Dipolar truncation in magic-angle spinning NMR recoupling experiments

Abstract

Quantitative solid-state NMR distance measurements in strongly coupled spin systems are often complicated due to the simultaneous presence of multiple noncommuting spin interactions. In the case of zeroth-order homonuclear dipolar recoupling experiments, the recoupled dipolar interaction between distant spins is attenuated by the presence of stronger couplings to nearby spins, an effect known as dipolar truncation. In this article, we quantitatively investigate the effect of dipolar truncation on the polarization-transfer efficiency of various homonuclear recoupling experiments with analytical theory, numerical simulations, and experiments. In particular, using selectively (13)C-labeled tripeptides, we compare the extent of dipolar truncation in model three-spin systems encountered in protein samples produced with uniform and alternating labeling. Our observations indicate that while the extent of dipolar truncation decreases in the absence of directly bonded nuclei, two-bond dipolar couplings can generate significant dipolar truncation of small, long-range couplings. Therefore, while alternating labeling alleviates the effects of dipolar truncation, and thus facilitates the application of recoupling experiments to large spin systems, it does not represent a complete solution to this outstanding problem.

FIG. 1.

Labeling schemes employed in the model tripeptides used to illustrate the effect of dipolar truncation. AGG-2 $\left(\text{Ala-}\left[2\text{-}{}^{13}\text{C}\right]\text{Gly-}\left[1\text{-}{}^{13}\text{C}\right]\text{Gly}\right)$ is a two-spin system with a dipolar coupling of 66 Hz, corresponding to a distance of 4.86 Å between nuclei 1 and 2. AGG-3 $\left(\text{Ala-}\left[1,2\text{-}{{}^{13}\text{C}}_2\right]\text{Gly-}\left[1\text{-}{}^{13}\text{C}\right]\text{Gly}\right)$ is a three-spin system formed by adding a third labeled nucleus (spin 3) to AGG-2, forming a strong dipolar coupling of 2.15 kHz with spin 2. The coupling between spins 1 and 3 is 150 Hz. GGV-3 $\left(\left[1\text{-}{}^{13}\text{C}\right]\text{Val-}\left[2\text{-}{}^{13}\text{C}\right]\text{Gly-}\left[1\text{-}{}^{13}\text{C}\right]\text{Gly}\right)$ is a three-spin system similar to AGG-3, but with the third labeled nucleus (spin 3) two bonds away from spin 2. GGV-3 has a weak coupling of 80 Hz corresponding to a distance of 4.56 Å between spins 1 and 2, and a medium coupling of 550 Hz corresponding to a distance of 2.43 Å between spins 2 and 3.

FIG. 2.

Simulated buildup curves of magnetization transfer from spin 2 (blue) to spin 1 (red) and spin 3 (green) in model spin systems AGG-2, AGG-3, and GGV-3 with various recoupling sequences. ZQ sequences: RFDR, ${\omega }_r/2\pi =10\text{kHz}$, ${\omega }_1=50\text{kHz}$; $\text{SR}{4}_4^1$, ${\omega }_r/2\pi =30\text{kHz}$, ${\omega }_1=30\text{kHz}$. DQ sequence: $\text{R}{12}_2^5$, ${\omega }_r/2\pi =15\text{kHz}$, ${\omega }_1=90\text{kHz}$. Mixed sequence: DRAWS, ${\omega }_r/2\pi =10\text{kHz}$, ${\omega }_1=85\text{kHz}$.

FIG. 3.

Cross sections of 2D RFDR correlation spectra through the diagonal peak of spin 2 for three different mixing times. The arrow indicates the cross peak between spin 2 (a $\text{C}\alpha$ carbon at 44 ppm) and the distant spin 1 (a carboxyl carbon at 175 ppm). The intensity of this cross peak is diminished in AGG-3 and GGV-3 compared to AGG-2, demonstrating the attenuation of polarization transfer due to the dipolar truncation effect.

FIG. 4.

Top: Experimental RFDR buildup curves for AGG-2, AGG-3, and GGV-3. Each data point is the integrated peak intensity of 2D correlation peaks normalized to the diagonal peak at zero mixing. RFDR experiments employed 50 kHz ${}^{13}\text{C}\pi$ pulses and 115 and 90 kHz ${}^1\text{H}$ decoupling fields during the mixing period and were performed at a MAS frequency of 8.929 kHz. Bottom: Numerical simulations of polarization transfer in AGG-2, AGG-3, and GGV-3 showing long-term behavior of RFDR mixing. These simulations included ${}^{13}\text{C}$ CSA parameters, eight neighboring ${}^1\text{H}$ spins, and experimental parameters identical to those performed in our experiments.