Optimal transcriptional regulation of cellular responses to sudden environmental shifts

Cellular responses to sudden changes in their environment require prompt expression of the correct levels of the appropriate enzymes. These enzymes are typically regulated by transcription factors that sense the presence of inducers and control gene expression for the duration of the response. The specific choice of regulatory strategy depends on the characteristics of each cell response, with the pattern of gene expression dictated by parameters such as the affinity of the transcription factor to its binding sites and the strength of the promoters it regulates. Although much is known about how gene regulation determines the dynamics of cell responses, we still lack a framework to understand how the many different regulatory strategies evolved in natural systems relate to the constraints imposed by the selective pressures acting in each particular case. Here, we analyze a dynamical model of a cell response where expression of a transcriptionally repressed enzyme is induced by a sudden exposure to its substrate. We identify strategies of gene regulation that optimize the response for different types of selective pressures, which we define as a set of costs associated with substrate, enzyme and repressor intracellular concentrations during the response. We find that regulated responses happen within a defined region in the parameter space. While responses to costly (toxic) substrates favor the usage of strongly self-regulated repressors, responses where expression of enzyme is more costly than its substrate favor the usage of constitutively expressed repressors. There is only a very narrow range of selective pressures that would favor weakly self-regulated repressors. This framework can be used to infer which costs and benefits are most critical in the evolution of natural examples of cellular responses, and to predict how a response can optimize its regulation when transported to a new environment with different demands.