Open AccessScaling laws of graphs of 3D protein structures
Author(s) -
Jure Pražnikar
Publication year - 2021
Publication title -
journal of bioinformatics and computational biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 1757-6334
pISSN - 0219-7200
DOI - 10.1142/s021972002050050x
Subject(s) - radius of gyration , exponent , scaling , mathematics , statistical physics , macromolecule , radius , graph , eccentricity (behavior) , combinatorics , geometry , physics , chemistry , computer science , polymer , law , linguistics , philosophy , biochemistry , computer security , nuclear magnetic resonance , political science
The application of graph theory in structural biology offers an alternative means of studying 3D models of large macromolecules such as proteins. The radius of gyration, which scales with exponent [Formula: see text], provides quantitative information about the compactness of the protein structure. In this study, we combine two proven methods, the graph-theoretical and the fundamental scaling laws, to study 3D protein models. This study shows that the mean node degree (MND) of the protein graphs, which scales with exponent 0.038, is scale-invariant. In addition, proteins that differ in size have a highly similar node degree distribution. Linear regression analysis showed that the graph parameters (radius, diameter, and mean eccentricity) can explain up to 90% of the total radius of gyration variance. Thus, the graph parameters of radius, diameter, and mean eccentricity scale match along with the same exponent as the radius of gyration. The main advantage of graph eccentricity compared to the radius of gyration is that it can be used to analyze the distribution of the central and peripheral amino acids/nodes of the macromolecular structure.