Cell cycle time series gene expression data encoded as cyclic attractors in Hopfield systems

Abstract

Modern time series gene expression and other omics data sets have enabled unprecedented resolution of the dynamics of cellular processes such as cell cycle and response to pharmaceutical compounds. In anticipation of the proliferation of time series data sets in the near future, we use the Hopfield model, a recurrent neural network based on spin glasses, to model the dynamics of cell cycle in HeLa (human cervical cancer) and S. cerevisiae cells. We study some of the rich dynamical properties of these cyclic Hopfield systems, including the ability of populations of simulated cells to recreate experimental expression data and the effects of noise on the dynamics. Next, we use a genetic algorithm to identify sets of genes which, when selectively inhibited by local external fields representing gene silencing compounds such as kinase inhibitors, disrupt the encoded cell cycle. We find, for example, that inhibiting the set of four kinases BRD4, MAPK1, NEK7, and YES1 in HeLa cells causes simulated cells to accumulate in the M phase. Finally, we suggest possible improvements and extensions to our model.

18 pages, 6 figures

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• Cell reprogramming modelled as transitions in a hierarchy of cell cycles
• Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks
• Network Hierarchy and Pattern Recovery in Directed Sparse Hopfield Networks
• Supervised and Unsupervised protocols for hetero-associative neural networks