document: A model of periodic oscillation for genetic regulatory systems In this paper , we focus on modeling and explaining periodic oscillations in gene-protein systems with a simple nonlinear model and on analyzing effects of time delay on the stability of oscillations . Our main model of genetic regulation comprises of a two-gene system with an autoregulatory feedback loop . We exploit multiple time scales and hysteretic properties of the model to construct periodic oscillations with jumping dynamics and analyze the possible mechanism according to the singular perturbation theory . As shown in this paper , periodic oscillations are mainly generated by nonlinearly negative and positive feedback loops in gene regulatory systems , whereas the jumping dynamics is generally caused by time scale differences among biochemical reactions . This simple model may actually act as a genetic oscillator or switch in gene-protein networks because the dynamics are robust for parameter perturbations or environment variations . We also explore effects of time delay on the stability of the dynamics , showing that the time delay generally increases the stability region of the oscillations , thereby making the oscillations robust to parameter changes . Two examples are also provided to numerically demonstrate our theoretical results
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extractive_keyphrases: modeling periodic oscillations nonlinear model time delay genetic regulation autoregulatory feedback loop hysteretic properties jumping dynamics singular perturbation theory biochemical reactions stability region
abstractive_keyphrases: gene-protein systems oscillations stability two-gene system nonlinearly negative feedback loops nonlinearly positive feedback loops genetic regulatory system bifurcation circadian rhythm relaxation oscillator