First-Passage Processes in Cellular Biology

Abstract

Many aspects of the behaviors of physical, chemical, and biological systems can be understood simply in terms of the dynamics of the averaged state variables and their deterministic evolution equations. Mathematical techniques for modeling and analyzing first passage (FP) processes were pioneered a few decades ago, in the context of non-equilibrium physical chemistry and chemical physics. This chapter presents and elucidates fundamentals of the FP formalism within a unified conceptual framework, which naturally integrates the existing techniques. It then discusses the applications with emphasis on the practical use of FP techniques in biophysical systems. The chapter focuses on covering a diverse set of analytical techniques; the number of reviewed biological applications and focuses on three specific areas: channel transport, receptor binding and adhesion, and single-cell growth and division. Simulation techniques that complement analytical approaches have played a crucial role in revealing the stochastic mechanisms of cells and molecules.