Ensembles, dynamics, and cell types: Revisiting the statistical mechanics perspective on cellular regulation

Abstract

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this subensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.* bornholdt@uni-bremen.de

Multiscale modeling of vertebrate limb development

“…Several features of developmental gene regulation resist modeling by conventional mathematical frameworks: lack of stoichiometry and mass action, and changeability of network topology, for example (reviewed in Newman, ). This prevents drawing any inferences about the global properties of the regulatory genome of an organism, for example, identifying its attractors with the organism's full array of cell types as has been proposed (Bornholdt & Kauffman, ; Kaneko & Yomo, ; Kauffman, ). Nevertheless, the bi‐ or tristability properties of Boolean or ordinary differential equation (ODE) networks with small numbers of experimentally relevant variables can serve as good heuristics for studying transitions between cell types that are adjacent to one another in a developmental lineage.…”

Self and the Brain. The Immune Metaphor

“…Contemporary systems biology aims to understand the rules governing dynamic regulatory networks across different scales (genes, RNA, proteins, cells, systems, metasystems, organism). Self-organization underlies a generic property of many complex networks and of gene regulatory networks in particular, which control cell ontogeny ( 16 , 17 ).…”

Regulatory Dynamics of Cell Differentiation Revealed by True Time Series From Multinucleate Single Cells

“…Single-cell analyses revealed complex dynamics of gene regulation in differentiating cells (Spiller et al, 2010;Junker and van Oudenaarden, 2014;Paul et al, 2015;Marr et al, 2016;Plass et al, 2018). It is believed that dynamic effects possibly superimposed by stochastic fluctuations in gene expression levels may play crucial roles in cell fate choice, commitment, and reprogramming (Graf and Enver, 2009;Huang et al, 2009;Zhou and Huang, 2011;FerrellJr., 2012;Il Joo et al, 2018;Bornholdt and Kauffman, 2019). Changes in gene expression over time have not been directly measured in single mammalian cells as cells are -for technical reasons -sacrificed during the analysis procedure and hence can be measured only once.…”