Analytical Solution of Gene Regulatory Networks

Abstract

We study gene regulatory networks that include the effect of multiple binary interactions, when various genes can activate or inhibit other genes, as well as of ternary interactions where two genes jointly affect the level of activity of a third gene. We also prove that Boolean identities for the activation state of a gene in terms of the activation level of another set of genes, can be represented, so that the overall probability of activation of any gene in the network can be computed in the presence of logical dependencies, and excitatory-inhibitory interactions between genes.