When translocation dynamics becomes anomalous

TL;DR

This paper investigates how non-Markovian dynamics with memory effects influence the translocation time distribution of ssDNA through membrane channels, challenging traditional Markovian models based on Brownian motion.

Contribution

It extends existing models by analyzing the impact of strong memory effects on translocation dynamics, providing a more accurate description of experimental observations.

Findings

Translocation time distribution is broader with memory effects.

Non-Markovian models better fit experimental data.

Memory effects significantly alter translocation dynamics.

Abstract

Recent single molecule experiments probing the passage process of a short single-stranded DNA (ssDNA) through a membrane channel (translocation) allow to measure the passage time distribution. Building on a recent modelling approach (D. K. Lubensky and D. R. Nelson, Biophys. J. 77, 1824 (1999)), which has been demonstrated to be valid for chains of up to $\simeq 300$ nucleotides and therefore well applies to the system we have in mind, we discuss the consequences if the associated dynamics is not of Markov origin, but if strong memory effects prevail during the translocation. Motivation is drawn from recent results indicating that the distribution of translocation times is broader than predicted by simple Markovian models based on Brownian motion.