Arrival time for the fastest among N switching stochastic particles
The first arrivals among N Brownian particles is ubiquitous in the life sciences, as it often triggers cellular processes from the molecular level. We study here the case where stochastic particles, which represent proteins or molecules can switch between two states inside the non-negative real line...
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| Veröffentlicht in: | The European physical journal. B, Condensed matter physics Condensed matter physics, 2022-07, Vol.95 (7), Article 113 |
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| container_title | The European physical journal. B, Condensed matter physics |
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| creator | Toste, S. Holcman, D. |
| description | The first arrivals among
N
Brownian particles is ubiquitous in the life sciences, as it often triggers cellular processes from the molecular level. We study here the case where stochastic particles, which represent proteins or molecules can switch between two states inside the non-negative real line. The switching process is modeled as a two-state Markov chain and particles can only escape in state 1. We estimate the fastest arrival time by solving asymptotically the Fokker–Planck equations for three different initial distributions: Dirac-delta, uniformly distributed and long-tail decay. The derived formulas reveal that the fastest particle avoids switching when the switching rates are much smaller than the diffusion time scale, but switches twice when the diffusion in state 2 is much faster than in state 1. The present results are compared to stochastic simulations revealing the range of validity of the derived formulas.
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| doi_str_mv | 10.1140/epjb/s10051-022-00366-1 |
| format | Article |
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N
Brownian particles is ubiquitous in the life sciences, as it often triggers cellular processes from the molecular level. We study here the case where stochastic particles, which represent proteins or molecules can switch between two states inside the non-negative real line. The switching process is modeled as a two-state Markov chain and particles can only escape in state 1. We estimate the fastest arrival time by solving asymptotically the Fokker–Planck equations for three different initial distributions: Dirac-delta, uniformly distributed and long-tail decay. The derived formulas reveal that the fastest particle avoids switching when the switching rates are much smaller than the diffusion time scale, but switches twice when the diffusion in state 2 is much faster than in state 1. The present results are compared to stochastic simulations revealing the range of validity of the derived formulas.
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N
Brownian particles is ubiquitous in the life sciences, as it often triggers cellular processes from the molecular level. We study here the case where stochastic particles, which represent proteins or molecules can switch between two states inside the non-negative real line. The switching process is modeled as a two-state Markov chain and particles can only escape in state 1. We estimate the fastest arrival time by solving asymptotically the Fokker–Planck equations for three different initial distributions: Dirac-delta, uniformly distributed and long-tail decay. The derived formulas reveal that the fastest particle avoids switching when the switching rates are much smaller than the diffusion time scale, but switches twice when the diffusion in state 2 is much faster than in state 1. The present results are compared to stochastic simulations revealing the range of validity of the derived formulas.
Graphic abstract</description><subject>Analysis</subject><subject>Brownian motion</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Diffusion rate</subject><subject>Extreme Value Statistics and Search in Biology: Theory and Simulations</subject><subject>Fluid- and Aerodynamics</subject><subject>Fokker-Planck equation</subject><subject>Markov chains</subject><subject>Markov processes</subject><subject>Mathematics</subject><subject>Particle decay</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Solid State Physics</subject><subject>Switches</subject><subject>Switching</subject><subject>Topical Review - Statistical and Nonlinear Physics</subject><issn>1434-6028</issn><issn>1434-6036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNqFkV1PwyAUhhujiZ-_wSZeedF5Tgu0vVwWdUsWTfy4JozCxtKVCWzqv5dZ4-KVIeEc4HnJC2-SXCIMEAncqPVyduMRgGIGeZ4BFIxleJCcIClIxuLy8LfPq-Pk1PslACBDcpKMhs6ZrWjTYFYq1dalYRGr8EH5kIqV7ebpQ-rfTZALE3sfrFzEUyPTtXCxtMqfJ0datF5d_NSz5PXu9mU0zqaP95PRcJpJQjBkZEYUYaiLstQCUbGSUUVmVVNriVIxipQ1VMS5krrBqgGhG6CqqEVNC9oUZ8l1f-9CtHztzEq4T26F4ePhlO_2gCDEL8EtRvaqZ9fOvm3iW_jSblwX7fGc1TkWDGgVqUFPzUWruOm0DU7IOBq1MtJ2Spu4PywR6poQyPcWfgSRCeojzMXGez55fvrLlj0rnfXeKf3rGYHvouO76HgfHY_R8e_o-M581St9VHRz5fbm_5N-ASItnQo</recordid><startdate>20220701</startdate><enddate>20220701</enddate><creator>Toste, S.</creator><creator>Holcman, D.</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><general>Springer-Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-5909-2566</orcidid><orcidid>https://orcid.org/0000-0001-9854-5014</orcidid></search><sort><creationdate>20220701</creationdate><title>Arrival time for the fastest among N switching stochastic particles</title><author>Toste, S. ; Holcman, D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c441t-4b4e461f377fa11e6765e4b8d9fc1ce65156d5a1568cfd18d0afd05e39a9535d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Analysis</topic><topic>Brownian motion</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Diffusion rate</topic><topic>Extreme Value Statistics and Search in Biology: Theory and Simulations</topic><topic>Fluid- and Aerodynamics</topic><topic>Fokker-Planck equation</topic><topic>Markov chains</topic><topic>Markov processes</topic><topic>Mathematics</topic><topic>Particle decay</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Solid State Physics</topic><topic>Switches</topic><topic>Switching</topic><topic>Topical Review - Statistical and Nonlinear Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Toste, S.</creatorcontrib><creatorcontrib>Holcman, D.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>The European physical journal. B, Condensed matter physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Toste, S.</au><au>Holcman, D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Arrival time for the fastest among N switching stochastic particles</atitle><jtitle>The European physical journal. B, Condensed matter physics</jtitle><stitle>Eur. Phys. J. B</stitle><date>2022-07-01</date><risdate>2022</risdate><volume>95</volume><issue>7</issue><artnum>113</artnum><issn>1434-6028</issn><eissn>1434-6036</eissn><abstract>The first arrivals among
N
Brownian particles is ubiquitous in the life sciences, as it often triggers cellular processes from the molecular level. We study here the case where stochastic particles, which represent proteins or molecules can switch between two states inside the non-negative real line. The switching process is modeled as a two-state Markov chain and particles can only escape in state 1. We estimate the fastest arrival time by solving asymptotically the Fokker–Planck equations for three different initial distributions: Dirac-delta, uniformly distributed and long-tail decay. The derived formulas reveal that the fastest particle avoids switching when the switching rates are much smaller than the diffusion time scale, but switches twice when the diffusion in state 2 is much faster than in state 1. The present results are compared to stochastic simulations revealing the range of validity of the derived formulas.
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| subjects | Analysis Brownian motion Complex Systems Condensed Matter Physics Diffusion rate Extreme Value Statistics and Search in Biology: Theory and Simulations Fluid- and Aerodynamics Fokker-Planck equation Markov chains Markov processes Mathematics Particle decay Physics Physics and Astronomy Solid State Physics Switches Switching Topical Review - Statistical and Nonlinear Physics |
| title | Arrival time for the fastest among N switching stochastic particles |
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