Abstract：
Establishing a mapping between the emergent biological properties and the repository of network structures has been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance that promotes regulation in the presence of environmental disturbances. This paper presents a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation with respect to external disturbances of arbitrary magnitude. Based on the prior information about the network, we frame precise mathematical conditions for adaptation using nonlinear systems theory. We first deduce the mathematical conditions for perfect adaptation for constant input disturbances. Subsequently, we translate these conditions to specific necessary structural requirements for adaptation in networks of small size and then extend to argue that there exist only two classes of architectures for a network of any size that can provide local adaptation in the entire state space, namely, incoherent feed-forward (IFF) structure and negative feedback loop with buffer node (NFB). The additional positiveness constraints further narrow the admissible set of network structures. This also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The proposed method does not assume any explicit knowledge of the underlying rate kinetics, barring some minimal assumptions. Finally, we also discuss the infeasibility of certain IFF networks in providing adaptation in the presence of downstream connections. Moreover, we propose a generic and novel algorithm based on non-linear systems theory to unravel the design principles for global adaptation. Detailed and extensive simulation studies corroborate the theoretical findings.
摘要：
在系统和合成生物学中，建立新兴生物学特性与网络结构存储库之间的映射关系很大。适应是一种至关重要的生物学特性，可以在环境干扰的情况下促进调节。本文提出了一种非线性系统理论驱动的框架，以确定针对任意大小的外部干扰进行完美适应的设计原则。根据有关网络的先验信息，我们使用非线性系统理论为适应构建了精确的数学条件。我们首先推导出完美适应恒定输入干扰的数学条件。随后，我们将这些条件转化为小型网络中适应的特定必要结构要求，然后扩展到认为，对于任何规模的网络，只有两类体系结构可以在整个状态空间中提供本地适应，即,非相干前馈(IFF)结构和带缓冲节点的负反馈环路(NFB)。额外的积极性约束进一步缩小了可接受的网络结构集。这也有助于在给定恒定输入扰动的情况下建立稳态的全局渐近稳定性。所提出的方法没有假设任何关于潜在速率动力学的明确知识，除了一些最小的假设。最后,我们还讨论了某些IFF网络在存在下游连接的情况下提供自适应的不可行性。此外，我们提出了一种基于非线性系统理论的通用和新颖的算法，以揭示全局适应的设计原则。详细而广泛的模拟研究证实了理论发现。
