Scale-Free Behaviour of Amino Acid Pair Interactions in Folded Proteins

The protein structure is a cumulative result of interactions between amino acid residues interacting with each other through space and/or chemical bonds. Despite the large number of high resolution protein structures, the “protein structure code” has not been fully identified. Our manuscript presents a novel approach to protein structure analysis in order to identify rules for spatial packing of amino acid pairs in proteins. We have investigated 8706 high resolution non-redundant protein chains and quantified amino acid pair interactions in terms of solvent accessibility, spatial and sequence distance, secondary structure, and sequence length. The number of pairs found in a particular environment is stored in a cell in an 8 dimensional data tensor. When plotting the cell population against the number of cells that have the same population size, a scale free organization is found. When analyzing which amino acid paired residues contributed to the cells with a population above 50, pairs of Ala, Ile, Leu and Val dominate the results. This result is statistically highly significant. We postulate that such pairs form “structural stability points” in the protein structure. Our data shows that they are in buried α-helices or β-strands, in a spatial distance of 3.8–4.3Å and in a sequence distance >4 residues. We speculate that the scale free organization of the amino acid pair interactions in the 8D protein structure combined with the clear dominance of pairs of Ala, Ile, Leu and Val is important for understanding the very nature of the protein structure formation. Our observations suggest that protein structures should be considered as having a higher dimensional organization.

蛋白质结构是氨基酸残基通过空间相互作用和/或化学键彼此作用的累积结果。尽管目前已解析大量高分辨率蛋白质结构，但“蛋白质结构编码”仍未被完全阐明。本研究提出一种全新的蛋白质结构分析方法，旨在揭示蛋白质中氨基酸残基对的空间堆积规则。我们对8706条高分辨率非冗余蛋白质链展开研究，从溶剂可及性、空间距离与序列距离、二级结构以及序列长度等维度对氨基酸残基对的相互作用进行量化分析。特定环境下出现的残基对数量被存储于一个8维数据张量的对应单元格中。当以单元格的种群数量为横轴、具有相同种群数量的单元格数目为纵轴绘图时，可观察到无标度组织特征。对种群数量大于50的单元格所对应的氨基酸残基对进行分析后发现，丙氨酸（Ala）、异亮氨酸（Ile）、亮氨酸（Leu）与缬氨酸（Val）组成的残基对占据主导地位，该结果具有极高的统计学显著性。我们推测此类残基对构成了蛋白质结构中的“结构稳定点”。实验数据表明，它们多存在于埋藏的α螺旋或β折叠股中，空间距离处于3.8–4.3Å范围内，且序列间隔大于4个残基。我们进一步推测，8维蛋白质结构框架下氨基酸残基对相互作用的无标度组织特征，加上丙氨酸、异亮氨酸、亮氨酸与缬氨酸残基对的显著主导性，对于理解蛋白质结构形成的本质具有重要意义。本研究结果提示，蛋白质结构应被视为具有更高维度的组织形式。