Monte Carlo simulations of a stochastic process with position-dependent resetting inspired by backtracked RNA polymerases

Abstract

The transcription of the genetic code features a transcriptional proofreading mechanism that inactivates a biological random walker, which consequently does a random walk or stochastically resets its position to the elongation-competent state. In this text, we discuss the different statistical features of a walker that is (1) unbiased and can stochastically reset from anywhere in a discrete lattice, (2) forward-biased and can only reset from within a certain region in the lattice, and (3) backward-biased and is likewise constrained to reset from specified lattice positions. In particular, we compute recovery time distributions, mean recovery times, and an eventual recovery probability.