  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.
