Cooperative Adaptive Responses in Gene Regulatory Networks with Many Degrees of Freedom

Masayo Inoue, Kunihiko Kaneko

Cells generally adapt to environmental changes by first exhibiting an immediate response and then gradually returning to their original state to achieve homeostasis. Although simple network motifs consisting of a few genes have been shown to exhibit such adaptive dynamics, they do not reflect the complexity of real cells, where the expression of a large number of genes activates or represses other genes, permitting adaptive behaviors. Here, we investigated the responses of gene regulatory networks containing many genes that have undergone numerical evolution to achieve high fitness due to the adaptive response of only a single target gene; this single target gene responds to changes in external inputs and later returns to basal levels. Despite setting a single target, most genes showed adaptive responses after evolution. Such adaptive dynamics were not due to common motifs within a few genes; even without such motifs, almost all genes showed adaptation, albeit sometimes partial adaptation, in the sense that expression levels did not always return to original levels. The genes split into two groups: genes in the first group exhibited an initial increase in expression and then returned to basal levels, while genes in the second group exhibited the opposite changes in expression. From this model, genes in the first group received positive input from other genes within the first group, but negative input from genes in the second group, and vice versa. Thus, the adaptation dynamics of genes from both groups were consolidated. This cooperative adaptive behavior was commonly observed if the number of genes involved was larger than the order of ten. These results have implications in the collective responses of gene expression networks in microarray measurements of yeast Saccharomyces cerevisiae and the significance to the biological homeostasis of systems with many components.