| Abstract: |
| Stochastic processes become more and more popular to model the mesoscopic biophysical dynamics, especially in single-cell biology. We proposed a fluctuating-rate model for the stochastic biochemical dynamics in a single cell, which is indeed piecewise deterministic Markov process. We also found that the fluctuating-rate model yields a nonequilibrium landscape function, which, similar to the energy function for equilibrium fluctuation, provides the leading orders of fluctuations around each phenotypic state, as well as the transition rates between the two phenotypic states. The rigorous proof needs to integrate the well-known Donsker-Varadhan theory and Feidlin-Wentzell theory in such an averaging case. We further apply this model to Lac operon, and show that
the stochastic gene-state switching can significantly broaden the environmental parameter ranges for the existence of bistability induced by positive feedback, which can be beneficial dealing with unpredictable environmental changes. We also demonstrate that the phenotype transition rates can help to distinguish two categories of bistability. |
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