Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular Regulation

TL;DR

This paper revisits Boolean network models of genetic regulation, highlighting their critical dynamics and scaling laws that predict cell type diversity based on DNA content, linking statistical mechanics to cellular differentiation.

Contribution

It demonstrates that critical Boolean networks accurately model cell type diversity and DNA content scaling, providing a theoretical framework connecting statistical mechanics and systems biology.

Findings

Number of attractors scales as DNA content^0.63

Number of cell types scales as DNA content^0.88

Critical Boolean networks predict key features of cell differentiation

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 sub-ensemble 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.