Analytical treatment of spin diffusion in a three-spin (AMX and ABX) system in the long-correlation-time (ω₀gt_c,»1) limit, for estimation of internuclear distances in macromolecules

Abstract

An analytical treatment of the spin-diffusion phenomenon in the NOE spectra of a homonuclear three-spin system in the long correlation time limit is presented. Explicit expressions for the transient NOE as a function of time have been obtained in a closed form for both weakly and strongly coupled spin systems. It is shown that the total NOE at a particular site can be effectively partitioned into two parts, the first part representing a "direct" contribution whose buildup is similar to the NOE in a two-spin case (at least in the initial stages) and the second part representing a "diffusive" contribution which is common to all the NOES. This has given insights into the role of spin diffusion in the shaping of NOE build-up curves and their geometry dependence. For the cases of uncoupled and weakly coupled spin systems an analysis of intrinsic errors in the estimation of interproton distances using the initial-slope approximation has been performed. The errors appear to be significantly high within the experimental ranges of mixing time. We suggest an alternative method whereby errors can be reduced, almost by an order of magnitude, and this involves estimating distances from the ? intercept of a linear least-squares fit of the NOE/t vs t data. This method is accurate even at longer mixing times. Experimental data supporting the above conclusions are presented.