Effect of Function Perturbation on the Steady-State Distribution of Genetic Regulatory Networks: Optimal Structural Intervention

The dynamics of a rule-based gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), there has been a significant amount of investigation into the effect of perturbing gene states, in particular, the design of intervention strategies based on finite- or infinite-horizon control polices. This paper considers the less investigated issue of function perturbations. A single function perturbation affects network dynamics and alters the long-run distribution, whereas any individual gene perturbation has only transient effects and does not change the long-run distribution. We derive analytic results for changes in the steady-state distributions of PBNs resulting from modifications to the underlying regulatory rules and apply the derived results to find optimal structural interventions to avoid undesirable states. The results are applied to a WNT5A network and a mammalian cell cycle related network, respectively, to achieve more favorable steady-state distributions and reduce the risk of getting into aberrant phenotypes.