Stochastic resetting in backtrack recovery by RNA polymerases

TL;DR

This paper models RNA polymerase backtrack recovery as a stochastic process involving diffusion and cleavage, providing exact formulas for recovery times and showing independence from lattice discreteness under certain conditions.

Contribution

It introduces a novel stochastic model of backtrack recovery using continuous-time random walks with stochastic resetting, deriving exact recovery time distributions.

Findings

Recovery time distributions are derived exactly.

Recovery times are independent of lattice discreteness at high diffusion rates.

The model links backtrack recovery to first-passage time and stochastic resetting concepts.

Abstract

Transcription is a key process in gene expression, in which RNA polymerases produce a complementary RNA copy from a DNA template. RNA polymerization is frequently interrupted by backtracking, a process in which polymerases perform a random walk along the DNA template. Recovery of polymerases from the transcriptionally-inactive backtracked state is determined by a kinetic competition between 1D diffusion and RNA cleavage. Here we describe backtrack recovery as a continuous-time random walk, where the time for a polymerase to recover from a backtrack of a given depth is described as a first-passage time of a random walker to reach an absorbing state. We represent RNA cleavage as a stochastic resetting process, and derive exact expressions for the recovery time distributions and mean recovery times from a given initial backtrack depth for both continuous and discrete-lattice descriptions of the random walk. We show that recovery time statistics do not depend on the discreteness of the DNA lattice when the rate of 1D diffusion is large compared to the rate of cleavage.