In computational structural biology, structure comparison is fundamental for our understanding of proteins. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. Based on the data we conclude that our program ProteinAlignmentObstruction provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs.

中文翻译：

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量化对蛋白质结构叠加的位阻和拓扑障碍

在计算结构生物学中，结构比较是我们了解蛋白质的基础。结构比较是例如算法上结构进化计算研究的起点，它指导我们根据氨基酸序列预测蛋白质结构的努力。用于蛋白质结构的结构比对的大多数方法最优化了比对和重叠的残基对之间的距离，即，线性内插过程中比对和重叠的残基对的距离。考虑到这种线性内插法，如果存在内插空间，引起空间冲突，或更严重的是改变已比较蛋白质骨架曲线的拓扑结构，则这些方法无法区分。为了区分这种情况，我们分析了两个对齐和重叠的骨架之间的线性插值。我们量化空间碰撞的数量，并在线性主干插值中找到所有自相交。为了确定自交点是否显着改变了蛋白质的主链曲线，我们提出了一种寻路算法，该算法检查线性插值附近是否存在自逃避路径。通过对Reidemeister运动的新颖解释来改变线性插值，从而构造一条新的路径，这种运动是基于在三维曲线上而不是在结图上工作的打结理论。该算法要么找到一条自动回避的路径，要么返回最小的基本自交点集。这些中的每一个都表明对齐的蛋白质结构的折叠之间存在显着差异。不出所料 我们发现至少一个基本的自交点将大多数未打结的结构与打结的结构分隔开，并且在通过无障碍线性插值连接的蛋白质中发现了更大的运动。我们还发现了具有不同螺纹的同源蛋白质的实例，并且我们发现了许多不同的折叠，这些折叠通过较长但简单的变形连接在一起。TM-align是限制性最强的对齐程序之一。使用标准参数时，它只能对齐叠加在5Ångström距离内的残基。我们在142068 TM对准中的对准部分之间发现了42165个拓扑障碍。因此，这种限制性对准过程仍然允许对准部分的拓扑不同。