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Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems

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

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Marcel Braukhoff

Bao Quoc Tang


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.


Braukhoff, M., Einav, A., & Quoc Tang, B. (2022). Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems. Nonlinearity, 35(4), Article 1876.

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


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Copyright Statement
Original content from this work may be used under the terms of the Creative Commons<br /> Attribution 3.0 licence. Any further distribution of this work must maintain attribution<br /> to the author(s) and the title of the work, journal citation and DOI.

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