Symmetry-based dipolar recoupling by optimal control: Band-selective experiments for assignment of solid-state NMR spectra of proteins

We present design of novel low-power homonuclear dipolar recoupling experiments for magic-angle-spinning solid-state NMR studies of proteins. The pulse sequences are developed by combining principles of symmetry-based dipolar recoupling and optimal control-based pulse sequence design. The scaffold of the pulse sequences is formed by known $CN$-type recoupling sequences, while the intrinsic sequence elements are designed using optimal control. This procedure allows for the development of high-performance pulse sequences demanding significantly weaker rf fields than previous symmetry-based pulse sequences while compensating for rf inhomogeneity and providing excitation over relevant ranges of chemical shifts for biological applications. The new recoupling experiments, referred to as optimal control $CN$ $(COCN)$⁠, are demonstrated numerically and experimentally by two-dimensional (2D) $C13–C13$ and three-dimensional (3D) $N15–C13–C13$ chemical shift correlation experiments on uniformly $C13$⁠, $N15$-labeled ubiquitin. Exploiting the double-quantum, band-selective dipolar recoupling properties of the $COCN$ experiments, we demonstrate significant sensitivity enhancement for 2D and 3D correlation spectra showing exclusively one- or two-bond correlations.