Control of asymmetric Hopfield networks and application to cancer attractors.

The asymmetric Hopfield model is used to simulate signaling dynamics in gene regulatory networks. The model allows for a direct mapping of a gene expression pattern into attractor states. We analyze different control strategies aimed at disrupting attractor patterns using selective local fields representing therapeutic interventions. The control strategies are based on the identification of signaling bottlenecks, which are single nodes or strongly connected clusters of nodes that have a large impact on the signaling. We provide a theorem with bounds on the minimum number of nodes that guarantee control of bottlenecks consisting of strongly connected components. The control strategies are applied to the identification of sets of proteins that, when inhibited, selectively disrupt the signaling of cancer cells while preserving the signaling of normal cells. We use an experimentally validated non-specific and an algorithmically-assembled specific B cell gene regulatory network reconstructed from gene expression data to model cancer signaling in lung and B cells, respectively. Among the potential targets identified here are TP53, FOXM1, BCL6 and SRC. This model could help in the rational design of novel robust therapeutic interventions based on our increasing knowledge of complex gene signaling networks.