Relaxation-matrix formalism for rotating-frame spin-lattice proton NMR relaxation and magnetization transfer in the presence of an off-resonance irradiation field.

The derivation of a generalized relaxation matrix equation for the off-resonance rotating-frame spin-lattice experiment, representing N macromolecular components, is presented. The applicability of the derived formalism was demonstrated using water proton off-resonance rotating-frame spin-lattice relaxation data obtained for calf lens cortical and nuclear homogenates, a tissue system characterized by the presence of both mobile and solid-like protein domains, whose relative amounts vary in a protein-concentration-dependent manner. Protein concentration and temperature were utilized as variables in the magnetization-transfer experiments. Curve fitting to obtain the relevant magnetization-transfer parameters was accomplished by simulated annealing and the method of steepest descents. In all cases, the best fit, as reflected by the smallest root-mean-square deviation, was obtained by assuming the presence of three components representing bulk-water and mobile and solid-like macromolecular components, characterized by Lorentzian (water and mobile protein) and Gaussian proton resonance lineshapes (solid-like protein). A two-component relaxation model gave unsatisfactory fits. Dilution of nuclear homogenate resulted in physically realistic changes in the derived magnetization-transfer parameters, which included a decrease in the fraction of solid-like protein, in agreement with previously published 13C NMR studies. Changes in magnetization-transfer parameters occurred as a result of the cold cataract phase transition in nuclear homogenate. The utility and limitations of the derived formalism are discussed.