Asymptotics and numerical analysis for enzymatic auxiliary reactions

Bersani, Alberto Maria; Borri, Alessandro; Tosti, Maria Elisa

doi:10.1007/s00161-020-00962-5

Cited by 2 publications

(1 citation statement)

References 53 publications

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“…Additionally, in [11] utilizing the same perturbation parameter as introduced in [10], the authors extended the uniform solution of the singular perturbation analysis to the first order. Furthermore, these techniques have been applied to other mechanisms of double substrate systems of reactions such as Goldbeter-Koshland switch [12] and auxiliary enzyme reactions [13].…”

Section: Introductionmentioning

confidence: 99%

The total quasi-steady-state for multiple alternative substrate reactions

Besya

Rao

2022

J Math Chem

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The Michaelis-Menten-Brigs-Haldane approximation and its extension, the total quasi-steady-state approximations (tQSSA) are famous assumptions for simplifications of mathematical modeling of enzyme-substrate reactions.These approximations and their validity conditions are well studied for a single substrate reaction system. However, the extension of these studies for the tQSSA of the general case of multiple substrate reactions is yet to be performed precisely due to the consequent non-linear expressions for tQSSA. In this paper, we introduce a linearization method for equations governing the tQSSA of multiple substrate reactions to obtain an analytical solution for the evolution of concentrations of reactants that is valid throughout the whole time period. In addition, we provide the validity conditions of the tQSSA for multiple substrate reaction systems using the singular perturbation analysis method.

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Section: Introductionmentioning

confidence: 99%

The total quasi-steady-state for multiple alternative substrate reactions

Besya

Rao

2022

J Math Chem

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Dynamic behavior of enzyme kinetics cooperative chemical reactions

Jan,

Shah,

Ahmad

et al. 2024

AIP Advances

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This article uses computational mathematics to investigate the dynamics of cooperative occurrences in chemical reactions inside living organisms. We study the dynamics of complex systems using mathematical models based on ordinary differential equations, paying special attention to chemical equilibrium and reaction speed. Explanations of cooperation, non-cooperation, and positive cooperation are presented in our study. We analyze the stabilities of equilibrium points by a systematic analysis that makes use of the Jacobian matrix and the threshold parameter R0. We next extend our investigation to evaluate global stability and the probability of the model. Variations in k3 have a notable effect on substrate concentration probabilities, indicating that it plays an important role in reaction kinetics. Reducing k3 highlights the substrate's critical contribution to the system by extending its presence in the concentration. We find that different results were obtained for cooperative behavior: higher reaction rates at different binding sites are correlated with positive cooperativity, while slower reactions are induced by negative cooperativity. The Adams–Bashforth method is used to show numerical and graphical solutions with the help of MATLAB. Tables and graphs are used to further explain the effects of the parameters. This study underlines how well ordinary differential equations may represent the complicated system dynamics found in chemical reactions. It also provides elusive insights into cooperative occurrences, which develops our understanding of the phenomenon and serves as a foundation for future research.

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Asymptotics and numerical analysis for enzymatic auxiliary reactions

Cited by 2 publications

References 53 publications

The total quasi-steady-state for multiple alternative substrate reactions

The total quasi-steady-state for multiple alternative substrate reactions

Dynamic behavior of enzyme kinetics cooperative chemical reactions

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