Stochastic activation in a genetic switch model
| Autor: | John Hertz, Alvaro Correales, Joanna Tyrcha |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
0301 basic medicine
Physics Bistability Molecular Networks (q-bio.MN) A protein FOS: Physical sciences First order 01 natural sciences Exponential function 03 medical and health sciences 030104 developmental biology Biological Physics (physics.bio-ph) FOS: Biological sciences 0103 physical sciences Path integral formulation 92C42 Quantitative Biology - Molecular Networks Physics - Biological Physics 010306 general physics Mathematical physics Stable state |
| DOI: | 10.48550/arxiv.1808.05003 |
| Popis: | We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced rare transitions between locally-stable states using a path integral formulation and Master and Chapman-Kolmogorov equations. As in simpler models for rare transitions, the rate has the form of the exponential of a quantity $S_0$ (a "barrier") multiplied by a prefactor $\eta$. We calculate $S_0$ and $\eta$ first in the bursting limit (where the ratio $\gamma$ of the protein and mRNA lifetimes is very large). In this limit, the calculation can be done almost entirely analytically, and the results are in good agreement with simulations. For finite $\gamma$ numerical calculations are generally required. However, $S_0$ can be calculated analytically to first order in $1/\gamma$, and the result agrees well with the full numerical calculation for all $\gamma > 1$. Employing a method used previously on other problems, we find we can account qualitatively for the way the prefactor $\eta$ varies with $\gamma$, but its value is 15-20% higher than that inferred from simulations. Comment: 26 pages, 9 figures; revised version: corrected a few typos, added a little new text at the beginning and the end, made small changes in some figures and captions |
| Databáze: | OpenAIRE |
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