We develop a theory of reversible diffusion-controlled reactions with generalized binding/unbinding kinetics. In this framework, a diffusing particle can bind to the reactive substrate after a random number of arrivals onto it, with a given threshold distribution. The particle remains bound to the substrate for a random waiting time drawn from another given distribution and then resumes its bulk diffusion until the next binding and so on. When both distributions are exponential, one retrieves the conventional first-order forward and backward reactions whose reversible kinetics is described by generalized Collins–Kimball’s (or back-reaction) boundary condition. In turn, if either of distributions is not exponential, one deals with generalized (non-Markovian) binding or unbinding kinetics (or both). Combining renewal technique with the encounter-based approach, we derive spectral expansions for the propagator, the concentration of particles, and the diffusive flux on the substrate. We study their long-time behavior and reveal how anomalous rarity of binding or unbinding events due to heavy tails of the threshold and waiting time distributions may affect such reversible diffusion-controlled reactions. Distinctions between time-dependent reactivity, encounter-dependent reactivity, and a convolution-type Robin boundary condition with a memory kernel are elucidated.
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7 June 2023
Research Article|
June 01 2023
Diffusion-controlled reactions with non-Markovian binding/unbinding kinetics
Denis S. Grebenkov
Denis S. Grebenkov
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing – original draft, Writing – review & editing)
Laboratoire de Physique de la Matière Condensée, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris
, 91120 Palaiseau, France
a)Author to whom correspondence should be addressed: denis.grebenkov@polytechnique.edu
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a)Author to whom correspondence should be addressed: denis.grebenkov@polytechnique.edu
J. Chem. Phys. 158, 214111 (2023)
Article history
Received:
February 14 2023
Accepted:
May 16 2023
Citation
Denis S. Grebenkov; Diffusion-controlled reactions with non-Markovian binding/unbinding kinetics. J. Chem. Phys. 7 June 2023; 158 (21): 214111. https://doi.org/10.1063/5.0146512
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