Department of Chemical and Physical Sciences and Institute for Optical Sciences, University of Toronto Mississauga, Mississauga, Ontario, Canada L5L 1C6.
J Theor Biol. 2010 Oct 21;266(4):723-38. doi: 10.1016/j.jtbi.2010.07.034. Epub 2010 Aug 3.
It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, "perfect" adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, "constructed" using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.
长期以来，控制理论家和工程师都知道，积分反馈控制导致并需要“完美”适应大多数系统中阶跃输入扰动。因此，在合成基因网络中实现这种强大的控制策略是一个有吸引力的前景。然而，遗传调控网络的性质（密度依赖性动力学和容易达到饱和的分子信号）意味着设计和构建这样的设备并不简单。在这项研究中，我们提出了一种通用的双启动子遗传调控网络，用于展示完美适应；我们的处理方法突出了实现遗传积分控制器所固有的挑战。我们还介绍了这个双启动子网络的一个具体实现的数值案例研究，“构建”使用了来自细菌大肠杆菌的常用部件。我们通过类比线性无阻尼谐振子来说明优化这个网络瞬态响应的可能性。最后，我们讨论了将这个双启动子网络扩展到比例积分控制器和一个能够在一阶蛋白质去除效应会破坏适应的条件下实现完美适应的三启动子网络。
