Accurate Electron-Nucleus Distances from Paramagnetic Relaxation Enhancements

Measurements of paramagnetic relaxation enhancements (PREs) in ¹H NMR spectra are an important tool to obtain long-range distance information in proteins, but quantitative interpretation is easily compromised by nonspecific intermolecular PREs. Here we show that PREs generated by lanthanides with anisotropic magnetic susceptibilities offer a route to accurate calibration-free distance measurements. As these lanthanides change ¹H chemical shifts due to pseudocontact shifts, the relaxation rates in the paramagnetic and diamagnetic state can be measured with a single sample that simultaneously contains the protein labeled with a paramagnetic and a diamagnetic lanthanide ion. Nonspecific intermolecular PREs are thus automatically subtracted when calculating the PREs as the difference in nuclear relaxation rates between paramagnetic and diamagnetic protein. Although PREs from lanthanides with anisotropic magnetic susceptibilities are complicated by additional cross-correlation effects and residual dipolar couplings (RDCs) in the paramagnetic state, these effects can be controlled by the choice of lanthanide ion and experimental conditions. Using calbindin D_9k with erbium, we succeeded in measuring intramolecular PREs with unprecedented accuracy, resulting in distance predictions with a root-mean-square-deviation of <0.9 Å in the range 11-24 Å.