The concept of effective correlation times for describing backbone motions in proteins.: Part I.: A residue-per-residue self-consistent analysis of multifield 15N relaxation parameters

This study is an extension of a recent work (Canet D, Barthe P, Mutzenhardt R Roumestand C. 2001. A comprehensive analysis of multifield N-15 relaxation parameters in proteins: Determination of N-15 chemical shift anisotropies. J Am Chem Soc 123:4567-4576) dealing with the exploitation of the three classical N-15 relaxation parameters (the longitudinal relaxation rate, R-1, the transverse relaxation rate, R-2, and the H-1-N-15 cross-relaxation rate, sigma(NH)) measured at several magnetic fields (at least two) in uniformly N-15-labeled proteins (the chosen example is the C12A-p8(MTCPI) protein whose relaxation parameters have been measured at five different fields). R-2 is iteratively corrected for exchange, so that the three parameters provide consistently the NH dipolar and N-15 csa (chemical shift anisotropy) contributions. The dipolar spectral densities are analyzed, residue by residue, according to the functional form a(d) + b(d)/1+omega(2)tau(eff)(2) (d for dipolar), where tau(eff) is an (effective) correlation time associated with the slow motion(s) sensed by the NH vector at the level of the residue to which it belongs. in comparison with the Lipari-Szabo approach, the coefficient b(d) can be identified with 2K(d)tau(eff)S(2), S being the generalized order parameter and K-d reflecting the amplitude of the dipolar mechanism (which, besides constants, involves 1/r(NH)(6)); a(d) is associated with fast local motions. The csa spectral densities appearing in the expressions of R-1 and R-2 can be analyzed according to b(csa)/1+omega(2)tau(eff)(2); b(csa); is proportional to b(d) (the proportionality factor depending on molecular quantities) and can yield N-15 csa values from the r(NH) value and from the knowledge of the angle between the two relevant tensors. Uncertainties are such that it is impossible (at least with the present data) to conclude about a possible variation of N-15 csa values along the protein backbone. (C) 2005 Wiley Periodicals, Inc.