Dual-band selective double cross polarization for heteronuclear polarization transfer between dilute spins in solid-state MAS NMR

Solid-State NMR: Methods for Biological Solids

In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.

A robust heteronuclear dipolar recoupling method comparable to TEDOR for proteins in magic-angle spinning solid-state NMR

In this letter, we propose a robust heteronuclear dipolar recoupling method for proteins in magic-angle spinning (MAS) solid-state NMR. This method is as simple, robust and efficient as the well-known TEDOR in the aspect of magnetization transfer between ¹⁵N and ¹³C. Deriving from our recent band-selective dual back-to-back pulses (DBP) (Zhang et al., 2016), this method uses new phase-cycling schemes to realize broadband DBP (Bro-DBP). For broadband ¹⁵N-¹³C magnetization transfer (simultaneous ¹⁵N→¹³C' and ¹⁵N→¹³Cα), Bro-DBP has almost the same ¹⁵N→¹³Cα efficiency while offers 30-40% enhancement on ¹⁵N→¹³C' transfer, compared to TEDOR. Besides, Bro-DBP can also be used as a carbonyl (¹³C')-selected method, whose ¹⁵N→¹³C' efficiency is up to 1.7 times that of TEDOR and is also higher than that of band-selective DBP. The performance of Bro-DBP is demonstrated on the N-formyl-[U-¹³C,¹⁵N]-Met-Leu-Phe-OH (fMLF) peptide and the U-¹³C, ¹⁵N labeled β1 immunoglobulin binding domain of protein G (GB1) microcrystalline protein. Since Bro-DBP is as robust, simple and efficient as TEDOR, we believe it is very useful for protein studies in MAS solid-state NMR.

Rapid convergence of optimal control in NMR using numerically-constructed toggling frames

We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.

Band-selective heteronuclear dipolar recoupling with dual back-to-back pulses in rotating solids

We propose a robust band-selective heteronuclear ¹⁵N-¹³C recoupling method using dual back-to-back (BABA) pulses (DBP). It contains four 90° pulses in each rotor period and corresponding phase cycling on each channel (¹³C and ¹⁵N). DBP aims at rapid band-selective heteronuclear magnetization transfer between ¹⁵N and ¹³Cα/¹³C', whose efficiency is close to that of the well-known SPECIFIC CP in membrane proteins with relatively short relaxation time in rotating frame (T_1ρ). Compared to SPECIFIC CP, DBP is very simple to set up and highly robust to RF variations. Thus, it can reduce the efforts in experimental optimization, especially for low-sensitive samples, and is very suitable for long-time or quantitative experiments. The efficacy of DBP is demonstrated by the E. coli diacylglycerol kinase (DAGK) proteoliposome. We anticipate that DBP would be useful for (segments of) membrane proteins that undergo the μs-ms timescale motions in magic-angle spinning (MAS) solid-state NMR.

Hybridizing cross-polarization with NOE or refocused-INEPT enhances the sensitivity of MAS NMR spectroscopy

Heteronuclear cross polarization (CP) has been commonly used to enhance the sensitivity of dilute low-γ nuclei in almost all solid-state NMR experiments. However, CP relies on heteronuclear dipolar couplings, and therefore the magnetization transfer efficiency becomes inefficient when the dipolar couplings are weak, as is often the case for mobile components in solids. Here, we demonstrate methods that combine CP with heteronuclear Overhauser effect (referred to as CP-NOE) or with refocused-INEPT (referred to as CP-RINEPT) to overcome the efficiency limitation of CP and enhance the signal-to-noise ratio (S/N) for mobile components. Our experimental results reveal that, compared to the conventional CP, significant S/N ratio enhancement can be achieved for resonances originating from mobile components, whereas the resonance signals associated with rigid groups are not significantly affected due to their long spin-lattice relaxation times. In fact, the S/N enhancement factor is also dependent on the temperature, CP contact time as well as on the system under investigation. Furthermore, we also demonstrate that CP-RINEPT experiment can be successfully employed to independently detect mobile and rigid signals in a single experiment without affecting the data collection time. However, the resolution of CP spectrum obtained from the CP-RINEPT experiment could be slightly compromised by the mandatory use of continuous wave (CW) decoupling during the acquisition of signals from rigid components. In addition, CP-RINEPT experiment can be used for spectral editing utilizing the difference in dynamics of different regions of a molecule and/or different components present in the sample, and could also be useful for the assignment of resonances from mobile components in poorly resolved spectra. Therefore, we believe that the proposed approaches are beneficial for the structural characterization of multiphase and heterogeneous systems, and could be used as a building block in multidimensional solid-state NMR experiments.

MAS solid state NMR of proteins: simultaneous ¹⁵N- ¹³CA and ¹⁵N- ¹³CO dipolar recoupling via low-power symmetry-based RF pulse schemes

The generation of efficient RN n (ν)s,(ν)k symmetry-based low-power RF pulse schemes for simultaneous (15)N-(13)CA and (15)N-(13)CO dipolar recoupling is demonstrated. The method involves mixing schemes employing phase and amplitude-modulated dual band-selective 180° pulses as basic "R" element and tailoring of the RF field-modulation profile of the 180° pulses so as to obtain efficient magnetisation transfer characteristics over the resonance offset range of the nuclei involved. Mixing schemes leading to simultaneous (15)N-(13)CA and (15)N-(13)CO dipolar recoupling would permit the one-shot acquisition of different chemical shift correlation spectra that are typically utilized for protein backbone resonance assignments and thereby save data acquisition time. At representative MAS frequencies the efficacies of the mixing schemes presented here have been experimentally demonstrated via the simultaneous acquisition of {3D CONH and 3D CANH}, {3D CONH and 3D CO(CA)NH} and {3D CONH, 3D CANH, 3D CO(CA)NH and 3D CA(CO)NH} spectra generated via the magnetisation transfer pathways (1)H → (13)CO → (15)N → (1)H (CONH), (1)H → (13)CA → (15)N → (1)H (CANH) and (1)H → (13)CO → (13)CA → (15)N → (1)H (CO(CA)NH) and (1)H → (13)CA → (13)CO → (15)N → (1)H (CA(CO)NH).

Asymmetric simultaneous phase-inversion cross-polarization in solid-state MAS NMR: relaxing selective polarization transfer condition between two dilute spins

Double cross polarization (DCP) has been widely used for heteronuclear polarization transfer between (13)C and (15)N in solid-state magic-angle spinning (MAS) NMR. However, DCP is such sensitive to experimental settings that small variations or deviations in RF fields would deteriorate its efficiency. Here, we report on asymmetric simultaneous phase-inversion cross polarization (referred as aSPICP) for selective polarization transfer between low-γ (13)C and (15)N spins. We have demonstrated through simulations and experiments using biological solids that the asymmetric duration in the simultaneous phase-inversion cross polarization scheme leads to efficient polarization transfer between (13)C and (15)N even with large chemical shift anisotropies in the presence of B1 field variations or mismatch of the Hartmann-Hahn conditions. This could be very useful in the aspect of long-duration experiments for membrane protein studies at high fields.

Pulse design for broadband correlation NMR spectroscopy by multi-rotating frames

We present a method for designing radio-frequency (RF) pulses for broadband or multi-band isotropic mixing at low power, suitable for protein NMR spectroscopy. These mixing pulses are designed analytically, rather than by numerical optimization, by repeatedly constructing new rotating frames of reference. We show how pulse parameters can be chosen frame-by-frame to systematically reduce the effective chemical shift bandwidth, but maintain most of the effective J-coupling strength. The effective Hartmann-Hahn mixing condition is then satisfied in a multi-rotating frame of reference. This design method yields multi-band and broadband mixing pulses at low RF power. In particular, the ratio of RF power to mixing bandwidth for these pulses is lower than for existing mixing pulses, such as DIPSI and FLOPSY. Carbon-carbon TOCSY experiments at low RF power support our theoretical analysis.

Utilizing afterglow magnetization from cross-polarization magic-angle-spinning solid-state NMR spectroscopy to obtain simultaneous heteronuclear multidimensional spectra

The time required for data acquisition and subsequent spectral assignment are limiting factors for determining biomolecular structure and dynamics using solid-state NMR spectroscopy. While strong magnetic dipolar couplings give rise to relatively broad spectra lines, the couplings also mediate the coherent magnetization transfer via the Hartmann-Hahn cross-polarization (HH-CP) experiment. This mechanism is used in nearly all backbone assignment experiments for carrying out polarization transfer between (1)H, (15)N, and (13)C. In this Article, we describe a general spectroscopic approach to use the residual or "afterglow" magnetization from the (15)N to (13)C selective HH-CP experiment to collect a second multidimensional heteronuclear data set. This approach allowed for the collection of two commonly used sequential assignment experiments (2D NCA and NCO or 3D NCACX and NCOCX) at the same time. Our "afterglow" technique was demonstrated with uniformly [(13)C,(15)N] and [1,3-(13)C] glycerol-labeled ubiquitin using instrumentation available on all standard solid-state NMR spectrometers configured for magic-angle-spinning. This method is compatible with several other sensitivity enhancement experiments and can be used as an isotopic filtering tool to reduce the spectral complexity and decrease the time needed for assignment.