| Noise is ubiquitous in dynamical systems. Its impact on the dynamics can be quite versatile, ranging from bad signal-to-noise ratios to qualitatively new phenomena such as oscillations of populations, which would be absent without noise. Here “noise” stands for stochastic fluctuations of various origin. Of particular interest are stochastic fluctuations in the context of biology. What is their role in the living cell as the basic unit of life? We shall focus on a prototypic dynamical unit which consists of only two species interacting in a non-linear way. This unit may be regarded as a coarse-grained description of a genetic circuit. For comparison we shall first discuss the case when these units are coupled on small network motifs in a deterministic description and then turn to a fully stochastic one. There we shall unravel the effect of demographic fluctuations and fluctuations in the reaction times. The power spectrum will show which source of stochastic behavior is dominant, in particular if the dynamics is very spiky. We shall compare analytic predictions with Gillespie simulations. We shall further point on the dependence of a coarse-grained description on inherent competing time scales, in our case realized by binding rates of genes as compared to the different decay rates of the two protein species. The results raise an interesting generic question about oscillatory genetic systems as they are realized in a number of natural systems, particularly and effectively in the form of the circuit considered here. |
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