On a Stochastic PDE Model for Epigenetic Dynamics

TL;DR

This paper introduces a stochastic PDE model to study epigenetic mutations influenced by environmental noise, with applications in cancer immunotherapy and plant cell fate, supported by mathematical analysis and optimal control strategies.

Contribution

It develops a novel stochastic PDE framework for epigenetic dynamics, incorporating noise effects and reversibility, with mathematical validation and potential therapeutic insights.

Findings

Mathematical validation of the stochastic PDE model.

Analysis of noise-induced epigenetic mutation reversibility.

Formulation of an optimal control problem for mutation reversal.

Abstract

We propose and analyze a stochastic model to investigate epigenetic mutations, i.e., modifications of the genetic information that control gene expression patterns in a cell but do not alter the DNA sequence. Epigenetic mutations are related to environmental fluctuations, which leads us to consider (additive) noise as the driving element for such mutations. We focus on two applications: firstly, cancer immunotherapy involving macrophages' epigenetic modifications that we call tumor microenvironment noise-induced polarizations, and secondly, cell fate determination and mutation of the flower Arabidopsis thaliana. Due to the technicalities involving cancer biology for the first case, we present only a general review of this topic and show the details in a separate manuscript since our principal concerns here are the mathematical results that are important to validate our system as an appropriate epigenetic model; for such results, we rely on the theory of Stochastic PDE, theory of large deviations, and ergodic theory. Moreover, since epigenetic mutations are reversible, a fact currently exploited to develop so-called epi-drugs to treat diseases like cancer, we also investigate an optimal control problem for our system to study the reversal of epigenetic mutations.