Gaussian closure and dynamical mean-field theory for self-avoiding heteropolymers

TL;DR

This paper develops a unified analytical framework using Gaussian closure and dynamical mean-field theory to study the conformational dynamics and contact probabilities of self-avoiding heteropolymers, including active polymers like chromatin.

Contribution

It introduces a self-consistent diffusion equation for polymer correlations derived from the Langevin equation, extending analytical treatments beyond linear response theory.

Findings

Validates the theory across coiled, globular, and self-avoiding polymers.

Predicts hyper-compacted fractal states in hydrodynamically coupled active polymers.

Provides a unified dynamical framework for diverse polymer conformations.

Abstract

Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the evolution of conformations, contact probabilities, and fluctuations within a dynamical mean-field theory. Starting with the Langevin equation of a hydrodynamically coupled and self-avoiding heteropolymer, the key idea is to focus on the two-point correlator as the lowest-order relevant observable. Truncating higher-order correlations via a Gaussian closure leads to a self-consistent diffusion equation for the chain correlations. The theory is validated by contrasting coiled, globular, and self-avoiding polymers within a single dynamical framework, and predicts hyper-compacted fractal states in hydrodynamically coupled active polymers such as chromatin.