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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society
2018
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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. |
format | Online Article Text |
id | pubmed-5908523 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT smithstephen modelreductionenablesturinginstabilityanalysisoflargereactiondiffusionmodels AT dalchauneil modelreductionenablesturinginstabilityanalysisoflargereactiondiffusionmodels |