Stochastic gene expression modeling with hill function for switch-like gene responses

Gene expression models play a key role to understand the mechanisms of gene regulation whose aspects are grade and switch-like responses. Though many stochastic approaches attempt to explain the gene expression mechanisms, the Gillespie algorithm which is commonly used to simulate the stochastic models hardly explain the switch-like behaviors of gene responses. In this study, we propose a stochastic gene expression model which can describe the switch-like behaviors of gene responses by employing Hill functions to the conventional Gillespie algorithm. We assume eight processes of gene expression and their biologically appropriate reaction rates are estimated based on published literatures. Our negative regulatory model shows that the modified Gillespie algorithm successfully describes the switch-like behaviors of gene responses, which is consistent with a published experimental study. We observe that the state of the system of the toggled switch model is rarely changed since the Hill function prevents the activation of involved proteins when their concentrations stay at low level. In ScbA/ScbR system which can control the antibiotic metabolite production of microorganisms, our proposed stochastic approach successfully models its switch-like gene response and oscillatory expressions.