Three pulse recoupling and phase jump matching

Simplified Preservation of Equivalent Pathways Spectroscopy

Inspired by the recently proposed transverse mixing optimal control pulses (TROP) approach for improving signal in multidimensional magic-angle spinning (MAS) NMR experiments, we present simplified preservation of equivalent pathways spectroscopy (SPEPS). It transfers both transverse components of magnetization that occur during indirect evolutions, theoretically enabling a √2 improvement in sensitivity for each such dimension. We compare SPEPS transfer with TROP and cross-polarization (CP) using membrane protein and fibril samples at MAS of 55 and 100 kHz. In three-dimensional (3D) (H)CANH spectra, SPEPS outperformed TROP and CP by factors of on average 1.16 and 1.69, respectively, for the membrane protein, but only a marginal improvement of 1.09 was observed for the fibril. These differences are discussed, making note of the longer transfer time used for CP, 14 ms, as compared with 2.9 and 3.6 ms for SPEPS and TROP, respectively. Using SPEPS for two transfers in the 3D (H)CANCO experiment resulted in an even larger benefit in signal intensity, with an average improvement of 1.82 as compared with CP. This results in multifold time savings, in particular considering the weaker peaks that are observed to benefit the most from SPEPS.

Recent progress in dipolar recoupling techniques under fast MAS in solid-state NMR spectroscopy

With the recent advances in NMR hardware and probe design technology, magic-angle spinning (MAS) rates over 100 ​kHz are accessible now, even on commercial solid NMR probes. Under such fast MAS conditions, excellent spectral resolution has been achieved by efficient suppression of anisotropic interactions, which also opens an avenue to the proton-detected NMR experiments in solids. Numerous methods have been developed to take full advantage of fast MAS during the last decades. Among them, dipolar recoupling techniques under fast MAS play vital roles in the determination of the molecular structure and dynamics, and are also key elements in multi-dimensional correlation NMR experiments. Herein, we review the dipolar recoupling techniques, especially those developed in the past two decades for fast-to-ultrafast MAS conditions. A major focus for our discussion is the ratio of RF field strength (in frequency) to MAS frequency, ν₁/ν_r, in different pulse sequences, which determines whether these dipolar recoupling techniques are suitable for NMR experiments under fast MAS conditions. Systematic comparisons are made among both heteronuclear and homonuclear dipolar recoupling schemes. In addition, the schemes developed specially for proton-detection NMR experiments under ultrafast MAS conditions are highlighted as well.

Optimization of band-selective homonuclear dipolar recoupling in solid-state NMR by a numerical phase search

Spin polarization transfers among aliphatic ¹³C nuclei, especially ¹³Cα-¹³Cβ transfers, permit correlations of their nuclear magnetic resonance (NMR) frequencies that are essential for signal assignments in multidimensional solid-state NMR of proteins. We derive and demonstrate a new radio-frequency (RF) excitation sequence for homonuclear dipolar recoupling that enhances spin polarization transfers among aliphatic ¹³C nuclei at moderate magic-angle spinning (MAS) frequencies. The phase-optimized recoupling sequence with five π pulses per MAS rotation period (denoted as PR5) is derived initially from systematic numerical simulations in which only the RF phases are varied. Subsequent theoretical analysis by average Hamiltonian theory explains the favorable properties of numerically optimized phase schemes. The high efficiency of spin polarization transfers in simulations is preserved in experiments, in part because the RF field amplitude in PR5 is only 2.5 times the MAS frequency so that relatively low ¹H decoupling powers are required. Experiments on a microcrystalline sample of the β1 immunoglobulin binding domain of protein G demonstrate an average enhancement factor of 1.6 for ¹³Cα → ¹³Cβ polarization transfers, compared to the standard ¹³C-¹³C spin-diffusion method, implying a two-fold time saving in relevant 2D and 3D experiments.

Two pulse recoupling

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called two pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block (π)_ϕ(π)_-ϕ where ϕ=π4n, and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to (π)_ϕ(π)_-ϕ(π)_π+ϕ(π)_π-ϕ. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ₁=3π8n,ϕ₂=π8n and n is number of blocks in a rotor period. The recoupling block is made robust to rf-inhomogeneity by extending it to [Formula: see text] and [Formula: see text] on two channels respectively. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for¹³C_α-¹³CO homonuclear recoupling in a sample of Glycine and ¹⁵N-¹³C_α heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-¹³C,¹⁵N]-Met-Leu-Phe-OH (MLF). Compared to R-sequences (Levitt, 2002), these sequences are more robust to rf-inhomogeneity and give better sensitivity, as shown in Fig. 3.

Four pulse recoupling

The paper describes a family of novel recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, called four pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block π2_0°3π2_ϕ°π2_180°+ϕ°3π2_180° where ϕ=πnϕ°=180°n, and n is number of blocks in a two rotor period. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ₁=3π2n,ϕ₂=π2n and n is number of blocks in a two rotor period. The recoupling pulse sequences mix the y magnetization. We show that four pulse recoupling is more broadband compared to three pulse recoupling [1]. Experimental quantification of this method is shown for ¹³C_α-¹³CO, homonuclear recoupling in a sample of Glycine and ¹⁵N-¹³C_α, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-¹³C,¹⁵N]-Met-Leu-Phe-OH (MLF).

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.

Recoupling pulse sequences with constant phase increments

The paper studies a family of recoupling pulse sequences in magic angle spinning (MAS) solid state NMR, that are characterized by constant phase increments at regular intervals. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. The homonuclear pulse sequence consists of a building block [Formula: see text] , where ϕ(p)=p(n-1)πn, where n is number of blocks in a rotor period and p=0,1,2,…. The pulse sequence repeats itself every rotor period when n is odd and every two rotor period when n is even. The heteronuclear recoupling pulse sequence consists of a building block [Formula: see text] and [Formula: see text] on channel I and S, where ϕ1(p)=p(2n-3)π2n,ϕ2(p)=p(2n-1)π2n and n is number of blocks in a rotor period. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for (13)Cα-(13)CO, homonuclear recoupling in a sample of Glycine and (15)N-(13)Cα, heteronuclear recoupling in Alanine. Application of this method is demonstrated on a sample of tripeptide N-formyl-[U-(13)C,(15)N]- Met-Leu-Phe-OH (MLF).