Biochemical reaction networks are subjected to large fluctuations attributable to small
molecule numbers, yet underlie reliable biological functions. Thus, it is important to
understand how regularity can emerge from noise. Here, we study the stochastic dynamics
of a self-repressing gene with arbitrarily long or short response time. We find that when the
mRNA and protein half-lives are approximately equal to the gene response time, fluctuations
can induce relatively regular oscillations in the protein concentration. To gain insight into this …

Biochemical reaction networks are subjected to large fluctuations attributable to small
molecule numbers, yet underlie reliable biological functions. Most theoretical approaches
describe them as purely deterministic or stochastic dynamical systems, depending on which
point of view is favored. Here, we investigate the dynamics of a self-repressing gene using
an intermediate approach based on a moment closure approximation of the master
equation, which allows us to take into account the binary character of gene activity. We …