A quantum spin approach to histone dynamics

TL;DR

This paper models histone modification dynamics using a quantum spin approach, revealing multiple stable states and the influence of spatial heterogeneity and correlated modifications in epigenetic regulation.

Contribution

It introduces a novel quantum spin framework to analyze histone modification dynamics, incorporating feedback, spatial effects, and multiple modification types.

Findings

Multiple stable histone states depend on modification sites.

Spatial heterogeneity affects histone state stability.

Correlated modifications lead to multistability.

Abstract

Post-translational modifications of histone proteins are an important factor in epigenetic control that serve to regulate transcription, depending on the particular modification states of the histone proteins. We study the stochastic dynamics of histone protein states, taking into account a feedback mechanism where modified nucleosomes recruit enzymes that diffuse to adjacent nucleosomes. We map the system onto a quantum spin system whose dynamics is generated by a non-Hermitian Hamiltonian. Making an ansatz for the solution as a tensor product state leads to nonlinear partial differential equations that describe the dynamics of the system. Multiple stable histone states appear in a parameter regime whose size increases with increasing number of modification sites. We discuss the role of the spatial dependance, and we consider the effects of spatially heterogeneous enzymatic activity. Finally, we consider multistability in a model of several types of correlated post-translational modifications.