An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation.Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuationsaffect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch isdirectly regulated by a noisy input signal, which is described as a non-negative mean-reverting diffusion process.This continuous process can be a good approximation of the discrete birth-death process and is much moreanalytically tractable.Within this setup, we apply the Feynman-Kac theorem to investigate the statistical featuresof the output switching dynamics. Consistent with our previous findings, the input noise is found to effectivelysuppress the input-dependent transitions.We show analytically that this effect becomes significant when the inputsignal fluctuates greatly in amplitude and reverts slowly to its mean.
展开▼
