{"title":"Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem","authors":"Alejandro Pérez Paz","doi":"10.1007/s11144-024-02703-0","DOIUrl":null,"url":null,"abstract":"<div><p>An analytic solution is presented for the simultaneous substrate elimination problem that combines Michaelis-Menten (MM) consumption with an irreversible homo-dimerization process. The implicit solution involves logarithm and inverse tangent functions and perfectly agrees with the numerical solution of the differential equation. A solution is also presented for the generalized dynamical problem that simultaneously combines MM kinetics with first and second-order processes. The exact expressions for the half-life and the area under the curve are also presented for these problems.</p></div>","PeriodicalId":750,"journal":{"name":"Reaction Kinetics, Mechanisms and Catalysis","volume":"137 5","pages":"2539 - 2560"},"PeriodicalIF":1.7000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reaction Kinetics, Mechanisms and Catalysis","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s11144-024-02703-0","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
An analytic solution is presented for the simultaneous substrate elimination problem that combines Michaelis-Menten (MM) consumption with an irreversible homo-dimerization process. The implicit solution involves logarithm and inverse tangent functions and perfectly agrees with the numerical solution of the differential equation. A solution is also presented for the generalized dynamical problem that simultaneously combines MM kinetics with first and second-order processes. The exact expressions for the half-life and the area under the curve are also presented for these problems.
期刊介绍：
Reaction Kinetics, Mechanisms and Catalysis is a medium for original contributions in the following fields:
-kinetics of homogeneous reactions in gas, liquid and solid phase;
-Homogeneous catalysis;
-Heterogeneous catalysis;
-Adsorption in heterogeneous catalysis;
-Transport processes related to reaction kinetics and catalysis;
-Preparation and study of catalysts;
-Reactors and apparatus.
Reaction Kinetics, Mechanisms and Catalysis was formerly published under the title Reaction Kinetics and Catalysis Letters.
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