Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness

Foundations of Static and Dynamic Absolute Concentration Robustness

Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg as robustness of equilibrium species concentration in a mass action dynamical system. Their aim was to devise a mathematical condition that will ensure robustness in the function of the biological system being modeled. The robustness of function rests on what we refer to as empirical robustness -- the concentration of a species remains unvarying, when measured in the long run, across arbitrary initial conditions. Even simple examples show that the ACR notion introduced in Shinar and Feinberg (here referred to as stat…

绝对浓度鲁棒性：代数与几何

Absolute concentration robustness: Algebra and geometry

针对生化系统绝对浓度鲁棒性（ACR）的判定难题，本文指出现有方法的不完整性，提出利用计算代数判定ACR的新方法，并在生化信号网络上验证了其有效性。

反应网络中的绝对浓度鲁棒性与多稳态：共存条件

Absolute Concentration Robustness and Multistationarity in Reaction Networks: Conditions for Coexistence

研究反应网络中多稳态与绝对浓度鲁棒性共存的条件，证明至多双分子网络共存需满足最低物种、络合物和反应数，并揭示小型双分子网络中ACR与非多稳态的等价关系。

Absolute concentration robustness in networks with low-dimensional stoichiometric subspace

A reaction system exhibits "absolute concentration robustness" (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this means that the positive part of the variety of the steady-state ideal lies entirely in a hyperplane of the form $x_i=c$, for some $c>0$. Deciding whether a given reaction system -- or those arising from some reaction network -- exhibits ACR is difficult in general, but here we show that for many simple networks, assessing ACR is straightforward. Indeed, our criteria for ACR can be performed by simply …

双稳态、绝对浓度鲁棒性及双稳态在双位无用循环中的表现

Bistability, Absolute Concentration Robustness, and Hysteresis in Dual-Site Futile Cycles with Bifunctional Enzymes

研究双位无用循环中双功能酶对系统动态特性的影响，揭示稳态存在性、数量及稳定性，以及双稳态和绝对浓度鲁棒性的表现。

生化系统中的渐近鲁棒性

Asymptotic Robustness in Biochemical Systems

本文提出渐近绝对浓度鲁棒性（aACR）概念，证明近似鲁棒性可仅由网络结构产生而无需精确ACR模体或参数微调，为分析广泛生化系统的鲁棒响应提供了严格实用的工具。

Biochemical network decomposition reveals absolute concentration robustness

Robustness of biochemical systems has become one of the central questions in Systems Biology, although it is notoriously difficult to formally capture its multifaceted nature. Maintenance of normal system function depends not only on the stoichiometry of the underlying interrelated components, but also on a multitude of kinetic parameters. For given parameter values, recent findings have aimed at characterizing the property of the system components to exhibit same concentrations in the resulting steady states, termed absolute concentration robustness (ACR). However, the existing method for det…

Network translation and steady state properties of chemical reaction systems

Network translation has recently been used to establish steady state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady state equivalent. In this work we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady state value of the …

化学反应网络的信息几何：Cramer-Rao界与绝对灵敏度的再探讨

Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited

本文利用信息几何的黎曼几何工具，证明绝对灵敏度为平衡流形切丛上的投影算子，导出多元Cramer-Rao界，并应用于IDHKP-IDH系统，揭示非理想热力学可产生超敏与负自我调控行为。

Complex balanced equilibria of weakly reversible poly-PL systems: existence, stability, and robustness

Poly-PL kinetic systems (PYK) are kinetic systems consisting of nonnegative linear combinations of power law functions. In this contribution, we analyze these kinetic systems using two main approaches: (1) we define a canonical power law representation of a poly-PL system, and (2) we transform a poly-PL system into a dynamically equivalent power law kinetic system that preserves the stoichiometric subspace of the system. These approaches led us to establish results that concern important dynamical properties of poly-PL systems that extend known results for generalized mass actions systems (GMA…

Delay stability of reaction systems

Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration networks with delays are presented.