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.

中文翻译：

---

大肠杆菌中 lexA 自动调节的参数适应度景观。

反馈机制是控制生理反应的基础。基因调控中的一个重要例子，称为负自动调节 (NAR)，当转录因子 (TF) 通过转录抑制抑制其自身产生时就会发生。这使得基因表达的更快速稳态控制成为可能。NAR 电路可能会进化以限制无偿基因表达的适应度成本。NAR 的关键生化反应可以使用启动子活性的数学模型进行参数化；然而，这种 NAR 模型主要是在与 TF 的目标基因断开的合成 NAR 电路的背景下进行研究的。因此，目前尚不清楚 NAR 参数在天然电路环境中的约束程度，其中 TF 目标基因可以对细胞产生适应性影响。为了量化这些约束，具有不同lexA- NAR电路参数的大肠杆菌菌株，并分析了对SOS响应功能和细菌适应性的影响。使用 NAR 的数学模型，这些实验数据用于计算 NAR 参数值并推导出参数适应度图。在没有反馈的情况下，由于高 LexA 浓度和较慢的 SOS“开启”动力学，DNA 损伤的存活率降低。然而，我们表明，即使在没有 DNA 损伤的情况下，lexA启动子也足够强大，在没有反馈的情况下，高水平的lexA表达会导致细胞的适应度成本。相反，超反馈可以模仿lexA删除，这也是代价高昂的。这项工作阐明了lexA-NAR 参数值能够平衡细胞对快速 SOS 响应激活的需求和限制其毒性。