Model-free analysis of stretched relaxation dispersions

Nuclear magnetic relaxation dispersion (NMRD) measurements can provide valuable information about the dynamics and structure of macromolecular solutions and other complex fluids. A large number of 1H NMRD studies of water in concentrated protein solutions and in semisolid biological samples have been reported. The observed dispersion usually extends over a wide frequency range and then cannot be described by a Lorentzian spectral density function. We propose here a model-free approach for analyzing such stretched dispersion profiles. Unlike the traditional empirical fitting procedures, the model-free approach is based on rigorous theory and produces parameters with well-defined physical significance. The model-free approach is validated with the aid of synthetic relaxation data, showing that it is robust and accurate, and is then applied to new water 1H NMRD data from solutions of the protein bovine pancreatic trypsin inhibitor (BPTI). By separating the static and dynamic information content of the relaxation dispersion, the model-free analysis shows that the dramatic salt effect observed in BPTI solutions is due almost entirely to a slowing down of protein rotation with little change of protein structure. An analysis of the same data in terms of the empirical dispersion function used in most 1H NMRD studies leads to a qualitatively different picture. We demonstrate that this widely used dispersion function is unphysical and that its parameters do not have the physical meaning usually ascribed to them.