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Updated: May 5, 2026

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Published on: September 26, 2016
Reversible diffusion-influenced reactions of an isolated pair on some two dimensional surfaces
1Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.
This study models reversible diffusion-influenced reactions in 2D. We derived survival probabilities for reversible reactions using irreversible reaction data, applicable to cell biology.
Area of Science:
- Chemical Kinetics
- Theoretical Chemistry
- Mathematical Biology
Background:
- Diffusion-influenced reactions are crucial in chemical and biological systems.
- Understanding reversible reactions requires accurate modeling of diffusion and reaction dynamics.
- Previous models often simplified reaction reversibility or spatial constraints.
Purpose of the Study:
- To develop a theoretical framework for reversible diffusion-influenced reactions in two dimensions.
- To derive exact and approximate expressions for survival probabilities in various 2D domains.
- To provide insights applicable to membrane-bound reactions in cell biology.
Main Methods:
- Utilizing convolution relations to link reversible and irreversible reaction survival probabilities.
- Applying the mean reaction time approximation for irreversible survival probability in confined spaces.
- Analyzing three distinct 2D spatial domains: infinite plane, annulus, and sphere surface.
Main Results:
- Obtained exact and approximate time-domain expressions for reversible reaction survival probability.
- Demonstrated the utility of convolution relations for simplifying complex reaction dynamics.
- Provided analytical solutions for specific geometries relevant to biological systems.
Conclusions:
- The developed method offers a robust approach to studying reversible diffusion-influenced reactions.
- The findings are directly relevant to understanding molecular interactions at cellular membranes.
- This work lays the groundwork for further investigations into complex reaction kinetics in biological contexts.
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