Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg\u00a0(Science 327:1389-1391, 2010) as robustness of equilibrium species concentration in a mass\u00a0action dynamical system. Their aim was to devise a mathematical condition that will ensure\u00a0robustness in the function of the biological system being modeled. The robustness of function\u00a0rests on what we refer to as empirical robustness\u00a0\u2014\u00a0the concentration of a species remains\u00a0unvarying, when measured in the long run, across arbitrary initial conditions. Even simple\u00a0examples show that the ACR notion introduced in Shinar and Feinberg\u00a0(here referred to as\u00a0<\/i>static ACR<\/b>) is neither necessary nor sufficient for empirical\u00a0robustness. To make a stronger connection with empirical robustness, we define\u00a0<\/i>dynamic\u00a0ACR<\/b>, a property related to long-term, global dynamics, rather than only to equilibrium\u00a0behavior. We discuss general dynamical systems with dynamic ACR properties as well as\u00a0parametrized families of dynamical systems related to reaction networks. In particular, we find necessary\u00a0and sufficient conditions for dynamic ACR in\u00a0complex balanced<\/b>\u00a0reaction networks, a class of\u00a0networks that is central to the theory of reaction networks.This is joint work with\u00a0<\/b><\/i>Badal Joshi (CSUSM)<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"
Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg\u00a0(Science 327:1389-1391, 2010) as robustness of equilibrium species concentration in a mass\u00a0action dynamical system. Their aim was to devise a mathematical … <\/p>\n