Universal Loop Statistics from Active Extrusion with Kinetic Barriers

TL;DR

This paper presents a kinetic theory for cohesin-driven loop extrusion on chromatin, revealing universal laws for loop sizes and distributions influenced by obstacles and extrusion symmetry.

Contribution

It introduces a unified framework for disorder-limited loop extrusion, accounting for active cohesin arms and obstacle effects, with predictions matching experimental data.

Findings

Mean loop size follows a universal law based on processivity and obstacle density.

One-sided extrusion results in a single-exponential loop-length distribution.

Experimental loop statistics show a peaked distribution consistent with the theory.

Abstract

We develop a kinetic theory of cohesin-driven loop extrusion on a disordered chromatin track with transient barriers. In the stationary state, the mean loop size is shown to obey a universal law determined by the bare processivity and a renormalized obstacle density. Beyond the mean, one-sided extrusion always yields a single-exponential loop-length distribution, whereas two-sided extrusion produces a finite sum of exponential modes and, generically, a peaked distribution. Experimental CTCF-anchored loop statistics exhibit such a peak, thereby providing a direct discriminator of extrusion symmetry. The theory therefore establishes a unified framework for disorder-limited loop extrusion and supports a scenario in which both cohesin arms actively operate in living cells.