Emmert-Streib Frank
Stowers Institute for Medical Research, Kansas City, Missouri 64110, USA.
J Comput Biol. 2006 Oct;13(8):1503-12. doi: 10.1089/cmb.2006.13.1503.
The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure--alpha-helix, antiparallel beta-sheet, and parallel beta-sheet--and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.
蛋白质结构的分类是一个重要且尚未解决的问题。本文的目的有三个方面。首先，我们利用Tutte多项式和homfly多项式之间的关系，表明可以通过算法计算给定平面图的Alexander-Conway多项式。其次，作为平面图的特殊情况，我们使用蛋白质结构的聚合物图。更确切地说，我们使用三维蛋白质结构的三个构建块——α-螺旋、反平行β-折叠和平行β-折叠——并通过为所有三个二级结构元素提供递推方程，解析计算它们相应聚合物图的Tutte多项式。第三，我们给出数值结果，将解析计算结果与算法的数值结果进行比较——不仅是为了测试一致性，也是为了证明所有分配的多项式都是二级结构元素的唯一标签。这为蛋白质结构的自动分类铺平了道路。
