Department of Mathematics, California State University San Marcos, San Marcos, USA.
Department of Mathematics, Texas A &M University, College Station, USA.
J Math Biol. 2024 Mar 1;88(3):36. doi: 10.1007/s00285-024-02060-5.
Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions required for a network of this type to have a species with absolute concentration robustness. We find that the robustness in a substrate is endowed by its interaction with a bifunctional enzyme, which is an enzyme that has different roles when isolated versus when bound as a substrate-enzyme complex. When isolated, the bifunctional enzyme promotes production of more molecules of the robust species while when bound, the same enzyme facilitates degradation of the robust species. These dual actions produce robustness in the large class of covalent modification networks. For each network of this type, we find the network conditions for the presence of robustness, the species that has robustness, and its robustness value. The unified approach of simultaneously analyzing a large class of networks for a single property, i.e. absolute concentration robustness, reveals the underlying mechanism of the action of bifunctional enzyme while simultaneously providing a precise mathematical description of bifunctionality.
生化共价修饰网络表现出一系列显著的稳态和动态特性，如多稳定性、振荡、超敏性和绝对浓度稳健性。本文重点研究了这种类型的网络具有绝对浓度稳健性的物种所需的条件。我们发现，基质的稳健性是由其与双功能酶的相互作用赋予的，双功能酶是一种在分离状态和作为基质-酶复合物结合状态时具有不同作用的酶。当分离时，双功能酶促进更多的稳健物种分子的产生，而当结合时，相同的酶促进稳健物种的降解。这些双重作用在大量的共价修饰网络中产生了稳健性。对于这种类型的每个网络，我们找到了存在稳健性的网络条件、具有稳健性的物种及其稳健性值。同时分析一大类网络的单一属性（即绝对浓度稳健性）的统一方法揭示了双功能酶作用的潜在机制，同时为双功能提供了精确的数学描述。
