  Coregulation of the expression of groups of genes has been extensively
demonstrated empirically in bacterial and eukaryotic systems. Such coregulation
can arise through the use of shared regulatory motifs, which allow the
coordinated expression of modules (and module groups) of functionally related
genes across the genome. Coregulation can also arise through the physical
association of multi-gene complexes through chromosomal looping, which are then
transcribed together. We present a general formalism for modeling coregulation
rules in the framework of Random Boolean Networks (RBN), and develop specific
models for transcription factor networks with modular structure (including
module groups, and multi-input modules (MIM) with autoregulation) and
multi-gene complexes (including hierarchical differentiation between multi-gene
complex members). We develop a mean-field approach to analyse the stability of
large networks incorporating coregulation, and show that autoregulated MIM and
hierarchical gene-complex models can achieve greater stability than networks
without coregulation whose rules have matching activation frequency. We provide
further analysis of the stability of small networks of both kinds through
simulations. We also characterize several general properties of the transients
and attractors in the hierarchical coregulation model, and show using
simulations that the steady-state distribution factorizes hierarchically as a
Bayesian network in a Markov Jump Process analogue of the RBN model.
