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Stochastic Hybrid Systems in Cellular Neuroscience
We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some d...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6104574/ https://www.ncbi.nlm.nih.gov/pubmed/30136005 http://dx.doi.org/10.1186/s13408-018-0067-7 |
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author | Bressloff, Paul C. Maclaurin, James N. |
author_facet | Bressloff, Paul C. Maclaurin, James N. |
author_sort | Bressloff, Paul C. |
collection | PubMed |
description | We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators. |
format | Online Article Text |
id | pubmed-6104574 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-61045742018-09-20 Stochastic Hybrid Systems in Cellular Neuroscience Bressloff, Paul C. Maclaurin, James N. J Math Neurosci Review We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators. Springer Berlin Heidelberg 2018-08-22 /pmc/articles/PMC6104574/ /pubmed/30136005 http://dx.doi.org/10.1186/s13408-018-0067-7 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Review Bressloff, Paul C. Maclaurin, James N. Stochastic Hybrid Systems in Cellular Neuroscience |
title | Stochastic Hybrid Systems in Cellular Neuroscience |
title_full | Stochastic Hybrid Systems in Cellular Neuroscience |
title_fullStr | Stochastic Hybrid Systems in Cellular Neuroscience |
title_full_unstemmed | Stochastic Hybrid Systems in Cellular Neuroscience |
title_short | Stochastic Hybrid Systems in Cellular Neuroscience |
title_sort | stochastic hybrid systems in cellular neuroscience |
topic | Review |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6104574/ https://www.ncbi.nlm.nih.gov/pubmed/30136005 http://dx.doi.org/10.1186/s13408-018-0067-7 |
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