How input fluctuations reshape the dynamics of a biological switching system.
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 non-negative 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 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.
IBM TJ Watson Research Center, PO Box 218, Yorktown Heights, New York 10598, USA.
Bo
B
Hu
David A
DA
Kessler
Wouter-Jan
WJ
Rappel
Herbert
H
Levine
D000465:Algorithms; D001671:Biochemistry / Q000379:methods*; D001703:Biophysics / Q000379:methods*; D004058:Diffusion; D008954:Models, Biological; D015233:Models, Statistical; D016011:Normal Distribution; D015398:Signal Transduction; D013269:Stochastic Processes; D013997:Time Factors