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

Abstract

One-bond 1JNH couplings have been measured in 15N-enriched human ubiquitin and range from 91.1 to 95.6 Hz. Measurements have been carried out using two different methods and at 1H 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 1JNH splitting that occur when the magnetic field strength is increased from 8.5 to 14 T. The dependence of the 1JNH splittings on the strength of the static magnetic field originates from two sources: a dynamic frequency shift caused by interference of the 15N chemical shift anisotropy and the 15N−1H 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 1JNH 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 1JNH splittings. This confirms that the random error in the measured data JNH 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 1JNH 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 cm3/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−Ni−Cαi plane which is about five times smaller than the out-of-plane distance predicted by ab initio calculations on a dipeptide analog in vacuum.