Quantifying epigenetic stability with minimum action paths

Amogh Sood and Bin Zhang
Phys. Rev. E 101, 062409 – Published 11 June 2020

Abstract

Chromatin can adopt multiple stable, heritable states with distinct histone modifications and varying levels of gene expression. Insight on the stability and maintenance of such epigenetic states can be gained by mathematical modeling of stochastic reaction networks for histone modifications. Analytical results for the kinetic networks are particularly valuable. Compared to computationally demanding numerical simulations, they often are more convenient at evaluating the robustness of conclusions with respect to model parameters. In this communication, we developed a second-quantization-based approach that can be used to analyze discrete stochastic models with a fixed, finite number of particles using a representation of the SU(2) algebra. We applied the approach to a kinetic model of chromatin states that captures the feedback between nucleosomes and the enzymes conferring histone modifications. Using a path-integral expression for the transition probability, we computed the epigenetic landscape that helps to identify the emergence of bistability and the most probable path connecting the two steady states. We anticipate the generalizability of the approach will make it useful for studying more complicated models that couple epigenetic modifications with transcription factors and chromatin structure.

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  • Received 28 February 2020
  • Accepted 21 May 2020

DOI:https://doi.org/10.1103/PhysRevE.101.062409

©2020 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsStatistical Physics & ThermodynamicsInterdisciplinary PhysicsNonlinear Dynamics

Authors & Affiliations

Amogh Sood and Bin Zhang*

  • Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *binz@mit.edu

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Vol. 101, Iss. 6 — June 2020

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