Feedback mechanisms are fundamental to the control of physiological responses. One important example in gene regulation, termed negative autoregulation (NAR), occurs when a transcription factor (TF) inhibits its own production through transcriptional repression. This enables more-rapid homeostatic control of gene expression. NAR circuits presumably evolve to limit the fitness costs of gratuitous gene expression. The key biochemical reactions of NAR can be parameterized using a mathematical model of promoter activity; however, this model of NAR has been studied mostly in the context of synthetic NAR circuits that are disconnected from the target genes of the TFs. Thus, it remains unclear how constrained NAR parameters are in a native circuit context, where the TF target genes can have fitness effects on the cell. To quantify these constraints, we created a panel of Escherichia coli strains with different lexA-NAR circuit parameters and analyzed the effect on SOS response function and bacterial fitness. Using a mathematical model for NAR, these experimental data were used to calculate NAR parameter values and derive a parameter-fitness landscape. Without feedback, survival of DNA damage was decreased due to high LexA concentrations and slower SOS "turn-on" kinetics. However, we show that, even in the absence of DNA damage, the lexA promoter is strong enough that, without feedback, high levels of lexA expression result in a fitness cost to the cell. Conversely, hyperfeedback can mimic lexA deletion, which is also costly. This work elucidates the lexA-NAR parameter values capable of balancing the cell's requirement for rapid SOS response activation with limiting its toxicity.IMPORTANCE Feedback mechanisms are critical to control physiological responses. In gene regulation, one important example, termed negative autoregulation (NAR), occurs when a transcription factor (TF) inhibits its own production. NAR is common across the tree of life, enabling rapid homeostatic control of gene expression. NAR behavior can be described in accordance with its core biochemical parameters, but how constrained these parameters are by evolution is unclear. Here, we describe a model genetic network controlled by an NAR circuit within the bacterium Escherichia coli and elucidate these constraints by experimentally changing a key parameter and measuring its effect on circuit response and fitness. This analysis yielded a parameter-fitness landscape representing the genetic network, providing a window into what gene-environment conditions favor evolution of this regulatory strategy.

Beverley C. Kozuch

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