Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Jain, Aditi, Kumar, Arun, Kumar Gupta, Arvind
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
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
_version_ 1784812255917899776
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
work_keys_str_mv AT jainaditi atheoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities
AT kumararun atheoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities
AT kumarguptaarvind atheoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities
AT jainaditi theoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities
AT kumararun theoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities
AT kumarguptaarvind theoreticalframeworktoanalysetheflowofparticlesinadynamicalsystemwithstochastictransitionratesandsitecapacities