Gene regulatory architecture in antibiotic resistance is optimized for specific dynamic regimens

Cellular responses to antibiotics face a fundamental trade-off: resistance must be deployed quickly enough to prevent the accumulation of drug inside the cell, but expression of resistance genes is costly in the absence of the drug. Therefore, antibiotic responses are typically regulated, controlling not only whether resistance is expressed, but also when, how strongly, and for how long. These regulatory strategies are implemented through the strength and arrangement of promoters and operators. However, it is still not clear how the dynamics of drug exposure select for specific regulatory strategies. Here, we develop a dynamical model of a typical antibiotic response, where a transcriptional repressor senses the drug and regulates expression of a resistance protein, coupled to the effects of the drug on cell growth and gene expression. We define a cost function that weighs the different burdens imposed on the cell over the course of the response, and perform in silico optimization of the regulatory parameters under different selective pressures for three architectures of increasing complexity: constitutive expression of resistance, repression by a constitutively expressed repressor, and repression by a self-regulated repressor. We find that strong drug exposures favor constitutive expression of resistance, high costs of basal expression favor repression by a constitutive repressor, and self-regulation of the repressor is favored only when the response must provide protection while also restraining overexpression of resistance. Stochastic simulations further show that self-regulation of the repressor protects cells against fluctuations in repressor levels, which cause unnecessary induction of resistance before exposure and failed induction after exposure. This framework links the dynamics of the environment to the evolution of gene regulation, providing a basis to predict which regulatory strategies are expected to arise under specific selective pressures.