Measuring 1H-1H and 1H-13C RDCs in methyl groups: example of pulse sequences with numerically optimized coherence transfer schemes

The optimization of coherence-transfer pulse-sequence elements (CTEs) is the most challenging step in the construction of heteronuclear correlation NMR experiments achieving sensitivity close to its theoretical maximum (in the absence of relaxation) in the shortest possible experimental time and featuring active suppression of undesired signals. As reported in the present article, this complex optimization problem in a space of high dimensionality turns out to be numerically tractable. Based on the application of molecular dynamics in the space of pulse-sequence variables, a general method is proposed for constructing optimized CTEs capable of transferring an arbitrary (generally non-Hermitian) spin operator encoding the chemical shift of heteronuclear spins to an arbitrary spin operator suitable for signal detection. The CTEs constructed in this way are evaluated against benchmarks provided by the theoretical unitary bound for coherence transfer and the minimal required transfer time (when available). This approach is used to design a set of NMR experiments enabling direct and selective observation of individual 1H-transitions in 13C-labeled methyl spin systems close to optimal sensitivity and using a minimal number of spectra. As an illustrative application of the method, optimized CTEs are used to quantitatively measure 1H-1H and 1H-13C residual dipolar couplings (RDCs) in a 17 kDa protein weakly aligned by means of Pf1 phages.