Direct Measurement of Dynamic Frequency Shift Induced by Cross‐Correlations in ¹⁵N‐Enriched Proteins

Abstract

We describe a new NMR experimental scheme that allows the direct determination of the dynamic frequency shift induced by chemical shift anisotropy/dipolar interaction (CSA/DD) cross-correlations in 15N-enriched proteins. Its principle consists of comparing two rates of polarisation transfer between the amide proton and nitrogen. The first rate, which is independent of the dynamic frequency shift, is based on a selective Hartmann-Hahn coherence transfer. The second rate, which depends on the dynamic frequency shift, is based on a free evolution of the transverse magnetisation. We report experimental validation of this approach by measuring the average dynamic frequency shift due to CSA/DD cross-correlations in the calcium-binding protein D9k. The method may also be applicable to the measurement of dynamic frequency shift induced by cross-correlations between the Curie spin and dipolar interactions.

Dipolar dynamic frequency shifts in multiple-quantum spectra of methyl groups in proteins: correlation with side-chain motion

“…Peak positions were determined by fitting cross-peak contours to elliptical shapes starting at 50% peak intensity, using the interactive peak-picking program PIPP 25 or via parabolic interpolation of intensities in the vicinity of the peak maximum; very similar results were obtained in both cases. The molecular tumbling correlation time of protein L in D 2 O at 25°C ( C D 4.97 ns; assumed isotropic) was obtained from a C value calculated from 15 N relaxation measurements performed on samples dissolved in H 2 O, as described previously, 21 and subsequently scaled by the ratio of viscosities of D 2 O to H 2 O at 25°C. Viscosity ratios can be obtained from tabulated values 26 or experimentally from ratios of translational diffusion constants measured for protein L samples in H 2 O and D 2 O at 25°C; ratios from either approach are in quantitative agreement.…”

“…for a 13 C-2 H spin-system the central carbon line shift is of the order of 6 Hz in the slowmotion limit at 600 MHz) and are readily observed in terms of an asymmetry in the multiplet structure. In the case of pairs of spin-1/2 particles, such as 15 N-1 H spin systems attached to macromolecules such as proteins, dipolar/chemical shift anisotropy interference gives rise to small shifts in multiplet components, of the order of several tenths of a hertz, that can be quantified. 14,15 These effects are of particular importance in the context of the measurement of residual dipolar couplings in molecules that are aligned via magnetic susceptibility anisotropy because they are of similar size to the couplings themselves.…”

“…In the case of pairs of spin-1/2 particles, such as 15 N-1 H spin systems attached to macromolecules such as proteins, dipolar/chemical shift anisotropy interference gives rise to small shifts in multiplet components, of the order of several tenths of a hertz, that can be quantified. 14,15 These effects are of particular importance in the context of the measurement of residual dipolar couplings in molecules that are aligned via magnetic susceptibility anisotropy because they are of similar size to the couplings themselves. 14 The relaxation properties of transitions in degenerate spin systems such as those in methyl groups are significantly influenced by cross-correlated dipole-dipole interactions.…”

Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software

“…Because the processing of correlation functions is done in full generality, the resulting relaxation rates also contain imaginary contributions, called dynamic frequency shifts (DFS), which originate from the fact that the imaginary part of the Fourier transform (17) is in general small, but non-zero [29]. Obtaining expressions for the DFS is even more difficult than for the relaxation rates, because the spectral density J(x) can no longer be assumed to be an even function, and the signs of frequencies therefore need to be controlled at every stage in the calculation.…”

“…Obtaining the correct argument signs in the correlation function is crucially important in the ongoing hunt for the experimental observation of relaxation-induced dynamic frequency shifts [29]. If we now choose to neglect the DFS and put the scalar coupling constant a to zero, we obtain the textbook rates for longitudinal relaxation, longitudinal cross-relaxation and transverse relaxation [31]:…”