Epigenetic Control and Reprogramming-Induced Potential Landscapes of Gene Regulatory Networks: A Quantitative Theoretical Approach

TL;DR

This work develops a quantitative extension of dynamical mean-field theory (DMFT) to gene regulatory networks (GRNs) that include slow epigenetic feedback. By introducing a slow epigenetic variable and deriving an average-field description, the study maps high-dimensional GRN dynamics onto effective local equations and a Newtonian-like autocorrelation framework with an epigenetically deformed potential landscape. It identifies regimes of stability and landscape deformation, showing how reprogramming-like epigenetic feedback can yield multiple attractors or spin-glass-like states, thus extending Waddington’s landscape to dynamically reconfigurable regulatory networks. The resulting framework offers a tractable tool for analyzing developmental processes, cell fate decisions, and reprogramming phenomena, with potential applications to single-cell data interpretation and theoretical explorations of epigenetic control in GRNs.

Abstract

We develop an extended Dynamical Mean Field Theory framework to analyze gene regulatory networks (GRNs) incorporating epigenetic modifications. Building on the Hopfield network model analogy to spin glass systems, our approach introduces dynamic terms representing DNA methylation and histone modification to capture their regulatory influence on gene expression. The resulting formulation reduces high-dimensional GRN dynamics to effective stochastic equations, enabling the characterization of both stable and oscillatory states in epigenetically regulated systems. This framework provides a tractable and quantitative method for linking gene regulatory dynamics with epigenetic control, offering new theoretical insights into developmental processes and cell fate decisions.

Figures (7)

• Figure 1: Potentials for Regime 1 for different values of $\theta$.
• Figure 2: Dependence of Regime 1 on different values of $\theta$, with $c=0$. The white dashed line indicates the location of the central maximum for each value of $\theta$.
• Figure 3: Potentials for Regime 2 for different values of $\theta$.
• Figure 4: Potentials for Regime 3 for different values of $\theta$.
• Figure 5: Dependence of Regime 3 on different values of $\theta$, with $c=0$. The white dashed line indicates the location of the intermediate maximum for each value of $\theta$.