Field theoretic methods applied to epigenetic models*

Chromosomal regions are known to adopt stable, heritable states which result in bistable gene expression without changes to the underlying DNA sequence. Such epigenetic control is a consequence of covalent modifications of histones. We introduced a (0+1)-dimensional kinetic model, wherein modified nucleosomes recruit enzymes that similarly modify neighbouring nucleosomes, to investigate the stability and heritability of the states. To make the model analytically tractable, we used the Doi-Peliti formalism, a second quantized description of the underlying master equation of a stochastic process such as the epigenetic problem at hand, that makes it amenable to attack via path integral methods such as semi-classical approximations, perturbation theory and renormalization group. Our model exhibits bistability, and using minimum action methods we can compute escape paths and probabilities between the two stable states. We are now coupling the model with a gene switch to quantify the developmental landscape of cell differentiation.