Effects of alternative connectivity on behavior of randomly constructed Boolean networks

Random Boolean networks (RBNs) were first introduced and used to model regulatory gene networks by Kauffman in 1969 and since then have been frequently used to model networks at various levels of biological organization. The standard model has a characteristic topology in which the network has N genes with an average of K input connections selected at random. We have used RBNs to examine regulatory gene networks with four different topologies, which are characterized by different rank distributions of output connections that vary from uniform to highly skewed. Among these is the topology of the standard model, which is included for purposes of comparison, and a topology with a power-law rank distribution, which is based on recent data for the regulatory gene network of the bacterium Escherichia coli. We also examine effects of bias in the distribution of Boolean functions for the network. The dynamical properties and mutual information of these networks depend not only on their size but also on their topology and Boolean functions. Networks with the more uniform rank distributions exhibit longer lengths of attractors, larger numbers of attractors, and less mutual information. Networks with the more skewed rank distributions have complementary properties. When viewed as biological decision-making networks, those with either the most uniform or the most skewed rank distributions have disadvantageous properties. The intermediate rank distribution exhibited by the regulatory gene network of E. coli avoids these disadvantages.