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Computing the Parameter Values for the Emergence of Homochirality in Complex Networks

The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those...

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Detalles Bibliográficos
Autores principales: Montoya, Andrés, Cruz, Elkin, Ágreda, Jesús
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6789494/
https://www.ncbi.nlm.nih.gov/pubmed/31540188
http://dx.doi.org/10.3390/life9030074
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author Montoya, Andrés
Cruz, Elkin
Ágreda, Jesús
author_facet Montoya, Andrés
Cruz, Elkin
Ágreda, Jesús
author_sort Montoya, Andrés
collection PubMed
description The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.
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spelling pubmed-67894942019-10-16 Computing the Parameter Values for the Emergence of Homochirality in Complex Networks Montoya, Andrés Cruz, Elkin Ágreda, Jesús Life (Basel) Article The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke’s system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs. MDPI 2019-09-15 /pmc/articles/PMC6789494/ /pubmed/31540188 http://dx.doi.org/10.3390/life9030074 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Montoya, Andrés
Cruz, Elkin
Ágreda, Jesús
Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title_full Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title_fullStr Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title_full_unstemmed Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title_short Computing the Parameter Values for the Emergence of Homochirality in Complex Networks
title_sort computing the parameter values for the emergence of homochirality in complex networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6789494/
https://www.ncbi.nlm.nih.gov/pubmed/31540188
http://dx.doi.org/10.3390/life9030074
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