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

Anthony Szedlak,Carlo Piermarocchi,Nicholas Smith,Spencer Sims,Giovanni Paternostro,Andrey Rzhetsky

doi:10.1371/journal.pcbi.1005849

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 AURKB, NEK1, TTK, and WEE1 causes simulated HeLa cells to accumulate in the M phase. Finally, we suggest possible improvements and extensions to our model.

Highlights

Proposed by Conrad Waddington in the 1950s [1] and Stuart Kauffman in the 1970s [2], analysis of biological processes such as cellular differentiation and cancer development using attractor models—dynamical systems whose configurations tend to evolve toward particular sets of states—has gained significant traction over the past decade [3,4,5,6,7,8,9,10,11,12]
Identifying gene inhibition targets to regulate cell cycle is important to the development of effective therapies
We create a dynamical model of the process of cell cycle using the Hopfield model and gene expression data from human cervical cancer cells and yeast cells

Summary

Introduction

Proposed by Conrad Waddington in the 1950s [1] and Stuart Kauffman in the 1970s [2], analysis of biological processes such as cellular differentiation and cancer development using attractor models—dynamical systems whose configurations tend to evolve toward particular sets of states—has gained significant traction over the past decade [3,4,5,6,7,8,9,10,11,12] One such attractor model, the Hopfield model [13], is a type of recurrent artificial neural network based on spin glasses. It has been used to directly model the dynamics of cellular differentiation and stem cell reprogramming [23, 24], targeted inhibition of genes in cancer gene regulatory networks [25], and cell cycle across various stages of cellular differentiation [26]

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Conclusion