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Classification of Polymer Structures by Graph Theory

机译：图论对聚合物结构的分类

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摘要

Compact polymers much as proteins obtain their unique conformation by appropriate nonbonded interactions among their monomer residues. Innumerable nonnative compact conformations are also possible, and it is essential to distinguish the native from the nonnative conformations. Toward this goal we have used graph-theoretic methods to classify polymer structures formed by noncovalent interactions. All compact structures on a 4 * 4 two-dimensional lattice and a few conformations on 3 * 3 * 3 cubic lattice have been investigated. The 69 compact conformations in 4 * 4 two- dimensional lattice are classified into 12 groups based on the highest eigenvalue and eigenvector. The complex graphs obtained for polymers in a 3 * 3 * 3 lattice space are analyzed. Their eigenvalues and eigenvector components are correlated with the branching structure and the center of the graph. The method has application in classifying real polymers such as proteins into their substructures, cluster, and domains.
机译：紧密的聚合物就像蛋白质一样，通过单体残基之间适当的非键相互作用获得其独特的构象。数不清的非本地构象也是可能的，区分非本地和非本地构象至关重要。为了达到这个目标，我们使用图论方法对由非共价相互作用形成的聚合物结构进行分类。研究了4 * 4二维晶格上的所有紧凑结构以及3 * 3 * 3立方晶格上的一些构象。基于最高特征值和特征向量，将4 * 4二维晶格中的69个紧密构象分为12组。分析了在3 * 3 * 3晶格空间中获得的聚合物的复数图。它们的特征值和特征向量分量与分支结构和图的中心相关。该方法可用于将诸如蛋白质之类的真实聚合物分类为其亚结构，簇和域。

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