narrow escape problem for diffusion in cellular microdomains
The study of the diffusive motion of ions or molecules in confined biological microdomains requires the derivation of the explicit dependence of quantities, such as the decay rate of the population or the forward chemical reaction rate constant on the geometry of the domain. Here, we obtain this exp...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS 2007-10, Vol.104 (41), p.16098-16103 |
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| creator | Schuss, Z Singer, A Holcman, D |
| description | The study of the diffusive motion of ions or molecules in confined biological microdomains requires the derivation of the explicit dependence of quantities, such as the decay rate of the population or the forward chemical reaction rate constant on the geometry of the domain. Here, we obtain this explicit dependence for a model of a Brownian particle (ion, molecule, or protein) confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. We call the calculation of the mean escape time the narrow escape problem. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Here, we present asymptotic formulas for the mean escape time in several cases, including regular domains in two and three dimensions and in some singular domains in two dimensions. The mean escape time comes up in many applications, because it represents the mean time it takes for a molecule to hit a target binding site. We present several applications in cellular biology: calcium decay in dendritic spines, a Markov model of multicomponent chemical reactions in microdomains, dynamics of receptor diffusion on the surface of neurons, and vesicle trafficking inside a cell. |
| doi_str_mv | 10.1073/pnas.0706599104 |
| format | Article |
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Singer, A ; Holcman, D</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c647t-283bfb312adbc60e5958b8cc5098e23afb462e44ecb20e841391bf1ba74530a83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Biological Sciences</topic><topic>Biophysical Phenomena</topic><topic>Biophysics</topic><topic>Calcium</topic><topic>Calcium - metabolism</topic><topic>Cells</topic><topic>Cellular biology</topic><topic>Chemical reactions</topic><topic>Cytoplasm - metabolism</topic><topic>Dendrites - metabolism</topic><topic>Dendritic spines</topic><topic>Diffusion</topic><topic>Geometry</topic><topic>Ions</topic><topic>Markov analysis</topic><topic>Markov Chains</topic><topic>Membrane Microdomains - metabolism</topic><topic>Models, Biological</topic><topic>Models, Neurological</topic><topic>Molecules</topic><topic>Neck</topic><topic>Neurons</topic><topic>Neurons - metabolism</topic><topic>Neuroscience</topic><topic>Physical Sciences</topic><topic>Receptors</topic><topic>Receptors, Cell Surface - metabolism</topic><topic>Subcellular Fractions - metabolism</topic><topic>Synapses - metabolism</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schuss, Z</creatorcontrib><creatorcontrib>Singer, A</creatorcontrib><creatorcontrib>Holcman, D</creatorcontrib><collection>AGRIS</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Animal Behavior Abstracts</collection><collection>Bacteriology Abstracts (Microbiology B)</collection><collection>Calcium & Calcified Tissue Abstracts</collection><collection>Chemoreception Abstracts</collection><collection>Ecology Abstracts</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Immunology Abstracts</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Oncogenes and Growth Factors Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Proceedings of the National Academy of Sciences - PNAS</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schuss, Z</au><au>Singer, A</au><au>Holcman, D</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>narrow escape problem for diffusion in cellular microdomains</atitle><jtitle>Proceedings of the National Academy of Sciences - PNAS</jtitle><addtitle>Proc Natl Acad Sci U S A</addtitle><date>2007-10-09</date><risdate>2007</risdate><volume>104</volume><issue>41</issue><spage>16098</spage><epage>16103</epage><pages>16098-16103</pages><issn>0027-8424</issn><eissn>1091-6490</eissn><abstract>The study of the diffusive motion of ions or molecules in confined biological microdomains requires the derivation of the explicit dependence of quantities, such as the decay rate of the population or the forward chemical reaction rate constant on the geometry of the domain. Here, we obtain this explicit dependence for a model of a Brownian particle (ion, molecule, or protein) confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. We call the calculation of the mean escape time the narrow escape problem. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Here, we present asymptotic formulas for the mean escape time in several cases, including regular domains in two and three dimensions and in some singular domains in two dimensions. The mean escape time comes up in many applications, because it represents the mean time it takes for a molecule to hit a target binding site. 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| subjects | Biological Sciences Biophysical Phenomena Biophysics Calcium Calcium - metabolism Cells Cellular biology Chemical reactions Cytoplasm - metabolism Dendrites - metabolism Dendritic spines Diffusion Geometry Ions Markov analysis Markov Chains Membrane Microdomains - metabolism Models, Biological Models, Neurological Molecules Neck Neurons Neurons - metabolism Neuroscience Physical Sciences Receptors Receptors, Cell Surface - metabolism Subcellular Fractions - metabolism Synapses - metabolism |
| title | narrow escape problem for diffusion in cellular microdomains |
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