Zero-quantum stochastic dipolar recoupling in solid state nuclear magnetic resonance

We present the theoretical description and experimental demonstration of a zero-quantum stochastic dipolar recoupling (ZQ-SDR) technique for solid state nuclear magnetic resonance (NMR) studies of C-13-labeled molecules, including proteins, under magic-angle spinning (MAS). The ZQ-SDR technique combines zero-quantum recoupling pulse sequence blocks with randomly varying chemical shift precession periods to create randomly amplitude-and phase-modulated effective homonuclear magnetic dipole-dipole couplings. To a good approximation, couplings between different C-13 spin pairs become uncorrelated under ZQ-SDR, leading to spin dynamics (averaged over many repetitions of the ZQ-SDR sequence) that are fully described by an orientation-dependent N x N polarization transfer rate matrix for an N-spin system, with rates that are inversely proportional to the sixth power of internuclear distances. Suppression of polarization transfers due to non-commutivity of pairwise couplings (i.e., dipolar truncation) does not occur under ZQ-SDR, as we show both analytically and numerically. Experimental demonstrations are reported for uniformly C-13-labeled L-valine powder (at 14.1 T and 28.00 kHz MAS), uniformly C-13-labeled protein GB1 in microcrystalline form (at 17.6 T and 40.00 kHz MAS), and partially labeled C-13-labeled protein GB1 (at 14.1 T and 40.00 kHz MAS). The experimental results verify that spin dynamics under ZQ-SDR are described accurately by rate matrices and suggest the utility of ZQ-SDR in structural studies of C-13-labeled solids. [http://dx.doi.org/10.1063/1.4749258]