Department of Mathematics, California State University San Marcos, San Marcos, USA.
Departments of Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison, Madison, USA.
J Math Biol. 2022 Oct 15;85(5):53. doi: 10.1007/s00285-022-01823-2.
Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg (Science 327:1389-1391, 2010) 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 (Science 327:1389-1391, 2010) (here referred to as static ACR) is neither necessary nor sufficient for empirical robustness. To make a stronger connection with empirical robustness, we define dynamic ACR, a property related to long-term, global dynamics, rather than only to equilibrium behavior. We discuss general dynamical systems with dynamic ACR properties as well as parametrized families of dynamical systems related to reaction networks. We find necessary and sufficient conditions for dynamic ACR in complex balanced reaction networks, a class of networks that is central to the theory of reaction networks.
绝对浓度稳健性（ACR）是由 Shinar 和 Feinberg（Science 327:1389-1391，2010）引入的，用于描述质量作用动力学系统中平衡物种浓度的稳健性。他们的目的是设计一种数学条件，以确保所建模的生物系统的功能具有稳健性。功能的稳健性取决于我们称之为经验稳健性的性质——在任意初始条件下，从长期来看，物种的浓度保持不变。即使是简单的例子也表明，Shinar 和 Feinberg（Science 327:1389-1391，2010）中引入的 ACR 概念（这里称为静态 ACR）既不是经验稳健性的必要条件，也不是充分条件。为了与经验稳健性建立更强的联系，我们定义了动态 ACR，这是一种与长期、全局动力学相关的性质，而不仅仅与平衡行为相关。我们讨论了具有动态 ACR 性质的一般动力系统以及与反应网络相关的参数化动力系统族。我们找到了在复杂平衡反应网络中动态 ACR 的必要和充分条件，复杂平衡反应网络是反应网络理论的核心网络之一。
