Predicting trait phenotypes from knowledge of the topology of gene networks

In many fields there is interest in manipulating genes and gene networks to realize improved trait phenotypes. The practicality of doing so, however, requires accepted theory on the properties of gene networks that is well-tested by empirical results. The extension of quantitative genetics to include models that incorporate properties of gene networks expands the long tradition of studying epistasis resulting from gene-gene interactions. Here we consider NK models of gene networks by applying concepts from graph theory and Boolean logic theory, motivated by a desire to model the parameters that influence predictive skill for trait phenotypes under the control of gene networks; N defines the number of graph nodes, the number of genes in the network, and K defines the number of edges per node in the graph, representing the gene-gene interactions. We define and consider the attractor period of an NK network as an emergent trait phenotype for our purposes. A long-standing theoretical treatment of the dynamical properties of random Boolean networks suggests a transition from long to short attractor periods as a function of the average node degree K and the bias probability P in the applied Boolean rules. In this paper we investigate the appropriateness of this theory for predicting trait phenotypes on random and real microorganism networks through numerical simulation. We show that: (i) the transition zone between long and short attractor periods depends on the number of network nodes for random networks; (ii) networks derived from metabolic reaction data on microorganisms also show a transition from long to short attractor periods, but at higher values of the bias probability than in random networks with similar numbers of network nodes and average node degree; (iii) the distribution of phenotypes measured on microorganism networks shows more variation than random networks when the bias probability in the Boolean rules is above 0.75; and (iv) the topological structure of networks built from metabolic reaction data is not random, being best approximated, in a statistical sense, by a lognormal distribution. The implications of these results for predicting trait phenotypes where the genetic architecture of a trait is a gene network are discussed.