Theory of relaxation of mobile water protons induced by protein NH moieties, with application to rat heart muscle and calf lens homogenates.

Kimmich and co-workers (cf., Winter, F., and R. Kimmich. 1982. Biochim. Biophys. Acta. 719:292-298) discovered peaks in the magnetic field-dependent longitudinal relaxation rate (1/T1) of water protons of muscle tissue, cells, and dehydrated protein in the field range 0.5-5 MHz (proton Larmor frequency), and argued that the peaks resulted from cross relaxation associated with quadrupolar splittings of the 14N nuclei of protein NH groups. More recently, analogous peaks were found in homogenates of calf eye lens (Beaulieu, C.F., J.I. Clark, R.D. Brown III, M. Spiller, and S. H. Koenig, 1987. Abstr. Soc. Magn. Res. Med., 6th, New York. 598-599), which are essentially concentrated protein solutions, and were measured with sufficient precision to allow resolution of the relaxation spectra into several peaks and the intrinsic linewidths to be determined. Here, we analyze these relaxation spectra, as well as earlier data on rat heart (Koenig, S. H., R. D. Brown III, D. Adams, D. Emerson, and C. G. Harrison. 1984. Invest. Radiol. 19:76-81) in some detail, and suggest a specific pathway for the cross relaxation to which we apply the theory of relaxation quantitatively. The view that emerges is that, at fields such that the proton Zeeman energy of the NH protons matches an 14N quadrupolar splitting, relaxation of these protons is by cross relaxation to the 14N nuclei which in turn transfer excess energy to the protein. The correlation time for the NH proton interaction is the T2 of the 14N nuclei, approximately 10(-6) s, whereas T1 of the NH protons is approximately 1.25 ms. At these energy level crossings, the NH protons become relaxation sinks for protons of rapidly exchanging (-3 x 109 s-1) water molecules hydrogen bonded to the same backbone carbonyl oxygens as the NH protons. The lifetime of this hydrogen bond (-3 x 10-10 s) then becomes the correlation time for the water proton-NH proton interaction which, though short, is much longer than the analogous correlation time (-5 x 10-12 s) in pure water; the enhanced interaction results in peaks in the field-dependent 1/ T, of the solvent protons. There are few data on the lifetime of such bonds, but the results here conform with the recent considerations of Bennett, H. F., R. D. Brown III, S. H. Koenig, and H. M. Swartz. 1987. Magn. Reson. Med. 4:93-111, regarding hydrogen bond lifetimes for water molecules bound to macromolecules. The recent precise field-dependent relaxation data, here combined with both a quantitative theory and the fact that the magnitude of the 14N peaks is very concentration sensitive, allow, at least for lens proteins, a study of protein-protein interactions difficult to investigate by other methods.