A Diffusion Equation Approach to Spin Diffusion in Biomolecules

A theoretical description of ‘H‘H dipolar nuclear spin relaxation in a multispin system has been worked out by forming a diffusion equat ion for a one-dimensional chain of equidistant spins. The spin-diffusion equat ion is formed from first principles by assuming nearest neighbor interactions for a molecule undergoing isotropic random reorientation. This equat ion descr ibes dilfusion only in the long correlation limit (for WT, > 1.118 ) and is solved for driven NOE experiments, for spins in a chain of infinite length (0 i x < cc ), or for spins in a chain of finite length (0 c x < L). The solutions are obtained using the method of the Laplace transform for specif ied initial and boundary conditions. The observed selectivity of the NOE transfer in driven NOE experiments on a biomolecule which has a correlation factor wr, 3 is indeed in conformity with the predictions obtained from the spin-diffusion equation. o 1989 Academic press, hc.