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

• We describe and explore a new class of asymmetric stochastic spin models in detail.
• The models provide a spin-like alternative to study nonequilibrium phenomena.
• The models provide a natural setup to study the spatial dynamics of reaction networks.
• We illustrate the application of the models to the repressilator, a synthetic GRN.
• Monte Carlo simulations reveal stationary state oscillations for the repressilator.

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 behaviour 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 behaviour.