Epigenetic feedback reshapes dynamical landscapes in gene regulatory networks

Understanding how gene regulatory networks (GRNs) give rise to stable and dynamic cellular states remains a central challenge in theoretical biology, particularly when slow epigenetic feedback reshapes the underlying regulatory landscape. While experimental approaches such as single-cell transcriptomics reveal rich dynamical behaviour, a tractable theoretical framework that links gene expression, epigenetic control, and collective dynamics remains challenging. Here, we develop an extended Dynamical Mean Field Theory (DMFT) framework for GRNs that incorporates epigenetic modifications as slow, feedback-driven variables. Building on the analogy between Hopfield networks and spin glass systems, we derive effective stochastic equations that reduce high-dimensional dynamics to a tractable form across multiple timescales. This formulation enables quantitative characterization of both stable and oscillatory regimes and reveals how epigenetic feedback reshapes the effective potential landscape governing cell fate decisions. Our model shows how epigenetic feedback regulation dynamically reshapes the Waddington landscape. Our results and methodology provide a unified theoretical framework for understanding developmental dynamics and epigenetic reprogramming in complex biological systems.