There are many different mathematical setups to model the dynamics of gene regulatory networks (GRNs), most based on Boolean networks or chemical kinetics ideas. Here we present an approach to model GRNs through a class of irreversible interacting particle systems called type-dependent stochastic spin models that depart from these traditions. The approach allows for a straightforward modeling of biochemical pathways at the level of promotion--inhibition circuitry, and 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 some stationary state properties of the repressilator, a synthetic three-gene network of transcriptional regulators that possesses a rich dynamical behavior .
We describe an approach to model biochemical reaction networks at the level of promotion-inhibition circuitry through a class of stochastic spin models that depart from the usual chemical kinetics setup and includes spatial and temporal density fluctuations in a most natural way. 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 some stationary state properties of the repressilator, a synthetic three-gene network of transcriptional regulators that possesses a rich dynamical behaviour .
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There are many different mathematical setups to model the dynamics of gene regulatory networks (GRNs), most based on Boolean networks or chemical kinetics ideas. Here we present
We describe
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GRNs
biochemical reaction networks at the level of promotion-inhibition circuitry
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irreversible interacting particle systems called type-dependent
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these traditions. The approach allows for a straightforward modeling of biochemical pathways at the level of promotion--inhibition circuitry, and a
the usual chemical kinetics setup and includes spatial and temporal density fluctuations in a most natural way. A
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behavior
behaviour