Meyer-Ortmanns H., Labavić D. (2013) Demographic Fluctuations and Inherent Time Scales in a Genetic Circuit. In: Gilbert T., Kirkilionis M., Nicolis G. (eds) Proceedings of the European Conference on Complex Systems 2012. Springer Proceedings in Complexity. Springer, Cham
We review results on a genetic circuit made out of a self-activating species A that activates its own repressor B in a negative feedback loop. We consider this motif in three descriptions: a deterministic coarse-grained one from the start, its stochastic pendant, and a stochastic version with an improved time resolution. We study the conditions under which we can derive the deterministic coarse-grained from the stochastic time-resolved version. As it can be shown from the time-resolved version, the regular oscillations which are found in a number of realizations of this motif, fade away for slow binding rates of the transcription factors to the promoter regions of the genes. Results of our Gillespie simulations match well with mean-field predictions if the averaging over states accounts for the inherent time scales. The occurrence of quasi-cycles in the stochastic descriptions raises the question as to which oscillations in natural systems are of mere demographic origin.