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

Source: [Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback](<https://www.sota2.com/research/paper/68fa3af21e209131ce8cec71>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:20:46.224Z

Authors: Chen Jia, Le Yi Wang, George G. Yin, Michael Q. Zhang

Published: 2019-08-30T19:21:01.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1909.00042>)

[PDF](<https://arxiv.org/pdf/1909.00042.pdf>)