Accepted Manuscript Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings Veera Mohana Rao Kakita, Eriks Kupče, Jagadeesh Bharatam PII: DOI: Reference:
S1090-7807(14)00327-9 http://dx.doi.org/10.1016/j.jmr.2014.11.006 YJMRE 5551
To appear in:
Journal of Magnetic Resonance
Received Date: Revised Date:
11 July 2014 10 November 2014
Please cite this article as: V.M.R. Kakita, E. Kupče, J. Bharatam, Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings, Journal of Magnetic Resonance (2014), doi: http://dx.doi.org/10.1016/j.jmr.2014.11.006
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Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings# Veera Mohana Rao Kakitaa Eriks Kupčeb and Jagadeesh Bharatama,* [a]
Centre for NMR & Structural Chemistry CSIR-Indian Institute of Chemical Technology Hyderabad, India-500 007
[b]
Bruker UK Limited, Banner Lane, Coventry, CV4 9GH, UK
Corresponding author Email: [email protected] Ph. No: +9140-27193976
# Dedicated to Professor V. S. S Sastry, University of Hyderabad, India on his 65th birthday
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Abstract
Unambiguous measurement of homonuclear scalar couplings (J) in multi-spin scalar network systems is not straightforward. Further, the direct measurement of J-couplings is obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA)dominated line broadening, even under the magic angle spinning (MAS). We present a new multiple frequency selective spin-echo method based on Hadamard matrix encoding, for simultaneous measurement of multiple homonuclear scalar couplings (J) in the solid-state. In contrast to the Hadamard encoded selective excitation schemes known for the solution-state, herein the selectivity is achieved during refocusing period. The Hadamard encoded refocusing scheme concurrently allows to create the spin-spin commutation property between number of spin-pairs of choice in uniformly labelled molecules, which, therefore avoids (1) the repetition of the double selective refocusing experiments for each spin-pair and (2) the synthesis of expensive selective labelled molecules. The experimental scheme is exemplified for determining 1JCC and 3JCC values in 13C6 L-Histidine.HCl molecule, which are found to be in excellent agreement with those measured in conventional double frequency selective refocusing mode as well as in the solution-state. This method can be simply extended to 2D/3D pulse schemes and be applied to small bio-molecular solids.
2
Introduction
Scalar spin-spin couplings (J) serve as powerful structural probes in NMR spectroscopy to map through-bond atomic connectivities and to gain insight into the local conformation as well as configuration of molecules. The measurements of J-couplings in solution-state are often straightforward from one-dimensional (1D) spectra due to the intrinsic resolution, whereas they are obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA) dominated line broadening, even under magic angle spinning (MAS). The double quantum (DQ) based [1] and J-resolved 2D-correlation techniques developed earlier for solid-state have allowed to observe J-multiplets in Jresolved dimension, for favourable cases [2-8]. Alternatively, in the past few years the strategic developments in solid-state MAS NMR techniques have aptly exploited the Jmodulation effect on spin-echoes, for precise measurement of J-couplings of hetero nuclear [9,10] or isolated / dilute homonuclear [11-16] spin-pairs and one-bond dipolar couplings (1DCC) [17], in small molecules. As these experiments were limited only to dilute spin systems or to isolated spinpairs, the corresponding J-coupling measurements were unambiguous and straightforward. On the other hand, the homonuclear spin-spin interactions in multiple spin network such as in uniformly isotope-enriched organic or bio-molecular solids, are complex, and the unambiguous measurements of individual couplings could be difficult. Recently, Cadars etal., [18] have applied a double frequency-selective spin-echo method under fast MAS, which enabled pair-wise measurement of J-couplings (1J and 2J) in uniformly isotope enriched polycrystalline solids.[19-21] This method, however, necessitates the experiments to be repeated for each spin-pair, which is more time consuming, particularly for multi-spin systems. In the present report, we discuss an alternative and versatile approach based on Hadamard matrix encoding/decoding [22-25], for precise and simultaneous recording of multiple homonuclear spin-spin couplings in uniformly spin-labelled solids, in a single experiment. In their original work, Kupce and Freeman have introduced frequency domain solution-state Hadamard NMR spectroscopy in one [25] and multi-dimensions [26-29], which involves selective frequency excitations in either direct or indirect dimensions that are encoded according to the Hadamard matrices.
This intriguing approach has revealed
attractive features over the conventional Fourier transform NMR spectroscopy such as, exclusion of undesired spectral regions / data-sampling, significant reduction in experimental 3
time as well as an enhancement in signal to noise ratio by a factor √2. On the other hand, the power and utility of the Hadamard encoding is only rarely explored in solid-state NMR, such as dipolar assisted rotational resonance (DARR) [30], saturation in deuterated solids [31] and proton local field [32] experiments. Herein, we adopt the Hadamard encoding strategy for selective refocusing instead of excitations in solid-state NMR, and exemplify for accurate measurement of 1JCC and 3JCC in uniformly 13C-labelled Histidine.HCl. To the best of our knowledge, this is the first report that demonstrates solid-state Hadamard NMR spectroscopy for measuring homonuclear scalar couplings in multi-spin systems in solids. Hadamard Encoding/Decoding: The Hadamard matrices HN (dimension N by N, satisfying N=4k, where k is an integer) are simple and consists of elements either +1or –1, which are usually represented by + or – signs, respectively.[26] The central theme of the Kupce-Freeman's frequency domain approach relies on simultaneous excitation of N frequencies (channels) of choice by an array of N individual frequency-selective soft pulses (combined into a polychromatic pulse), that are coded according to the signs (+ or –) in the rows of a Hadamard matrix. The + or – signs correspond to setting the phase of the irradiation channels to positive or negative, respectively. For the selection of eight resolved resonances N=8, a Hadamard matrix of 8 X 8 (H8) is represented as:
A total of N experiments are need to be recorded with phase encoding according to the Hadamard matrix of N. Therefore, the operation necessitates eight scans with each scan carrying the respective sign coding given in the rows of the H8 matrix. A composite response generated at the end of each scan is comprised of NMR signal components corresponding to the selected chemical sites. However, as the sign pattern is different for each scan, an
4
appropriate linear combination of these scans results in only the desired individual resonance, while the signals from other channels are vanished. For example, the subtraction of the scans (3+4+7+8) from (1+2+5+6), yields a trace exhibiting only the signal from channale-3. The similar process is repeated for the other encoded resonances. In the other sense, as the Hadamard matrix is real and symmetric (HN =HN T=HN -1), the pre-encoded NMR signals are decoded according to the columns of the same Hadamard matrix, H4 (Hadamard Transformation).
The smart NMR spectral-tailoring approach has been successfully
incorporated into various other experimental schemes, for example, excitation sculpting [33], DOSY [34, 35], multi voxel/slice-selective imaging [36, 37], single-scan TOCSY [38], and also applied to quantum computations [39, 40]. As shown below, we have extended this approach for Hadamard encoded multiplex refocusing in the solid-state.
Materials and Experimental details
The solid-state NMR experiments are conducted on 1:5 mixtures of uniformly
13
C-
labelled L-Histidine.HCl (Cambridge Isotopes Laboratories, MA, USA) and its natural analogue, to minimize the inter-molecular dipolar interactions. The mixture is tightly filled in 4 or 2.5 mm Zirconia rotors and spun at 8 kHz. The CP/MAS NMR experiments are conducted on Varian (Agilent) Unity-Inova 400 MHz and Bruker Avance-III 500 MHz spectrometers.
Results and Discussion
Hadamard encoded multiple frequency selective refocusing (HE-MSR):
Figure 1.I describes the Hadamard encoded multiple frequency refocusing (HE-MSR) scheme employed in the present study. In contrast to the direct selective multiplex excitation method discussed above, herein the initial excitation is accomplished by a conventional nonselective hard pulse followed by a HE-polychromatic refocusing pulse comprised of Gaussian π-pulses corresponding to the frequencies of choice. It implies that the selectivity is achieved during the refocusing, instead of during the excitation. The frequency of each refocusing pulse is an offset from the carrier, which need not be equally spaced or continuous. While the size of a Hadamard matrix, N should be multiple of 4, the number of actual chemical sites of interest could often differ from this condition. In such cases, a nearest 5
Hadamard matrix is employed.
For example, in order to encode the total of six
13
C
resonances of Histidine, the matrix H8 has to be applied. On the other hand, as shown in Figure 1.II, for a selection of only four chemical sites of Histidine, viz., (i) C1, C4, C5 and C6 or (ii) C2, C3, C5 and C6, a Hadamard matrix of 4X4 (H4) is sufficient. Prior to the integration of the individual selective refocusing pulses into a polychromatic sequence, the respective radio frequency pulses are encoded according the signs + or – in the rows of the H4 matrix. This operation is realized by altering the phase of the individual refocusing pulses between x (0o) and y (90o), over four scans. Accordingly, in each scan, the resultant complex spin echo pattern for the four different 13C sites has shown positive and negative intensities, respectively (Figure 1.II(b-e)). As described above, the patterns over four scans (or multiples of 4 scans) are simplified by decoding (Hadamard transform) according to the signs in the columns of the Hadamard matrix. For example, combining the amplitudes of all four scans, i.e., e+d+c+b, resulted in only one signal corresponding to C6, while other signals are rejected (Figure 1.III(f)). Similarly, other linear combinations of the scans, in accordance with H4 matrix, have resulted in C4, C1 and C5 signals as shown in Figures 1.III(g), 1.III(h), 1.III(i), respectively. This combination also leads to an improvement in the signal to noise ratio by square-root of N.
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Figure.1: I) Hadamard encoded multiple selective refocusing (HE-MSR) scheme: The 13C, 1 H optimized 90° pulse widths are 3.0 and 3.2µs, respectively. The recycle delay is 3s. The transverse magnetization is created by using ramped cross polarization from 1H to 13C at a contact time of 5 ms. During the pulsing and acquisition periods, SPINAL-64 decoupling is applied at 83 KHz nutation frequency. An 8-step phase cycle is employed on the 13C channel: φ1= x, -x; φ2= x, x, y, y, -x, -x, -y, -y and φrec= x, -x, -x, x. A total 8 (multiple of 4) acquisitions are made for each data set (scan), b, c, d and e for improved signal to noise ratio. Gaussian shaped 180o pulses of length 4.5 ms covering a band width of 200 Hz are used for simultaneous refocusing. The corresponding time shift correction [19] value is 1.08 ms, which equals to the shaped pulse width at 76.69% of its maximum height. The τ/2 values are incremented as the integer multiples of rotor periods at 8 kHz sample spinning frequency. II) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5-C6) of 13C6 LHistidine.HCl (a) and the corresponding HE-MSR traces (b-e) for a C6-C5-C4-C1 spin combination that are encoded according to the signs in the rows of the Hadamard matrix (H4). The H4 matrix employed is depicted for easy reference. The + and - signs in the matrix correspond to alternating the phase of the selective refocusing pulses between x (0o) and y (90o), respectively. Appropriate linear combinations of e, d, c and b have yielded traces with only C6, C4, C1 and C5 resonances as shown in III (f-i), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. IV) Fitting of the spin-echo modulations of C6 (j) and C4 (k) in the C1-C4-C5-C6 combination to equation-1 has resulted in 1JC5-C6 and 1JC1-C4, respectively in a single experiment. The numbering of carbon atoms is given according to the BMRB nomenclature (www.bmrb.wisc.edu). HE-MSR and simultaneous measurements of multiple JCC: The spin-echo modulations of each resonance site in the HE-MSR traces are recorded by systematically varying the echo time and the scalar couplings are computed for the desired set of spin pairs, by using the equation (1): S (τ) ∝cos {πJ (τ-τsh)} exp (-τ /T2) (1) Here T2 is the spin-spin relaxation time constant, τ is the spin-echo evolution time and τsh is a shift correction applied to the shaped pulse to account for the suppression of MQ coherences [18, 19, 41, 42]. As the J-evolution is absent when only one frequency is selected, it is evident from equation (1) that the evolution of the signal amplitude is predominantly governed by T2, which can be expressed as So (τ) ∝exp (-τ/T2)
(2)
7
In principle, for a conventional spin-echo spectrum representing all the chemical sites, the spin-echo modulations may be complex due to simultaneous J-interactions with the nearby spins. However, as the C3 spin, which shares direct one-bond scalar interaction with C5 and C4 is omitted from the spin selection C6-C5-C4-C1 of 13C-Histidine, it is reasonable to assume that the predominant scalar interactions are limited only to C6-C5 and C4-C1 pairs, which therefore can be considered as isolated commuting spin-pairs. Accordingly, the JC5-C6 and JC4-C1 values are computed from the echo modulations of C5 or C6 and C1or C4, which are found to be 56.8±0.2 Hz (Figure 1.IV(j)), and 72.5±0.5 Hz (Figure 1.IV(k)), respectively. These JC5-C6 and JC1-C4 values are further verified with those obtained from independent twospin selections: C5-C6 and C4-C1 are found to be consistent. On the other hand, for the C1C4-C3 spin selection, C4 is commonly coupled to both C1 and C3, therefore its echo modulation is found to be complex due to the simultaneous evolution under two Jinteractions (Figure 2.III(i)). However, this situation is simplified by analyzing the spin-echo modulations of C3 (Figure 2.III(j)) and C1 (Figure 2.III(k)) to obtain 1JC3-C4 (47.8±2.0 Hz) and 1JC1-C4 (74.8±1.0 Hz), respectively. The same procedure has been repeated for the other three spin combinations: C1-C2-C4, C4-C3-C5 and C3-C5-C6 and the respective 1JCC are estimated (for details please see the supporting information). It is assumed that the exponential T2 spin-relaxation decay for a specific spin is almost similar in all the possible combinations. The fitted T2 value (equation-1) obtained for a specific spin is found to be similar for different combinations, which is in accordance with the above assumption (please see Table S1 of supporting information). For example, the T2 value of C6 is about 24.0 ±1.0 ms for all the encoded combinations, C5-C6, C1-C4-C5-C6, C2-C3-C5-C6 and C3-C5-C6, suggesting that the 1JCC modulations are predominantly due to these one-bond scalar couplings only. Nevertheless, it is known from solution-state NMR studies that Histidine exhibits three-bond 3JC2-C3 of about 5 Hz [43] and the C3 evolution (1JC3-C5) analyzed from C2-C3-C5-C6 spin selection can have a weak contribution from C2-C3. As explained below, from the same C2-C3-C5-C6 encoded set, the long range 3JC2-C3 is also simultaneously determined by analysing the echo modulation of C2. The error estimation and confidence limits are derived by considering the experimental noise for each trajectory of the spin-echo (for details please see the supporting information).
8
Figure 2: I) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5C6) of 13C6 L-Histidine.HCl (a) and the corresponding HE-MSR traces (b-e) for C3-C4-C1 spin combination that are encoded according to the signs in the rows of the Hadamard matrix, H4 . II) Appropriate linear combinations of e, d, c and b have yielded traces with only C4, C1 and C3 resonances as shown in II(f-h), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. III) The spin-echo modulation of C4 (i) is complex due to its simultaneous J-evolution with C3 and C1, which makes the analysis difficult. Whereas, fitting of the Hadamard edited spin-echo modulations of C1 (j) and C3 (k) to the equation (1) has resulted in 1JC1-C4 and 1JC3-C4, respectively in a single experiment. Long range 3JCC coupling: The magnitude of the long rage couplings such as, 3JC2-C3 is rather small and the spin-echo modulation (exponential decay) is expected to be predominantly due to the T2 relaxation and hence the estimation of JCC from the equation (1) is not easy. However, from the equations (1) and (2), the ratio of spin echo modulations S(τ)/So(τ)∝cos(πJ(τ-τsh))can be computed, which yields the spin-echo evolution term with the contribution due to T2 relaxation suppressed [20]. This simplification allows to determine the small J-coupling values. Accordingly, for the C2-C3-C5-C6 combination (Figure 3.I and Figure 3.II), the 3JC2-C3 value (4.4±0.2 Hz) is estimated (Figure 3.III(l)), which is consistent with that derived by encoding only C2-C3 (N=2) pair and also with that reported earlier (by using double-selective refocusing pulses) [20]. Except 3JC2-C3, no long-range scalar couplings 9
of significant magnitude are observed for U-13CHistidine.HCl. Further, as shown in Figure 3.III(m), the 1JCC and 3JCCvalues obtained through HE-MSR method are found to be in excellent agreement with those measured in the solution-state [43].
Figure 3: I) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5C6) of 13C6 L-Histidine.HCl (a) and the corresponding HE-MSR traces (b-e) for C6-C5-C3C2 spin combination that are encoded according to the signs in the rows of the Hadamard matrix, H4 . II) Appropriate linear combinations of e, d, c and b have yielded traces with only C6, C2, C5 and C3 resonances as shown in (f-i), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. III) Fitting of the spin-echo modulations of C6 (j) and C3 (k) to the equation (1) in the C2-C3-C5-C6 encoding has resulted in 1JC5-C6 and 1JC3-C5, respectively in a single experiment. The variation of the C2 signal intensity S(τ) in the C6-C5-C3-C2 combination is found to be predominantly exponential decay (closed circles •) due to the dominant T2 relaxation, with a minor component due to J-interactions. This is closely comparable to the pure T2-relaxation decay of C2 (So(τ), open circles ) (l). As discussed in the text, the ratio of the S(τ) and So (τ) (crosses X) of the two modulations has allowed to estimate 3JC2-C3. The solid line represents the best fit to the S/So=A cos (πJτ). The excellent correlation between nJCC values derived from solution-state and HE-MSR solid-state, is shown in (m).
Conclusions
Direct measurement of homonuclear spin-spin couplings in the solid-state, particularly for uniformly labelled samples, is hampered due to the inherent dipolar and CSAdominated line broadening, even under the magic angle spinning (MAS) and this exercise is
10
more complex in multi-spin solids, which make the measurements difficult. In order to address this, herein we have discussed a new and versatile multiple frequency selective refocusing scheme based on Hadamard encoding (HE-MSR). The HE-MSR approach does not require pair-wise measurements of spin-spin couplings or a set of specially synthesized 13
C2 labelled molecules. The efficacy of this method is exemplified for simultaneous and
unambiguous measurement of multiple
13
C-13C scalar couplings (both small and large) in
uniformly 13C labelled Histidine. HCl. Further, this method can be extended to 2D/3D NMR schemes, particularly for small bio-molecular solids.
Acknowledgements The authors thank Prof. Malcolm Levitt (University of Southampton, UK) and Prof. Bernhard Blümich (RWTH, Aachen, Germany) for useful discussions. KVMR and BJ thank CSIR-IICT, India for financial support.
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Graphical abstract Manuscript: " Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings” by Kakita et al.,
Highlights •
Hadamard encoded multiple selective refocusing scheme for solid-state NMR
•
Simultaneously allows commutation of spin-spin interactions in multi-spin systems
•
Precise measurement of multiple JCC couplings uniformly 13C-labelled solids
•
Method can be extended to the measurement of dipolar couplings and 2D/3D schemes
•
Applicable to small biomolecular solids
15
S1090-7807(14)00327-9 http://dx.doi.org/10.1016/j.jmr.2014.11.006 YJMRE 5551
To appear in:
Journal of Magnetic Resonance
Received Date: Revised Date:
11 July 2014 10 November 2014
Please cite this article as: V.M.R. Kakita, E. Kupče, J. Bharatam, Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings, Journal of Magnetic Resonance (2014), doi: http://dx.doi.org/10.1016/j.jmr.2014.11.006
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Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings# Veera Mohana Rao Kakitaa Eriks Kupčeb and Jagadeesh Bharatama,* [a]
Centre for NMR & Structural Chemistry CSIR-Indian Institute of Chemical Technology Hyderabad, India-500 007
[b]
Bruker UK Limited, Banner Lane, Coventry, CV4 9GH, UK
Corresponding author Email: [email protected] Ph. No: +9140-27193976
# Dedicated to Professor V. S. S Sastry, University of Hyderabad, India on his 65th birthday
1
Abstract
Unambiguous measurement of homonuclear scalar couplings (J) in multi-spin scalar network systems is not straightforward. Further, the direct measurement of J-couplings is obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA)dominated line broadening, even under the magic angle spinning (MAS). We present a new multiple frequency selective spin-echo method based on Hadamard matrix encoding, for simultaneous measurement of multiple homonuclear scalar couplings (J) in the solid-state. In contrast to the Hadamard encoded selective excitation schemes known for the solution-state, herein the selectivity is achieved during refocusing period. The Hadamard encoded refocusing scheme concurrently allows to create the spin-spin commutation property between number of spin-pairs of choice in uniformly labelled molecules, which, therefore avoids (1) the repetition of the double selective refocusing experiments for each spin-pair and (2) the synthesis of expensive selective labelled molecules. The experimental scheme is exemplified for determining 1JCC and 3JCC values in 13C6 L-Histidine.HCl molecule, which are found to be in excellent agreement with those measured in conventional double frequency selective refocusing mode as well as in the solution-state. This method can be simply extended to 2D/3D pulse schemes and be applied to small bio-molecular solids.
2
Introduction
Scalar spin-spin couplings (J) serve as powerful structural probes in NMR spectroscopy to map through-bond atomic connectivities and to gain insight into the local conformation as well as configuration of molecules. The measurements of J-couplings in solution-state are often straightforward from one-dimensional (1D) spectra due to the intrinsic resolution, whereas they are obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA) dominated line broadening, even under magic angle spinning (MAS). The double quantum (DQ) based [1] and J-resolved 2D-correlation techniques developed earlier for solid-state have allowed to observe J-multiplets in Jresolved dimension, for favourable cases [2-8]. Alternatively, in the past few years the strategic developments in solid-state MAS NMR techniques have aptly exploited the Jmodulation effect on spin-echoes, for precise measurement of J-couplings of hetero nuclear [9,10] or isolated / dilute homonuclear [11-16] spin-pairs and one-bond dipolar couplings (1DCC) [17], in small molecules. As these experiments were limited only to dilute spin systems or to isolated spinpairs, the corresponding J-coupling measurements were unambiguous and straightforward. On the other hand, the homonuclear spin-spin interactions in multiple spin network such as in uniformly isotope-enriched organic or bio-molecular solids, are complex, and the unambiguous measurements of individual couplings could be difficult. Recently, Cadars etal., [18] have applied a double frequency-selective spin-echo method under fast MAS, which enabled pair-wise measurement of J-couplings (1J and 2J) in uniformly isotope enriched polycrystalline solids.[19-21] This method, however, necessitates the experiments to be repeated for each spin-pair, which is more time consuming, particularly for multi-spin systems. In the present report, we discuss an alternative and versatile approach based on Hadamard matrix encoding/decoding [22-25], for precise and simultaneous recording of multiple homonuclear spin-spin couplings in uniformly spin-labelled solids, in a single experiment. In their original work, Kupce and Freeman have introduced frequency domain solution-state Hadamard NMR spectroscopy in one [25] and multi-dimensions [26-29], which involves selective frequency excitations in either direct or indirect dimensions that are encoded according to the Hadamard matrices.
This intriguing approach has revealed
attractive features over the conventional Fourier transform NMR spectroscopy such as, exclusion of undesired spectral regions / data-sampling, significant reduction in experimental 3
time as well as an enhancement in signal to noise ratio by a factor √2. On the other hand, the power and utility of the Hadamard encoding is only rarely explored in solid-state NMR, such as dipolar assisted rotational resonance (DARR) [30], saturation in deuterated solids [31] and proton local field [32] experiments. Herein, we adopt the Hadamard encoding strategy for selective refocusing instead of excitations in solid-state NMR, and exemplify for accurate measurement of 1JCC and 3JCC in uniformly 13C-labelled Histidine.HCl. To the best of our knowledge, this is the first report that demonstrates solid-state Hadamard NMR spectroscopy for measuring homonuclear scalar couplings in multi-spin systems in solids. Hadamard Encoding/Decoding: The Hadamard matrices HN (dimension N by N, satisfying N=4k, where k is an integer) are simple and consists of elements either +1or –1, which are usually represented by + or – signs, respectively.[26] The central theme of the Kupce-Freeman's frequency domain approach relies on simultaneous excitation of N frequencies (channels) of choice by an array of N individual frequency-selective soft pulses (combined into a polychromatic pulse), that are coded according to the signs (+ or –) in the rows of a Hadamard matrix. The + or – signs correspond to setting the phase of the irradiation channels to positive or negative, respectively. For the selection of eight resolved resonances N=8, a Hadamard matrix of 8 X 8 (H8) is represented as:
A total of N experiments are need to be recorded with phase encoding according to the Hadamard matrix of N. Therefore, the operation necessitates eight scans with each scan carrying the respective sign coding given in the rows of the H8 matrix. A composite response generated at the end of each scan is comprised of NMR signal components corresponding to the selected chemical sites. However, as the sign pattern is different for each scan, an
4
appropriate linear combination of these scans results in only the desired individual resonance, while the signals from other channels are vanished. For example, the subtraction of the scans (3+4+7+8) from (1+2+5+6), yields a trace exhibiting only the signal from channale-3. The similar process is repeated for the other encoded resonances. In the other sense, as the Hadamard matrix is real and symmetric (HN =HN T=HN -1), the pre-encoded NMR signals are decoded according to the columns of the same Hadamard matrix, H4 (Hadamard Transformation).
The smart NMR spectral-tailoring approach has been successfully
incorporated into various other experimental schemes, for example, excitation sculpting [33], DOSY [34, 35], multi voxel/slice-selective imaging [36, 37], single-scan TOCSY [38], and also applied to quantum computations [39, 40]. As shown below, we have extended this approach for Hadamard encoded multiplex refocusing in the solid-state.
Materials and Experimental details
The solid-state NMR experiments are conducted on 1:5 mixtures of uniformly
13
C-
labelled L-Histidine.HCl (Cambridge Isotopes Laboratories, MA, USA) and its natural analogue, to minimize the inter-molecular dipolar interactions. The mixture is tightly filled in 4 or 2.5 mm Zirconia rotors and spun at 8 kHz. The CP/MAS NMR experiments are conducted on Varian (Agilent) Unity-Inova 400 MHz and Bruker Avance-III 500 MHz spectrometers.
Results and Discussion
Hadamard encoded multiple frequency selective refocusing (HE-MSR):
Figure 1.I describes the Hadamard encoded multiple frequency refocusing (HE-MSR) scheme employed in the present study. In contrast to the direct selective multiplex excitation method discussed above, herein the initial excitation is accomplished by a conventional nonselective hard pulse followed by a HE-polychromatic refocusing pulse comprised of Gaussian π-pulses corresponding to the frequencies of choice. It implies that the selectivity is achieved during the refocusing, instead of during the excitation. The frequency of each refocusing pulse is an offset from the carrier, which need not be equally spaced or continuous. While the size of a Hadamard matrix, N should be multiple of 4, the number of actual chemical sites of interest could often differ from this condition. In such cases, a nearest 5
Hadamard matrix is employed.
For example, in order to encode the total of six
13
C
resonances of Histidine, the matrix H8 has to be applied. On the other hand, as shown in Figure 1.II, for a selection of only four chemical sites of Histidine, viz., (i) C1, C4, C5 and C6 or (ii) C2, C3, C5 and C6, a Hadamard matrix of 4X4 (H4) is sufficient. Prior to the integration of the individual selective refocusing pulses into a polychromatic sequence, the respective radio frequency pulses are encoded according the signs + or – in the rows of the H4 matrix. This operation is realized by altering the phase of the individual refocusing pulses between x (0o) and y (90o), over four scans. Accordingly, in each scan, the resultant complex spin echo pattern for the four different 13C sites has shown positive and negative intensities, respectively (Figure 1.II(b-e)). As described above, the patterns over four scans (or multiples of 4 scans) are simplified by decoding (Hadamard transform) according to the signs in the columns of the Hadamard matrix. For example, combining the amplitudes of all four scans, i.e., e+d+c+b, resulted in only one signal corresponding to C6, while other signals are rejected (Figure 1.III(f)). Similarly, other linear combinations of the scans, in accordance with H4 matrix, have resulted in C4, C1 and C5 signals as shown in Figures 1.III(g), 1.III(h), 1.III(i), respectively. This combination also leads to an improvement in the signal to noise ratio by square-root of N.
6
Figure.1: I) Hadamard encoded multiple selective refocusing (HE-MSR) scheme: The 13C, 1 H optimized 90° pulse widths are 3.0 and 3.2µs, respectively. The recycle delay is 3s. The transverse magnetization is created by using ramped cross polarization from 1H to 13C at a contact time of 5 ms. During the pulsing and acquisition periods, SPINAL-64 decoupling is applied at 83 KHz nutation frequency. An 8-step phase cycle is employed on the 13C channel: φ1= x, -x; φ2= x, x, y, y, -x, -x, -y, -y and φrec= x, -x, -x, x. A total 8 (multiple of 4) acquisitions are made for each data set (scan), b, c, d and e for improved signal to noise ratio. Gaussian shaped 180o pulses of length 4.5 ms covering a band width of 200 Hz are used for simultaneous refocusing. The corresponding time shift correction [19] value is 1.08 ms, which equals to the shaped pulse width at 76.69% of its maximum height. The τ/2 values are incremented as the integer multiples of rotor periods at 8 kHz sample spinning frequency. II) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5-C6) of 13C6 LHistidine.HCl (a) and the corresponding HE-MSR traces (b-e) for a C6-C5-C4-C1 spin combination that are encoded according to the signs in the rows of the Hadamard matrix (H4). The H4 matrix employed is depicted for easy reference. The + and - signs in the matrix correspond to alternating the phase of the selective refocusing pulses between x (0o) and y (90o), respectively. Appropriate linear combinations of e, d, c and b have yielded traces with only C6, C4, C1 and C5 resonances as shown in III (f-i), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. IV) Fitting of the spin-echo modulations of C6 (j) and C4 (k) in the C1-C4-C5-C6 combination to equation-1 has resulted in 1JC5-C6 and 1JC1-C4, respectively in a single experiment. The numbering of carbon atoms is given according to the BMRB nomenclature (www.bmrb.wisc.edu). HE-MSR and simultaneous measurements of multiple JCC: The spin-echo modulations of each resonance site in the HE-MSR traces are recorded by systematically varying the echo time and the scalar couplings are computed for the desired set of spin pairs, by using the equation (1): S (τ) ∝cos {πJ (τ-τsh)} exp (-τ /T2) (1) Here T2 is the spin-spin relaxation time constant, τ is the spin-echo evolution time and τsh is a shift correction applied to the shaped pulse to account for the suppression of MQ coherences [18, 19, 41, 42]. As the J-evolution is absent when only one frequency is selected, it is evident from equation (1) that the evolution of the signal amplitude is predominantly governed by T2, which can be expressed as So (τ) ∝exp (-τ/T2)
(2)
7
In principle, for a conventional spin-echo spectrum representing all the chemical sites, the spin-echo modulations may be complex due to simultaneous J-interactions with the nearby spins. However, as the C3 spin, which shares direct one-bond scalar interaction with C5 and C4 is omitted from the spin selection C6-C5-C4-C1 of 13C-Histidine, it is reasonable to assume that the predominant scalar interactions are limited only to C6-C5 and C4-C1 pairs, which therefore can be considered as isolated commuting spin-pairs. Accordingly, the JC5-C6 and JC4-C1 values are computed from the echo modulations of C5 or C6 and C1or C4, which are found to be 56.8±0.2 Hz (Figure 1.IV(j)), and 72.5±0.5 Hz (Figure 1.IV(k)), respectively. These JC5-C6 and JC1-C4 values are further verified with those obtained from independent twospin selections: C5-C6 and C4-C1 are found to be consistent. On the other hand, for the C1C4-C3 spin selection, C4 is commonly coupled to both C1 and C3, therefore its echo modulation is found to be complex due to the simultaneous evolution under two Jinteractions (Figure 2.III(i)). However, this situation is simplified by analyzing the spin-echo modulations of C3 (Figure 2.III(j)) and C1 (Figure 2.III(k)) to obtain 1JC3-C4 (47.8±2.0 Hz) and 1JC1-C4 (74.8±1.0 Hz), respectively. The same procedure has been repeated for the other three spin combinations: C1-C2-C4, C4-C3-C5 and C3-C5-C6 and the respective 1JCC are estimated (for details please see the supporting information). It is assumed that the exponential T2 spin-relaxation decay for a specific spin is almost similar in all the possible combinations. The fitted T2 value (equation-1) obtained for a specific spin is found to be similar for different combinations, which is in accordance with the above assumption (please see Table S1 of supporting information). For example, the T2 value of C6 is about 24.0 ±1.0 ms for all the encoded combinations, C5-C6, C1-C4-C5-C6, C2-C3-C5-C6 and C3-C5-C6, suggesting that the 1JCC modulations are predominantly due to these one-bond scalar couplings only. Nevertheless, it is known from solution-state NMR studies that Histidine exhibits three-bond 3JC2-C3 of about 5 Hz [43] and the C3 evolution (1JC3-C5) analyzed from C2-C3-C5-C6 spin selection can have a weak contribution from C2-C3. As explained below, from the same C2-C3-C5-C6 encoded set, the long range 3JC2-C3 is also simultaneously determined by analysing the echo modulation of C2. The error estimation and confidence limits are derived by considering the experimental noise for each trajectory of the spin-echo (for details please see the supporting information).
8
Figure 2: I) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5C6) of 13C6 L-Histidine.HCl (a) and the corresponding HE-MSR traces (b-e) for C3-C4-C1 spin combination that are encoded according to the signs in the rows of the Hadamard matrix, H4 . II) Appropriate linear combinations of e, d, c and b have yielded traces with only C4, C1 and C3 resonances as shown in II(f-h), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. III) The spin-echo modulation of C4 (i) is complex due to its simultaneous J-evolution with C3 and C1, which makes the analysis difficult. Whereas, fitting of the Hadamard edited spin-echo modulations of C1 (j) and C3 (k) to the equation (1) has resulted in 1JC1-C4 and 1JC3-C4, respectively in a single experiment. Long range 3JCC coupling: The magnitude of the long rage couplings such as, 3JC2-C3 is rather small and the spin-echo modulation (exponential decay) is expected to be predominantly due to the T2 relaxation and hence the estimation of JCC from the equation (1) is not easy. However, from the equations (1) and (2), the ratio of spin echo modulations S(τ)/So(τ)∝cos(πJ(τ-τsh))can be computed, which yields the spin-echo evolution term with the contribution due to T2 relaxation suppressed [20]. This simplification allows to determine the small J-coupling values. Accordingly, for the C2-C3-C5-C6 combination (Figure 3.I and Figure 3.II), the 3JC2-C3 value (4.4±0.2 Hz) is estimated (Figure 3.III(l)), which is consistent with that derived by encoding only C2-C3 (N=2) pair and also with that reported earlier (by using double-selective refocusing pulses) [20]. Except 3JC2-C3, no long-range scalar couplings 9
of significant magnitude are observed for U-13CHistidine.HCl. Further, as shown in Figure 3.III(m), the 1JCC and 3JCCvalues obtained through HE-MSR method are found to be in excellent agreement with those measured in the solution-state [43].
Figure 3: I) Comparisons between conventional full-CP/MAS spectrum (C1-C2-C3-C4-C5C6) of 13C6 L-Histidine.HCl (a) and the corresponding HE-MSR traces (b-e) for C6-C5-C3C2 spin combination that are encoded according to the signs in the rows of the Hadamard matrix, H4 . II) Appropriate linear combinations of e, d, c and b have yielded traces with only C6, C2, C5 and C3 resonances as shown in (f-i), respectively. The JCC scalar couplings are computed from the modulation of the respective spin-echoes. III) Fitting of the spin-echo modulations of C6 (j) and C3 (k) to the equation (1) in the C2-C3-C5-C6 encoding has resulted in 1JC5-C6 and 1JC3-C5, respectively in a single experiment. The variation of the C2 signal intensity S(τ) in the C6-C5-C3-C2 combination is found to be predominantly exponential decay (closed circles •) due to the dominant T2 relaxation, with a minor component due to J-interactions. This is closely comparable to the pure T2-relaxation decay of C2 (So(τ), open circles ) (l). As discussed in the text, the ratio of the S(τ) and So (τ) (crosses X) of the two modulations has allowed to estimate 3JC2-C3. The solid line represents the best fit to the S/So=A cos (πJτ). The excellent correlation between nJCC values derived from solution-state and HE-MSR solid-state, is shown in (m).
Conclusions
Direct measurement of homonuclear spin-spin couplings in the solid-state, particularly for uniformly labelled samples, is hampered due to the inherent dipolar and CSAdominated line broadening, even under the magic angle spinning (MAS) and this exercise is
10
more complex in multi-spin solids, which make the measurements difficult. In order to address this, herein we have discussed a new and versatile multiple frequency selective refocusing scheme based on Hadamard encoding (HE-MSR). The HE-MSR approach does not require pair-wise measurements of spin-spin couplings or a set of specially synthesized 13
C2 labelled molecules. The efficacy of this method is exemplified for simultaneous and
unambiguous measurement of multiple
13
C-13C scalar couplings (both small and large) in
uniformly 13C labelled Histidine. HCl. Further, this method can be extended to 2D/3D NMR schemes, particularly for small bio-molecular solids.
Acknowledgements The authors thank Prof. Malcolm Levitt (University of Southampton, UK) and Prof. Bernhard Blümich (RWTH, Aachen, Germany) for useful discussions. KVMR and BJ thank CSIR-IICT, India for financial support.
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Graphical abstract Manuscript: " Solid-state Hadamard NMR spectroscopy: Simultaneous measurements of multiple selective homonuclear scalar couplings” by Kakita et al.,
Highlights •
Hadamard encoded multiple selective refocusing scheme for solid-state NMR
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Simultaneously allows commutation of spin-spin interactions in multi-spin systems
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Precise measurement of multiple JCC couplings uniformly 13C-labelled solids
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Method can be extended to the measurement of dipolar couplings and 2D/3D schemes
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Applicable to small biomolecular solids
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