Type-dependent irreversible stochastic spin models for genetic regulatory networks at the level of promotion-inhibition circuitry

TL;DR

This paper introduces a stochastic spin model framework to simulate genetic regulatory networks, capturing spatial and temporal fluctuations, and demonstrates its application on a synthetic oscillatory gene network using Monte Carlo simulations.

Contribution

The paper presents a novel spin-based modeling approach for genetic regulation that incorporates density fluctuations and agent behavior, with a specific application to the repressilator network.

Findings

Model captures promotion-inhibition circuitry dynamics.

Simulation reveals stationary state properties of the repressilator.

Framework is adaptable to other genetic networks.

Abstract

We describe an approach to model genetic regulatory networks at the level of promotion-inhibition circuitry through a class of stochastic spin models that includes spatial and temporal density fluctuations in a natural way. The formalism can be viewed as an agent-based model formalism with agent behavior ruled by a classical spin-like pseudo-Hamiltonian playing the role of a local, individual objective function. A particular but otherwise generally applicable choice for the microscopic transition rates of the models also makes them of independent interest. To illustrate the formalism, we investigate (by Monte Carlo simulations) some stationary state properties of the repressilator, a synthetic three-gene network of transcriptional regulators that possesses oscillatory behavior.