A Model for the Evolution of Networks of Genes

An organism persists through the activity of structural genes, which is co-ordinated by clusters of coupled regulatory genes. During evolution, changes of coupling within a cluster can increase the reliability with which its structural genes perform a task. To study the evolution of coupling, we have simulated and analyzed a stochastic model for a simple problem. The assumptions of the model are these: A network of regulatory genes co-ordinates the synthesis of four structural proteins, which associate in distinct heterodimers that form a heterotetramer. Mutation in cisregulatory regions produces transitions among 64 types of network. In a population, each network reproduces in proportion to its fitness, which depends on its probability (reliability) of synthesizing the tetramer. Fitness-dependent attrition keeps the size of the population constant. Regulatory genes occur in a sequence of levels; each level is associated with a different family of transcription factors. The following results emerge: Because different messengers within a family can give networks with the same connectivity, the 64 types of networks cluster into eight equivalence classes. During evolution with a low mutation rate, high-fitness classes can be approached through various paths on a fitness landscape. With a higher mutation rate, networks remain more uniformly distributed among the 64 types, and lower-fitness networks remain preponderant. An initially homogeneous population becomes more heterogeneous through mutation, but selection according to fitness later reduces its diversity. During this process the dispersion of the population over the possible networks increases, then decreases as the population approaches a unique steady state.