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Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene: a deterministic approach

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 thereby obtain deterministic equations that describe how nonlinearity feeds back fluctuations into the mean-field equations, providing insight into the interplay of determinism and stochasticity. This allows us to identify regions of parameter space where fluctuations induce relatively regular oscillations.