Cargando…
A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics
In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites....
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2017
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5568237/ https://www.ncbi.nlm.nih.gov/pubmed/28832591 http://dx.doi.org/10.1371/journal.pone.0182178 |
_version_ | 1783258820499210240 |
---|---|
author | Zarai, Yoram Margaliot, Michael Tuller, Tamir |
author_facet | Zarai, Yoram Margaliot, Michael Tuller, Tamir |
author_sort | Zarai, Yoram |
collection | PubMed |
description | In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation. |
format | Online Article Text |
id | pubmed-5568237 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-55682372017-09-09 A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics Zarai, Yoram Margaliot, Michael Tuller, Tamir PLoS One Research Article In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation. Public Library of Science 2017-08-23 /pmc/articles/PMC5568237/ /pubmed/28832591 http://dx.doi.org/10.1371/journal.pone.0182178 Text en © 2017 Zarai et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Zarai, Yoram Margaliot, Michael Tuller, Tamir A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title | A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title_full | A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title_fullStr | A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title_full_unstemmed | A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title_short | A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics |
title_sort | deterministic mathematical model for bidirectional excluded flow with langmuir kinetics |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5568237/ https://www.ncbi.nlm.nih.gov/pubmed/28832591 http://dx.doi.org/10.1371/journal.pone.0182178 |
work_keys_str_mv | AT zaraiyoram adeterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics AT margaliotmichael adeterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics AT tullertamir adeterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics AT zaraiyoram deterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics AT margaliotmichael deterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics AT tullertamir deterministicmathematicalmodelforbidirectionalexcludedflowwithlangmuirkinetics |