Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems

Braukhoff, Marcel; Einav, Amit; Quoc Tang, Bao

Abstract

In this work we investigate the convergence to equilibriumfor mass action reactiondiffusion systemswhich model irreversible enzyme reactions. Using the standard entropy method in this situation is not feasible as the irreversibility of the system implies that the concentrations of the substrate and the complex decay to zero. The key idea we utilise in this work to circumvent this issue is to introduce a family of cut-off partial entropy-like functionals which, when combined with the dissipation of a mass like term of the substrate and the complex, yield an explicit exponential convergence to equilibrium. This method is also applicable in the case where the enzyme and complex molecules do not diffuse, corresponding to chemically relevant situation where these molecules are large in size.

Citation

Braukhoff, M., Einav, A., & Quoc Tang, B. (2022). Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems. Nonlinearity, 35(4), Article 1876. https://doi.org/10.1088/1361-6544/ac4d84

• Journal Article Type: Article
• Acceptance Date: Jan 20, 2022
• Online Publication Date: Feb 24, 2022
• Publication Date: 2022-04
• Deposit Date: Jan 21, 2022
• Publicly Available Date: May 25, 2022
• Journal: Nonlinearity
• Print ISSN: 0951-7715
• Electronic ISSN: 1361-6544
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 35
• Issue: 4
• Article Number: 1876
• DOI: https://doi.org/10.1088/1361-6544/ac4d84
• Public URL: https://durham-repository.worktribe.com/output/1216300