ANALYSIS OF INTERNALLY RESTRICTED CORRELATED ROTATIONS IN PEPTIDES AND PROTEINS USING C-13 AND N-15 NMR RELAXATION DATA

The study of protein internal motions from analysis of C-13 and N-15 N MR relaxation data and auto- and crosscorrelation spectral densities i s being pursued in many labs. Model-free approaches and derived motion al order parameters are normally used to interpret NMR relaxation data and internal mobility in proteins and peptides. Correlated motions ca n substantially modify the behavior of NMR auto- and cross-correlation spectral density functions and the values of derived motional order p arameters. Here, a simple model is proposed to describe small amplitud e (less than about 60 degrees or 1 rad), internally restricted correla ted rotations (IRCR) in peptides and proteins in order to analyze orde r parameters. Bond rotations are represented by vectors whose motions are correlated by a correlation coefficient, c(ij), which is the cosin e of the angle between these vectors. Order parameters for NH, CalphaH and CbetaH bond motions have been calculated from molecular dynamics simulations performed on short peptides with well-defined alpha-helix and beta-sheet structures in order to derive values for c(ij). General equations relating dipolar auto- and cross-correlation order paramete rs for CalphaH, CbetaH, and NH bonds to c(ij) have been derived. The s ign of c(ij) depends on the specific motional correlation within a par ticular molecular conformation. For glycine phi, psi rotations, the si gn of c(ij) can be derived from analysis of dipolar auto- and cross-co rrelation order parameters. Long-range motional correlations are obser ved with hydrogen bonds modulating internal mobility. In general, back bone NH order parameters, S-NH(2), are more sensitive to structure tha n are CalphaH order parameters, S-CH(2). S-CH(2) is increased and (SNH )-N-2 is decreased when correlation coefficients c(psi phi) and c(phi psi) are decreased and increased, respectively.