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On a characterization of the folding of proteins
Author(s) -
Randić Milan,
Krilov Goran
Publication year - 1999
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1999)75:6<1017::aid-qua6>3.0.co;2-c
Subject(s) - eigenvalues and eigenvectors , folding (dsp implementation) , distance matrix , characterization (materials science) , measure (data warehouse) , quotient , protein folding , matrix (chemical analysis) , combinatorics , euclidean distance , mathematics , chemistry , physics , geometry , data mining , computer science , quantum mechanics , biochemistry , electrical engineering , engineering , optics , chromatography
We consider a characterization of the folding of 3‐D model proteins. Using as the input the geometry of molecules, we first construct a distance/distance matrix in which element i , j is given by the quotient of the Euclidean and the graph theoretical distance between the two vertices. The leading eigenvalue of the D / D matrix gives a measure of the folding of the protein structure. Using higher powers of the elements of D / D matrices, we generate the corresponding leading eigenvalue λ( k ) for different exponents ( k =1, 2, 3,…). So, derived invariants represent a characterization of the folding of a structure—here, model proteins. The derived invariants are analogous to the characterization of proteins based on the average distance, referred to as a protein profile. The folding index ϕ=λ/ n , that is, the leading eigenvalue, is normalized to the number of “points” representing the structure. Structures that are more folded have a smaller folding index. We illustrate the use of the folding indices to measure the degree of similarity of molecules. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 1017–1026, 1999