The backbone of a protein is typically represented as either a C α -polyline, a three-dimensional (3D) polyline that passes through the C α atoms, or a tuple of ϕ,ψ pairs while its fold is usually assigned using the 3D topological arrangement of the secondary structure elements (SSEs). It is tricky to obtain the SSE composition for a protein from the C α -polyline representation while its 3D SSE arrangement is not apparent in the two-dimensional (2D) ϕ,ψ representation. In this article, we first represent the backbone of a protein as a pc-polyline that passes through the centers of its peptide planes. We then analyze the pc-polylines for six different sets of proteins with high quality crystal structures. The results show that SSE composition becomes recognizable in pc-polyline presentation and consequently the geometrical property of the pc-polyline of a protein could be used to assign its secondary structure. Furthermore, our analysis finds that for each of the six sets the total length of a pc-polyline increases linearly with the number of the peptide planes. Interestingly a comparison of the six regression lines shows that they have almost identical slopes but different intercepts. Most interestingly there exist decent linear correlations between the intercepts of the six lines and either the average helix contents or the average sheet contents and between the intercepts and the average backbone hydrogen bonding energetics. Finally, we discuss the implications of the identified correlations for structure classification and protein folding, and the potential applications of pc-polyline representation to structure prediction and protein design.

中文翻译：

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代表蛋白质骨架的pc多义线的表征。

蛋白质的骨架通常表示为Cα-折线，穿过Cα原子的三维（3D）折线或ϕ，ψ对的元组，而其折叠通常使用3D拓扑指定二级结构元素（SSE）的排列。从Cα-多义线表示获得蛋白质的SSE组成是棘手的，而其3D SSE排列在二维（2D）ϕ，ψ表示中并不明显。在本文中，我们首先将蛋白质的骨架表示为穿过其肽平面中心的pc-polyline。然后，我们分析了具有高质量晶体结构的六组不同蛋白质的pc多义线。结果表明，SSE成分在pc-polyline呈现中变得可识别，因此蛋白质pc-polyline的几何性质可用于分配其二级结构。此外，我们的分析发现，对于六组中的每组，pc-polyline的总长度都随肽平面的数量线性增加。有趣的是，对这6条回归线的比较表明，它们的斜率几乎相同，但截距却不同。最有趣的是，六条线的截距与平均螺旋含量或平均片材含量之间以及截距与平均主链氢键能之间存在良好的线性相关性。最后，我们讨论了已确定的相关性对结构分类和蛋白质折叠的影响，