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Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems

Braukhoff, Marcel and Einav, Amit and Quoc Tang, Bao (2022) 'Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems.', Nonlinearity., 35 (4). p. 1876.


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.

Item Type:Article
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Publisher statement:Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Date accepted:20 January 2022
Date deposited:21 January 2022
Date of first online publication:24 February 2022
Date first made open access:25 May 2022

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