A.-M. Moșneagu†, I. Stoleriu‡
Abstract: Enzyme-catalysed reactions are chemical reactions within cells in which the rate of the reaction is signi cantly increased through the action of enzymes. They are usually part of large and complex biochemical networks, which form the central processing units of the living cell. Enzymatic reactions often operate on multiple time scales, which can be characterized as being either fast or slow. The quasi steadystate approximation (QSSA) utilizes time scale separation to project these complex models onto lower-dimensional slow manifolds. In this paper, we investigate the validity of a quasi steady-state assumption for enzyme-catalysed biochemical reactions with competitive inhibition that are subject to a constant substrate input. Necessary and su cient conditions for the validity of these assumptions were derived and were shown to be dependent, among others, on the substrate input. The validity conditions are numerically veri ed using the classical RungeKutta method.
MSC: 92C45; 92-10; 34C20; 34D05; 34E13
keywords: enzyme kinetics; inhibition; quasi steady-state; open system; multiple time scales; validity conditions.
DOI 10.56082/annalsarscimath.2023.1-2.383
†anamaria.mosneagu@uaic.ro; Alexandru Ioan Cuza University of Iasi, Faculty of Mathematics, Bvd. Carol I, No. 11, 700506 Iasi, Romania; Alexandru Ioan Cuza University of Iasi, Research Center with Integrated Techniques for Atmospheric Aerosol Investigation in Romania, RECENT AIR, Laboratory of astronomy and astrophysics, Astronomy Observatory, 5-7 Mihail Sadoveanu, 700490 Iasi, Romania; Acknowledgment is given to infrastructure support from the Operational Program Competitiveness 20142020, Axis 1, under POC/448/1/1 Research infrastructure projects for public R&D institutions/Sections F 2018, through the Research Center with Integrated Techniques for Atmospheric Aerosol Investigation in Romania (RECENT AIR) project, under grant agreement MySMIS no. 127324;
‡iulian.stoleriu@uaic.ro; Faculty of Mathematics, Alexandru Ioan Cuza University of Iasi, Bvd. Carol I, No. 11, 700506 Iasi, Romania
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
