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A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities
We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9579774/ https://www.ncbi.nlm.nih.gov/pubmed/36277836 http://dx.doi.org/10.1098/rsos.220698 |
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author | Jain, Aditi Kumar, Arun Kumar Gupta, Arvind |
author_facet | Jain, Aditi Kumar, Arun Kumar Gupta, Arvind |
author_sort | Jain, Aditi |
collection | PubMed |
description | We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment. |
format | Online Article Text |
id | pubmed-9579774 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-95797742022-10-20 A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities Jain, Aditi Kumar, Arun Kumar Gupta, Arvind R Soc Open Sci Mathematics We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment. The Royal Society 2022-10-19 /pmc/articles/PMC9579774/ /pubmed/36277836 http://dx.doi.org/10.1098/rsos.220698 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Mathematics Jain, Aditi Kumar, Arun Kumar Gupta, Arvind A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title | A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title_full | A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title_fullStr | A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title_full_unstemmed | A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title_short | A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
title_sort | theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities |
topic | Mathematics |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9579774/ https://www.ncbi.nlm.nih.gov/pubmed/36277836 http://dx.doi.org/10.1098/rsos.220698 |
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