Conformational statistics of non-equilibrium polymer loops in Rouse model with active loop extrusion

TL;DR

This study analyzes the statistical properties of DNA loops extruded by protein motors, revealing how non-equilibrium dynamics influence loop conformations and showing that different motor types produce similar loop characteristics.

Contribution

It introduces a dimensionless parameter controlling the transition between equilibrium and non-equilibrium loop conformations in the Rouse model with active extrusion.

Findings

The loop conformation depends on the ratio of relaxation time to extrusion time.

Two-sided and one-sided motors generate similar loop properties.

Theoretical predictions match asymptotic behaviors in different extrusion regimes.

Abstract

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in statistics of the extruded loop. Besides, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits.