A CoD-based reduction algorithm for designing stationary control policies on Boolean networks

Abstract

Gene regulatory networks serve as models from which to derive therapeutic intervention strategies, in particular, stationary control policies over time that shift the probability mass of the steady state distribution (SSD) away from states associated with undesirable phenotypes. Derivation of control policies is hindered by the high-dimensional state spaces associated with gene regulatory networks. Hence, network reduction is a fundamental issue for intervention. The network model that has been most used for the study of intervention in gene regulatory networks is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks (BNs) with perturbation. In this article, we propose an algorithm that reduces a BN with perturbation, designs a control policy on the reduced network and then induces that policy to the original network. The coefficient of determination (CoD) is used to choose a gene for deletion, and a reduction mapping is used to rewire the remaining genes. This CoD-reduction procedure is used to construct a reduced network, then either the previously proposed mean first-passage time (MFPT) or SSD stationary control policy is designed on the reduced network, and these policies are induced to the original network. The efficacy of the overall algorithm is demonstrated on networks of 10 genes or less, where it is possible to compare the steady state shifts of the induced and original policies (because the latter can be derived), and by applying it to a 17-gene gastrointestinal network where it is shown that there is substantial beneficial steady state shift. The code for the algorithms is available at: http://gsp.tamu.edu/Publications/supplementary/ghaffari10a/ Please Contact Noushin Ghaffari at nghaffari@tamu.edu for further questions. Supplementary data are available at Bioinformatics online.