Control of Asymmetric Hopfield Networks and Application to Cancer Attractors

Abstract

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.

Novel Hybrid Phenotype Revealed in Small Cell Lung Cancer by a Transcription Factor Network Model That Can Explain Tumor Heterogeneity

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“…This approach is grounded in the mathematical interpretation of Waddington’s epigenetic landscape (12,13), whereby attractors correspond to biological differentiation states or stable phenotypes. Based on this view, it has previously been proposed that malignant phenotypes in cancer correspond to attractors (14,15), and some have suggested “differentiation therapy” from malignant to benign attractors as a possible treatment strategy (14–17). …”

Modeling Basins of Attraction for Breast Cancer Using Hopfield Networks

“…In cancer-related reports, Hopfield networks have been used to identify attractors associated with cancer subtypes (Maetschke and Ragan, 2014) and stages (Taherian Fard and Ragan, 2017). Moreover, Szedlak et al (2014) have used asymmetric Hopfield networks to test densely connected nodes as therapeutic targets and inferred the minimum number of genes necessary for treatment. Meanwhile, Cantini and Caselle (2019) developed a methodology to identify molecular similarities to stratify cancer patients and improve their therapies.…”

A Complex Systems Analysis of Cancer Networks

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