document: Dynamics of the firing probability of noisy integrate-and-fire neurons Cortical neurons in vivo undergo a continuous bombardment due to synaptic activity , which acts as a major source of noise . We investigate the effects of the noise filtering by synapses with various levels of realism on integrate-and-fire neuron dynamics . The noise input is modeled by white -LRB- for instantaneous synapses -RRB- or colored -LRB- for synapses with a finite relaxation time -RRB- noise . Analytical results for the modulation of firing probability in response to an oscillatory input current are obtained by expanding a Fokker-Planck equation for small parameters of the problem-when both the amplitude of the modulation is small compared to the background firing rate and the synaptic time constant is small compared to the membrane time constant . We report the detailed calculations showing that if a synaptic decay time constant is included in the synaptic current model , the firing-rate modulation of the neuron due to an oscillatory input remains finite in the high-frequency limit with no phase lag . In addition , we characterize the low-frequency behavior and the behavior of the high-frequency limit for intermediate decay times . We also characterize the effects of introducing a rise time to the synaptic currents and the presence of several synaptic receptors with different kinetics . In both cases , we determine , using numerical simulations , an effective decay time constant that describes the neuronal response completely
doc_bio_tags: O O O B I O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: firing probability cortical neurons synaptic activity noise filtering synaptic time constant membrane time constant phase lag synaptic receptors
abstractive_keyphrases: noisy integrate-and-fire neurons white noise colored noise fokker-planck equation numerical simulation