Predicting rare events in chemical reactions: application to skin cell proliferation

Abstract

In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory can be used to predict rare events in chemical reactions. As an example, we apply our approach to a recently proposed model on cell proliferation with relevance to skin cancer [P.B. Warren, Phys. Rev. E {\bf 80}, 030903 (2009)]. In particular, we provide an analytical explanation for the form of the exponential exponent observed in the onset rate of uncontrolled cell proliferation.