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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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Life |
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| Online Access: | https://www.mdpi.com/2075-1729/9/3/74 |
| _version_ | 1811187834614185984 |
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| author | Andrés Montoya Elkin Cruz Jesús Ágreda |
| author_facet | Andrés Montoya Elkin Cruz Jesús Ágreda |
| author_sort | Andrés Montoya |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T14:10:13Z |
| format | Article |
| id | doaj.art-5f43c4f5e8f045eda78ab804ef15d44e |
| institution | Directory Open Access Journal |
| issn | 2075-1729 |
| language | English |
| last_indexed | 2024-04-11T14:10:13Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Life |
| spelling | doaj.art-5f43c4f5e8f045eda78ab804ef15d44e2022-12-22T04:19:45ZengMDPI AGLife2075-17292019-09-01937410.3390/life9030074life9030074Computing the Parameter Values for the Emergence of Homochirality in Complex NetworksAndrés Montoya0Elkin Cruz1Jesús Ágreda2Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá D. C. 111321, ColombiaDepartamento de Química, Universidad Nacional de Colombia, Bogotá D. C. 111321, ColombiaDepartamento de Química, Universidad Nacional de Colombia, Bogotá D. C. 111321, ColombiaThe 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.https://www.mdpi.com/2075-1729/9/3/74models of biological homochiralitymirror symmetry-breakingalgorithmic problemssemialgebraic definitionsstoichiometric network analysis |
| spellingShingle | Andrés Montoya Elkin Cruz Jesús Ágreda Computing the Parameter Values for the Emergence of Homochirality in Complex Networks Life models of biological homochirality mirror symmetry-breaking algorithmic problems semialgebraic definitions stoichiometric network analysis |
| 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 | models of biological homochirality mirror symmetry-breaking algorithmic problems semialgebraic definitions stoichiometric network analysis |
| url | https://www.mdpi.com/2075-1729/9/3/74 |
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