Evaluation of loop formation dynamics in a chromatin fiber during chromosome condensation

TL;DR

This study models the thermal-driven dynamics of chromatin loop formation during chromosome condensation, providing a detailed iterative map of loop growth influenced by physical energies and interactions.

Contribution

It introduces a novel iterative map approach to quantify chromatin loop growth dynamics based on physical energy calculations and mean-field theory.

Findings

Loop growth length decreases over time reaching condensin size.

Loop formation energy is comparable to thermal energy, influencing growth.

Loop growth dynamics can be modeled as a motor protein-like power stroke.

Abstract

Chromatin fibers composed of DNA and proteins fold into consecutive loops to form rod-shaped chromosome in mitosis. Although the loop growth dynamics is investigated in several studies, its detailed processes are unclear. Here, we describe the time evolution of the loop length for thermal-driven loop growth processes as an iterative map by calculating physical quantities involved in the processes. We quantify the energy during the chromatin loop formation by calculating the free energies of unlooped and looped chromatins using the Domb-Joyce model of a lattice polymer chain incorporating the bending elasticity for thermal-driven loop growth processes. The excluded volume interaction among loops is integrated by employing the mean-field theory. We compare the loop formation energy with the thermal energy and evaluate the growth of loop length via thermal fluctuation. By assuming the dependence of the excluded volume parameter on the loop length, we construct an iterative map for the loop growth dynamics. The map demonstrates that the growth length of the loop for a single reaction cycle decreases with time to reach the condensin size, where the loop growth dynamics can be less stochastic and be regarded as direct power stroke of condensin as a kind of motor proteins.