Røgen Peter
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Asmussens Allé, Building 322, Kongens Lyngby, Denmark.
Algorithms Mol Biol. 2021 Feb 27;16(1):1. doi: 10.1186/s13015-020-00180-3.
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.
在计算结构生物学中，结构比较是我们理解蛋白质的基础。例如，从算法角度来看，结构比较是结构进化计算研究的起点，并且它指导我们从氨基酸序列预测蛋白质结构的工作。大多数蛋白质结构的结构比对方法会优化比对和叠加残基对之间的距离，即线性插值过程中比对和叠加残基移动的距离。考虑到这种线性插值，这些方法不会区分是否有插值空间、是否会导致空间冲突，或者更严重的是，是否会改变所比较蛋白质主链曲线的拓扑结构。
为了区分这些情况，我们分析了两条比对和叠加后的主链之间的线性插值。我们量化了空间冲突的数量，并找出线性主链插值中的所有自相交点。为了确定自相交点是否显著改变了蛋白质的主链曲线，我们提出了一种路径查找算法，该算法检查在线性插值的邻域内是否存在一条避免自相交的路径。通过使用纽结理论中对三维曲线而非纽结图的雷德迈斯特移动的一种新颖解释来改变线性插值，从而构建一条新路径。该算法要么找到一条避免自相交的路径，要么返回一组最小的基本自相交点。其中每一个都表明比对的蛋白质结构折叠之间存在显著差异。正如预期的那样，我们发现至少有一个基本自相交点将大多数无纽结结构与一个纽结结构区分开来，并且我们发现在通过无阻碍线性插值连接的蛋白质中存在更大的构象变化。我们还发现了同源蛋白质以不同方式穿线的例子，并且我们发现许多不同的折叠通过更长但简单的变形连接在一起。TM-align是最具限制性的比对程序之一。使用标准参数时，它仅比对叠加距离在5埃以内的残基。我们在142068次TM-align比对中的比对部分之间发现了42165个拓扑阻碍。因此，这种限制性的比对过程仍然允许比对部分存在拓扑差异。
基于这些数据，我们得出结论，我们的程序ProteinAlignmentObstruction为仅基于比对和叠加残基对之间距离的比对分数提供了重要的额外信息。
