Elsevier

Journal of Magnetic Resonance

Volume 281, August 2017, Pages 162-171
Journal of Magnetic Resonance

Two pulse recoupling

https://doi.org/10.1016/j.jmr.2017.06.004Get rights and content

Highlights

  • We present a family of broadband recoupling pulse sequences, called two pulse recoupling.

  • These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments.

  • We show these sequences are robust to rf-inhomogeneity and chemical shift dispersion.

  • We present solid state NMR experiments that use two pulse recoupling.

Abstract

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 (π)ϕ1(π)-ϕ1 and (π)ϕ2(π)-ϕ2 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 (π)ϕ1(π)-ϕ1(π)π+ϕ1(π)π-ϕ1 and (π)ϕ2(π)-ϕ2(π)π+ϕ2(π)π-ϕ2 on two channels respectively. The recoupling pulse sequences mix the z magnetization. Experimental quantification of this method is shown for 13Cα-13CO homonuclear recoupling in a sample of Glycine and 15N-13Cα 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.

Introduction

Nuclear magnetic resonance (NMR) spectroscopy opens up the possibility of studying insoluble protein structures such as membrane proteins, fibrils, and extracellular matrix proteins which are difficult to analyze using conventional atomic-resolution structure determination methods, including liquid-state NMR and X-ray crystallography [1], [2], [3], [4], [5], [6]. Recoupling pulse sequences that enable transfer of magnetization between coupled spins is the workhorse of all these experiments, either as a means to obtain structural information (e.g., internuclear distances) or as a means to improve resolution as building blocks in multiple-dimensional correlation experiments. The present paper describes some new methodology development for design of recoupling pulse sequences and demonstration of their use in correlation experiments.

To put this work in proper context, and motivate the proposed new methodology, we look at development of dipolar recoupling. The work of Tycko [7], [8], [9] on DRAMA initiated homonuclear dipolar recoupling methods in solids. This was followed by methods like Rotational Resonance [10], [11] and RFDR [12]. Later came gamma encoded recoupling in HORROR [13], and its adiabatic version DREAM [14]. Further developments include, DRAWS [15] and MELODRAMA [16]. Subsequently, there was development of C7 [17], POSTC7 [19], SPC5 [18] and CMR7 [20]. Recently Levitt [24] and co-workers have further developed symmetry based pulse sequences. Some new work in recoupling includes, CMRR [28], [29], phase alternating recoupling [25] and most recently TPR and FPR recoupling [21], [22]. If we study sequences like C7, POSTC7, SPC5, CMR7, Symmetry sequences, CMRR and TPR and FPR recoupling, we find they have a common design principle. A strong rf-field is used to eliminate chemical shifts and make the sequence broadband. Furthermore, this strong rf-field is used to demodulate a second oscillating field which performs recoupling. The second oscillating field comes about by principled phase changes in these sequences. To add to this family, we propose in this paper, a new two phase modulated recoupling, we call TOPR. The sequence is interesting from simplicity of its design for broadband recoupling and robustness to rf-inhomogeneity. Compared to symmetry based R-sequences, [24] these sequences are more robust to rf-inhomogeneity and give better sensitivity, as shown in Fig. 3. Furthermore, TOPR adds to our repertoire of recoupling sequences and to our understanding of recoupling which is fundamental to solid state NMR.

The paper is organized as follows. In Section 2, we describe TOPR, a novel approach to homonuclear recoupling that recouple dipolar coupled spins under Magic angle spinning (MAS) experiments. TOPR experiments are broadband and robust to rf-inhomogeneity. This work extends recently developed techniques for broadband homonuclear recoupling as reported in the [21], [25], [26], [28], [29], [30]. In Section 3, we describe these methods in the context of heteronuclear experiments. In the context of heteronuclear spins, the recoupling is achieved by matching the syncronized phases on the two rf-channels (analogous to Hartmann-Hahn matching of the rf-power commonly seen in heteronuclear recoupling experiments [31]). Section 4 describes experimental verification of the proposed techniques. We conclude in Section 5 by comparing TOPR with state of the art pulse sequences.

Section snippets

TOPR in homonuclear spins

Consider two homonuclear spins, I and S, under magic angle spinning condition [13]. In a rotating frame, rotating with both the spins at their common Larmor frequency, the Hamiltonian of the spin system takes the formH(t)=ωI(t)Iz+ωS(t)Sz+ωIS(t)(3IzSz-I·S)+2πA(t)(cosϕ(t)Fx+sinϕ(t)Fy),where the operator Fx=Ix+Sx, and ωI(t) and ωS(t) represent the chemical shift for the spins I and S respectively and ωIS(t) represents the time varying couplings between the spins under magic-angle spinning. These

Phase matching and heteronuclear recoupling

Consider two coupled heteronuclear spins I and S under magic angle spinning condition [31]. The spins are irradiated with rf fields at their Larmor frequencies along say the x direction. In a double-rotating Zeeman frame, rotating with both the spins at their Larmor frequency, the Hamiltonian of the system takes the formH(t)=ωI(t)Iz+ωS(t)Sz+ωIS(t)2IzSz+Hrf(t),where ωI(t),ωS(t), and ωIS(t) represent time-varying chemical shifts for the two spins I and S and the coupling between them,

Experimental results

All experiments were performed on a 750 MHz spectrometer (1H Larmor frequency of 750 MHz) equipped with a triple resonance 3.2 mm probe. Uniformly 13C labeled sample of Glycine and uniformly 13C, 15N-labeled sample of Alanine were used in the full volume of standard 3.2 mm rotor at ambient temperature for homonuclear and heteronuclear experiments respectively. Uniformly 13C, 15N-labeled sample of MLF was used for both homonuclear and heteronuclear recoupling experiments. The experiments used 2 s

Conclusion

In this paper we introduced a class of recoupling pulse sequences, which rest on the principle of second oscillating field [21], [25], [26], [28], [29], [32]. A strong field is used to eliminate chemical shifts and make the sequence broadband. Furthermore this strong rf-field is used to demodulate a second oscillating field which performs recoupling. In our design, the second oscillating field comes about by principled phase changes which are described in the paper. The recoupling sequences

Acknowledgement

The authors would like to thank the HFNMR lab facility at IIT Bombay where the data was collected.

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