All organisms must be able to adapt to changes in the environment. To this end, they have developed sophisticated regulatory mechanisms to ensure homeostasis. Control engineers, who must design similar regulatory systems, have developed a number of general principles that govern feedback regulation. These lead to constraints which impose trade-offs that arise when developing controllers to minimize the effect of external disturbances on systems. Here, we review some of these trade-offs, particularly Bode’s integral formula. We also highlight its connection to information theory, by showing that the constraints in sensitivity minimization can be cast as limitations on the information transmission through a system, and these have their root in causality. Finally, we look at how these constraints arise in two biological systems: glycolytic oscillations and the energy cost of perfect adaptation in a bacterial chemotactic pathway.

所有生物都必须能够适应环境的变化。为此，他们开发了复杂的监管机制来确保体内平衡。必须设计类似调节系统的控制工程师已经制定了一些管理反馈调节的一般原则。这些会导致约束，这些约束会在开发控制器时产生权衡，以尽量减少外部干扰对系统的影响。在这里，我们回顾了其中的一些权衡，尤其是 Bode 积分公式。我们还强调了它与信息论的联系，通过表明灵敏度最小化的约束可以被视为对通过系统的信息传输的限制，这些都源于因果关系。最后，我们看看这些限制是如何在两个生物系统中出现的：