Fractional Calculus in Epigenetics

Abstract

DNA methylation, a pivotal epigenetic modification, plays a critical role in regulating gene expression. Understanding its dynamics with age is essential for elucidating ageing processes and developing biomarkers. This short note presents a theoretical framework for modelling DNA methylation dynamics using a fractional calculus approach, extending standard exponential models to accommodate the complex, heterogeneous nature of methylation changes over time. The fractional-calculus representation of the methylation process, described by the fractional-order differential equation and its solution based on the Mittag-Leffler function, not only provides better results in the sense of R2, RMSE, and MSE criteria but also offers a more general model, where the standard exponential model is only one special case.