Exact Identification of Topologically Essential Interactions in the Networks Derived from Perturbation Experiments

Abstract

Perturbation screens (e.g. by gene knock-downs) are one of the most promising tools available for discovering the structure of complex biological networks. Considerable obstacle in understanding the results of such screens stems from inability to distinguish the indirect effects of a perturbation from the direct effects. Thus, networks derived from typical perturbation screen are significantly more complex than true underlying networks. The problem of identifying minimal core network topology consistent with results of perturbation screen (i.e. discriminating between direct and indirect effects of a perturbation) has been accurately formulated previously but despite the attempts to solve it, only approximate methods with severe limitations have been developed. Here, we report a novel approach that is based on the theory of self-avoiding random walks which allows one to find an exact solution to the problem: given experimentally derived network one can identify core network(s) consistent with original network (note that for sufficiently complex network, more than one core network is possible). By introducing novel matrix representation of the network topology we reduce the problem of identifying core underlying networks to the counting of self-avoiding random walks in the original network, thus allowing exact solution for any input network topology. We describe application of our approach to synthetic data obtained by simulating artificially constructed networks, as well as to the results of real perturbation screens performed in yeast and mammalian systems.