Distribution of first-reaction times with target regions on boundaries of shell-like domains

  • We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.

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Author details:Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiDGND
Title of parent work (German):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
Publication series (Volume number):Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (1255)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Postprint
Date of first publication:2022/07/25
Publication year:2021
Publishing institution:Universität Potsdam
Release date:2022/07/25
Tag:approximate methods; diffusion; first-passage time; first-reaction time; shell-like geometries
Article number:123049
Number of pages:23
First page:1
Last Page:23
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access
License (German):License LogoCC BY - Namensnennung, 4.0 International
External remark:Bibliographieeintrag der Originalveröffentlichung/Quelle
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