Markov Chain Modeling of Polymer Translocation Through Pores

TL;DR

This paper develops an exact Markov chain model for polymer translocation through pores, providing insights into finite size effects, scaling exponents, and validating the approach with numerical simulations.

Contribution

It introduces a Markov chain framework with specific transition probabilities to analyze polymer translocation, refining existing relaxation models and addressing finite size effects.

Findings

Previous Langevin simulation results can be recovered with mobility corrections

Dynamical scaling exponents approach asymptotic values slowly with polymer length

Markov chain approach is validated through numerical simulations

Abstract

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities which satisfy a specific balance constraint provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are taken into account and that (ii) the dynamical scaling exponents have a slow approach to their predicted asymptotic values as the polymer's length increases. We also address, along with strong support from additional numerical simulations, a critical discussion which points in a clear way the viability of the Markov chain approach put forward in this work.