Effects of the DNA state fluctuation on single-cell dynamics of self-regulating gene

TL;DR

This paper develops a dynamical mean-field theory to analyze how DNA state fluctuations influence stochastic gene expression dynamics in single cells, revealing complex behaviors like oscillations and noise variations.

Contribution

It introduces a novel theoretical framework that explicitly incorporates nonequilibrium DNA fluctuations to predict diverse single-cell dynamical phenomena.

Findings

Frequent DNA state changes lead to small effective temperature and reduced noise.

Infrequent DNA state changes cause large effective temperature and enhanced noise.

The theory predicts oscillatory decay and anomalous relaxation times in gene expression dynamics.

Abstract

A dynamical mean-field theory is developed to analyze stochastic single-cell dynamics of gene expression. By explicitly taking account of nonequilibrium and nonadiabatic features of the DNA state fluctuation, two-time correlation functions and response functions of single-cell dynamics are derived. The method is applied to a self-regulating gene to predict a rich variety of dynamical phenomena such as anomalous increase of relaxation time and oscillatory decay of correlations. Effective "temperature" defined as the ratio of the correlation to the response in the protein number is small when the DNA state change is frequent, while it grows large when the DNA state change is infrequent, indicating the strong enhancement of noise in the latter case.