Correlated Motions Analysis from Molecular Dynamics Trajectories: Statistical Accuracy on the Determination of Canonical Correlation Coefficients

摘要

A numerical study of the accuracy on the determination of a unique global canonical correlation coefficient C between two groups of random variables is presented as a function of the number of variables of both groups (n and m, respectively), of the sampling size N and of the actual level of correlation C between the groups. The method used to estimate C has been already described (Briki, F.; Genest, D. Biophys Chem 1994, 52, 35-43; and J Biomol Struct Dynam 1995, 12, 1063-1082), and is implemented in the home made program TECOR. To check the accuracy on the estimation of C for given values of n, m, N, and C, samples of the random variables are synthesized (with known C), then TECOR is used to get an estimated value M of the global canonical coefficient, which is compared to the actual value C. Special attention is paid to the application of the method to the analysis from molecular dynamics simulation trajectories of concerted motions of two groups of atoms (not larger than about 20 atoms) in the course of internal deformation of biopolymers. It is found that there is a good agreement between M and C for moderate and high correlation (C>=0.35), provided that at least about 2000 configurations are stored during the molecular dynamics simulation. If C is smaller than 0.35, the method can overestimate its value if the number of configurations is not increased, especially for larger groups.