Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks

TL;DR

This paper uncovers a fundamental link between the relaxation rates of gene expression and the feedback type in autoregulatory gene networks, enabling inference of feedback signs from expression dynamics.

Contribution

It establishes a novel relation between relaxation rates and feedback signs using a stochastic model, providing a new method to infer network topology from data.

Findings

Positive feedback slows relaxation kinetics.

Negative feedback speeds up relaxation.

The spectral gap relates to feedback sign.

Abstract

The transient response to a stimulus and subsequent recovery to a steady state are the fundamental characteristics of a living organism. Here we study the relaxation kinetics of autoregulatory gene networks based on the chemical master equation model of single-cell stochastic gene expression with nonlinear feedback regulation. We report a novel relation between the rate of relaxation, characterized by the spectral gap of the Markov model, and the feedback sign of the underlying gene circuit. When a network has no feedback, the relaxation rate is exactly the decaying rate of the protein. We further show that positive feedback always slows down the relaxation kinetics while negative feedback always speeds it up. Numerical simulations demonstrate that this relation provides a possible method to infer the feedback topology of autoregulatory gene networks by using time-series data of gene expression.