A master-equation approach to the description of proton-driven spin diffusion from crystal geometry using simulated zero-quantum lineshapes

Abstract

Measurements of proton-driven carbon-13 spin diffusion (PDSD) by NMR spectroscopy are a central component of structural analyses of biomolecules in the solid-state. However, the quantitative link between experimental PDSD data and structural information is difficult to make. Here we observe that a master-equation approach can be used to model full PDSD dynamics accurately in polycrystalline ¹³C-labelled L-histidine·HCl·H₂O under magic-angle spinning. In the master-equation approach, PDSD rates and effective dipolar couplings are related by a function of the carbon–carbon zero-quantum lineshapes; we find that numerical simulations of the zero-quantum lineshapes are sufficiently accurate so as to allow the calculation of PDSD rates that are in good agreement with the measured rates, directly from crystal geometry and with no adjustable parameters. Finally, using carbon–carbon internuclear distances we illustrate the potential of the master-equation approach for structural studies. Generalisation of these results to proton-driven carbon-13 spin diffusion in more complex molecular systems is readily envisaged.