Spin Diffusion in Biomolecules. Effect of Higher-Order Terms in Transient NOE Experiments

The proton-proton nuclear Overhauser effect in recent years has become a powerful tool for the study of solution structure of organic and bimolecular (1-4). The transfer of magnetization from one spin to another, monitored as NOE, crucially depends on motional processes governing relaxation and interspin distances. The proton-proton NOE is positive for molecules, which reorient at a rate fast compared to the Larmor frequency and negative for molecules, which reorient at a slower rate (5). For large molecules, such as biomolecules, generally the later situation prevails. Under this condition, the magnetization is also able to migrate to long distances within the molecule by a hopping mechanism termed spin diffusion. It has been shown recently that a second-order diffusion equation can indeed be formulated for a one-dimensional chain of equidistant spins to describe spin diffusion in biomolecules (6).This spindiffusion equation was solved analytically for the driven NOE experiment, in which the magnetization of a spin is continuously saturated. It was also shown that the second-order diffusion equation describes adequately the magnetization-transport process in driven NOE experiment