合成生物学中的积分反馈：负平衡突变
Integral feedback in synthetic biology: Negative-equilibrium catastrophe
摘要：
合成生物学的一个中心目标是设计分子控制器，以稳定和准确的方式操纵细胞内网络的动力学。为了解决细胞内网络的详细知识是不可用的，积分反馈控制器（IFC）已被提出用于控制分子丰度的事实。这些控制器可以保持精度，尽管在受控网络的不确定性。然而，只有在保持稳定性的情况下，才能实现这种理想的特征。在本文中，我们表明，分子IFC可以遭受一个危险的不稳定性称为负平衡灾难（NEC），即所有的非负平衡消失的作用下的控制器，和一些分子丰度炸毁。我们表明，单分子IFC不存在由于NEC。然后，我们推导出一个家庭的双分子国际金融公司的不确定的单分子网络时，任何数量的分子物种，受到控制，对NEC的保障。然而，当IFC应用于不确定的双分子（因此大多数细胞内）网络，我们表明，防止NEC一般成为一个棘手的问题，相互作用的分子物种的数量增加。
英文摘要：
A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the fact that detailed knowledge about intracellular networks is unavailable, integral-feedback controllers (IFCs) have been put forward for controlling molecular abundances. These controllers can maintain accuracy in spite of the uncertainties in the controlled networks. However, this desirable feature is achieved only if stability is also maintained. In this paper, we show that molecular IFCs can suffer from a hazardous instability called negative-equilibrium catastrophe (NEC), whereby all nonnegative equilibria vanish under the action of the controllers, and some of the molecular abundances blow up. We show that unimolecular IFCs do not exist due to a NEC. We then derive a family of bimolecular IFCs that are safeguarded against NECs when uncertain unimolecular networks, with any number of molecular species, are controlled. However, when IFCs are applied on uncertain bimolecular (and hence most intracellular) networks, we show that preventing NECs generally becomes an intractable problem as the number of interacting molecular species increases.
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