A Systematic Review of Mathematical Modelling of Epigenetic Regulatory Mechanisms in Gene Expression: Methods, Architectures, and Future Research Directions

Abstract

Epigenetic regulation plays a fundamental role in controlling gene expression without altering the underlying DNA sequence. Mechanisms such as DNA methylation, histone modification, and chromatin remodelling dynamically influence transcriptional activity and cellular differentiation. Mathematical modelling, particularly using differential equations and dynamical systems, has emerged as a powerful framework for understanding these complex regulatory processes. This systematic review examines advances between 2018 and 2023 in modelling epigenetic regulatory mechanisms governing gene expression. Recent studies demonstrate that ordinary differential equation (ODE) models are widely used to describe temporal dynamics of gene regulatory networks (GRNs), while stochastic and fractional models capture variability and memory effects in epigenetic processes. Additionally, hybrid and multiscale models integrating gene regulation with epigenetic feedback loops have significantly improved predictive capability. Mathematical models allow the analysis of nonlinear regulatory circuits, feedback loops, and attractor states that determine cellular phenotypes. Emerging approaches include data-driven parameter estimation, machine learning-assisted differential equation models, and integration of single-cell sequencing data. Despite these advancements, challenges remain in parameter estimation, data integration, and model validation due to the complexity of epigenetic systems. This review synthesizes modelling approaches, compares architectures, and identifies future research directions such as multiscale integration, hybrid AI–mechanistic modelling, and personalized epigenetic modelling.