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The characterization of pc ‐polylines representing protein backbones
Author(s) -
Wang Lincong,
Zhang Yao,
Zou Shuxue
Publication year - 2020
Publication title -
proteins: structure, function, and bioinformatics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.699
H-Index - 191
eISSN - 1097-0134
pISSN - 0887-3585
DOI - 10.1002/prot.25803
Subject(s) - representation (politics) , crystallography , combinatorics , composition (language) , helix (gastropod) , protein secondary structure , folding (dsp implementation) , mathematics , chemistry , topology (electrical circuits) , computer science , biology , biochemistry , ecology , linguistics , philosophy , electrical engineering , politics , snail , political science , law , engineering
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.