Two-component systems (TCS) are signal transduction systems in bacteria and many other organisms that relay the sensory signal to genetic components. TCS consist of two proteins: a histidine kinase and a response regulator that the histidine kinase activates. This seemingly simple machinery can generate complex regulatory dynamics that enables the level of gene expression that matches the input signal: many TCS response regulators act on their own genes as transcription factors, resulting in a positive autoregulation mechanism. This regulation, in return, modulates the transcription factor activity as a function of the input signal. Positive autoregulation does not necessarily result in positive feedback. Sensitivity to autoregulation is quantified as the output level amplification resulting from the positive autoregulation mechanism. Another structural property of these systems is formally characterized as “robustness”: in a robust TCS, the output of the system is solely a function of the input signal. Thus, a robust TCS remains insensitive to fluctuations in the concentrations of its protein components and, this way, maintains the precision in the output transcription factor activity in response to input stimulus. In this paper, we show with a formal model that TCS operate on a spectrum of inverse correlation between robustness and sensitivity to autoregulation. Our model predicts that the modulation by positive autoregulation is a function of loss in TCS robustness, for example, by spontaneous dephosphorylation of the histidine kinase. Consequently, the loss in robustness provides a proportional modulation by positive autoregulation to widen the response range with a scaled amplification of the output. At the other end of the spectrum, in the presence of a strictly robust TCS machinery, amplification of the transcription factor activity by autoregulation is diminished. We show that our results are in agreement with published experimental results. Our results suggest that these TCS evolve to converge at a trade-off between robustness and positive autoregulation.

双成分系统 (TCS) 是细菌和许多其他生物体中的信号转导系统，可将感觉信号传递给遗传成分。TCS 由两种蛋白质组成：组氨酸激酶和组氨酸激酶激活的反应调节剂。这种看似简单的机制可以产生复杂的调节动力学，使基因表达水平与输入信号相匹配：许多 TCS 反应调节因子作为转录因子作用于它们自己的基因，从而产生积极的自动调节机制。作为回报，这种调节调节转录因子活性作为输入信号的函数。积极的自动调节并不一定会导致积极的反馈。对自动调节的敏感性被量化为由正自动调节机制产生的输出水平放大。这些系统的另一个结构特性被正式描述为“鲁棒性”：在鲁棒的 TCS 中，系统的输出仅仅是输入信号的函数。因此，稳健的 TCS 对其蛋白质成分浓度的波动仍然不敏感，并且通过这种方式，保持输出转录因子活性对输入刺激的响应的精确度。在本文中，我们用一个正式的模型展示了 TCS 在鲁棒性和对自动调节的敏感性之间的反相关谱上运行。我们的模型预测，通过正向自动调节进行的调节是 TCS 稳健性丧失的函数，例如，通过组氨酸激酶的自发去磷酸化。最后，鲁棒性的损失通过正向自动调节提供比例调制，以扩大响应范围，并按比例放大输出。另一方面，在存在严格稳健的 TCS 机制的情况下，自动调节对转录因子活性的放大作用减弱。我们表明我们的结果与已发表的实验结果一致。我们的结果表明，这些 TCS 演变为在稳健性和积极的自动调节之间进行权衡。