Cargando…
An algebraic characterization of self-generating chemical reaction networks using semigroup models
The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann’s autocatalytic sets, Hordijk and Steel have constructed the versatile formalism...
Autor principal: | |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2023
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10113333/ https://www.ncbi.nlm.nih.gov/pubmed/37071214 http://dx.doi.org/10.1007/s00285-023-01899-4 |
_version_ | 1785027816777056256 |
---|---|
author | Loutchko, Dimitri |
author_facet | Loutchko, Dimitri |
author_sort | Loutchko, Dimitri |
collection | PubMed |
description | The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann’s autocatalytic sets, Hordijk and Steel have constructed the versatile formalism of catalytic reaction systems (CRS) to model and to analyze such self-generating networks, which they named reflexively autocatalytic and food-generated. Recently, it was established that the subsequent and simultaenous catalytic functions of the chemicals of a CRS give rise to an algebraic structure, termed a semigroup model. The semigroup model allows to naturally consider the function of any subset of chemicals on the whole CRS. This gives rise to a generative dynamics by iteratively applying the function of a subset to the externally supplied food set. The fixed point of this dynamics yields the maximal self-generating set of chemicals. Moreover, the set of all functionally closed self-generating sets of chemicals is discussed and a structure theorem for this set is proven. It is also shown that a CRS which contains self-generating sets of chemicals cannot have a nilpotent semigroup model and thus a useful link to the combinatorial theory of finite semigroups is established. The main technical tool introduced and utilized in this work is the representation of the semigroup elements as decorated rooted trees, allowing to translate the generation of chemicals from a given set of resources into the semigroup language. |
format | Online Article Text |
id | pubmed-10113333 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-101133332023-04-20 An algebraic characterization of self-generating chemical reaction networks using semigroup models Loutchko, Dimitri J Math Biol Article The ability of a chemical reaction network to generate itself by catalyzed reactions from constantly present environmental food sources is considered a fundamental property in origin-of-life research. Based on Kaufmann’s autocatalytic sets, Hordijk and Steel have constructed the versatile formalism of catalytic reaction systems (CRS) to model and to analyze such self-generating networks, which they named reflexively autocatalytic and food-generated. Recently, it was established that the subsequent and simultaenous catalytic functions of the chemicals of a CRS give rise to an algebraic structure, termed a semigroup model. The semigroup model allows to naturally consider the function of any subset of chemicals on the whole CRS. This gives rise to a generative dynamics by iteratively applying the function of a subset to the externally supplied food set. The fixed point of this dynamics yields the maximal self-generating set of chemicals. Moreover, the set of all functionally closed self-generating sets of chemicals is discussed and a structure theorem for this set is proven. It is also shown that a CRS which contains self-generating sets of chemicals cannot have a nilpotent semigroup model and thus a useful link to the combinatorial theory of finite semigroups is established. The main technical tool introduced and utilized in this work is the representation of the semigroup elements as decorated rooted trees, allowing to translate the generation of chemicals from a given set of resources into the semigroup language. Springer Berlin Heidelberg 2023-04-18 2023 /pmc/articles/PMC10113333/ /pubmed/37071214 http://dx.doi.org/10.1007/s00285-023-01899-4 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Loutchko, Dimitri An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title | An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title_full | An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title_fullStr | An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title_full_unstemmed | An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title_short | An algebraic characterization of self-generating chemical reaction networks using semigroup models |
title_sort | algebraic characterization of self-generating chemical reaction networks using semigroup models |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10113333/ https://www.ncbi.nlm.nih.gov/pubmed/37071214 http://dx.doi.org/10.1007/s00285-023-01899-4 |
work_keys_str_mv | AT loutchkodimitri analgebraiccharacterizationofselfgeneratingchemicalreactionnetworksusingsemigroupmodels AT loutchkodimitri algebraiccharacterizationofselfgeneratingchemicalreactionnetworksusingsemigroupmodels |