Facilitated diffusion in a crowded environment: from kinetics to stochastics

Facilitated diffusion is a fundamental search process used to describe the problem of a searcher protein finding a specific target site over a very large DNA strand. In recent years macromolecular crowding has been recognized to affect this search process. In this paper, we bridge between two different modelling methodologies of facilitated diffusion: the physics-oriented kinetic approach, which yields the reaction rate of the search process, and the probability-oriented stochastic approach, which yields the probability distribution of the search duration. We translate the former approach to the latter, ascertaining that the two approaches yield coinciding results, both with and without macromolecular crowding. We further show that the stochastic approach markedly generalizes the kinetic approach by accommodating a vast array of search mechanisms, including mechanisms having no reaction rates, and thus being beyond the realm of the kinetic approach.