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Biochemical reaction networks are subjected to large fluctuationsattributable to small molecule numbers, yet underlie reliable biologicalfunctions. Most theoretical approaches describe them as purely deterministic orstochastic dynamical systems, depending on which point of view is favored.Here, we investigate the dynamics of a self-repressing gene using anintermediate approach based on a moment closure approximation of the masterequation, which allows us to take into account the binary character of geneactivity. We thereby obtain deterministic equations that describe hownonlinearity feeds back fluctuations into the mean-field equations, providinginsight into the interplay of determinism and stochasticity. This allows us toidentify regions of parameter space where fluctuations induce relativelyregular oscillations.

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