  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 fluctuations
affect the stochastic dynamics of a simple biological switch. In our model, the
on transition rate of the switch is directly regulated by a noisy input signal,
which is described as a nonnegative mean-reverting diffusion process. This
continuous process can be a good approximation of the discrete birth-death
process and is much more analytically tractable. Within this new setup, we
apply the Feynman-Kac theorem to investigate the statistical features of the
output switching dynamics. Consistent with our previous findings, the input
noise is found to effectively suppress the input-dependent transitions. We show
analytically that this effect becomes significant when the input signal
fluctuates greatly in amplitude and reverts slowly to its mean.
