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We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary spin variables. Treating both the protein number and gene expression state variables stochastically and on equal footing, we propose a mapping that connects the molecular level description of networks to the binary representation. We construct a phase diagram indicating when...
We present a self-consistent field approximation approach to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on an equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad...
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