Lundgren Martin, Niemi Antti J, Sha Fan
Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108 Uppsala, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061909. doi: 10.1103/PhysRevE.85.061909. Epub 2012 Jun 11.
Folded proteins have a modular assembly. They are constructed from regular secondary structures like α helices and β strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure. In complement to the widely employed Ramachandran plot that is based on toroidal geometry, our approach utilizes the geometry of a two sphere. Unlike the more conventional approaches that describe only a given peptide unit, ours is capable of describing the entire backbone environment including the neighboring peptide units. It maps the positions of each atom to the surface of the two-sphere exactly how these atoms are seen by an observer who is located at the position of the central C_{α} atom. At each level of side-chain atoms we observe a strong correlation between the positioning of the atom and the underlying local secondary structure with very little if any variation between the different amino acids. As a concrete example we analyze the left-handed helix region of nonglycyl amino acids. This region corresponds to an isolated and highly localized residue independent sector in the direction of the C_{β} carbons on the two-sphere. We show that the residue independent localization extends to C_{γ} and C_{δ} carbons and to side-chain oxygen and nitrogen atoms in the case of asparagine and aspartic acid. When we extend the analysis to the side-chain atoms of the neighboring residues, we observe that left-handed β turns display a regular and largely amino acid independent structure that can extend to seven consecutive residues. This collective pattern is due to the presence of a backbone soliton. We show how one can use our visualization techniques to analyze and classify the different solitons in terms of selection rules that we describe in detail.
折叠蛋白具有模块化组装结构。它们由规则的二级结构构建而成，如α螺旋和β链，这些二级结构通过环连接在一起。在此，我们开发了一种适用于描述这种模块化结构的可视化技术。作为基于环形几何的广泛使用的拉氏图的补充，我们的方法利用了双球面的几何结构。与仅描述给定肽单元的更传统方法不同，我们的方法能够描述包括相邻肽单元在内的整个主链环境。它将每个原子的位置精确映射到双球面上，就如同位于中心Cα原子位置的观察者所看到的这些原子的样子。在侧链原子的每个层次上，我们观察到原子的定位与潜在的局部二级结构之间存在很强的相关性，不同氨基酸之间的差异很小或几乎没有差异。作为一个具体例子，我们分析了非甘氨酸氨基酸的左手螺旋区域。该区域对应于双球面上Cβ碳方向上一个孤立且高度局部化的残基独立区域。我们表明，残基独立定位延伸到Cγ和Cδ碳，在天冬酰胺和天冬氨酸的情况下还延伸到侧链氧和氮原子。当我们将分析扩展到相邻残基的侧链原子时，我们观察到左手β转角呈现出一种规则且在很大程度上与氨基酸无关的结构，这种结构可以延伸到七个连续残基。这种集体模式是由于主链孤子的存在。我们展示了如何使用我们的可视化技术，根据我们详细描述的选择规则来分析和分类不同的孤子。
