On the applicability of deterministic approximations to model genetic circuits

Abstract

Theoretical results and simulations support the idea that deterministic models provide an acceptable description only for large numbers of molecules. In the context of GRN, which usually involve a small number of molecules, such arguments might lead to disregard deterministic models as unsuitable representations. We found, however, strong evidences that justify their use to model self-regulatory genetic circuits, even for small number of molecules. In fact, we show that under some conditions, a stochastic system showing a switching-like behaviour (manifested on a bimodal distribution) nearly coincides with a deterministic counterpart exhibiting bistability. Moreover, and contrary to what it might be expected, we find situations involving large numbers of molecules where the deterministic model results into a poor approximation. The analysis and methods presented are expected to help selecting the most adequate system’s representation