process with unknown mechanism, one wants to discover whether it is chemically
driven [99]. In fact, a quantification of the deviation from reversibility could reveal the
source of external energy supply. Finally, for system with breakdown of detailed balance,
the event ordering from statistical analysis provides insights toward molecular mechanism
[100].
The concept of detailed balance also exists in chemistry [64, 101, 102]. But it is essentially
different from the same term known in statistics. The chemical detailed balance requires that
a set of linear and nonlinear reactions forming a reaction cycle has zero cycle flux in
chemical equilibrium. This chemical detailed-balance is expressed in terms of
concentrations of the reactants, which are deterministic quantities. There is no probability
involved in this statement. If all the reactions are unimolecular, however, then a chemical
reaction system in terms of the law of mass action is equivalent to a continuous-time
Markov chain. Only in this case the chemical and the probabilistic detailed balance
conditions are the same.
6 Polymer dynamics and Gaussian processes
Polymer dynamics is another highly successful theory based on stochastic processes [103,
104]. A polymer chain in aqueous solution is modelled by a string of identical beads
connected by harmonic springs. The Langevin equation for the kth bead ( k = 1, 2, …, N) is
(24)
in which α is the spring constant, m and ζ are the mass and damping coefficient of a bead,
and Bk(t) are i.i.d. Wiener processes, again representing the collisions with the solvent.
Usually the mechanical system is under overdamped condition, e.g., mα ≪ ζ2, in which the
acceleration is negligible. Then equation (24) is simplified to
(25)Qian and Kou Page 21
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This is a multi-dimensional OU process. A polymer molecule presented by such a dynamics
is called a Gaussian chain .
One uses the boundary condition X0(t) = 0 to represent a tethered polymer end, and XN(t) =
XN+1(t) to represent a free polymer end. To study (25), an elegant approach is to
approximate it by a stochastic partial differential equation (SPDE):
in which
represents a spatio-temporal white noise. With the boundary conditions
X(0, t) = 0 and
, Fourier transform yields
in which each normal mode
and
Each ξj(t) is an OU process; its stationary distribution has variance
Therefore, X(s, t) is a Gaussian random field with stationary variance
One strong prediction of the Gaussian polymer theory is that the end-to-end distance of a
long polymer should be scaled as the square-root of its molecular weight M. This result hasQian and Kou Page 22
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become the standard against which a real polymer is classified: When a polymer is dissolved
in a “bad” solvent, its conformation is more collapsed, and thus its end-to-end distance
might scale as Mν with ν < 1/2. On the other hand, due to physical exclusion among polymer
segments, a real polymer in a “good” solvent is expected to be more expanded with ν > 1/2.
Indeed, the problem of excluded-volume effect in polymer theory has been a major topic in
chemistry and in mathematics. Paul Flory received the 1974 Nobel Prize in Chemistry for
his studies leading to a ν = 3/4. The rigorous mathematical work on this subject, known as
self-avoiding random walks , was carried out by Wendelin Werner, who received 2006 Fields
Medal for related work.
6.1 Tethered particle motion measuring DNA looping
Polymer theory has been widely applied in modeling biomacromolecules, especially DNA
[105]. In 1990s, Gelles, Sheetz, and their colleagues have developed a single-molecule
method to study transcription and DNA looping, called tethered particle motion (TPM)
[106, 107]. This time, the trajectory a Brownian motion particle, attached to a piece of DNA,
is followed. The statistical movements of the particle, therefore, provide informations on the
DNA flexibility, length, etc. The theory for the TPM requires a boundary condition at XN
that is different from Eq. (25), taking into account of the much larger particle that serves as
the optical marker [108, 109].
6.2 Rubber elasticity and entropic force
The Gaussian chain theory owes its great success to the Central Limit Theorem (CLT). The
end-to-end distance of a polymer chain can be thought as a sum of N i.i.d. random segment
lk, 1 ≤ k ≤ N, where N is proportional to the total molecular weight M. As long as l has a
distribution with finite second moment, then [103]
in which, due to spatial symmetry, it is assumed that E[lj · lk] = σ2δjk.
We like to point out that the elasticity of rubber is not due to any other molecular
interaction, to a large extent, but simply a consequence of this statistical behavior of a
Gaussian chain. The end-to-end distance is asymptotically a Gaussian random variable with
variance Nσ2:
Let one end of a chain be attached. Then the stochastic chain dynamics, on average, pulls the
free end from less probable position toward more probable position: This is called “entropicQian and Kou Page 23
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force” in polymer physics. In fact, reversing the Boltzmann's Law, there is an equivalent
harmonic “entropy potential energy” U(x) = kBTx2/(2Nσ2) with springer constant kBT/(Nσ2).
6.3 Potential of mean force and conditional probability
Stationary probability giving rise to an equivalent “force” is one of the fundamental insights
from polymer chemistry. A key concept in statistical chemistry, first developed by John
Kirkwood in 1930s [110], is the potential of mean force , which we shall discuss in this
subsection. It is essentially an incarnation of the conditional probability.
To illustrate the idea, let us again consider the Langevin equation for an overdamped particle
in a potential U(x):
The corresponding Kolmogorov forward equation, for probability density function fX(x, t) is
(26)
in which the − U′(x) term represents a potential force acting on the Brownian particle.
Now let us consider a Brownian particle in a 3-dimensional space without any force. If one
is only interested in the distance of the Brownian particle to the origin: R(t), then the pdf
fR(r, t) follows a Kolmogorov forward equation:
(27)
Comparing equation (27) to (26), we see that the stochastic motion of R(t) experiences an
equivalent force 2 kBT/r, with a potential function UR(r) = −2 kBT ln r. This is again an
entropic force, and the corresponding UR(r) is called potential of mean force . We recognize
that the entropic force arises essentially from a change of measure, therefore, it is
fundamentally rooted in the theory of probability. The potential of mean force UR(r) should
be understood as
(28)
Eq. (28) is again applying the Boltzmann's law in reverse, relating an energy to probability.Qian and Kou Page 24
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7 Statistical description of general stochastic dynamics
7.1 Chemical kinetic systems as a paradigm for complex dynamics
It is arguable that, since the work of Kramers, chemists are among the first groups to fully
appreciate the nature of separation of time scales in complex dynamics: while the rapid
atomic movements in a molecule is extremely fast on the order pico- to femto-seconds, a
chemical reaction which involves passing through a saddle point in the energy landscape, on
this time scale is a rare event. From this realization, the notions of transition state and
reaction coordinate have become two of the most elusive, yet extremely important concepts
distinctly chemical. They are even more important in biophysics, which, among others, deals
with the transitions between conformational states of proteins. Although not being widely
articulated, this is the appropriate statistical treatment of any dynamic system with a
separation of time scales due to statistical multi-modality.
7.2 General Markov dynamics with irreversible thermodynamics
Ever since the work of Kolmogorov, reversible, or symmetric Markov process has been
widely studied both in theory and in applications. Detailed balance is one of the most
important concepts in the theory of MCMC. On the other hand, the notion of entropy has
grown increasingly prominent in the general discussions on complex systems, usually in
connection to the information theory.
The central role of irreversible Markov description of complex biophysical processes is now
firmed established. In recent years, it has also become clear that entropy, and entropy
production, are essential concepts in irreversible, often stationary, Markov processes. In this
section, we give a concise description of this emergent statistical dynamic theory . We shall
only present the key results and leave out all the mathematical proofs, which can be found in
the literature [15, 111, 112, 113].
Consider a diffusion process with its Kolmogorov forward equation in the form of
(29)
We assume that it has an ergodic, differentiable stationary density fness(x), x ∈ Ω. Then one
can define two essential thermodynamic quantities: internal energy of the system U(x) = −ln
fness(x) and entropy of the entire system
Then one has the expected value of the U and the so called generalized free energy Ψ [f(x, t)]
= E[U] − S:Qian and Kou Page 25
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(30)
As a relative entropy, the importance of Ψ ≥ 0 is widely known. Then one has the following
set of equations that constitute a theory of irreversible thermodynamics :
(31a)
(31b)
(31c)
(31d)
(31e)
The first equation in (31a) can be interpreted as an energy balance equation, with the non-
negative Ein and ep as a source and a sink. ep is called entropy production. The second
equation in (31a) is an entropy balance equation, with heat exchange hex can be either
positive or negative. dΨ/dt ≤ 0 is the second law of thermodynamics.
For a reversible Markov process, Ein(t) = 0 for all t. Its stationary version has J(x) = 0 for all
x and ep = hex = 0. This is know as chemico-thermodynamic equilibrium in biophysics. In
general, in a nonequilibrium steady state, ∇ · Jness = 0 but Jness ≠ 0.
We now turn our attention to the dynamic equation (29). Its generator is ℒ* = ∇ · D(x) ∇ +
b(x) ∇. Introducing inner product
then the linear differential operator ℒ* can be decomposed into
, a symmetric
and an anti-symmetric part. Correspondingly, one has the operator in (29), ℒ = ℒs + ℒa:
(32a)
(32b)
In connection to the thermodynamics in (31), a diffusion process with pure ℒs has Ein(t) = 0;
a process with pure ℒa has dΨ/dt = 0 for all t. Noting that the operator in (32b) is actuallyQian and Kou Page 26
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hyperbolic rather than elliptic: it is a generalization of a conservative, classical Hamiltonian
dynamics [113]. Eq. (32a) of course is a generalization of the heat kernel. The generalized
Markov dynamics, therefore, unifies the Newtonian conservative and Fourier's dissipative
dynamics.
Thermodynamics, and the notions of dissipative and conservative dynamics have been the
cornerstone of classical physics. We now see that they emerge from a statistical description
of Markov processes. It will be an exciting challenge to the practicing statisticians to apply
this new-found stochastic perspective in modeling dynamic data.
How to use these mathematical relations in (31)? We give a speculative example: Consider a
stochastic biophysical process Xt in stationarity and assume we know its stationary density
fness(x). Now one carries out a measurement at time t0 and observes Xt0 = x0 ± ∊.
Conditioning on this information, the process is no longer stationary; and the system in fact
possesses an amount of “chemical energy”, which can be utilized for t > t0. According to the
thermodynamic theory, the amount of energy is Ψ[f(x, t0)] = – ln ( fness(x0)/(2∈)). This result
is consistent with information theory. How to calibrate this mathematical result against
energy in joules and calories, however, is a challenge.
8 Summary and Outlooks
Biological dynamics are complex. Uncertainty is one of the hallmarks of complex behavior,
either in the cause(s) of an occurred event, or in the prediction of its future – modeling and
predicting weather is one example. This intuitive sense in fact can be mathematically
justifies: Voigt [114] has shown that the generalized free energy Ψ defined in (30) is
monotonically decreasing if a dynamics is stochastic with uncertainty in the future, or is
deterministic but non-invertable with uncertainty in the past (i.e., many-to-one in discrete
time). Ψ is conserved in one-to-one dynamics such as determined by differential equations!
In contrast to the deterministic view of classical physics with certainty, quantitative
descriptions of biological systems and processes require a statistical perspective [115], as
testified in many successful theories and discoveries from population genetics, genomics,
and bioinformatics. In the context of single-molecule biophysics, where one zooms in on
individual molecules to study their behavior and interactions, one at a time, this stochastic
view is ever so fundamental: the random motion of and interaction between molecules in
time and space are necessarily described by stochastic processes. We have seen in this
review that the basic laws and understanding of statistical mechanics naturally lead to many
stochastic processes that govern the behavior of the underlying single-molecule system, but
more importantly the understanding and advances in stochastic processes theory motivate
new physical and chemical concepts – entropy production in nonequilibrium steady state
developed from studying irreversible Markov processes is one such example. The statistical
inference of single-molecule experimental data, ranging from exploratory data analysis,
testing stochastic models to the estimation of model parameters, has the distinctive feature
that the data are typically not the familiar i.i.d. (or independence) type. Often the underlying
stochastic-process model does not offer closed-form likelihood; even numerical evaluations
are difficult in many models; missing data, in the form of missing components/states or
state-aggregation, are prevalent owing to the experimental limitations. There are many openQian and Kou Page 27
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problems in stochastic model building, theoretical investigation of stochastic processes,
testing a stochastic model and the estimation of model parameters. The development in
stochastic-process theory and the statistical analysis of stochastic-process data will in turn
provide new modeling and data-analysis tools for biologists, chemists and physicists. We
believe the many open problems present great opportunities for statisticians and probabilists,
not only to provide correlations and distributions, but to actually determine mechanistic
causality through statistical analysis.
Stochastic process is a more natural language than classical differential equations for
chemical and biochemical dynamics at the levels of single molecules and individual cells. It
is still not widely appreciated that many of the key notions in chemistry echo important
concepts in the theory of probability: transition state as the “origin” of a rare event, chemical
potential as a form of stationary probability, Gaussian chain as a consequence of the Central
Limit Theorem, and potential of mean force as a manifestation of conditional probability, to
name a few. All these chemical concepts have fundamental roots in statistics, though most
of them were developed independently by chemists without the explicit usage of modern
theory of probability and stochastic processes.
8.1 Mechanism, entropic force and statistics
Before closing, we would like to discuss a philosophical point one inevitably encounters in
statistical modeling of complex dynamic data. A fundamental reason to study dynamics in
classical sciences is to establish causal relations between events in the sense that modern
scientific understanding demands a “mechanism” beyond mere statistical correlations.
However, non-deterministic dynamics with random elements raises a very different kind of
“understanding”: a force that exerts on a population level might not exist at all on an
individuals level; the former is an emergent phenomenon.
Taking the celebrated Fick's law as an example. For a large collection of i.i.d. Brownian
particles with diffusion coefficient D, their density flux clearly follows J(x, t) = −D ∇c(x, t)
where c(x, t) is the concentration of the particle. A net movement of the particle population
is due to “more particles moving from a high-concentration region to a low-concentration
region than the reverse”, while every particle moves in completely random direction. There
is a “Fickean force” pushing the particle population; but this force is not acting on any one
individual in the population. Therefore, this Fickean force is a simple example of the
concept of entropic force discussed in Sec. 6.2. In fact, noting D = kBT/ζ, J(x, t) can be
expressed as (1/ ζ)∇S(x, t) × c(x, t) where S(x, t) = − kBT ln c(x, t) is a form of energy if one
applies the Boltzmann's law in reverse.
This simple example illustrates that in statistical understanding of stochastic dynamics, one
needs to be able to appreciate a fundamentally novel type of “law of force” that has no
mechanical counterpart. This is the notion of entropy first developed by physicists in
thermodynamics. But its significance goes far beyond molecular physics; so is the Second
Law that accompanies it. In fact, we believe these concepts are firmly grounded in the
domain of probability and statistics. More and deeper investigations are clearly needed.Qian and Kou Page 28
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Acknowledgments
The authors thank Professor Sunney Xie for fruitful collaborations and many inspiring discussions and for sharing
experimental data. S. C. Kou's research was supported in part by the NIH/NIGMS grant R01GM090202.
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Rev. Sci. Instrum. 93, 015101 (2022); https://doi.org/10.1063/5.0072346 93, 015101
© 2022 Author(s).A setup for studies of photoelectron
circular dichroism from chiral molecules in
aqueous solution
Cite as: Rev. Sci. Instrum. 93, 015101 (2022); https://doi.org/10.1063/5.0072346
Submitted: 22 September 2021 • Accepted: 14 December 2021 • Published Online: 10 January 2022
Published open access through an agreement with Fritz Haber Institut der Max-Planck-Gesellschaft
Sebastian Malerz ,
Henrik Haak ,
Florian Trinter , et al.
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A setup for studies of photoelectron circular
dichroism from chiral molecules
in aqueous solution
Cite as: Rev. Sci. Instrum. 93, 015101 (2022); doi: 10.1063/5.0072346
Submitted: 22 September 2021 •Accepted: 14 December 2021 •
Published Online: 10 January 2022
Sebastian Malerz,1Henrik Haak,1
Florian Trinter,1,2
Anne B. Stephansen,1,a)Claudia Kolbeck,1,b)
Marvin Pohl,1,c)Uwe Hergenhahn,1
Gerard Meijer,1
and Bernd Winter1,d)
AFFILIATIONS
1Molecular Physics Department, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
2FS-PETRA-S, Deutsches Elektronen-Synchrotron (DESY), Notkestraße 85, 22607 Hamburg, Germany
a)Current address: Seaborg Technologies, Titangade 11, 2200 Copenhagen, Denmark.
b)Current address: sonUtec GmbH, Mittlere-Motsch-Straße 26, 96515 Sonneberg, Germany.
c)Current address: Department of Chemistry, University of California, Berkeley, CA 94720, USA.
d)Author to whom correspondence should be addressed: [email protected]
ABSTRACT
We present a unique experimental design that enables the measurement of photoelectron circular dichroism (PECD) from chiral molecules
in aqueous solution. The effect is revealed from the intensity difference of photoelectron emission into a backward-scattering angle relative
to the photon propagation direction when ionizing with circularly polarized light of different helicity. This leads to asymmetries (normalized
intensity differences) that depend on the handedness of the chiral sample and exceed the ones in conventional dichroic mechanisms by orders
of magnitude. The asymmetry is largest for photon energies within several electron volts above the ionization threshold. A primary aim is
to explore the effect of hydration on PECD. The modular and flexible design of our experimental setup EASI (Electronic structure from
Aqueous Solutions and Interfaces) also allows for detection of more common photoelectron angular distributions, requiring distinctively
different detection geometries and typically using linearly polarized light. A microjet is used for liquid-sample delivery. We describe EASI ’s
technical features and present two selected experimental results, one based on synchrotron-light measurements and the other performed in the
laboratory, using monochromatized He-II αradiation. The former demonstrates the principal effectiveness of PECD detection, illustrated for
prototypic gas-phase fenchone. We also discuss the first data from liquid fenchone. In the second example, we present valence photoelectron
spectra from liquid water and NaI aqueous solution, here obtained from a planar-surface microjet (flatjet). This new development features a
more favorable symmetry for angle-dependent photoelectron measurements.
©2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0072346
I. INTRODUCTION
A. General considerations
Photoelectron spectroscopy (PES) studies from liquids and par-
ticularly from water and aqueous solutions, mostly in conjunction
with a liquid microjet,1,2have contributed tremendously to our cur-
rent understanding of the aqueous-phase electronic structure. An
experimental focus has been on core-level PES,2,3with far less studies
directed at the lowest ionization energies, although the latter govern
chemical reactivity.4,5Core-level spectra, typically measured with
tunable soft-x-ray photons from synchrotron radiation beamlines,have identified chemical shifts of solutes, pH-dependent protona-
tion and de-protonation,6–8solvent and solute interfacial depth
profiles,9,10as well as several non-local electronic relaxation pro-
cesses, such as intermolecular Coulombic decay (ICD).11In most of
these studies, electrons with some tens to hundreds of eV kinetic
energy (KE) were detected. Single-photon ionization-threshold phe-
nomena in the aqueous phase, corresponding to generation of
photoelectrons with kinetic energies typically smaller than 20 eV,
have barely been addressed.12This is despite their significant rel-
evance, including the increase in photoionization cross sections
near an ionization edge, the yet to be demonstrated liquid-phase
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post-collision interaction (PCI),13,14or the potential presence of
photoelectron circular dichroism (PECD)15–19in the ionization
of liquids. Enabling the exploration of near-threshold ionization
phenomena, and particularly aqueous-phase PECD, has been a
major motivation to build EASI (Electronic structure from Aqueous
Solutions and Interfaces), a unique, versatile liquid-microjet photo-
electron spectroscopy setup.
Our interest in PECD is motivated by the fact that it uniquely
connects the molecular electronic structure to chirality.15The effect
manifests as a forward–backward asymmetry in the photoelectron
emission intensity from chiral molecules, measured with respect
to the propagation direction⇀
kof circularly polarized light (CPL),
the sign of which depends on the helicity of the ionizing radiation
(leftorright -handed, l-CPL or r-CPL). The magnitude of PECD
is expressed via the chiral anisotropy parameter b1. Furthermore,
the PECD mechanism is solely based on electric dipole transition
amplitudes, which leads to much stronger effects than found in con-
ventional circular dichroism methods.19Since chirality is a universal
property, and of particular importance for biochemically relevant
complexes in aqueous solution, it is highly desirable to quantify
PECD in an aqueous environment and understand the molecules’
possible chiral imprint on their solvation shells.
The principal geometry of a PECD measurement is illustrated
in Fig. 1(a). However, application to the liquid phase requires that
several experimental and technical hurdles are overcome, calling for
novel and dedicated experimental designs. For gas-phase targets,
PECD studies can be readily and very efficiently performed with a
velocity map imaging (VMI) spectrometer,20which provides high
electron collection efficiency by simultaneous and angle-resolved
acquisition of the electron signal in all emission directions. How-
ever, currently available VMI spectrometers are not compatible with
liquid jets for several reasons: (1) A liquid jet represents a dielectricfilament of improperly defined charge state, thus introducing unde-
sired electric-field perturbations near the actual ionization region.
(2) For sole geometrical reasons, VMI cannot image the full pho-
toelectron angular distribution (PAD) from a cylindrical jet since
photoelectrons born inside the solution engage in multiple electron-
scattering processes, mostly with water molecules.12These electrons
may even be directed away from the liquid–vacuum interface into
the solution, or if reaching the detector, they will contribute to a
signal background that will be difficult to quantify. Using a planar
liquid microjet (see Sec. III B) might be advantageous since elec-
trons would be detected from a single surface orientation rather than
from a curved surface. Admittedly though, an increased water vapor
pressure from a flatjet is likely to result in additional disturbing
electron scattering. (3) An additional, more technical complica-
tion arises from the considerable background vapor pressure in a
liquid-jet (LJ) experiment, which for highly volatile water and aque-
ous solutions may well be in the ∼10−3mbar (for the flatjet) to
10−5mbar range. Correspondingly, the successful implementation
of the VMI technique with a liquid-jet target remains a challenging
technical goal. A first approach toward a technical realization has
been attempted very recently for non-electrically conductive solu-
tions. Yet, particularly the consequences of electron scattering in
the liquid phase have been barely elaborated on.21The same chal-
lenges hold for COLTRIMS-type setups, which also have a history of
providing important results on gas-phase PECD22but have yet to be
implemented with liquid-phase targets.
Here, we take a more conventional, simpler, and currently
feasible approach by using a state-of-the-art hemispherical elec-
tron analyzer (HEA) equipped with a differentially pumped pre-
lens section (capable of near-ambient pressure experiments)2and
mounted in a geometry compliant with the requirements of PECD
detection. Magnetic fields in the region where the liquid jet is
FIG. 1. Sketch of the relevant principal symmetry axes and respective angles for PES experiments using circularly polarized light (a) or linearly (horizontally) polarized light
(b); also see Eqs. (1)–(3). The green circle indicates the ionization region. In panel (a), the important parameter is the angle θspanned between the propagation direction
(wave vector, ⃗k) of the circularly polarized light and the electron detection axis, shown here for detection in the direction opposite to⇀
k(backward-scattering geometry). In
panel (b), the important parameter is the angle φspanned between the electric field vector⇀
Eand the electron detection axis, shown here in the plane perpendicular to the
floor plane and the photon propagation direction (dipole plane).
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ionized are carefully shielded by a full μ-metal encasement, enabling
the detection of photoelectrons and elastically and inelastically scat-
tered electrons down to near-zero-eV kinetic energy with quanti-
tative accuracy,12,23as required for studying any (near) ionization-
threshold phenomena. This includes the measurement of the
low-energy cutoff and low-energy tail in a water or aqueous-solution
PE spectrum.12,23In addition, in gas-phase studies, PECD was found
to be most prominent at electron kinetic energies smaller than
∼15 eV.15–19
A major drawback imposed by the geometric constraints in a
liquid-jet experiment is that the dichroic effect, resulting in differ-
ent intensities emitted in forward and backward directions, can-
not be directly and simultaneously measured. Instead, the signal
intensity, obtained at a (necessarily) fixed detection angle of our
hemispherical electron analyzer, has to be collected for alternating
CPL helicity. A similar detection scheme has been previously used
to demonstrate core-level PECD in the gas phase.24Yet, extension
to liquid-jet PECD (LJ-PECD) experiments entails major technical
considerations and developments, which will be detailed below.
A suitable radiation source for our PECD experiments is
the synchrotron radiation delivered from a helical undulator (e.g.,
APPLE-II).25,26However, the flexible design of EASI also enables
PAD measurements to be carried out using linearly polarized syn-
chrotron radiation. For this purpose, EASI is devised to detect
signals within the plane perpendicular to the propagation of the light
[“dipole plane,” see Fig. 1(b)] at three alternative fixed detection
angles: 0○(horizontal, in the floor plane, parallel to the polarization
vector), 54.7○(magic angle), and 90○(perpendicular to the floor and
polarization vector). These optional geometries are relevant when
only linear horizontal polarization is available, which is the case
for many beamlines at synchrotron-light facilities. Photoelectrons
from most orbitals are emitted preferentially in the direction of the
polarization vector,27while electrons from Auger or ICD processes
typically feature an isotropic emission pattern.28Then, choosing the
0○-geometry for photoelectrons and 90○-geometry for Auger elec-
trons will yield relatively larger intensities of the respective spectral
ranges. The 54.7○-geometry is used to explicitly suppress any angular
distribution effects (see below), for instance, when comparing rela-
tive signal intensities from ionization of different orbitals for quanti-
tative analysis of relative solute concentration. If linear polarization
with a variable orientation of the polarization ellipse is available,
any detection angle within 0○–90○can be realized for any of the
three geometries, and photoelectron angular distributions (PADs)
can be fully mapped out allowing for a determination of the common
(dipolar) anisotropy parameter, β, from aqueous solution of both
the water solvent and solute. This parameter can reveal hydrogen-
bonding-induced orbital structural changes at the solution–vacuum
interface29and also provides insight into the molecular structure at
such interfaces.30
In the following, we will describe the overall design of EASI and
its components, including the main technical specifications and its
principal detection geometries. We close by presenting experimental
results to highlight the performance of EASI . These include core-
level PECD measurements from gas- and liquid-phase fenchone and
regular valence PE spectra obtained from a planar microjet (flatjet)
using unpolarized He-II α(40.814 eV) radiation. It is useful though
to first review the aforementioned anisotropy parameters, which are
relevant for PAD and specifically PECD experiments.B. Photoelectron angular distributions
in single-photon ionization
The directional anisotropy of the photoemission process from
molecules has played a decisive role in the conceptual design of
EASI . We, therefore, review here the main aspects determining
PADs. We restrict ourselves to single-photon photoionization of a
randomly oriented target within the dipole approximation by light in
a pure polarization state p, with p=+1 designating l-CPL in the sense
of the optical convention, p=0 linear, and p=−1 corresponding to
r-CPL.24,31The PAD describes differential photoelectron intensities
as a function of the angle between a principal symmetry axis and the
detection direction. In the case of unpolarized light or CPL, the sym-
metry axis is the light-propagation direction⇀
k[Fig. 1(a)], whereas
for linearly polarized light (LPL), it is the direction of the electric
field vector⇀
E[Fig. 1(b)]. In the following, we distinguish these cases
by denoting the respective angles as θandφ.
PADs are uniquely connected with several important
electronic-structure properties, for instance, photoionization
dynamics, based on interfering photoelectron partial waves. Cou-
pling of the electron and photon angular momenta introduces
certain symmetry properties and constraints. These symmetry
conditions of the experiment determine which terms in the angular
distribution function contribute to the PAD. In the following we
restrict ourselves to the electric dipole approximation. The influence
of magnetic and higher-order electric multipoles on the PADs
of linear molecules for single-photon photoionization at photon
energies below 1 keV was experimentally found to be small.32,33We
expect the same also for chiral-specific non-dipole terms, as derived
in Ref. 34. This has been discussed in some detail in Ref. 35. The
angular distribution function for perfectly linearly polarized light
(LPL) can then be written in the form36–38
I(φ)∝1+βP2(cosφ), (1)
where P2(x)is the second-order Legendre polynomial which pro-
vides the non-isotropic part of the overall distribution and φis the
angle between the linear polarization vector⇀
Eand the direction of
photoelectron emission [Fig. 1(b)]. The anisotropy parameter βis
constrained to values −1≤β≤+2 specifying the magnitude of the
emission anisotropy, which ranges from a pure cos2(φ)to a sin2(φ)
form, and therefore possesses mirror symmetry about the principal
symmetry axis which is always the polarization vector. For CPL, the
PAD is governed by a similar expression (valid only for non-chiral
targets, see below),
I(θ)∝1−β
2P2(cosθ), (2)
with θdefined as the angle between the photon propagation vector
⇀
kand the direction of photoelectron emission [see Fig. 1(a)]. The
second Legendre polynomial has a zero crossing at x=cos(54.7○). At
this particular (magic) angle, the measured differential cross section
for any transition will become independent of its β-value and thus
proportional to its total cross section.
Less widely recognized is that these equations are just special
(though common) sub-cases of a more general expression,39,40
Ip(θ)∝1+bp
1P1(cosθ)+bp
2P2(cosθ). (3)
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The equation is written with the understanding that the variable θ
is replaced by φin the linearly polarized case. The coefficients bp
n
are determined by the photoionization dynamics and depend on the
photon polarization state pand the radial dipole amplitudes between
the molecular initial and ionized state. For the P2(x)terms, this
leads to the relation β=b0
2=−2b±1
2. Moreover, b0
1=0, while b±1
1also
vanishes for achiral molecules; in such circumstances, this general
expression (3) reduces to the well-known former forms (1) and (2).
Particularly relevant for the present work is that for the specific
case of a chiral molecule ionized with CPL, the P1(x)(first-order
Legendre polynomial) coefficients no longer vanish for symmetry
reasons.39Furthermore, they switch signs with respect to a change
of light polarization: b+1
1=−b−1
1. The same change in sign of the b±1
1
coefficient is also encountered upon changing the enantiomer.39,40
AsP1(cosθ)=cosθ, the largest asymmetry (largest PECD effect)
can be observed at θ=0○(or 180○). This is, however, elusive for a
non-gaseous sample because of the existence of a liquid–gas inter-
face and the associated electron scattering inside the liquid.12On the
other hand, the PECD asymmetry vanishes in the dipole plane (at
θ=90○), which is the standard (and only) electron detection
arrangement realized in currently existing LJ-PES setups. The exten-
sion to off-dipole plane detection [Fig. 1(a)] was hence the main
motivation for constructing a new setup.II. EXPERIMENTAL
A.EASI —General features
EASI is a state-of-the-art setup for angle-resolved photo-
electron spectroscopy from a liquid microjet, typically used in
conjunction with monochromatic linearly or circularly polarized
extreme ultraviolet (XUV) to soft-x-ray radiation. For labora-
tory experiments, also (essentially) unpolarized radiation from a
monochromatized helium plasma-discharge source, yielding the
He-I α(21.218 eV), He-I β(23.087 eV), He-I γ(23.743 eV), He-II
α(40.814 eV), He-II β(48.372 eV), or He-II γ(51.017 eV) emission
lines, can be used. Figure 2(a) presents the principal arrangement
of the EASI instrument for the case of electron detection in the
floor plane—which is one of the geometries suited for b2PAD
measurements—and using variable linearly polarized light (LPL).
This is the standard configuration for laboratory experiments with
He-I/II radiation and the most compact form adopted when moving
EASI between the home laboratory and synchrotron-radiation facil-
ities. In Fig. 2(b), a rendered graphic of EASI in its unique position
for LJ-PECD experiments with CPL is shown. Here, the HEA (detec-
tion axis, green arrow) is tilted away from the propagation direction
of the CPL [red arrow; compare Fig. 1(a)], forming an angle of θ
=130○. At this angle, the PECD asymmetry, ∼(I+1(θ)−I−1(θ)), will
FIG. 2. Rendered drawing of EASI in its most compact (smallest enclosed volume, travel) arrangement (a) and in its “PECD-arrangement” with θ=130○(b). In the orientation
shown in (a), the liquid jet (blue arrow) travels from top to bottom. The jet direction is parallel to the entrance slit into the hemisphere. In (b), the jet enters horizontally; the
HEA unit is now rotated 90○about the lens axis (green arrow) such that the entrance slit is again parallel to the jet. The most important components are labeled as follows:
Interaction Chamber (IC); Electron Lens System (ELS); Hemispherical Electron Analyzer (HEA); Turbomolecular Pump (TP#); Cryo Pump (CP); Ice Crusher (CR); Liquid
Jet (LJ); and Jet Catching Unit (JC). The Differential Pumping (DP) stage will be shown in more detail in Fig. 4, and the mounted VUV He-discharge light source can be
seen in Fig. 6. The total weight of EASI is 1232 kg; the weight of the base frame is 232 kg. Transformation between the EASI default configurations is facilitated by the
compact cuboidal frame (indicated by green dashed lines), containing the core of EASI , which can be detached from its base frame to be freely moved in space. For each
setting, a different side (face) of the cuboid sits on the lower base frame. The interaction region, i.e., point of ionization, is at the same vertical distance from the floor in any
orientation. Lifting, tilting, and rotating the cuboid unit is typically crane-assisted.
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be reduced by a factor of ∣cos(130○)∣≅0.64 from its maximum value
atθ=0○or 180○. Due to spatial constraints, especially the dimension
(size) of the HEA unit and the extension of synchrotron radiation
beamline components, it was technically impossible to implement
the analyzer at a smaller θ-angle. Note that positioning the HEA
to detect PECD electrons in the forward direction (i.e., at θ=50○)
is not an option because electrons cannot be detected from the far
side of the liquid-jet target. This is due to the combination of strong
light absorption in the dense liquid and the small electron escape
depth,1,12the latter making PES distinctively surface sensitive.
Our detection angle of 130○is close to a zero crossing of the
second Legendre polynomial at θ=180○−54.7○=125.3○[P2(cos
125.3○)=0], with the important and favorable side effect that the
angular dependence of the electron intensity on the dipolar para-
meter βis suppressed [Eq. (2)]. This is indeed crucial when using
CPL in this “PECD” setup for achiral targets, allowing for a mean-
ingful comparison of signal intensities arising from ionization of
orbitals of different symmetry. A common application is to quantify
relative intensities of different core-level peaks, often in the context
of mapping solvent and solute species’ distributions in solution.1,2
The aforementioned two other EASI configurations, corre-
sponding to φ=54.7○(magic angle) and 90○detection within the
dipole plane [compare Fig. 1(b)], i.e., in combination with horizon-
tally LPL, are sketched in Fig. 3. As explained above, measuring at
just the magic angle is advantageous for many routine studies, while
for some measurements, it is desirable to maximize or minimize rel-
ative signal contribution from a particular orbital symmetry, and this
is best realized by choosing either φ=0○or 90○.
The modular concept of EASI allows for a fairly easy trans-
formation between the various geometries. In each configuration,
suitable ports allow the photon beam as well as the liquid jet
to enter the interaction chamber such that the ionization spot is
at the same height from the floor, not requiring any height re-
adjustment at a given beamline. However, when changing between
FIG. 3. Sketches showing EASI without the cuboidal frame in the φ=54.7○
(a) and φ=90○(b) configurations in the x–y (dipolar) plane defined in Fig. 1(b).
As in Fig. 2, in each configuration, electrons are detected perpendicular to the flow
direction of the liquid jet. Red dots indicate the ionization point associated with
synchrotron radiation propagating perpendicular to the figure plane, towards the
observer. The horizontal electric field vector⇀
E(in the case of horizontally LPL) is
also indicated.configurations, the system must be vented, and several components
must be re-arranged or rotated. Typically, for a given experimental
run period of several days or longer, a single setting is used. Switch-
ing to another setting can be completed within 3–4 h with the help
of a crane, and the experiment can be resumed. Our experiments do
not require any bake-out. Moreover, while the main experimental
chamber is vented, the pressure inside the HEA and in the section
containing the electron lens system is allowed to increase into the
low mbar range. The necessary high-vacuum conditions for a LJ-PES
experiment can be re-established within ∼5 min.
We now consider Fig. 2(a) in more detail, identifying the
main components of the setup. These are (i) the interaction
vacuum chamber (IC), which houses the liquid microjet (LJ)
and is equipped with multiple cryo- (CP) and turbomolecular
pumps (TP#) (their number, #, varies upon experimental demand);
(ii) the electron detector, consisting of a differentially pumped elec-
tron pre-lens system (ELS) for near-ambient-pressure operation
and the hemispherical electron analyzer (HEA); (iii) a multistage
differential pumping unit (DP) that is only used for studies at syn-
chrotron facilities; and (iv) a helium-discharge, high-intensity vac-
uum ultraviolet (VUV) source, only mounted for laboratory studies.
A description of the most-relevant components will be provided in
the following subsections (Secs. II B–II F).
B. Interaction chamber
The custom-made 211-mm-diameter and 600-mm long cylin-
drical IC is made of grade 304 corrosion-resistant steel. A total of
11 ConFlat (CF) ports of size CF40 and four ports of size CF100 are
arranged on the outer surface of the IC such that they point toward
the interaction center of the chamber. Different ports can be used
for photons to enter or to mount a cylindrical or flat-surface liq-
uid microjet and the respective jet-catcher unit depending on the
specific EASI geometric arrangement. The intended occupancy of
the ports in a given geometry is indicated in Figs. 2 and 3 by the
red (photon-beam axis), green (electron-detection axis), and blue
(LJ-flow axis) arrows/dots.
In order to effectively shield induced magnetic fields and the
Earth’s magnetic field at the interaction point (red dots in Fig. 3),
which is of major concern for the quantitative detection of low-
kinetic-energy electrons, we mounted an additional μ-metal superal-
loy shielding ( μSH), a cylindrical inset within the cylindrical IC that
forms an inner layer over its entire length. Typical magnetic fields
measured at the interaction point of liquid jet and light are ∼0.5μT
for the horizontal and 0.3 μT for the vertical components. The μSH
incorporates 13 30-mm and two 40-mm diameter holes on its sur-
face, positioned such that the ports on the IC have an unobstructed
view on the interaction point. The two larger ports are used for the
liquid jet and provide enough space for its positioning. Fixations of
theμSH shield are made of titanium. At one end, the IC connects
via a CF200 flange to the magnetic shield of the lens system of the
analyzer, giving EASI the elongated appearance. A view into the IC
and the μSH, along the cylinder and electron detection axis of the
hemispherical energy analyzer, is shown in Fig. 6(a).
In order to achieve a sufficient vacuum base pressure in the IC,
∼5⋅10−5mbar for typical liquid-jet experiments, two turbomolec-
ular pumps [TP1 and TP2; see Fig. 2(a)] are mounted ∼400 mm
downstream of the analyzer orifice. TP1 is a 1360 l/s (Pfeiffer ATH
1603 M) TP, and TP2 is a 790 l/s (Pfeiffer HiPace®800 M) TP. Each
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TP is backed by one corrosion-resistive 10 l/s scroll pump (Edwards
xDS35i C). Main pumping of the evaporating liquid jet is, how-
ever, accomplished by at least one additional cryo pump (CP). When
operating a cylindrical microjet in the laboratory, we use a single CP,
consisting of a cylindrical liquid-nitrogen (LN 2) trap made of stain-
less steel with a surface area of ∼1000 cm2. This is CP1 in Fig. 2(a).
The pumping speed of CP1 for water vapor is ∼10 000 l/s for a pris-
tine trap surface,41i.e., exceeding the capacity of TP1 and TP2 by
nearly an order of magnitude. If required, for instance, when oper-
ating a liquid flatjet with much higher evaporation rates and for
synchrotron-light experiments, up to three LN 2-traps can be added.
Alternatively, a recirculating system for liquid collection can be used
instead of a liquid-nitrogen cold trap, as we detail in Sec. II E.
C. Electron detection
The electron analyzer used with EASI , a Scienta Omicron
HiPP-3, is a high-energy-resolution state-of-the-art HEA with
200 mm central radius of the hemisphere. It has rather similar
properties as its predecessor, which has been described in detail pre-
viously.42Here, we review the main features and highlight several
new ones. One characteristic is the separate pre-lens that pro-
vides efficient differential pumping, in conjunction with two further
differential-pressure stages within the HiPP-3 lens system, and the
electron optics for PES imaging. The HEA can operate over a large
pressure range, including typical 10−4to 10−5mbar pressures under
standard liquid-jet conditions, but also sustaining pressures as high
as 5–30 mbar in the IC. This enables the probing of liquid sur-
faces other than those associated with liquid jets or jets within
some gaseous (near-ambient-pressure) environment. To provide
the required vacuum conditions, each stage of the electron lens
is pumped by two 255 l/s turbomolecular pumps (Pfeiffer HiPace
300 M), labeled TP3, TP4, etc., in Fig. 2(a), with each given pair of
TPs being backed by one 10 l/s scroll pump (Edwards xDS35i C).
The pre-lens is equipped with a small front aperture (orifice or
skimmer, representing the first differential pumping stage) at the tip
of a graphite-covered titanium analyzer cone, that permits electrons
to enter the analyzer. The opening angle of the front cone is 45○
[see Fig. 6(b) below], which is sufficiently steep to position the liq-
uid jet in close proximity. The slim front-cone design also provides
sufficient space for the exit capillary of the He-discharge source,
requiring a short working distance (see below).
Different orifice sizes are available, although we almost exclu-
sively use an 800- μm orifice for liquid-jet experiments. This small
opening allows for an elevated maximum pressure in the IC and at
the same time effectively protects the lens system from contamina-
tion arising from the volatile-sample environment. The acceptance
angle is∼±15○, with the accurate value depending on the retarda-
tion ratio, eKE/E p(see below). In all cases, this angle is smaller than
the±26.6○geometric acceptance for the nearly point-sized liquid-jet
sample in front of the 800- μm orifice. The HiPP-3 analyzer is capable
of covering a ∼2–1500 eV electron kinetic-energy detection range.
Extension to even higher kinetic energies can be achieved when
using a higher-voltage power supply. The (pre-)lens design—having
a first skimmer followed by a second one—enables operation of the
analyzer in two different modes, the swift acceleration mode and the
normal transmission mode. For realization of the former, the second
skimmer is held at a potential, while it is grounded for the normalmode. In the swift mode, electrons are thus accelerated as soon as
they enter the analyzer, which greatly reduces the inelastic scattering
of the photoelectrons with the dense water-gas environment, thus
enhancing the transmission at near-ambient-pressure conditions. In
addition, this mode increases the angular acceptance (an aspect less
relevant when using a small entrance-cone orifice) in both ultra-high
vacuum and mbar pressure conditions. In combination, this leads to
an increase in signal of up to a factor of ten compared to traditional
lens modes.
The energy resolution and the electron transmission are deter-
mined by the size of the entrance slit into the hemisphere (selectable
between 0.1 and 4.0 mm using nine different straight slits) and by
the pass energy, E p, with the latter being restricted to pre-set values
depending on the lens mode used. For instance, in the transmission
mode, E pcan be selected from 20, 50, 100, 200, and 500 eV, cov-
ering an electron kinetic-energy range of 20–1500 eV. With 20 eV
pass energy and 500 eV kinetic energy, an energy resolution bet-
ter than 15 meV full width at half maximum (FWHM) is specified;
note, however, that in the case of aqueous solutions, most PES peaks
are considerably wider due to an intrinsic distribution of hydra-
tion/solvation configurations of different energies. Other available
modes include the angular ( ±9○parallel angular range; 100–1500 eV
kinetic-energy range) and spatial (20–1500 eV kinetic-energy range)
modes. The latter mode is specified to achieve a spatial resolution
<10μm for kinetic energies below 1200 eV. For measurements from
a cylindrical liquid microjet, the spatial mode is of little relevance,
but this mode will be exploited in upcoming characterizations of
planar microjets where several properties (including jet thickness,
solute concentration, and temperature) might vary when probing
the liquid sheet along the flow direction.43,44
Another unique lens mode of the HiPP-3 is the UPS upgrade,
which enables low-kinetic-energy measurements with high energy
resolution and a simultaneous increase of electron transmission.
This adds the following features: energy resolution <5 meV FWHM
at 5 eV pass energy and 10 eV kinetic energy; pass energies 2, 5, 10,
and 20 eV; kinetic-energy ranges of near-zero to 60 eV (UPS mode),
near-zero to 100 eV (angular mode), and near-zero to 20 eV (spatial
mode). It is the former mode, typically using E p=20 eV, which is
indispensable for the near-threshold measurements, i.e., the main
mission of EASI . Here, the detection of electron energies smaller
than E pis accomplished by a custom-made lens table developed by
Scienta Omicron.
The actual electron detector unit at the exit of the hemisphere
consists of a stack of two 40 mm-diameter microchannel plates
(MCPs) in a Chevron arrangement, combined with a phosphor
screen (type P46) to image the position of electron hits in two dimen-
sions. The screen image is recorded through a viewport by a CCD
camera (Basler scA 1400-17gm; acquiring 17 frames per second)
placed outside of the vacuum vessel. A rectangular section of this
image is divided into a maximum of 1064 energy channels in the
energy-dispersive and 1000 channels in the non-dispersive direc-
tion, which for some lens modes corresponds to a spatial or angular
coordinate at the interaction center. The camera may either count
illuminated pixels above a certain threshold to determine the num-
ber of detected electrons (pulse-counting-mode) or generate the
spectrum from interpreting the gray-scale levels of the CCD image
(ADC-mode). To obtain the absolute count rate from the recorded
ADC spectra, a calibration factor (multiple counting factor, MCF)
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must be determined before measurements, individually for each pass
energy. In routine operation, we use the gray-scale mode.
D. Differential pumping chamber
In synchrotron-radiation measurements employing a liquid jet,
a highly efficient differential pumping unit (DP) must be placed
between the IC and the beamline, since in the latter a pressure
requirement of 10−9to 10−10mbar usually must be met (as com-
pared to the typical 10−4to 10−5mbar pressure in the IC or con-
siderably worse, 10−3mbar, in the case of flatjets or near-ambient-
pressure studies). For EASI , we designed a novel highly compact
three-stage DP, which is shown in Fig. 4. The total length is only
355 mm, allowing accommodation of this unit even at beamlines
with a relatively short focal length. Each stage is pumped sepa-
rately. The first one, close to the interaction chamber (low-vacuum
side), is pumped by one 255 l/s TP (Pfeiffer HiPace 300 M), while
FIG. 4. (a) Sketch of the differential pumping unit (DP), including dimensions and
mounting orientation onto the IC in the “PECD” configuration [compare Fig. 2(b)].
(b) Close-up view of the DP. The main components are labeled as introduced in
the text: stages 1–3; view ports 1–4 (VP1, VP2, etc.); capillaries 1–3; camera; and
cryo pumps (CPs; only one can be seen from this viewing angle). A single-crystal
cerium (III)-doped yttrium aluminum garnet (YAG:Ce) screen of 0.1 mm thickness
and 20 mm diameter is placed on the far side of the IC for visual inspection of the
beam position, as it emits visible light when hit by UV light or x rays.45the other two stages are each pumped by one 90 l/s TP (Leybold
TURBOVAC 90i). All three pumps are backed by a single 10 l/s scroll
pump (Edwards xDS35i C). In order to increase the pumping speed
and to more efficiently pump water vapor, we additionally use two
LN 2traps (cryo pumps; CP in Fig. 4), each with a surface area of
∼580 cm2. With that, we maintain a 10−9to 10−10mbar pressure in
the connecting beamline chamber even for mbar-range pressure in
the IC.
The photon beam propagates through the DP via three
20-mm long stainless-steel capillaries, which connect the stages. On
the high- and low-vacuum sides, we use a capillary of 3 and 8 mm
inner diameter, respectively; the capillaries can be easily exchanged
if required by the experimental conditions. To aid alignment of the
whole unit, we coated the ends of the capillaries facing the beamline
with fluorescence powder (Honeywell LUMINUX Green B 43-3),
and the green-glowing spot allows the position of the light beam to
be tracked and observed through dedicated viewports (VPs).
Two further elements for beam monitoring are mounted inside
the IC: a retractable gold mesh (Precision Eforming, 333 LPI) for
quantitative monitoring of the photon flux shortly downstream of
the interaction point and a YAG:Ce screen for visual inspection of
the photon beam shape.
E. Liquid jets and alignment
Vacuum liquid microjets are produced by pushing water (or
other solvents or solutions) through a micrometer-sized orifice into
vacuum.1,4,46We usually use 15–30 μm inner-diameter quartz-glass
capillaries of ∼3 cm length, made in-house, to obtain cylindrical
microjets. At times, we also use platinum plates (30 μm inner diam-
eter; 2 mm outer diameter), similar to what has been reported
in our early LJ-PES studies.47,48Resulting jet velocities are in the
20–80 ms−1range, depending on the given experimental conditions.
More recently, we have also generated planar-surface microjets by
colliding two cylindrical jets at a suitable angle, analogous to the
design described in Ref. 44. Several different capillary materials,
including quartz, have been tested. In the exemplary photoelectron
spectra from a liquid-water planar jet which will be presented below,
65-μm inner-diameter polyether ether ketone (PEEK) tubes were
used, at a 46○collision angle.
The liquid to be pushed through the capillary is pumped
through PEEK interconnected tubing of different inner diameters,
130 and 800 μm, by a high-performance liquid chromatography
pump (HPLC; Shimadzu LC-20AD), equipped with four inlets to
accommodate quick switching between different solutions. A sketch
of our standard liquid-jet setup is shown in Fig. 5(a). The HPLC
takes in filtered solutions channeled via an in-line Shimadzu DGU-
20A 5Rdegasser to enable the simultaneous preparation of different
solutions. The high-pressure side of the HPLC is connected to the
jet holder via ∼5 m of PEEK tubing, which is interrupted by several
Teflon®inter-connecting tubing segments of different inner diam-
eter, as experience showed this to dampen occasional oscillatory
throughput variations of the HPLC operating in the low-pressure
regime. Under these conditions, typical flow rates are 0.4 ml/min
up to 1.5 ml/min, corresponding to 5–30 bars pressure in the tub-
ing for (cylindrical) liquid-jet experiments at solution temperatures
of 10○C. In a given set of experiments, the flow rate is typically
constant, adjusted by HPLC backing pressure, which depends on
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FIG. 5. (a) Schematic of the standard liquid-jet setup, showing the jet rod, HPLC pump, liquid-nitrogen cold trap, and electric connections for biasing or grounding the liquid
jet. (b) Rendered graphic of a liquid-jet catcher/recirculation unit. The liquid-jet-injecting glass capillary and the jet catching cone with 500 μm orifice at<7 mm distance from
the capillary tip in the direction of the flowing jet are mounted on a common support. Mutual jet and catcher positions are mechanically adjustable. The bronze catcher cone
is typically held at 80○C (associated heat pipes are shown) to prevent clogging of its orifice upon water ice formation; details of pumping on the catcher side are not shown.
This slim and compact design (using several components of Microliquids design, now Advanced Microfluidic Systems GmbH—AdMiSys)49fits into the same ports of the
cylindrical shielding ( μSH) used for jet operation without a recirculating unit. (c) Schematic of the stainless-steel connector which is in contact with the aqueous solution. For
grounding the liquid jet, the connector is linked to the grounded HEA, and for biasing the jet, the connector is electrically linked to a power supply on a common ground with
the HEA.
solution viscosity and temperature as well as jet diameter. Control
and stabilization of the jet temperature is accomplished by flowing
a water–ethanol volume mixture (30:70) through a cooling jacket of
the jet rod. Toward this end, a closed-flow temperature-stabilized
cycle is maintained by a chiller unit (Julabo CORIO CD-200F). Typ-
ically, the temperature is set between 4 and 20○C depending on the
experiment. A small but unquantified difference of the set tempera-
ture to the actual temperature at the point of expansion may occur
because the cooling jacket ends few centimeters before the actual
nozzle.
In vacuum, the produced laminar liquid microjet quickly cools
by evaporation. Eventually, it disintegrates into droplets and freezes,
and the resulting spray is collected downstream of the flow. For a
jet traveling horizontally, we typically use a regular LN 2cold trap of
similar design as the cryo pumps described above.3,47In case the jet
travels vertically from top to bottom [see Fig. 2(a)], it is terminated
by a steel cylinder submerged in a liquid-nitrogen bath. A note-
worthy technical detail is that at some suitable position, ∼100 mm
upstream of the respective catching unit, a motorized rotating wire-
frame, with a shape resembling a kitchen mixer, is placed [CR in
Fig. 2(a)]. This unit nebulizes the liquid flow and prevents ice needles
growing back from the cold-trap surface toward the jet capillary, i.e.,
opposite to the flow direction. This also helps to maintain a rather
homogeneous coverage of the cold surface which slows down thedecrease in pump efficiency and considerably extends the available
measurement time between venting-and-cleaning cycles.
The liquid-jet rod, the supporting metallic unit for a cylin-
drical single jet, consists of an inner tube with a socket to hold
the quartz capillary, PEEK tubing, and an upstream connector [see
Fig. 5(a)]. These parts are sleeved with an outer tube to stabi-
lize the construction, also acting as a jacket for the coolant liquid.
This whole unit, a modified Microliquids design (now Advanced
Microfluidic Systems GmbH—AdMiSys),49is mounted on a high-
precision x-y-z-manipulator (Hositrad, MA2000 series). All parts of
the jet-assembly unit that immerse into the magnetically shielded
region of the IC are made of titanium or other non-magnetic mate-
rials, typically tungsten, copper, or aluminum. Parts (except for the
quartz capillary) in the vicinity of the ionization region have been
graphite-coated to assure a common electric potential. All of these
parts are fully electrically insulated from the liquid sample solu-
tions. As mentioned above, we can alternatively operate the liquid
jet as a recirculating system, based on collecting the liquid jet before
freezing. Our system is similar to those previously reported,50,51
consisting of a catcher, of ∼1 cm3size, made of bronze which is
connected via stainless-steel tubing to a solution reservoir con-
tainer; see schematic in Fig. 5(b). The liquid jet shoots into the
500- μm orifice of the cone of the catcher after <7 mm travel in vac-
uum. The advantage of a recirculating unit, other than recycling or
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recovering the solution, is the reduction of pressure in the main
IC and, even more important for our experiments, the deposition
of volatile species from the solution on the chamber walls can be
reduced to achieve more temporally stable vacuum conditions.
Given the micrometer-sized diameter of the liquid jet, highly
accurate positioning of the jet is mandatory and is accomplished
using a high-precision x-y-z manipulator (Hositrad, MA2000
series), modified by the manufacturer to achieve a spatial resolu-
tion of 2.5 μm with a repeatability of 1.25 μm. To visually monitor
the liquid-microjet performance and its position, we use two Basler
acA2440-35- μm cameras in combination with suitable telescopes.
One camera (equipped with a NAVITAR NMV-100 objective and
a 15-mm spacer) is aligned to the rotational symmetry axis of the
electron-analyzer lens and observes whether the liquid jet is centered
in front of the HEA first skimmer. The typical jet-to-skimmer dis-
tance is 500–800 μm to match the imaging distance of the HEA lens
system; at the same time, this distance corresponds to a suitable elec-
tron transfer length between the liquid jet and analyzer at the typical
10−4to 10−5mbar water vapor pressure in the IC.1A view seen by
this camera, although in the presence of a flatjet sample, is shown in
Fig. 6(a). The other camera (combined with a RICOH FL-BC7528-
9M objective) is directed at the jet and the HEA entrance cone at
an angle perpendicular to the detection axis (see Fig. 4). With this
combination of two cameras, we can accurately re-position the jet
for each measurement, in any of EASI ’s geometric arrangements.
In order to obtain meaningful liquid-jet photoelectron spec-
tra, we have to assure that the solutions have a sufficient electrical
conductivity. Neat liquid water and many aqueous solutions con-
taining no ions are, however, poorly conductive, and a tiny amount
of salt needs to be added, as discussed previously.1Another effect
of salt addition is the compensation of electrokinetic charging of
the jet surface.52,53In a related context, molecular dipoles at the
solution surface can also give rise to surface charging. Any quan-
titative information on the energetics [absolute binding energies
(BE)] of the ionized solute and solvent then requires that the jet is
either properly grounded to the HEA or that a stable bias voltage is
applied, as recently discussed.12,23To connect the liquid jet to the
electrostatic potential of the analyzer, we have inserted a stainless-
steel through-connector (as used with HPLCs) in the high-pressure
side of the PEEK line, at a few tens of millimeters upstream of the
liquid-jet holder. This design, detailed in Fig. 5(c), turned out to
provide a much lower contact resistance compared to earlier ver-
sions, in which the electrical contact to the solution was provided
by a gold wire. For PES experiments from a biased liquid jet, the
solution is fully electrically insulated from any other potential and
only connected to a high-precision power supply. We use a Rohde
& Schwarz HMP 4030 high-precision voltage source or for higher
voltages (60–300 V) a Delta Electronics ES 0300-0.45 power supply.
F. Helium lamp
A helium plasma-discharge source (Scienta Omicron VUV5k)
enables LJ-PES valence measurements in the laboratory. Here, we
greatly benefit from the aforementioned HEA VUV lens-mode. This
combination has been recently applied to determine absolute lowest
ionization energies of water and solutes.23,54The VUV5k, equipped
with differential pumping, is operated with helium 6.0, and liquid
FIG. 6. (a) Photograph of the view into the IC along the lens axis of the HEA
and centered on the analyzer cone with its 800- μm orifice. In front of the ori-
fice, a water flatjet, 1.2 mm long and 0.6 mm wide, is seen. The thickness of
the jet is∼20–25 μm. A subsequent chain of pairwise orthogonal leaves, forming
downstream along the flow direction, is not resolved by the camera used here for
jet alignment. The flatjet is formed by two colliding cylindrical jets, each with 65 μm
inner diameter and a 46○collision angle; simultaneously changing the diameters
of the cylindrical jets can be used to adjust the size and thickness of the planar
jet. Above the flatjet, one of the two PEEK capillaries generating the colliding cylin-
drical jets can be seen. At the left-hand side, the focusing capillary, receiving light
from the VUV discharge source, is shown at a working distance of ∼5 mm. The
angle between the detector axis and the VUV photon beam is 110○. (b) Schematic
of a top view of the same situation, showing the angle αbetween the surface plane
of the first flatjet leaf and the direction of electron detection.
nitrogen-cooling of the connecting gas-line removes water residu-
als and contaminant gases. A given discharge line—we primarily use
He-I α(21.218 eV), He-II α(40.814 eV), and He-II β(48.372 eV)—is
selected by an 80 ×30 mm2toroidal grating with 1200 lines/mm.
The monochromatic radiation is then directed into a collimating
300- μm-inner-diameter (75-mm-long) glass capillary, producing a
300×300 μm2focus at 5 mm focal length, which corresponds
to the distance between capillary exit and liquid jet (see Fig. 6).
The total photon flux at the ionization region, without grating and
focusing capillary implemented, is ∼3⋅1014photons/s, and the flux
of the focused He-I αphoton beam, using the 300- μm capillary,
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Figure 1.
A typical enzyme kinetics can be written as a sequence of biochemical steps as in Eq. 19, or
from a single enzyme perspective, a cycle as illustrated here. Note that the second order rate
constants
and
in (19) are replaced by pseudo-first-order rate constants
and
,
respective. The simplest statistical kinetic model is to consider this system as a continuous-
time, discrete-state Markov process. More sophisticated model, when there are sufficient
data, could be a semi-Markov model with arbitrary, non-exponential sojourn time for each
of the three states [63].Qian and Kou Page 34
Annu Rev Stat Appl . Author manuscript; available in PMC 2014 July 07.
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Figure 2.
A discrete schematic illustrating the Markovian kinetics of a single enzyme molecule with
conformational fluctuations.Qian and Kou Page 35
Annu Rev Stat Appl . Author manuscript; available in PMC 2014 July 07.
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El texto completo de este trabajo no se encuentra disponible por no haber sido
facilitado aún por su autor, por restricciones de copyri ght, o por no existir una
versión digital
The full text of this item is not available because it has not been provided by its author yet; because there are copyright re strictions; or because a digital version
does not exist
| 0a5de272f149e04fcbfdb8d24fb47e8d0d0106ba | page_0000 |
DNA Profiling Using Solid-State Nanopores: Detection of DNA-
Binding Molecules
Meni Wanunu , Jason Sutin , and Amit Meller*
Department of Biomedical Engineering, Boston University, Boston Massachusetts 02215
Abstract
We present a novel single-molecule method for rapidly evaluating small-molecule binding to
individual DNA molecules using nanopores fabricated in ultrathin silicon membranes. A measurable
shift in the residual ion current through a ~3.5 nm pore results from threading of a dye-intercalated
DNA molecule, as compared to the typical residual current of native DNA. The average level of the
residual current can be used to directly quantify the fraction of bound molecules to DNA, providing
a new way to determine binding isotherms. Spatial sensitivity is also demonstrated by designing a
two-segment DNA molecule that contains small-molecule binding sites in one of its two segments.
Translocations of such molecules exhibit two current levels upon incubation with a DNA-binding
dye, caused by selectively bound dye in one of the DNA segments. Our results, as shown here with
four different dyes, coincide well with bulk fluorescence measurements performed under identical
conditions. The nanopore approach for “reading-out” molecular binding along a DNA molecule,
combined with the miniscule amounts of DNA required and the potential for scalability using
nanopore arrays, provide a novel platform for future applications in analytical drug screening.
Selection of small molecules that bind genomic DNA or other nucleic acids with high
specificity is a central requirement for drug development, necessitating new in vitro methods
for rapid and low-cost assessment of the binding affinity and location of drugs along DNA
molecules.1,2 While conventional, bulk spectroscopic tools (e.g., NMR, crystallography, mass
spectrometry) have yielded a wealth of information on small-molecule binding to
macromolecules,3 membrane-embedded nanopores have enjoyed remarkable success as
nucleic acid analyzers. For example, membrane embedded alpha-hemolysin channels have
been used to thread and detect variations in nucleic acid sequences,4 to investigate DNA–
protein interactions,5 and to follow enzyme processivity.6 In addition, chiral nanopores of
subnanometer dimensions have been used to discriminate enantiomeric drugs in solution,7 as
well as to discriminate among the different mononucleotides in solution.8 Solid-state nanopores
have only recently taken the stage as more versatile, synthetic analogs of protein channels,
owing to their mechanical robustness and size tunability. Several applications of solid-state
nanopores in biophysics have already been demonstrated, such as characterization of DNA
duplexes by electromechanical unzipping,9 detection of DNA/protein complexes,10 and
characterization of proteins11 and DNA.12–14
In this paper, we show that sub-5 nm solid-state nanopores can be used to quantitatively profile
the binding of small molecules to both double-stranded DNA (dsDNA) and single-stranded
DNA (ssDNA) molecules, potentially facilitating the detection of DNA/drug complexes with
spatial sensitivity along the biopolymer. We present the first demonstration that the residual
*To whom correspondence should be addressed. [email protected].
Supporting Information Available: (1) Details on the experimental setup and (2) fluorescence titration data. This material is available
free of charge via the Internet at http://pubs.acs.org.
NIH Public Access
Author Manuscript
Nano Lett . Author manuscript; available in PMC 2010 May 16.
Published in final edited form as:
Nano Lett . 2009 October ; 9(10): 3498±3502. doi:10.1021/nl901691v.
NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript | c26bc6ac6551247e8b6764807d8f8abc2c04240e | page_0000 |
ion current signal through a nanopore during dsDNA translocation is highly affected by the
amount of intercalated small molecules, which give the DNA/intercalator complex a bulkier
structure than that of native DNA. Furthermore, we demonstrate the capability of using
nanopores to discriminate within a DNA molecule among native and small molecule-bound
regions, achieved using a ssDNA molecule containing two regions with different affinities
toward a cyanine dye. Nucleic acid-binding fluorophores were used here to validate our
nanopore data with bulk fluorescence measurements, illustrating the analytical capabilities of
the nanopore method. Moreover, as we show here, our method offers a set of unique advantages
over conventional techniques, such as not requiring chemical labeling with fluorescent
reporters (which can often interact with DNA), detecting small molecule/DNA binding with
high spatial resolution, and offering single-molecule sensitivity and rapid analysis.
Our setup, shown in Figure 1, is based on a Si-chip device containing a 20-nm-thick silicon
nitride window, through which a nanoscale pore is drilled using the electron beam of a
transmission electron microscope (TEM).15,16 A TEM image of a 3.5 nm pore used here is
also shown. The cis and trans chambers, separated by the membrane, are filled with 1 M KCl
electrolyte buffered to pH 8, such that an electrolyte junction between the chambers forms at
the nanopore. When a voltage is applied across the membrane, the baseline ion current is
measured ( io). This current is reduced when a DNA molecule threads into the pore and linearly
translocates through it, driven by the electric field. Reduction of the current signal during
translocation is caused by the steric/electrostatic effects of the DNA segment inside the broad
region of the nanopore, which due to its hourglass shape has an approximate length of 7 nm.
16 We have previously shown that the average translocation speed is a strong function of the
pore diameter, such that a short DNA fragment (100–1000 bp) translocates through a 3.5 nm
pore with an average speed of ~0.3 μs/bp, yielding a current signal well within our measurement
time resolution (~12 μs).14 Each recorded ion current transient corresponds to the translocation
(or collision, see ref 14 for details) of a single-molecule and is characterized by its average
current amplitude Δib = ῑo − ῑb, where ῑb and ῑo are average blocked-state and open-state
currents for each translocation event, respectively (see Figure 1). Unless otherwise indicated,
for each experiment we have collected thousands of single-molecule translocations to obtain
Δib distributions, the average threading rate, and translocation time distributions.
Small Molecule Intercalation into Double-Stranded DNA
Intercalation is a common binding mode of many molecules to DNA, in which the molecule
inserts itself between two adjacent basepairs.17 We first studied current signatures for a 400
bp DNA fragment translocating through a 3.5 nm pore, exposed to three intercalating dyes with
different affinities to DNA (see Figure 2a). Typical single-molecule traces for a free 400 bp
DNA fragment exhibit a single characteristic blocked current level of amplitude ~1 nA (Figure
2b), whereas for increasing ethidium bromide (EtBr) concentrations, we observe a deeper
blockade level of amplitude ~1.5 nA (red level, Figure 2b). Interestingly, for increasing EtBr
concentrations, a greater fraction of the event duration corresponds to the deeper blockage
level, suggesting a correlation of the mean event amplitude, Δib, with EtBr loading. The larger
blockade amplitude may be related to the EtBr loading fraction, since EtBr is known to widen
the normal B-DNA cross section by about 15%.18 In addition, partial charge neutralization of
the DNA from the positively charged EtBr may result in release of counterions from the DNA
backbone, further reducing the effective ion concentration in the pore. The open pore current
did not change by more than 0.2% for all EtBr concentrations.
A more detailed correlation of Δib with EtBr loading is shown by nanopore titration
experiments. As shown in Figure 3a, we have added aliquots of EtBr to the cis sample chamber
and recorded >2000 translocations at each EtBr concentration. The surface plot in Figure 3a
shows histograms of the event blockade amplitude from thousands of molecules per EtBrWanunu et al. Page 2
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concentration, as a function of EtBr concentration. As we have previously reported, the major
and minor Gaussian populations in each histogram correspond to translocations and collisions
(brief current blockades with smaller event amplitudes of ~0.75 nA, attributed to DNA
molecules that are not fully threaded into the pore), respectively.14 As the EtBr concentration
increases, a noticeable shift in the position of the major peak of the current amplitude (red,
defined here as ΔIb, see Figure 3a) is seen with negligible change in the collision peak (purple).
The effect of EtBr on ΔIb suggests that the translocation signal is extremely sensitive to the
additive fraction on the DNA. The dependence of ΔIb on EtBr concentration is shown in Figure
3b, displaying >25% increase in the average event amplitude in the EtBr concentration range
used. Analogous binding fraction curves obtained from fluorescence experiments performed
in bulk are superimposed on the nanopore data set (see Supporting Information for fluorescence
measurements) and show excellent agreement with a measured dissociation constant Kd = 14.7
μM.
In order to evaluate the generality of the nanopore method, we repeated the experiments
performed with EtBr using two other DNA intercalator dyes, propidium (Pr2+) and ethidium
homodimer (EtHD2+). These dyes display stronger binding affinities to B-DNA as compared
to EtBr, mainly due to their double charge. As described above for EtBr, the peak event
amplitudes ΔIb were measured for each of these dyes. Figure 4 displays the dependence of
ΔIb on dye concentrations for propidium (a) and for ethidium homodimer (b). Bulk
fluorescence measurements of binding to the same DNA molecules are overlaid, displaying
good agreement with the nanopore measurements. We also note that as expected, the
EtHD2+ displayed a stronger shift (>50%) in the event amplitude, due to its bulkier structure.
As with the EtBr experiments, the addition of either PR2+ or EtHD2+ did not appreciably change
the open pore current.
Charged DNA intercalators are also known to affect the mobility of DNA in an electric field.
For example, it is well known that a DNA stained with EtBr displays retarded mobility in gel
electrophoresis as compared to unstained DNA, due to the decreased effective charge and
increased stiffness of the polymer.19 These molecular changes to DNA structure upon binding
of cationic intercalators have resulted in similar trends with our nanopores. In Table 1, average
capture rates (normalized to concentration) and translocation times are given, both before and
after the addition of intercalator to saturation. First, we note that average capture rates decreased
by a factor of 3–5 upon intercalation of Et+, Pr2+, or EtHD2+. Furthermore, a closer look at
average translocation times reveals a slightly higher degree of retardation for the divalent
intercalators EtHD and PrI (factor of 5–6) than for EtBr (factor of 4), expected for a DNA with
a greater charge reduction. These findings are consistent with the reduced gel electrophoretic
mobility of the intercalator/DNA complex (see Supporting Information), manifested in the case
of nanopores by suppression of DNA capture and slowed transport through the pore. Apart
from the reduced effective charge of the intercalator/DNA complex, other factors that may
contribute to slowing down may be (1) increased contour length (and stiffness) of the
intercalator/DNA complex,20 (2) increased interactions of the complex with the pore walls,
already shown to reduce the DNA velocity in small pores,14 (3) increased stall force of the
intercalator/DNA complex, which has a larger cross-section than free DNA, arising from
hydrodynamic drag inside the pore.21–23
Interaction with Single-Stranded DNA
In this part of our study we have used a 2.2 nm pore (see Figure 5a) to probe the interaction of
single -stranded DNA molecules with the cyanine dye SYBR Green II (SGII), an RNA-selective
stain that preferentially intercalates into single-stranded DNA over double-stranded DNA
(Invitrogen Corp., Carlsbad, CA). SGII has particularly low affinity toward a deoxyadenine
homopolymer (see Supporting Information), presumably because the purine bases of theWanunu et al. Page 3
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homopolymer undergo extensive stacking interactions, resulting in a helical secondary
structure.24,25 Using fluorescence measurements, we have determined the binding affinity of
SGII to poly(dA) to be >50 times smaller than for a random sequence (see Supporting
Information). Since SGII binds with high affinity to a random single-stranded DNA sequence,
for our nanopore experiments we have designed a two-segment dA 50dN50 molecule (see
Supporting Information for sequence) for which SGII provides spatial contrast along the
molecule by binding only to the “random sequence” dN region (see Figure 5a). As a negative
control, the response of the dA 50dN50 to SGII was compared to a dA 60 homopolymer molecule.
In Figure 5b, a typical concatenated set of translocation events for dA 60 through a 2.2 nm pore
is shown, both before and after the addition of SGII to the cis chamber. All experiments here
were carried out at 5 °C, in order to reduce translocation speeds and to stabilize the poly(dA)
secondary structure. As expected, these experiments do not reveal any differences in the poly
(dA) translocation properties before and after the addition of SGII with both exhibiting mean
current amplitudes of ~0.58 nA and a peak translocation time of ~80 μs. In contrast, typical
translocation events for the dA 50dN50 sample with SGII (Figure 5d) display strikingly long
translocation times and exhibit a second, deeper blocked current level. The all-point histograms
for these events clearly show that the deeper blockade is a discrete level with an amplitude of
0.96 nA, much greater than the blockade amplitude for the DNA alone (0.60–0.62 nA).
The translocation time distributions for the dA 60 and dA 50dN50 samples, shown in Figure 6a,b,
respectively, show that SGII binding considerably slows the translocation process (histograms
shown in log time units). While the mean translocation time scales for dA 60 both before and
after the addition of SGII were 0.11 ± 0.03 ms, mean translocation times for dA 50dN50
increased from 0.25 ± 0.04 ms to 7.1 ± 1.0 ms upon SGII binding. A closer inspection of the
relative time scales of the two blocking levels reveals that >80% of a typical event is spent at
the shallow blockade amplitude ( i = 0.74 nA). It is also interesting to note that for the vast
majority of events (>95%), the shallow blockade level precedes the deeper blockade level.
These findings suggest that entry of the dA 50 portion of the molecule is favored over entry of
the bulkier SGII-bound dN 50 portion. This favored entry can be also rationalized by considering
the positive charge of SGII, which may decrease the overall charge of the dN 50 region upon
binding SGII, and/or condense the DNA structure to a coil. Although we do not have an exact
mechanism to account for the long dwell times, we note two main possibilities: (1) SGII-
binding results in formation of secondary structure by condensing the DNA, thereby stalling
the translocation process, or (2) the SGII-bound DNA is bulky enough to interact with the SiN
membrane and the pore. However, since the translocation events suggest that the poly(dA)
portion is in the pore for most of the translocation process, we favor the explanation that SGII-
binding induces secondary structure which stalls entry of the dN 50 portion of the molecule into
the pore. This conclusion is consistent with the literature, as certain DNA-binding molecules,
including clinical drugs, have been shown to induce secondary structure in single-stranded
DNA molecules.26
In summary, we have developed a novel, high-throughput single-molecule method for
evaluating small molecule binding to DNA. Our method was validated using a set of DNA
intercalating fluorophores for which we obtained a complementary set of fluorescence titration
curves. For double-stranded DNA, we used three intercalating dyes with different binding
affinities to DNA in the range Kd = 10−7−10−5 M. Single-molecule current traces for partially
intercalated DNA reveal bilevel shapes with deeper blockades correlated to the fraction of
intercalator molecules bound to the DNA and with deeper blockades for larger dyes. The mean
fraction of deeper blockades, which corresponds very well to the fraction of bound dye as
measured by fluorescence, allows binding curves for DNA-binding drugs to be obtained at
high sensitivity. Furthermore, we have shown that binding of small molecules to single-
stranded DNA can be analyzed using 2 nm pores, revealing clear differences between the regionWanunu et al. Page 4
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of the ssDNA molecule that binds the fluorophores and a poly(dA) region that does not bind
the dye. Nanopore profiling of DNA interactions with small molecules is extremely rapid, uses
only ~103–104 DNA copies, and can be performed using short or long DNAs. Since the method
is essentially “label-free”, that is, it does not require fluorogenic or radioactive probes, it is
well-suited for future discovery of high affinity, sequence-specific nucleic acid-targeting drugs
for epigenetic profiling and applications in environmental and molecular toxicity.
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
Acknowledgments
We acknowledge useful discussion with M. Frank-Kamenetskii, help in sample preparation from B. McNally and J.
Larkin, and financial support from NIH award HG-004128, and NSF award PHY-0646637. We thank A. Squires for
comments on the manuscript.
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Figure 1.
Solid-state nanopore setup for detecting the binding of small molecules to DNA. A pair of
electrodes in solution is used to thread individual DNA molecules through a nanopore while
recording the current of an electrolyte. Left: a TEM image of a 3.5 nm pore fabricated in an
ultrathin silicon nitride membrane. Magnified oval: 3D rendering of a 3.5 nm nanopore with
ethidium-intercalated double-stranded DNA. Bottom: ion current signal from DNA
translocating through a 3.5 nm pore, in which the downward transients correspond to
translocation of double-stranded DNA molecules (the time between events was reduced for
clarity). For explanation of the definitions, see text.Wanunu et al. Page 7
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Figure 2.
(a) Chemical structures of ethidium (Et+), propidium (Pr2+) and ethidium homodimer
(EtHD2+). (b) Representative single-molecule 400 bp DNA translocation events through a 3.5
nm pore at different EtBr concentrations, showing a deeper blocking current amplitude for the
DNA/Et+ complex ( V = 300 mV for all experiments).Wanunu et al. Page 8
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Figure 3.
Nanopore titration of a DNA/EtBr complex. (a) Current amplitude histograms for a 400 bp
DNA fragment as a function of EtBr concentration. A shift to increasing amplitudes is seen
for the translocation peak (major population, red), whereas the collision peak (minor
population, purple) remains unchanged. (b) The peak current amplitude value ( ΔIb) for
ethidium/DNA as a function of ethidium concentration. Each point in the graph is determined
from >2000 translocations events, and the error bars are smaller than the marker size. The
overlaid curve is a best fit to the fraction bound dye obtained from fluorescence measurements
(right axis, see Supporting Information), exhibiting good agreement with the nanopore data.Wanunu et al. Page 9
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Figure 4.
Nanopore titration of 400 bp DNA using propidium (a) and ethidium homodimer (b). The peak
current amplitude value ( ΔIb) is plotted as a function of dye concentrations (symbols). The
overlaid curves are best fit to the fraction bound dye obtained from fluorescence measurements
(right axis, see Supporting Information).Wanunu et al. Page 10
Nano Lett . Author manuscript; available in PMC 2010 May 16.
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Figure 5.
Nanopore detection of small-molecule binding to single-stranded DNA. (a) TEM image of a
2.2 nm pore, and the molecules used in this study. Since SYBR Green II (SGII) binds to poly
(dA) with very low affinity, dA 60 was used as a negative control and dA 50dN50 as a positive
control. (b) Typical translocation events for dA 60, before and after the addition of SGII to the
cis chamber (side histogram is an all-point histogram of the current data). Typical translocation
events for dA 50dN50, before and after the addition of SGII, are shown in (c) and (d),
respectively. The two-step events prevalent after SGII binding were characterized by
amplitudes of 0.58 and 0.96 nA, corresponding to dA 50 and SGII-bound dN 50, respectively
(see text).Wanunu et al. Page 11
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Figure 6.
Translocation-time distributions for dA 60 (a) and dA 50dN50 (b), both before and after the
addition of excess SGII (see text for discussion).Wanunu et al. Page 12
Nano Lett . Author manuscript; available in PMC 2010 May 16.
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