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

TL;DR

This paper uses Kramers escape theory within the chemical Langevin framework to predict rare events in chemical reactions, specifically applied to a model of skin cell proliferation related to cancer.

Contribution

It introduces an analytical approach to predict rare events in chemical systems using Kramers escape theory, applied to a biological cell proliferation model.

Findings

Analytical explanation for the exponential rate of uncontrolled cell proliferation

Application of Kramers escape theory to biological reaction systems

Prediction of rare events in skin cell proliferation model

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.