Towards a full quantitative description of single-molecule reaction kinetics in biological cells
- The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it is typically very broad in many biological situations, thus, the mean FPT canThe first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it is typically very broad in many biological situations, thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.…
Author details: | Denis S. GrebenkovORCiD, Ralf MetzlerORCiDGND, Gleb OshaninORCiD |
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DOI: | https://doi.org/10.1039/c8cp02043d |
ISSN: | 1463-9076 |
ISSN: | 1463-9084 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/29873351 |
Title of parent work (English): | Physical chemistry, chemical physics : a journal of European Chemical Societies |
Publisher: | Royal Society of Chemistry |
Place of publishing: | Cambridge |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/05/21 |
Publication year: | 2018 |
Release date: | 2021/11/17 |
Volume: | 20 |
Issue: | 24 |
Number of pages: | 9 |
First page: | 16393 |
Last Page: | 16401 |
Funding institution: | Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [ME 1535/7-1, ME 1535/6-1]; French National Research AgencyFrench National Research Agency (ANR) [ANR-13-JSV5-0006-01]; Foundation for Polish Science within an Alexander von Humboldt Polish Honorary Research Fellowship |
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 |