Review and application of group theory to molecular systems biology.

Edward A Rietman, Robert L Karp, Jack A Tuszynski
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引用次数: 26

Abstract

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.

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群论在分子系统生物学中的回顾与应用。
在本文中,我们提供了一些数学思想的回顾,这些思想可以帮助我们更好地理解生命和非生命系统之间的界限。我们专注于群论和抽象代数应用于分子系统生物学。在本文中,我们简要地描述了可能存在的开放性问题。在遗传密码方面,我们提出有可能使用微扰理论来探索进化基因组的64维时空流形中的邻近可能性。关于代数图论,我们讨论几个次要的开放问题。关于网络动力学和类群形式化,我们认为网络图可能不是理解表现型的主要焦点,而是网络动力学的相空间。我们给出了C6网络及其相空间网络的一个简单例子。我们设想细胞的分子网络实际上是一个由超循环和反馈电路组成的复杂网络,它可以在高维空间中得到更好的表现。我们推测,根据自同构分解的分析,靶向分子网络中在相空间中起关键作用的节点可能是一种更好的药物发现和治疗癌症的方法。
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Theoretical Biology and Medical Modelling
Theoretical Biology and Medical Modelling MATHEMATICAL & COMPUTATIONAL BIOLOGY-
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审稿时长
6-12 weeks
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.
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