化学反应网络中的Cramer-Rao界与绝对灵敏度
Cramer-Rao bound and absolute sensitivity in chemical reaction networks
AI总结：
针对化学反应网络中与基无关的绝对灵敏度构建问题，本文借助准热稳态与指数族分布的类比证明多元Cramer-Rao界，给出绝对灵敏度矩阵的线性代数表征，并在IDHKP-IDH系统中验证结论、揭示隐藏对称性。
摘要：
化学反应网络（CRN）是一类用于理解生物功能的重要模型，可用于研究细胞信息处理、代谢通路的鲁棒性与调控、昼夜节律等诸多生物过程。然而，描述某一特定功能的CRN并非孤立运作，而是更大规模网络的一部分，因此会持续受到外部变化的影响。在Shinar、Alon与Feinberg于2009年发表在《SIAM应用数学期刊》的《化学反应网络中的灵敏度与鲁棒性》一文中，研究了CRN对线性守恒量变化的响应（即灵敏度），并提出了如何构建绝对（即与基无关的）灵敏度的问题。本文通过应用信息几何方法，给出了这样的构建方式。其核心思路是追踪特定化学物质的浓度变化如何传播至稳态下所有化学物质的浓度变化，这一关系被编码在绝对灵敏度矩阵中。作为主要技术工具，本文证明了适用于CRN的多元Cramer-Rao界，该界基于准热稳态与概率分布指数族之间的类比。由此得到了准热CRN的绝对灵敏度矩阵的线性代数表征。作为实例，本文通过对浓度空间进行大量随机采样，从解析和数值层面分析了IDHKP-IDH乙醛酸旁路调控系统的核心模块，验证了实验中已知的IDH酶鲁棒性结论，并揭示了分布层面的隐藏对称性，为CRN鲁棒性分析提供了参考框架。
英文摘要：
Chemical reaction networks (CRN) comprise an important class of models to understand biological functions such as cellular information processing, the robustness and control of metabolic pathways, circadian rhythms, and many more. However, any CRN describing a certain function does not act in isolation but is a part of a much larger network and as such is constantly subject to external changes. In [Shinar, Alon, and Feinberg. "Sensitivity and robustness in chemical reaction networks." SIAM J App Math (2009): 977-998.], the responses of CRN to changes in the linear conserved quantities, called sensitivities, were studied in and the question of how to construct absolute, i.e., basis-independent, sensitivities was raised. In this article, by applying information geometric methods, such a construction is provided. The idea is to track how concentration changes in a particular chemical propagate to changes of all concentrations within a steady state. This is encoded in the matrix of absolute sensitivities. As the main technical tool, a multivariate Cramer-Rao bound for CRN is proven, which is based on the the analogy between quasi-thermostatic steady states and the exponential family of probability distributions. This leads to a linear algebraic characterization of the matrix of absolute sensitivities for quasi-thermostatic CRN. As an example, the core module of the IDHKP-IDH glyoxylate bypass regulation system is analyzed analytically and numerically by extensive random sampling of the concentration space. The experimentally known findings for the robustness of the IDH enzyme are confirmed and a hidden symmetry at the level of distributions is revealed, providing a blueprint for the analysis of the robustness properties of CRNs.
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