Department of Chemical, Food, Pharmaceutical and Pharmacological Sciences (DiSCAFF), University of Piemonte Orientale Amedeo Avogadro, Novara, Italy.
PLoS One. 2011 Apr 13;6(4):e18693. doi: 10.1371/journal.pone.0018693.
Polymers can be modeled as open polygonal paths and their closure generates knots. Knotted proteins detection is currently achieved via high-throughput methods based on a common framework insensitive to the handedness of knots. Here we propose a topological framework for the computation of the HOMFLY polynomial, an handedness-sensitive invariant. Our approach couples a multi-component reduction scheme with the polynomial computation. After validation on tabulated knots and links the framework was applied to the entire Protein Data Bank along with a set of selected topological checks that allowed to discard artificially entangled structures. This led to an up-to-date table of knotted proteins that also includes two newly detected right-handed trefoil knots in recently deposited protein structures. The application range of our framework is not limited to proteins and it can be extended to the topological analysis of biological and synthetic polymers and more generally to arbitrary polygonal paths.
聚合物可以被建模为开放的多边形路径，它们的封闭会产生纽结。目前，通过基于不对手性敏感的常见框架的高通量方法来检测纽结蛋白。在这里，我们提出了一种用于 HOMFLY 多项式计算的拓扑框架，HOMFLY 多项式是一种对手性敏感的不变量。我们的方法将多分量约简方案与多项式计算相结合。在对表格化纽结和链接进行验证后，我们将该框架应用于整个蛋白质数据库，并结合了一组选定的拓扑检查，这些检查可以排除人为纠缠的结构。这导致了一个最新的纽结蛋白表，其中还包括最近在蛋白质结构中发现的两个新的右手三叶结。我们的框架的应用范围不仅限于蛋白质，它可以扩展到生物和合成聚合物的拓扑分析，更一般地说，可以扩展到任意的多边形路径。
