Predicting attractors from spectral properties of stylized gene regulatory networks

Abstract

How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these networks and then argue for the function of these features using mechanistic modelling. Here we establish the foundation of an alternative approach by studying the correlation of eigenvectors with synthetic gene expression data simulated with a basic and popular model of gene expression dynamics -- attractors of Boolean threshold dynamics in signed directed graphs. Eigenvectors of the graph Laplacian are known to explain collective dynamical states (stationary patterns) in Turing dynamics on graphs. In this study, we show that eigenvectors can also predict collective states (attractors) for a markedly different type of dynamics, Boolean threshold dynamics, and category of graphs, signed directed graphs. However, the overall predictive power depends on details of the network architecture, in a predictable fashion. Our results are a set of statistical observations, providing the first systematic step towards a further theoretical understanding of the role of eigenvectors in dynamics on graphs.

arXiv commentMain text: 14 pages, 11 figures. Supplements: 22 pages, 16 figures. Submitted to: Physical Review E

References in corpus (18)

• The Yeast Cell-Cycle Network Is Robustly Designed
• Boolean network model predicts cell cycle sequence of fission yeast
• Turing patterns in network-organized activator-inhibitor systems
• Turing patterns on networks
• Genetic networks with canalyzing Boolean rules are always stable
• Topology of biological networks and reliability of information processing
• Logic and connectivity jointly determine criticality in biological gene regulatory networks
• Biological Regulatory Networks are Minimally Frustrated
• Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development
• Topology regulates pattern formation capacity of binary cellular automata on graphs
• Outer-totalistic cellular automata on graphs
• Spectral dimension reduction of complex dynamical networks
• Scaling in a general class of critical random Boolean networks
• The phase diagram of random threshold networks
• Spin glass behavior of the antiferromagnetic Ising model on a scale-free network
• Reliability of genetic networks is evolvable
• Sensitive Dependence of Optimal Network Dynamics on Network Structure
• The 3D genome shapes the regulatory code of developmental genes