On the applicability of deterministic approximations to model genetic circuits*

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.