{"title":"群论在分子系统生物学中的回顾与应用。","authors":"Edward A Rietman, Robert L Karp, Jack A Tuszynski","doi":"10.1186/1742-4682-8-21","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.</p>","PeriodicalId":51195,"journal":{"name":"Theoretical Biology and Medical Modelling","volume":" ","pages":"21"},"PeriodicalIF":0.0000,"publicationDate":"2011-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/1742-4682-8-21","citationCount":"26","resultStr":"{\"title\":\"Review and application of group theory to molecular systems biology.\",\"authors\":\"Edward A Rietman, Robert L Karp, Jack A Tuszynski\",\"doi\":\"10.1186/1742-4682-8-21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.</p>\",\"PeriodicalId\":51195,\"journal\":{\"name\":\"Theoretical Biology and Medical Modelling\",\"volume\":\" \",\"pages\":\"21\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/1742-4682-8-21\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Biology and Medical Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1186/1742-4682-8-21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Biology and Medical Modelling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/1742-4682-8-21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Review and application of group theory to molecular systems biology.
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.
期刊介绍:
Theoretical Biology and Medical Modelling is an open access peer-reviewed journal adopting a broad definition of "biology" and focusing on theoretical ideas and models associated with developments in biology and medicine. Mathematicians, biologists and clinicians of various specialisms, philosophers and historians of science are all contributing to the emergence of novel concepts in an age of systems biology, bioinformatics and computer modelling. This is the field in which Theoretical Biology and Medical Modelling operates. We welcome submissions that are technically sound and offering either improved understanding in biology and medicine or progress in theory or method.