Magnetic Field Dependence of Nitrogen−Proton J Splittings in 15N-Enriched Human Ubiquitin Resulting from Relaxation Interference and Residual Dipolar Coupling

Abstract

One-bond 1 J NH couplings have been measured in 15 N-enriched human ubiquitin and range from 91.1 to 95.6 Hz. Measurements have been carried out using two different methods and at 1 H frequencies of 360, 500, and 600 MHz. The best method yields a precision of ca 0.02 Hz, and permits reliable measurement of the small changes (<0.3 Hz) in 1 J NH splitting that occur when the magnetic field strength is increased from 8.5 to 14 T. The dependence of the 1 J NH splittings on the strength of the static magnetic field originates from two sources: a dynamic frequency shift caused by interference of the 15 N chemical shift anisotropy and the 15 N− 1 H dipolar coupling relaxation mechanisms, and a dipolar contribution caused by a small degree of alignment resulting from the anisotropic magnetic susceptibility of the diamagnetic protein. Best fitting of the measured data yields an orientation-independent decrease of 0.11 Hz in the 1 J NH splittings at 600 MHz relative to 360 MHz, in perfect agreement with theoretical predictions for the magnitude of the dynamic frequency shift. When fitting the measured J values to the theoretical model, containing only the dynamic frequency shift and dipolar coupling contributions, the reduced error in the statistical F-test is smaller than one, assuming a 0.02 Hz rms error in the experimental 1 J NH splittings. This confirms that the random error in the measured data J NH values does not exceed 0.02 Hz, and that effects other than the dipolar coupling and dynamic frequency shift are not detectable. Dependence of the change in 1 J NH on the orientation of the N−H bond vector within the molecular frame yields experimentally determined axial and rhombic magnetic shielding susceptibility anisotropies of −2.1 × 10 - 28 and 0.7 × 10 - 28 cm 3 /molecule, respectively. A small improvement of the fit is observed when the amide proton is positioned at a distance above or below the C‘ i - 1 −N i −C α i plane which is about five times smaller than the out-of-plane distance predicted by ab initio calculations on a dipeptide analog in vacuum.