Modeling stochastic dynamics of genetic oscillators
Date
2022
Authors
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Publisher
University of Delaware
Abstract
Inside living cells, sustained and precise oscillations in the levels of certain genes are essential for timekeeping for many biological processes. Gene expressions are often characterized by large fluctuations arising from the probabilistic nature of biochemical reactions occurring at few molecular copy numbers. How cells produce robust oscillations amid such fluctuations is an intriguing question. In this thesis, we try to understand the origin of robust oscillations. ☐ The minimal requirements for creating sustained gene oscillations are a time delay and negative feedback. A well-known gene oscillator with delayed negative feedback is the Goodwin oscillator, which involves the dynamics of three species. First, we investigated how the interplay between time delay and feedback strength controls the stochastic dynamics of the Goodwin oscillator using mathematical tools and stochastic simulations. Then, motivated by the circadian clock, the gene oscillator that synchronizes physiological events with the day-night pattern, we studied stochasticity in the Goodwin oscillations in the presence of external periodic driving. Finally, we investigated an activator-repressor-based gene oscillator to address how high-affinity nonspecific binding of activator can control the emergence of sustained oscillations.
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Keywords
Goodwin oscillator, Robust oscillations, Genetic oscillators, Stochastic dynamics, Biochemical reactions, Stochasticity