Detection of long-range concerted motions in protein by a distance covariance

We asses the ability of a distance correlation coefficient (DiCC), calculated from distance covariance, for detecting long-range concerted motion in proteins. We establish a set of criteria for ideal correlation coefficient values based on the coefficient of determination in multi-dimension, R². We compare in detail DiCC and conventional coefficients against these criteria. We demonstrate that in contrast to conventional correlation coefficients, which capture long-distance correlation adequately only with certain restrictions in multi-dimension, DiCC reflects appropriate correlation in both one- and multi-dimension. Finally we demonstrate the usefulness of DiCC for assessing long-distance correlated fluctuation in protein dynamics.