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Genetic regulatory networks control ontogeny. For fifty years Booleannetworks have served as models of such systems, ranging from ensembles ofrandom Boolean networks as models for generic properties of gene regulation toworking dynamical models of a growing number of sub-networks of real cells. Atthe same time, their statistical mechanics has been thoroughly studied. Here werecapitulate their original motivation in the context of current theoreticaland empirical research. We discuss ensembles of random Boolean networks whosedynamical attractors model cell types. A sub-ensemble is the critical ensemble.There is now strong evidence that genetic regulatory networks are dynamicallycritical, and that evolution is exploring the critical sub-ensemble. Thegeneric properties of this sub-ensemble predict essential features of celldifferentiation. In particular, the number of attractors in such networksscales as the DNA content raised to the 0.63 power. Data on the number of celltypes as a function of the DNA content per cell shows a scaling relationship of0.88. Thus, the theory correctly predicts a power law relationship between thenumber of cell types and the DNA contents per cell, and a comparable slope. Wediscuss these new scaling values and show prospects for new research lines forBoolean networks as a base model for systems biology.

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