Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback

TL;DR

This paper analyzes stochastic gene expression in a coupled positive-negative feedback circuit, revealing a triphasic bifurcation, noise reduction, and deriving analytic steady-state distributions under different limits.

Contribution

It introduces a minimal coupled gene circuit model with positive and negative feedback, providing new analytic solutions for protein distributions and noise decomposition.

Findings

Triphasic stochastic bifurcation observed with feedback ratio increase

Coupled feedback amplifies mean expression but reduces noise

Analytic steady-state distributions derived for different macroscopic limits

Abstract

Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation upon the increasing ratio of the positive and negative feedback strengths is observed, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the L\'{e}vy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained in [Chaos 26:043108, 2016]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model proposed in [Phys. Rev. Lett. 97:168302, 2006]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit and a complete decomposition of noise in terms of five different biophysical origins is provided.