Structural intervention of gene regulatory networks by general rank-k matrix perturbation

One of the ultimate objectives of studying gene regulatory networks is to derive potential intervention strategies to avoid aberrant cellular behavior. Boolean networks (BNs) and their stochastic extension, probabilistic Boolean networks (PBNs), provide a convenient framework to design different types of intervention strategies. In this paper, we focus on studying structural intervention, in which we perturb regulatory Boolean functions to alter the long-term network dynamics to obtain desirable behavior. Specifically, we extend our previous work that derives optimal structural intervention for rank-1 function perturbations to more general solutions for arbitrary rank-k function perturbations. The analytic solution is derived using the Sherman-Morrison-Woodbury (SMW) formula. We apply the derived structural intervention to a mutated mammalian cell cycle network. Our results show that our intervention strategy correctly identifies the main targets to stop uncontrolled cell growth in the mutated cell cycle network.