Using Effective Empirical Sub-Networks to Move Equilibria of Gene Networks

Abstract

Many biological processes are governed by the action of networks of genes, proteins, and other molecules. We ask how the equilibrium of such a gene network $\calN_0$ can be moved from an initial, perhaps undesirable, state ∃\calP_0$ to a pre-determined state $\calP_{aim}$ through external (pharmacological) intervention. The input for our analyses are the expression levels of genes in $\calP_0$ and $\calP_{aim}$, as well as those of sets of their genetic perturbations. We first find genes that are differentially expressed between the two groups, and partition them into clusters that are weakly coupled to each other. Since genes within cluster are strongly coupled, their expression levels change coherently between genetic perturbations. We asume that all genes within a cluster can be moved by appropriate changes in a few. We thus construct a subset $\calN_S$ that contains a small number of genes from each cluster. We next show how “effective” interactions between nodes of $\calN_S$ can be computed using expression levels of genes in $\calP_0$ and all its single knockout mutants. We argue that geometrical constraints imposed by the construction makes the solutions of $\calN_S$ close to those of $\calN_0$. This proximity of solutions allows us to compute how the equilibrium can be moved from $\calP_0$ to, or as close as possible to, $\calP_{aim}$.