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Model reduction enables Turing instability analysis of large reaction–diffusion models

Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted...

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Detalles Bibliográficos
Autores principales: Smith, Stephen, Dalchau, Neil
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5908523/
https://www.ncbi.nlm.nih.gov/pubmed/29540540
http://dx.doi.org/10.1098/rsif.2017.0805
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author Smith, Stephen
Dalchau, Neil
author_facet Smith, Stephen
Dalchau, Neil
author_sort Smith, Stephen
collection PubMed
description Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species. In this paper, we suggest a method for reducing large biochemical systems that relies on removing the non-diffusible species, leaving only the diffusibles in the model. Such model reduction enables analysis to be conducted on a smaller number of differential equations. We provide conditions to guarantee that the full system forms patterns if the reduced system does, and vice versa. We confirm our technique with three examples: the Brusselator, an example proposed by Turing, and a biochemically plausible patterning system consisting of 17 species. These examples show that our method significantly simplifies the study of pattern formation in large systems where several species can be considered immobile.
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spelling pubmed-59085232018-04-20 Model reduction enables Turing instability analysis of large reaction–diffusion models Smith, Stephen Dalchau, Neil J R Soc Interface Life Sciences–Mathematics interface Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species. In this paper, we suggest a method for reducing large biochemical systems that relies on removing the non-diffusible species, leaving only the diffusibles in the model. Such model reduction enables analysis to be conducted on a smaller number of differential equations. We provide conditions to guarantee that the full system forms patterns if the reduced system does, and vice versa. We confirm our technique with three examples: the Brusselator, an example proposed by Turing, and a biochemically plausible patterning system consisting of 17 species. These examples show that our method significantly simplifies the study of pattern formation in large systems where several species can be considered immobile. The Royal Society 2018-03 2018-03-14 /pmc/articles/PMC5908523/ /pubmed/29540540 http://dx.doi.org/10.1098/rsif.2017.0805 Text en © 2018 The Authors. http://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/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Life Sciences–Mathematics interface
Smith, Stephen
Dalchau, Neil
Model reduction enables Turing instability analysis of large reaction–diffusion models
title Model reduction enables Turing instability analysis of large reaction–diffusion models
title_full Model reduction enables Turing instability analysis of large reaction–diffusion models
title_fullStr Model reduction enables Turing instability analysis of large reaction–diffusion models
title_full_unstemmed Model reduction enables Turing instability analysis of large reaction–diffusion models
title_short Model reduction enables Turing instability analysis of large reaction–diffusion models
title_sort model reduction enables turing instability analysis of large reaction–diffusion models
topic Life Sciences–Mathematics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5908523/
https://www.ncbi.nlm.nih.gov/pubmed/29540540
http://dx.doi.org/10.1098/rsif.2017.0805
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