细胞外信号调节激酶（ERK）在细胞中控制多个关键过程，并受到人类癌症、先天性异常、免疫疾病和神经发育综合征中突变的影响。ERK的催化活性需要经由上游激酶的双重磷酸化，该过程可由两个顺序的麦氏—门登（MM）步骤描述。从动力学数据中估计全过程机制中各个反应速率常数一直很具有挑战性。在本文中，我们提出了一种基于ERK活化的相平面表示的参数估计方法，该方法易于解析，可得出详细机制中的六个反应速率常数的两个组合。这些组合反映了两个连续磷酸化的特异性比率和单磷酸化底物在第二次磷酸化之前与酶结合不解离的概率。所提出的方法提供了一种比较扰乱ERK活化和功能的突变效应的语言。作为示例，我们使用相平面表示来分析在异型条件下的双重磷酸化，此时两种酶变种竞争同一底物。 版权所有 © 2023 作者。由Elsevier Inc.发表并保留所有权利。

The Extracellular signal Regulated Kinase (ERK) controls multiple critical processes in the cell and is deregulated by mutations in human cancers, congenital abnormalities, immune diseases, and neurodevelopmental syndromes. Catalytic activity of ERK requires dual phosphorylation by an upstream kinase, in a mechanism that can be described by two sequential Michaelis-Menten (MM) steps. The estimation of individual reaction rate constants from kinetic data in the full mechanism has proved challenging. Here, we present an analytically tractable approach to parameter estimation that is based on the phase plane representation of ERK activation and yields two combinations of six reaction rate constants in the detailed mechanism. These combinations correspond to the ratio of the specificities of two consecutive phosphorylations and the probability that monophosphorylated substrate does not dissociate from the enzyme before the second phosphorylation. The presented approach offers a language for comparing the effects of mutations that disrupt ERK activation and function in vivo. As an illustration, we use the phase plane representation to analyze dual phosphorylation under heterozygous conditions, when two enzyme variants compete for the same substrate.Copyright © 2023 The Authors. Published by Elsevier Inc. All rights reserved.