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Speeding up the measurement of one-bond scalar (1J) and residual dipolar couplings (1D) by using non-uniform sampling (NUS)
Journal of Magnetic Resonance 216 (2012) 134–143
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Speeding up the measurement of one-bond scalar (1J) and residual dipolar couplings (1D) by using non-uniform sampling (NUS) Christina M. Thiele a,⇑, Wolfgang Bermel b a b
Clemens Schöpf Institut für Organische Chemie und Biochemie, Technische Universität Darmstadt, Petersenstr. 22, 64287 Darmstadt, Germany Bruker Biospin GmbH, Silberstreifen 4, 76287 Rheinstetten, Germany
a r t i c l e
i n f o
Article history: Received 17 November 2011 Revised 12 January 2012 Available online 1 February 2012 Keywords: NMR Coupling constant measurement Non-uniform sampling J-scaling Partial alignment Compressed sensing
a b s t r a c t The accurate and precise measurement of one-bond scalar and residual dipolar coupling (RDC) constants is of prime importance to be able to use RDCs for structure determination. If coupling constants are to be extracted from the indirect dimension of HSQC spectra a significant saving of measurement time can be achieved by non-uniform sampling (NUS). Coupling constants can either be obtained with the same precision as in traditionally acquired spectra in a fraction of the measurement time or the precision can be significantly improved if the same amount of measurement time as for traditionally acquired spectra is invested. The application of NUS for the measurement of 1J (scalar coupling constants) and 1T (total couplings constants) from different kinds of x1-coupled spectra (including also J-scaled ones) is examined in detail and the possible gains in time or resolution are discussed. When using the newly proposed compressed sensing (CS) algorithm for processing, the quality of the spectra is comparable to the traditionally sampled ones. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Due to their global orientation information content (residual) dipolar couplings (RDCs) have shown significant impact on the structure determination of biomolecular [1,2] and organic compounds [3–6]. (R)DCs are anisotropic NMR parameters, which become observable if the compound in question is (marginally) oriented with respect to the magnetic field. If the degree of order is very small (order parameters S 10 4–10 5), the dipolar coupling interaction D is scaled down by the same factor and is thus small with respect to scalar coupling constants J [7]. If this is the case (D < J) these are then called residual dipolar couplings. In these cases the dipolar coupling constants (D) are obtained from the difference in line splitting between anisotropic (T = J + 2D) and isotropic samples (J). As they are calculated from the difference of two coupling constants it is of prime importance to measure scalar coupling constants (J) and total coupling constants (T) as accurately and precisely as possible. For organic compounds – the class of compounds this article is focussed on but not necessarily limited to – the most widespread used RDCs are the one bond 1H–13C RDCs (1DC–H). If one decides to measure the 1J/1T directly as frequency difference, there is a multitude of methods with different underlying ⇑ Corresponding author. Fax: +49 6151 16 72081. E-mail address: [email protected] (C.M. Thiele). URL: http://www.thielelab.de (C.M. Thiele). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jmr.2012.01.008
principles such as IPAP, spin-state selection, and E.COSY, to do so [8–15]. Whether it is best to obtain the frequency difference from the indirect (x1) or direct (x2) dimension of 2D HSQC spectra depends on many factors, such as relaxation properties of the compound in question, signal dispersion, degree of alignment of the oriented sample and thus size of 1H–1H dipolar coupling constants and many more. Both methods have their advantages and drawbacks. Acquisition of HSQC spectra with coupling evolution in the direct dimension is clearly the faster way, allows for almost unlimited digital resolution and also allows the assignment of coupling constants in methylene pairs. Problems with anti-phase contributions due to a mismatch of delay in the INEPT transfer step and the total coupling constant in aligned samples [16] can efficiently be eliminated by using CLIP/CLAP HSQC [17] or IPAP [13] approaches. Especially the CLIP-HSQC has been extremely useful in our hands and the results as far as accuracy and precision of coupling constants obtained within this publication are concerned will be compared with this ‘‘gold standard’’. It might however happen that one of the above factors (especially large 1H–1H dipolar couplings in methylene groups seem to be a key problem in organic compounds) prevents the ‘‘quick’’ measurement of RDCs from the direct dimension and thus the measurement needs to be performed with coupling evolution in the indirect dimension. This is then usually performed by removing the 180° 1H pulse in the middle of the evolution period as has been proposed by different groups [18,19] (see Fig. 2b) leading
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(b)
(a) trad. (FFT)
(c) 20%
(d) 30%
40%
10
δ (13C)
15 20 25 30 35 40 45 50 55 60 65 70 75 [ppm] [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0
δ (1H) Fig. 1. x1-Coupled HSQC (for the pulse sequence see Fig. 2a) of an isotropic sample of (+)-IPC recorded (a) traditionally with 4k complex points, (b) 20% of 4k (20%/4k/819), (c) 30% of 4k (30%/4k/1228) and (d) 40% of 4k (40%/4k/1638).
to a spectrum in which the signal is split by 1JC–H/1TC–H in the indirect dimension. The troublesome 1H–1H coupling, however, evolves exclusively in x2 and thus does not disturb the 1JC–H coupling constant measurement in x1. One (potential) problem, however, remains: Not only 1JC–H/1TC–H couplings evolve during t1, but also long range C–H couplings. These lead to an additional broadening or even splitting in x1 and are thus a potential source of error when extracting RDCs. It was shown, that these can very efficiently be removed by using the G-BIRD(r) module [20–22]. To achieve a resolution also in x1 comparable to the one possible in x2 a very large number of increments needs to be recorded, which is very time-consuming. Already from the very beginning [18] it was perceived that, by using J-scaling the number of increments can be reduced significantly. Another very effective way to reduce the number of increments in (the) indirect dimension(s) of multi-dimensional data sets is the concept of reducing the number of sampled time domain data points via non-uniform sampling (NUS) [23–30], or nonlinear sampling (NLS) [31,32]. These methods differ from the conventional sampling scheme, in which the time domain data points are sampled linearly in an equidistant manner (Nyquist grid), by either acquiring only a given subset of theses points (on grid) in a random fashion (NUS) or by sampling a reduced number of data points off the Nyquist grid (NLS). Both methods allow the reduction of the number of sampled time domain data points and thus lead to significant time savings. Naturally the time-saving is the bigger, the higher the dimensionality of the data set is. This boosted the possibility of obtaining high-dimensionality data sets of biomolecular compounds (even up to 5D) [28,32,33] in reasonable time, including also experiments for the measurement of coupling constants (mostly from three dimensional NMR-spectra) [34–37]. As time saving was not expected to be significant for two dimensional spectra, very few applications of sparse sampling for
two-dimensional data sets have been published so far [38,39]. Very recently a compressed sensing (CS) algorithm has been proposed for the efficient processing of non-uniformly sampled 2D data sets [40,41]. We set out to investigate whether NUS in combination with CS can also improve the measurement of scalar and residual dipolar coupling constants in organic compounds from two dimensional x1-coupled HSQC spectra. A detailed investigation on the optimal and minimal ‘‘sparseness’’ of data sets, the potential saving in time and/or increase in resolution (at the same experimental time as for the conventionally sampled datasets) was conducted for different methods for measuring one-bond coupling constants in the indirect dimension of HSQC spectra (also including J-scaled ones).
2. Materials and methods 2.1. NMR sample preparation The solute used in this study was (+)-Isopinocampheol (IPC), which is commercially available from Sigma–Aldrich and was used as purchased (see Scheme 1, including numbering of atoms used throughout this publication). Both samples used were sealed after three pump–freeze–thaw cycles to guarantee constant conditions. The isotropic sample contained 54 mg (+)-IPC in CDCl3, the anisotropic sample was prepared as follows: The corresponding amount of high-molecular weight poly-c-benzyl-L-glutamate (HMW-PBLG, 50 mg polymer, Mn = 470.000 g/mol; Mw = 1.000.000 g/mol; [42]) was weighed into the NMR sample tube, IPC (23 mg) and the organic co-solvent CDCl3 were added to give a 7.5% w/w concentration of PBLG. A [d6]DMSO capillary was added to provide the lock signal. The polymer was allowed to dissolve overnight and the sample centrifuged back and forth until the 2H signals were sharp and the line widths constant. The quadrupolar splitting (DmQ) of
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(a)
(b)
(c)
(d)
Fig. 2. Pulse sequences for x1-coupled HSQC spectra used: (a) x1-coupled HSQC obtained by removing the 1H p-pulse in the middle of the evolution period [18]; (b) x1coupled HSQC using a G-BIRD(r)-element to remove 1H–13C long range couplings [20]; (c) x1-coupled HSQC with G-BIRD(r)-element and scaling; (d) x1-coupled HSQC with GBIRD(r)-element, scaling and double quantum J-evolution for the measurement of coupling constants in CH2 groups [45]. Narrow filled rectangles are hard p/2 pulses, wide filled rectangles p-pulses. Narrow shaped filled pulses on 13C are adiabatic inversion pulses (chirp pulses of 60 kHz sweep width, 500 ls duration, 20% smoothing, 1000 points were used here), wide shaped filled pulses are adiabatic refocusing pulses (composite smoothed chirp pulse consisting of three elements with an R ratio of 1:2:1, each with 60 kHz sweep width and 20% smoothing, a length ratio of 500 ls, 1 ms, 500 ls (1:2:1) and a total duration of 2 ms were used here); open shaped pulses on 13C are 720-10010-BIP (broad band inversion) pulses of length 160 ls [46]. Phases of pulses as indicated; gradients of 1 ms duration were used for echo–antiecho selection, GARP4 [47] decoupling was used; D1 (D1 = 1/(41J), INEPT) and D2 (D2 = 1/(21J), G-BIRD(r)) were adjusted for 1J = 145 Hz (unless indicated otherwise), the scaling factor j for J-evolution in (c) and (d) was set to 8.
the solvent was 211 Hz (at 298 K) and remained constant over several months (change in splitting of maximum 1.24 Hz over 11 d and 7 h measurement time). 2.2. NMR experiments All experiments were performed on a 600 MHz Bruker Avance III NMR spectrometer (Bruker Biospin, Rheinstetten) under Topspin 3.0 equipped with a TXI (H–C,N) probe with z gradient. Temperature was set to 298 K for all experiments. The number of scans was 2, the relaxation delay was set to 2 s in all experiments. Unless otherwise stated the delays used for transfer of magnetization via one-bond coupling were set for a 145 Hz coupling constant. CLIP-HSQC spectra [17], in which coupling constants are obtained from splittings in x2, were acquired with 8k complex data points over a spectral width of 11 ppm in x2 to give a FID resolution of 0.4 Hz. In x1 128 complex data points over 82.8 ppm spectral width were (more than) sufficient to prevent overlap. In both dimensions a p/2-shifted sine-squared window function and zero filling by a factor of 2 was applied. x1-Coupled experiments (with or without BIRD-module, with or without scaling) were performed with the pulse sequences shown in Fig. 2 and the same spectral widths as above. In x2 1k complex data points were sampled. In x1 the number of complex data points varied (depending on pulse sequence, sparseness and desired resolution, see below, Figs. 1 and 3–6, Tables 1–4) between
Scheme 1. (+)-Isopinocampheol (IPC).
512 or 4k complex points for traditionally sampled data and between 30% out of 512 complex points and 25%/16k complex points leading to between 153 and 4k complex points to be acquired with total experimental times of 23 min to 10 h 40 min. In the remainder of the text x%/y/z will denote the number of complex points being x% out of y points leading to z acquired complex points. In both dimensions a p/2-shifted sine-squared window function and zero filling by a factor of 2 was applied. 2.3. Sampling scheme and processing of NUS data sets The list of points to be acquired was calculated using the program nussampler [43] based on the maximum number of t1 points
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trad. (FFT)
(a)
NUS
(b)
23.0
(13C)
23.5 24.0 24.5
1 -coupled HSQC (a)
25.0 25.5 [ppm]
(d)
(c)
23.0 23.5 24.0
HSQC BIRD (b)
24.5 25.0 25.5 [ppm]
0.93 0.92 0.91 [ppm]
0.93 0.92 0.91 [ppm]
(1H) Fig. 3. Section of the C9 methyl group of (+)-IPC in isotropic solution and corresponding extracted columns from x1-coupled HSQC (a and b) and BIRD-HSQC (c and d) spectra recorded under traditional sampling scheme (a and c) and using NUS with 30% of 4k (30%/4k/1228) complex points (b and d).
and a given percentage. The points are randomly distributed within this range. For the processing of the data, first a Fourier transformation is applied along the acquisition dimension. The data are further processed by compressed sensing [35] using the IRLS algorithm with norm = 0. This will sort the data points according to the normal grid, reconstruct the points not measured and is followed by a FT along the indirect dimension [44]. 2.4. Measurement of coupling constants Scalar or total coupling constants were obtained from the spectra by extracting rows (in the case of CLIP) or columns (in all other cases), copying them and shifting them with respect to each other until the best possible overlap of the respective multiplet component was obtained. The error was determined by shifting the line to both sides until it was clearly discernible that the overlap was not acceptable anymore. 3. Results and discussion 3.1. x1-Coupled HSQC and sampling density We started our investigation by varying the degree of sparseness (see Fig. 1) in the most simple pulse sequence for the measurement of RDCs in x1-coupled HSQCs, in which the p-pulse on protons in the middle of the evolution period is removed (see Fig. 2a) [18,19]. The extracted coupling constants are compared with the ones obtained from the x2-coupled CLIP-HSQC [17]. Thus we chose 4k complex points for this initial test to reach a resolution that makes extracted coupling constants comparable to the CLIP-HSQC. We have recorded the x1-coupled HSQC traditionally (Fig. 1a), with only 20% (Fig. 1b), 30% (Fig. 1c) and 40% (Fig. 1d) of the traditionally sampled data points. We were not able to discern any difference between the quality of traditionally sampled spectra (10 h 40 min) and those obtained by using different degrees of sparseness (by visual inspection of the spectra and extracting columns and overlaying them). Also, coupling constants extracted from the NUS data sets do not differ from the ones obtained from the traditionally sampled ones (data
not shown). Thus coupling constants can – in principle – be extracted from sparsely sampled x1-coupled HSQC data sets and as little as 20% of the traditionally sampled data points (2 h) are clearly sufficient using the compressed sensing algorithm for processing. When increasing the sparseness further (10%), either artefacts (such as cross peaks arising from COSY transfer) start to disappear (which generally would be a nice situation, but might indicate that important information is also lost) or phase problems start to occur, which might lead to errors in the extraction of coupling constants. Thus for x1-coupled HSQC the minimum requirement on sparseness is 20% of 4k (20%/4k/819) complex points. As has been reported previously, long-range C–H couplings (nJC–H/nTC–H) also evolve during t1 and can thus lead to a broadening of resonances. This is a potential source of errors in the extracted coupling constants [20]. With the high resolution we chose we even see fully resolved multiplets (see Fig. 3a and b) for most of the resonances. As the number of signals increases significantly when long-range couplings are resolved, we decided to choose the conservative 30% sparseness for the further investigation, which nevertheless provides a time saving of 70%. When comparing the 1J coupling constants extracted from CLIPHSQC (column 1, Table 1) with the ones from x1-coupled HSQC (column 2 of Table 1), we observed that – as long as the long-range couplings are resolved (which is the case for C4, C7–C10) – coupling constants of the same size with almost equal precision and accuracy can be obtained. If, however, lines are only broadened by long-range couplings systematic deviations occur as is the case for C1, C2, C3 and C5. As has been observed previously [20,48] for methylene groups the individual coupling constants cannot be extracted from x1coupled HSQC as the central anti phase peaks overlap or cancel. In the anisotropic phase this problem is alleviated, but not fully resolved as the central peaks are quite broad and are thus not base line separated. This leads to rather large errors. One possible solution for the CH2 group problem [45] will be examined later (see below). NUS cannot only be used to reduce experimental time for a given digital resolution, but also to increase resolution for a given experiment time. Thus we also recorded spectra with 25% out of 16k complex data points (25%/16k/4k), to find out whether the
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isotropic HSQC-BIRD
(a)
anisotropic J-scaled HSQC-BIRD =8
(b)
HSQC-BIRD
(c)
J-scaled HSQC-BIRD =8 (13C)
(d)
[ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0
(1H) Fig. 4. (a and c) BIRD-HSQC (sequence b) and (b and d) BIRD-HSQC with scaling (sequence c, j = 8) for the isotropic (a, b) and anisotropic sample (c, d) of IPC.
errors observed are due to the limited resolution. As can be seen from Table 1 (column 3) the deviations are still present for the same coupling constants. The same is true for the 1T coupling constants (see Table 2), although deviations are generally larger due to the broader lines in the anisotropic phase. Such a high number of increments would never be recorded for conventionally sampled spectra and we have expected to be limited by relaxation. With the compound and sample preparation method chosen here, we did not observe severe losses due to relaxation in this study (neither for the isotropic nor for the anisotropic sample). 3.2. x1-HSQC with BIRD We believed that the deviations observed above are due to not resolved long-range couplings and thus turned our attention towards a pulse sequence that was especially designed to remove C–H long range couplings – namely the x1-coupled HSQC with G-BIRD(r)-element [20]. The pulse sequence is shown in Fig. 2b; a section from the isotropic spectra (trad. and NUS) together with the corresponding column is shown in Fig. 3c and d, the full spectrum of the isotropic and anisotropic sample is shown in Fig. 4a and c. As can be seen in Fig. 3c and d, lines are much sharper, also leading to much higher S/N. Again no difference can be discerned between the traditionally sampled spectra (10 h 40 min) and the ones recorded with 30% of the increments (30%/4k/1228, 3 h 10 min). When comparing the coupling constants extracted from the BIRD-HSQC with the CLIP it can be seen that for the isotropic sample the match is almost perfect. For the anisotropic sample, there is only one coupling constant for which the values extracted from
BIRD-HSQC and CLIP-HSQC are not in perfect agreement. Already at this rather low degree of alignment lines of several C–H pairs are severely broadened by 1H–1H dipolar couplings in the CLIP, which leads to a rather large error margin for some of the coupling constants. For the isotropic sample the methylene group problem remains, but in the anisotropic sample at least one of the central lines is sharp enough to lead to a reliably extractable coupling constant. As can be seen from the columns in Fig. 3c and d, there are some artefacts present in the spectra. These have already been observed in the initial publication [18] and are due to a mismatch in the BIRD element (variation of 1J/1T coupling). As was already observed by Feher et al. these artefacts appear in the center of the multiplet and can thus be identified easily and in our case did not impede the extraction of coupling constants. As above we investigated, whether it is not only possible to save time with NUS, but also to increase resolution. Thus we recorded spectra with 25% out of 16k complex data points (25%/16k/4k, same experimental time as the traditionally sampled one). When doing so we obtained spectra with astonishing resolution and extremely sharp lines, thus leading to very precise and accurate coupling constants (compare column 1 and 5 of Tables 1 and 2). After we had seen, that 30% of 4k complex points lead to excellent spectra with much higher S/N than in the x1-coupled HSQC, we realized that for this sequence it might be possible to reduce the number of points further. We found out, that even for 5% sparseness (out of 4k, 5%/4k/204) excellent spectra with more than sufficient S/N are obtained, thus reducing the experimental time from 10 h 40 min to 31 min without any significant loss in spectral quality. Piqued by this observation, we then investigated, whether it is possible to also increase the sparseness in the highly resolved spectra (16k complex points). Down to 1.25% out of 16k (1.25%/
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(a)
(b)
BIRD HSQC(b) trad.
J-scaled BIRD HSQC(c) trad., =8 512 1h20
4k 10h40 (1JCH1 + 1JCH2 )
[ppm]
40.5
(c)
40.0
39.5
39.0
38.5
38.0
[ppm]
J-scaled BIRD HSQC(c) NUS, =8
(d)
48 46 44 42 40 38 36 34 32 30 28
J-scaled BIRD HSQC(c) NUS, =8 25%/2k 1h20
30%/512 23min
[ppm]
48 46 44 42 40 38 36 34 32 30 28
[ppm]
48 46 44 42 40 38 36 34 32 30 28
(13C) Fig. 5. Columns of the CH2 group at C4 of the isotropic (+)-IPC sample extracted from (a) the traditionally sampled BIRD-HSQC (sequence b, 4k complex points), (b) the traditionally sampled J-scaled BIRD-HSQC (sequence c, j = 8, 512 complex points), (c) J-scaled BIRD-HSQC with NUS (sequence c, j = 8, 30% (30%/512/153), (d) J-scaled BIRDHSQC with NUS (sequence c, j = 8, 25% (25%/2k/512). The relative intensities of lines (resulting from the INEPT transfer) are opposite when going from the BIRD-HSQC to the BIRD-HSQC with scaling. This is due to the different number of p-pulses (see Fig. 2b and c) and could be corrected for if necessary.
16k/204, 31 min) no difference in the spectra is discernible. Below that, artefacts start disappearing again. Thus for this sequence it is not only possible to reduce experimental time by NUS, or increase resolution; it is also possible to do both at the same time: increase resolution to 16k complex points and reduce experimental time to 31 min. This is of course only true as long as relaxation and sensitivity are not an issue, neither was critical here. At first glance this large difference between the minimum number of sampled data points in x1-coupled HSQC and its BIRD variant is surprising. It can, however, be nicely explained by the large difference in numbers of frequencies observed in the two spectra. During the work with NUS we got the impression that the following rule of thumb can be proposed: The number of complex points sampled should be higher than the number of signals expected (see also Ref. [49]). For the measurement of coupling constants the same is essentially true with two restrictions: (a) the number of frequencies (including all splitting by long-range couplings) and not just the number of signals expected needs to be taken into account; (b) if one wants to make sure not to loose any information also the additional frequencies resulting from artefacts (like COSY cross peaks in HSQC) need to be considered. As splittings resulting from long-range couplings are efficiently removed by the BIRD module, the number of frequencies and thus demand on sampled data points is drastically reduced in x1-coupled HSQCs with BIRD. It has to be highlighted at this point that using 1.25% out of 16k data points in the x1-coupled HSQC leads to couplings as accurate and precise as from the CLIP-HSQC in as little as 31 min !
3.3. x1-Coupled HSQC with G-BIRD(r)-element and scaling Already from the very beginning of the measurement of RDCs in
x1-coupled HSQCs it was recognized, that the number of increments can be significantly reduced if J-scaling is used. We have combined this idea with the BIRD-HSQC. The resulting pulse sequence is shown in Fig. 2c. We investigated whether this pulse sequence also allows a significant time saving and whether this time saving can even be increased by using NUS. To have comparability with pulse sequence b (BIRD-HSQC) we used a scaling factor of j = 8. As can be seen in Figs. 4 and 5a and b, the high spectral quality of the BIRD-HSQC is retained, while the splitting is multiplied by 8. This leads already to a significant time saving (1 h 20 min vs. 10 h 40 min) at the same resolution for J. Of course, in cases of less welldispersed signals, overlap can occur. The couplings extracted for the isotropic and anisotropic sample can be found in Table 3. As can be seen the couplings for the isotropic and for the anisotropic sample (with exception of the same coupling constant as above) match perfectly to the ones extracted from CLIP HSQC. The same investigation concerning NUS as above was also conducted using this pulse sequence. In Fig. 5 columns for C4 are extracted for the isotropic sample and again the two concepts: (a) reduction of measurement time by NUS (30%/512/153, Fig. 5c and b) increase of resolution by NUS (25%/2k/512, Fig. 5d) are compared to the traditionally sampled J-scaled BIRD-HSQC (1k, Fig. 5b). As can be seen both approaches lead to spectra of excellent quality.
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(a)
(b)
BIRD HSQC(b) trad.
J-scaled BIRD HSQC with MQ-evolution (d) trad., =8
4k 10h40
512 1h20
CH1
[ppm] 40.5 40.0
(c)
39.5
39.0
38.5
38.0
48 46 44 42 40 38 36 34 32 30 28
[ppm]
J-scaled BIRD HSQC with MQ-evolution (d) NUS, =8
(d)
JCH2
1
J-scaled BIRD HSQC with MQ-evolution (d) NUS, =8
30%/512 23min
[ppm]
25%/2k 1h20
48 46 44 42 40 38 36 34 32 30 28
48 46 44 42 40 38 36 34 32 30 28
[ppm]
(13C) Fig. 6. Columns of the CH2 group at C4/H4a = H1 of the isotropic (+)-IPC sample extracted from (a) the traditionally sampled BIRD-HSQC (sequence b, 4k complex points), (b) the traditionally sampled J-scaled BIRD-HSQC with DQ-evolution (sequence d, j = 8, 512 complex points), (c) J-scaled BIRD-HSQC with DQ-evolution with NUS (sequence d, j = 8, 30%/512/153), (d) J-scaled BIRD-HSQC with DQ-evolution with NUS (sequence d, j = 8, 25%/2k/512). In b, c and d only the passive C–H (1JC–H2=H4s) coupling together with the geminal H–H coupling is observed.
Table 1 Comparison of 1JC–H coupling constants extracted from CLIP-HSQC (column 1), x1-coupled HSQC (column 2, 3) and x1-coupled HSQC with G-BIRD(r) (column 4, 5) using traditional sampling (column 2, 4) and NUS (25%/16k/4k, column 3, 5) for the isotropic sample of (+)-IPC. Pulse sequence (# in Fig. 2)
CLIP HSQC
x1-Coupled HSQC (a)
Sampl. scheme/# of data points
8k (in x2)
Traditional 4ka,b 1
13
Coupling C1 C2 C3 C4 C5 C7 C8 C9 C10
H1 H2 H3 H4s H4a H5 H7s H7a H8 H9 H10
d( C)
d( H)
1
47.83 47.69 71.59
1.79 1.93 4.06 2.5 1.71 1.93 2.37 1.04 1.21 0.91 1.13 FIDres:
140.87 ± 0.2 126.54 ± 0.1 141.98 ± 0.1 126.54 ± 0.2 126.95 ± 0.1 141.14 ± 0.1 135.12 ± 0.1 136.95 ± 0.1 124.63 ± 0.1 123.65 ± 0.1 124.86 ± 0.1 0.4
39 41.77 34.37 27.68 23.7 20.74
1
JC–H (Hz)
JC–H (Hz)
BIRD-HSQC (b) NUS (25%/16k/4k)b 1
JC–H (Hz)
Traditional 4ka,b
NUS (25%/16k/4k)b
1
1
JC–H (Hz)
JC–H (Hz)
144.76 ± 0.5 128.01 ± 1 144.25 ± 1
144.92 ± 0.5 128.21 ± 0.5 144.52 ± 2
140.92 ± 0.5 126.6 ± 0.2 142.04 ± 0.2
140.91 ± 0.2 126.58 ± 0.1 141.99 ± 0.1
253.6 ± 0.5
253.48 ± 0.5
253.44 ± 0.2
253.45 ± 0.1
143.56 ± 1
143.77 ± 2
141.24 ± 0.2
141.2 ± 0.1
272.52 ± 0.5
272.14 ± 0.3
272.03 ± 0.2
272.07 ± 0.1
124.55 ± 0.5 123.61 ± 0.5 124.76 ± 0.5 1.52
124.65 ± 0.2 123.69 ± 0.2 124.74 ± 0.2 0.38
124.58 ± 0.2 123.58 ± 0.2 124.8 ± 0.2 1.52
124.62 ± 0.1 123.65 ± 0.1 124.83 ± 0.1 0.38
a Spectra recorded under traditional conditions and using 30% NUS (30%/4k/1228) are identical; thus coupling constants are also identical to the ones from traditionally sampled spectra and are not listed. b Only the sum of couplings to methylene protons can be extracted from these spectra as the difference in couplings is too small to lead to observable/evaluable anti-phase patterns.
When we tried to increase the sparseness further (as above), we realized that 30% (30%/512/153, 23 min) is the minimum, for the higher resolution 20% (20%/2k/408, 64 min) is the lower limit of the data we recorded. We believe that 15% would also have led to satisfactory results. As this sparseness was not recorded, we chose to report the conservative values.
3.4. x1-Coupled HSQC with G-BIRD(r)-element, scaling and double quantum J-evolution As can be nicely seen in Fig. 5, again individual coupling constants for CH2 groups are not accessible for the isotropic sample from the J-scaled BIRD-HSQC as was the case for all other x1-coupled HSQC
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Table 2 Comparison of 1TC–H couplings extracted from CLIP-HSQC (column 1), x1-coupled HSQC (column 2,3) and x1-coupled HSQC with G-BIRD(r) (column 4,5) using traditional sampling (column 2, 4) and NUS (25%/16k/4k, column 3, 5) for the anisotropic sample of (+)-IPC. Pulse sequence (Fig. 2)
CLIP HSQC
x1-Coupled HSQC (a)
Sampl. scheme/# of data points Coupling
8k (in x2) 1 TC–H (Hz)
Traditional 4ka,b 1 TC–H (Hz)
NUS (25%/16k/4k) 1 TC–H (Hz)
1
Traditional 4ka,b TC–H (Hz)
NUS (25%/16k/4k) 1 TC–H (Hz)
C1 C2 C3
166.37 ± 3 115.07 ± 1 162.22 ± 0.5 148.99 ± 0.4 117.99 ± 0.4 130.97 ± 0.3 141.86 ± 0.5 104.48 ± 0.5 130.57 ± 0.4 118.14 ± 0.2 124.1 ± 0.2 0.4
168.3 ± 1 117.7 ± 1 165 ± 1 151.48 ± 2 117 ± 3 134.9 ± 1 139 ± 5d 105 ± 5d 130.62 ± 1 117.58 ± 1 123.71 ± 1 1.52
168.25 ± 0.5 117.14 ± 0.5 164.46 ± 0.5 148.97 ± 1 117.78 ± 1 134.38 ± 1 137 ± 5d 110 ± 5d 130.2 ± 0.5 118.17 ± 0.5 123.89 ± 0.5 0.38
165.04 ± 0.2 115.4 ± 0.2 162.79 ± 0.2 149.48 ± 0.2 117.55 ± 0.2 131.55 ± 0.2 142 ± 2 103.8 ± 2 130.78 ± 0.2 117.69 ± 0.2 123.79 ± 0.2 1.52
164.75 ± 0.2 115.02 ± 0.2 161.83 ± 0.1 148.4 ± 0.1 118.05 ± 0.1 130.98 ± 0.2 142.3 ± 0.2 104.94 ± 0.2 130.22 ± 0.1 118.15 ± 0.2 123.92 ± 0.1 0.38
H1 H2 H3 H4s H4a H5 H7sc H7ac H8 H9 H10 FIDres:
C4 C5 C7 C8 C9 C10
BIRD-HSQC (b)
a Spectra recorded under traditional conditions and using 30% NUS (30%/4k/1228) are identical; thus couplings are also identical to the ones from traditionally sampled spectra and are not listed. b Couplings were extracted from spectra with different D1 (and D2 in the case of the BIRD-HSQC). Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts in BIRD-HSQC, see text), such that for the 25% NUS (25%/16k/4k) spectra we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. c The H–H total coupling constant is ca. 40 Hz, which makes extraction from CLIP error prone. d The center peaks (anti-phase) are not completely base line separated. Thus the error given is a conservative estimate.
Table 3 Comparison of 1JC–H and 1TC–H couplings extracted from CLIP HSQC (column 1, 4) and J-scaled HSQC-BIRD (sequence c) using traditional sampling (512, j = 8, column 2, 5) and NUS (25%/2k/512, j = 8, column 3, 6) for the isotropic (columns 1, 2, 3) and anisotropic sample (columns 4, 5, 6) of (+)-IPC. Sample
Isotropic
Pulse sequence (Fig. 2)
CLIP HSQC
J-scaled HSQC-BIRD
Sampl. scheme/# of points
8k (in x2)
Traditional 512a,b
NUS (25%/2k/512)b
8k (in x2)
Traditional 512c
NUS (25%/2k/512)
1
1
1
1
1
140.97 ± 0.25 126.57 ± 0.25 142.01 ± 0.25
140.89 ± 0.1 126.56 ± 0.1 142.01 ± 0.1
166.37 ± 3 115.07 ± 1 162.22 ± 0.5 148.99 ± 0.4 117.99 ± 0.4 130.97 ± 0.3 141.86 ± 0.5 104.48 ± 0.5 130.57 ± 0.4 118.14 ± 0.2 124.1 ± 0.2 0.4
165.18 ± 0.5 115.05 ± 0.5 161.28 ± 0.5 149.13 ± 0.5 117.94 ± 0.5 131.28 ± 0.5 142.19 ± 0.5 104.6 ± 0.5 130.49 ± 0.5 118.15 ± 0.5 124.03 ± 0.5 1.52
165.21 ± 0.1 114.90 ± 0.1 161.80 ± 0.1 148.36 ± 1d 118.03 ± 1d 131.00 ± 0.1 142.39 ± 1d 104.92 ± 1d 130.18 ± 0.1 118.22 ± 0.1 123.95 ± 0.1 0.38
13
Coupling C1 C2 C3 C4 C5 C7 C8 C9 C10
H1 H2 H3 H4s H4a H5 H7se H7ae H8 H9 H10
d( C)
d( H)
1
47.83 47.69 71.59
1.79 1.93 4.06 2.5 1.71 1.93 2.37 1.04 1.21 0.91 1.13 FIDres:
140.87 ± 0.2 126.54 ± 0.1 141.98 ± 0.1 126.54 ± 0.2 126.95 ± 0.1 141.14 ± 0.1 135.12 ± 0.1 136.95 ± 0.1 124.63 ± 0.1 123.65 ± 0.1 124.86 ± 0.1 0.4
39 41.77 34.37 27.68 23.7 20.74
1
JC–H (Hz)
Anisotropic
JC–H (Hz)
CLIP HSQC
JC–H (Hz)
253.45 ± 0.25
253.40 ± 0.1
141.29 ± 0.25
141.19 ± 0.1
272.07 ± 0.25
272.09 ± 0.1
124.56 ± 0.25 123.72 ± 0.25 124.87 ± 0.25 1.52
124.60 ± 0.1 123.65 ± 0.1 124.84 ± 0.1 0.38
TC–H (Hz)
J-scaled HSQC-BIRD
TC–H (Hz)
TC–H (Hz)
a Spectra recorded under traditional conditions and using 30% NUS (30%/512/153) are identical; thus couplings are also identical to the ones from traditionally sampled spectra and are not listed. b Only the sum of couplings to methylene protons can be extracted from the isotropic spectra as the difference in couplings is too small to lead to observable/evaluable anti-phase patterns. c Couplings were extracted from spectra with different D1 and D2. Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts due to J mismatch in the BIRD), such that for the 25% NUS (25%/2k/512) spectra we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. d The center peaks (anti-phase) are not completely base line separated. Thus the error given is a conservative estimate. e The H–H total coupling constant (in the anisotropic sample) is ca. 40 Hz, which makes extraction from CLIP error prone.
spectra investigated here. Among many other solutions [11–14,50], one clever solution to this problem uses the evolution of DQ magnetization, BIRD and J-scaling [20]. For a detailed description of the pulse sequence (Fig. 2d) the reader is referred to the original literature, here it should suffice to say, that one special property of multi quantum coherences (MQC) is used, namely that they are not modulated by the coupling between the active spins involved in them, but only evolve under the coupling of passive spins. Thus signals for CH2 groups are observed, in which the cross peak (of one geminal proton H1) carries the JC–H2 coupling constant of the (other geminal) passive spin (H2). An additional splitting by the geminal H1–H2 coupling constant is observed.
Using this pulse sequence we again performed the same tasks: recording a traditionally sampled spectrum (again using the scaling factor j = 8 to provide comparability), the fast NUS (30%/512/ 153) and the highly resolved NUS (25%/2k/512) ones (see Fig. 6). As can be seen in Fig. 6, the passive coupling (1JC–H2) can be obtained from the signal of the active spin (C–H1), together with the geminal 1H–1H coupling 2JH1–H2. When considering the line-shape observed in Fig. 6, which originate from 1H–1H coupling evolution of geminal protons during the BIRD module, it is quite surprising that a comparison of the values extracted from these spectra with those obtained from CLIP reveals almost perfectly accurate and precise coupling constants (see Table 4).
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Table 4 Comparison of 1JC–H and 1TC–H couplings extracted from CLIP HSQC (column 1, 4) and J-scaled HSQC-BIRD with DQ-evolution (sequence d) using traditional sampling (512, j = 8, column 2, 5) and NUS (25%/2k/512, j = 8, column 3, 6) for the isotropic (columns 1, 2, 3) and anisotropic sample (columns 4, 5, 6) of (+)-IPC. For completeness 2JH–H protons are also given. Sample
Isotropic
Pulse sequence (Fig. 2)
CLIP HSQC
J-scaled HSQC-BIRD, with DQ (d)
CLIP HSQC
Sampl. scheme/# of points
8k (in x2)
Traditional 512a
NUS (25%/2k/512)
8k (in x2)
Traditional 512b
NUS (25%/2k/512)
1
1
1
1
1
148.99 ± 0.4 117.99 ± 0.4
149.28 ± 1 118.03 ± 1 13.4 ± 2 142.28 ± 1 104.33 ± 1 36.5 ± 2 1.52
148.48 ± 1 117.85 ± 1 13.4 ± 1.25 142.14 ± 0.25 105.23 ± 0.25 35.6 ± 1.25 0.38
13
Coupling C4 H4s C7 H7s
H4s H4a H4a H7sc H7ac H7a
1
d( C)
d( H)
1
39
2.5 1.71
126.54 ± 0.2 126.95 ± 0.1
34.37
2.37 1.04
135.12 ± 0.1 136.95 ± 0.1
FIDres:
0.4
JC–H (Hz)
Anisotropic
JC–H (Hz)
126.56 ± 0.25 126.95 ± 0.25 14.3 ± 0.25 134.96 ± 0.25 137.15 ± 0.25 9.6 ± 0.25 1.52
JC–H (Hz)
126.53 ± 0.25 126.94 ± 0.13 14.0 ± 0.25 135.14 ± 0.13 136.98 ± 0.13 9.7 ± 0.25 0.38
TC–H (Hz
141.86 ± 0.5 104.48 ± 0.5 0.4
J-scaled HSQC-BIRD, with DQ (d)
TC–H (Hz)
TC–H (Hz)
a
Couplings from 30% NUS (30%/512/153) are essentially identical to the ones from traditionally sampled spectra (±0.2 Hz) and are not listed. Couplings were extracted from spectra with different D1 and D2. Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts due to J-mismatch in the BIRD), such that for the 25% NUS spectra /25%/2k/512) we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. c The H–H total coupling constant (in the anisotropic sample) is ca. 40 Hz, which makes extraction from CLIP error prone. b
The investigation concerning reduction of measurement time by NUS and increasing resolution by NUS was also conducted using this pulse sequence. In Fig. 6 columns for H4–H4a are extracted for the isotropic sample and for the NUS spectra: 30% (30%/512/153), Fig. 6c and 25% (25%/2k/512), Fig. 6d, which are compared to the traditionally sampled J-scaled BIRD-HSQC with DQ evolution (512 complex points, Fig. 6b). When we tried to increase the sparseness further, we saw that 30% (30%/512/153, 23 min) is the minimum, for the higher resolution 20% (20%/2k/408, 1 h) is the lower limit. 4. Conclusion We have investigated whether non-uniform sampling (NUS) in combination with the recently proposed compressed sensing (CS) algorithm for processing allows improving the measurement of one-bond scalar and total/residual dipolar couplings from different kinds of x1-coupled HSQCs. Two main points were investigated: Speeding up the measurement by reducing the number of sampled data points at the same digital resolution (time saving). Improving the resolution by sampling the same amount of data points as in traditionally sampled spectra but at a much higher digital resolution (resolution improvement). Both approaches yielded – in our eyes – spectacular improvements without any loss in spectral quality as long as the minimum requirements with respect to sparseness of the data was respected (number of sampled points > number of expected frequencies). When care was taken to remove long-range couplings by using the BIRD-HSQC and/or its J-scaled variants even a combination of the two upper approaches was possible (reduction of number of sampled data points at the same time as increasing resolution) making the measurement of couplings in x1 equally fast as in x2, while conserving accuracy and precision. This way an alternative for problems occurring in cases of large 1H–1H dipolar couplings (as is frequently observed in methylene groups) is offered. While we investigated these methods with a focus on small organic molecules in organic solvents, the extension to other cases should be straight forward. Acknowledgments C.M.T thanks the European Research Council (ERC, Starting Grant RDC@catalysis) for financial support. The authors thank To-
bias Montag for the preparation of the isotropic and anisotropic sample used in this study.
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Contents lists available at SciVerse ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Speeding up the measurement of one-bond scalar (1J) and residual dipolar couplings (1D) by using non-uniform sampling (NUS) Christina M. Thiele a,⇑, Wolfgang Bermel b a b
Clemens Schöpf Institut für Organische Chemie und Biochemie, Technische Universität Darmstadt, Petersenstr. 22, 64287 Darmstadt, Germany Bruker Biospin GmbH, Silberstreifen 4, 76287 Rheinstetten, Germany
a r t i c l e
i n f o
Article history: Received 17 November 2011 Revised 12 January 2012 Available online 1 February 2012 Keywords: NMR Coupling constant measurement Non-uniform sampling J-scaling Partial alignment Compressed sensing
a b s t r a c t The accurate and precise measurement of one-bond scalar and residual dipolar coupling (RDC) constants is of prime importance to be able to use RDCs for structure determination. If coupling constants are to be extracted from the indirect dimension of HSQC spectra a significant saving of measurement time can be achieved by non-uniform sampling (NUS). Coupling constants can either be obtained with the same precision as in traditionally acquired spectra in a fraction of the measurement time or the precision can be significantly improved if the same amount of measurement time as for traditionally acquired spectra is invested. The application of NUS for the measurement of 1J (scalar coupling constants) and 1T (total couplings constants) from different kinds of x1-coupled spectra (including also J-scaled ones) is examined in detail and the possible gains in time or resolution are discussed. When using the newly proposed compressed sensing (CS) algorithm for processing, the quality of the spectra is comparable to the traditionally sampled ones. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Due to their global orientation information content (residual) dipolar couplings (RDCs) have shown significant impact on the structure determination of biomolecular [1,2] and organic compounds [3–6]. (R)DCs are anisotropic NMR parameters, which become observable if the compound in question is (marginally) oriented with respect to the magnetic field. If the degree of order is very small (order parameters S 10 4–10 5), the dipolar coupling interaction D is scaled down by the same factor and is thus small with respect to scalar coupling constants J [7]. If this is the case (D < J) these are then called residual dipolar couplings. In these cases the dipolar coupling constants (D) are obtained from the difference in line splitting between anisotropic (T = J + 2D) and isotropic samples (J). As they are calculated from the difference of two coupling constants it is of prime importance to measure scalar coupling constants (J) and total coupling constants (T) as accurately and precisely as possible. For organic compounds – the class of compounds this article is focussed on but not necessarily limited to – the most widespread used RDCs are the one bond 1H–13C RDCs (1DC–H). If one decides to measure the 1J/1T directly as frequency difference, there is a multitude of methods with different underlying ⇑ Corresponding author. Fax: +49 6151 16 72081. E-mail address: [email protected] (C.M. Thiele). URL: http://www.thielelab.de (C.M. Thiele). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jmr.2012.01.008
principles such as IPAP, spin-state selection, and E.COSY, to do so [8–15]. Whether it is best to obtain the frequency difference from the indirect (x1) or direct (x2) dimension of 2D HSQC spectra depends on many factors, such as relaxation properties of the compound in question, signal dispersion, degree of alignment of the oriented sample and thus size of 1H–1H dipolar coupling constants and many more. Both methods have their advantages and drawbacks. Acquisition of HSQC spectra with coupling evolution in the direct dimension is clearly the faster way, allows for almost unlimited digital resolution and also allows the assignment of coupling constants in methylene pairs. Problems with anti-phase contributions due to a mismatch of delay in the INEPT transfer step and the total coupling constant in aligned samples [16] can efficiently be eliminated by using CLIP/CLAP HSQC [17] or IPAP [13] approaches. Especially the CLIP-HSQC has been extremely useful in our hands and the results as far as accuracy and precision of coupling constants obtained within this publication are concerned will be compared with this ‘‘gold standard’’. It might however happen that one of the above factors (especially large 1H–1H dipolar couplings in methylene groups seem to be a key problem in organic compounds) prevents the ‘‘quick’’ measurement of RDCs from the direct dimension and thus the measurement needs to be performed with coupling evolution in the indirect dimension. This is then usually performed by removing the 180° 1H pulse in the middle of the evolution period as has been proposed by different groups [18,19] (see Fig. 2b) leading
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(b)
(a) trad. (FFT)
(c) 20%
(d) 30%
40%
10
δ (13C)
15 20 25 30 35 40 45 50 55 60 65 70 75 [ppm] [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0
δ (1H) Fig. 1. x1-Coupled HSQC (for the pulse sequence see Fig. 2a) of an isotropic sample of (+)-IPC recorded (a) traditionally with 4k complex points, (b) 20% of 4k (20%/4k/819), (c) 30% of 4k (30%/4k/1228) and (d) 40% of 4k (40%/4k/1638).
to a spectrum in which the signal is split by 1JC–H/1TC–H in the indirect dimension. The troublesome 1H–1H coupling, however, evolves exclusively in x2 and thus does not disturb the 1JC–H coupling constant measurement in x1. One (potential) problem, however, remains: Not only 1JC–H/1TC–H couplings evolve during t1, but also long range C–H couplings. These lead to an additional broadening or even splitting in x1 and are thus a potential source of error when extracting RDCs. It was shown, that these can very efficiently be removed by using the G-BIRD(r) module [20–22]. To achieve a resolution also in x1 comparable to the one possible in x2 a very large number of increments needs to be recorded, which is very time-consuming. Already from the very beginning [18] it was perceived that, by using J-scaling the number of increments can be reduced significantly. Another very effective way to reduce the number of increments in (the) indirect dimension(s) of multi-dimensional data sets is the concept of reducing the number of sampled time domain data points via non-uniform sampling (NUS) [23–30], or nonlinear sampling (NLS) [31,32]. These methods differ from the conventional sampling scheme, in which the time domain data points are sampled linearly in an equidistant manner (Nyquist grid), by either acquiring only a given subset of theses points (on grid) in a random fashion (NUS) or by sampling a reduced number of data points off the Nyquist grid (NLS). Both methods allow the reduction of the number of sampled time domain data points and thus lead to significant time savings. Naturally the time-saving is the bigger, the higher the dimensionality of the data set is. This boosted the possibility of obtaining high-dimensionality data sets of biomolecular compounds (even up to 5D) [28,32,33] in reasonable time, including also experiments for the measurement of coupling constants (mostly from three dimensional NMR-spectra) [34–37]. As time saving was not expected to be significant for two dimensional spectra, very few applications of sparse sampling for
two-dimensional data sets have been published so far [38,39]. Very recently a compressed sensing (CS) algorithm has been proposed for the efficient processing of non-uniformly sampled 2D data sets [40,41]. We set out to investigate whether NUS in combination with CS can also improve the measurement of scalar and residual dipolar coupling constants in organic compounds from two dimensional x1-coupled HSQC spectra. A detailed investigation on the optimal and minimal ‘‘sparseness’’ of data sets, the potential saving in time and/or increase in resolution (at the same experimental time as for the conventionally sampled datasets) was conducted for different methods for measuring one-bond coupling constants in the indirect dimension of HSQC spectra (also including J-scaled ones).
2. Materials and methods 2.1. NMR sample preparation The solute used in this study was (+)-Isopinocampheol (IPC), which is commercially available from Sigma–Aldrich and was used as purchased (see Scheme 1, including numbering of atoms used throughout this publication). Both samples used were sealed after three pump–freeze–thaw cycles to guarantee constant conditions. The isotropic sample contained 54 mg (+)-IPC in CDCl3, the anisotropic sample was prepared as follows: The corresponding amount of high-molecular weight poly-c-benzyl-L-glutamate (HMW-PBLG, 50 mg polymer, Mn = 470.000 g/mol; Mw = 1.000.000 g/mol; [42]) was weighed into the NMR sample tube, IPC (23 mg) and the organic co-solvent CDCl3 were added to give a 7.5% w/w concentration of PBLG. A [d6]DMSO capillary was added to provide the lock signal. The polymer was allowed to dissolve overnight and the sample centrifuged back and forth until the 2H signals were sharp and the line widths constant. The quadrupolar splitting (DmQ) of
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(a)
(b)
(c)
(d)
Fig. 2. Pulse sequences for x1-coupled HSQC spectra used: (a) x1-coupled HSQC obtained by removing the 1H p-pulse in the middle of the evolution period [18]; (b) x1coupled HSQC using a G-BIRD(r)-element to remove 1H–13C long range couplings [20]; (c) x1-coupled HSQC with G-BIRD(r)-element and scaling; (d) x1-coupled HSQC with GBIRD(r)-element, scaling and double quantum J-evolution for the measurement of coupling constants in CH2 groups [45]. Narrow filled rectangles are hard p/2 pulses, wide filled rectangles p-pulses. Narrow shaped filled pulses on 13C are adiabatic inversion pulses (chirp pulses of 60 kHz sweep width, 500 ls duration, 20% smoothing, 1000 points were used here), wide shaped filled pulses are adiabatic refocusing pulses (composite smoothed chirp pulse consisting of three elements with an R ratio of 1:2:1, each with 60 kHz sweep width and 20% smoothing, a length ratio of 500 ls, 1 ms, 500 ls (1:2:1) and a total duration of 2 ms were used here); open shaped pulses on 13C are 720-10010-BIP (broad band inversion) pulses of length 160 ls [46]. Phases of pulses as indicated; gradients of 1 ms duration were used for echo–antiecho selection, GARP4 [47] decoupling was used; D1 (D1 = 1/(41J), INEPT) and D2 (D2 = 1/(21J), G-BIRD(r)) were adjusted for 1J = 145 Hz (unless indicated otherwise), the scaling factor j for J-evolution in (c) and (d) was set to 8.
the solvent was 211 Hz (at 298 K) and remained constant over several months (change in splitting of maximum 1.24 Hz over 11 d and 7 h measurement time). 2.2. NMR experiments All experiments were performed on a 600 MHz Bruker Avance III NMR spectrometer (Bruker Biospin, Rheinstetten) under Topspin 3.0 equipped with a TXI (H–C,N) probe with z gradient. Temperature was set to 298 K for all experiments. The number of scans was 2, the relaxation delay was set to 2 s in all experiments. Unless otherwise stated the delays used for transfer of magnetization via one-bond coupling were set for a 145 Hz coupling constant. CLIP-HSQC spectra [17], in which coupling constants are obtained from splittings in x2, were acquired with 8k complex data points over a spectral width of 11 ppm in x2 to give a FID resolution of 0.4 Hz. In x1 128 complex data points over 82.8 ppm spectral width were (more than) sufficient to prevent overlap. In both dimensions a p/2-shifted sine-squared window function and zero filling by a factor of 2 was applied. x1-Coupled experiments (with or without BIRD-module, with or without scaling) were performed with the pulse sequences shown in Fig. 2 and the same spectral widths as above. In x2 1k complex data points were sampled. In x1 the number of complex data points varied (depending on pulse sequence, sparseness and desired resolution, see below, Figs. 1 and 3–6, Tables 1–4) between
Scheme 1. (+)-Isopinocampheol (IPC).
512 or 4k complex points for traditionally sampled data and between 30% out of 512 complex points and 25%/16k complex points leading to between 153 and 4k complex points to be acquired with total experimental times of 23 min to 10 h 40 min. In the remainder of the text x%/y/z will denote the number of complex points being x% out of y points leading to z acquired complex points. In both dimensions a p/2-shifted sine-squared window function and zero filling by a factor of 2 was applied. 2.3. Sampling scheme and processing of NUS data sets The list of points to be acquired was calculated using the program nussampler [43] based on the maximum number of t1 points
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trad. (FFT)
(a)
NUS
(b)
23.0
(13C)
23.5 24.0 24.5
1 -coupled HSQC (a)
25.0 25.5 [ppm]
(d)
(c)
23.0 23.5 24.0
HSQC BIRD (b)
24.5 25.0 25.5 [ppm]
0.93 0.92 0.91 [ppm]
0.93 0.92 0.91 [ppm]
(1H) Fig. 3. Section of the C9 methyl group of (+)-IPC in isotropic solution and corresponding extracted columns from x1-coupled HSQC (a and b) and BIRD-HSQC (c and d) spectra recorded under traditional sampling scheme (a and c) and using NUS with 30% of 4k (30%/4k/1228) complex points (b and d).
and a given percentage. The points are randomly distributed within this range. For the processing of the data, first a Fourier transformation is applied along the acquisition dimension. The data are further processed by compressed sensing [35] using the IRLS algorithm with norm = 0. This will sort the data points according to the normal grid, reconstruct the points not measured and is followed by a FT along the indirect dimension [44]. 2.4. Measurement of coupling constants Scalar or total coupling constants were obtained from the spectra by extracting rows (in the case of CLIP) or columns (in all other cases), copying them and shifting them with respect to each other until the best possible overlap of the respective multiplet component was obtained. The error was determined by shifting the line to both sides until it was clearly discernible that the overlap was not acceptable anymore. 3. Results and discussion 3.1. x1-Coupled HSQC and sampling density We started our investigation by varying the degree of sparseness (see Fig. 1) in the most simple pulse sequence for the measurement of RDCs in x1-coupled HSQCs, in which the p-pulse on protons in the middle of the evolution period is removed (see Fig. 2a) [18,19]. The extracted coupling constants are compared with the ones obtained from the x2-coupled CLIP-HSQC [17]. Thus we chose 4k complex points for this initial test to reach a resolution that makes extracted coupling constants comparable to the CLIP-HSQC. We have recorded the x1-coupled HSQC traditionally (Fig. 1a), with only 20% (Fig. 1b), 30% (Fig. 1c) and 40% (Fig. 1d) of the traditionally sampled data points. We were not able to discern any difference between the quality of traditionally sampled spectra (10 h 40 min) and those obtained by using different degrees of sparseness (by visual inspection of the spectra and extracting columns and overlaying them). Also, coupling constants extracted from the NUS data sets do not differ from the ones obtained from the traditionally sampled ones (data
not shown). Thus coupling constants can – in principle – be extracted from sparsely sampled x1-coupled HSQC data sets and as little as 20% of the traditionally sampled data points (2 h) are clearly sufficient using the compressed sensing algorithm for processing. When increasing the sparseness further (10%), either artefacts (such as cross peaks arising from COSY transfer) start to disappear (which generally would be a nice situation, but might indicate that important information is also lost) or phase problems start to occur, which might lead to errors in the extraction of coupling constants. Thus for x1-coupled HSQC the minimum requirement on sparseness is 20% of 4k (20%/4k/819) complex points. As has been reported previously, long-range C–H couplings (nJC–H/nTC–H) also evolve during t1 and can thus lead to a broadening of resonances. This is a potential source of errors in the extracted coupling constants [20]. With the high resolution we chose we even see fully resolved multiplets (see Fig. 3a and b) for most of the resonances. As the number of signals increases significantly when long-range couplings are resolved, we decided to choose the conservative 30% sparseness for the further investigation, which nevertheless provides a time saving of 70%. When comparing the 1J coupling constants extracted from CLIPHSQC (column 1, Table 1) with the ones from x1-coupled HSQC (column 2 of Table 1), we observed that – as long as the long-range couplings are resolved (which is the case for C4, C7–C10) – coupling constants of the same size with almost equal precision and accuracy can be obtained. If, however, lines are only broadened by long-range couplings systematic deviations occur as is the case for C1, C2, C3 and C5. As has been observed previously [20,48] for methylene groups the individual coupling constants cannot be extracted from x1coupled HSQC as the central anti phase peaks overlap or cancel. In the anisotropic phase this problem is alleviated, but not fully resolved as the central peaks are quite broad and are thus not base line separated. This leads to rather large errors. One possible solution for the CH2 group problem [45] will be examined later (see below). NUS cannot only be used to reduce experimental time for a given digital resolution, but also to increase resolution for a given experiment time. Thus we also recorded spectra with 25% out of 16k complex data points (25%/16k/4k), to find out whether the
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isotropic HSQC-BIRD
(a)
anisotropic J-scaled HSQC-BIRD =8
(b)
HSQC-BIRD
(c)
J-scaled HSQC-BIRD =8 (13C)
(d)
[ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0 [ppm] 3.5 3.0 2.5 2.0 1.5 1.0
(1H) Fig. 4. (a and c) BIRD-HSQC (sequence b) and (b and d) BIRD-HSQC with scaling (sequence c, j = 8) for the isotropic (a, b) and anisotropic sample (c, d) of IPC.
errors observed are due to the limited resolution. As can be seen from Table 1 (column 3) the deviations are still present for the same coupling constants. The same is true for the 1T coupling constants (see Table 2), although deviations are generally larger due to the broader lines in the anisotropic phase. Such a high number of increments would never be recorded for conventionally sampled spectra and we have expected to be limited by relaxation. With the compound and sample preparation method chosen here, we did not observe severe losses due to relaxation in this study (neither for the isotropic nor for the anisotropic sample). 3.2. x1-HSQC with BIRD We believed that the deviations observed above are due to not resolved long-range couplings and thus turned our attention towards a pulse sequence that was especially designed to remove C–H long range couplings – namely the x1-coupled HSQC with G-BIRD(r)-element [20]. The pulse sequence is shown in Fig. 2b; a section from the isotropic spectra (trad. and NUS) together with the corresponding column is shown in Fig. 3c and d, the full spectrum of the isotropic and anisotropic sample is shown in Fig. 4a and c. As can be seen in Fig. 3c and d, lines are much sharper, also leading to much higher S/N. Again no difference can be discerned between the traditionally sampled spectra (10 h 40 min) and the ones recorded with 30% of the increments (30%/4k/1228, 3 h 10 min). When comparing the coupling constants extracted from the BIRD-HSQC with the CLIP it can be seen that for the isotropic sample the match is almost perfect. For the anisotropic sample, there is only one coupling constant for which the values extracted from
BIRD-HSQC and CLIP-HSQC are not in perfect agreement. Already at this rather low degree of alignment lines of several C–H pairs are severely broadened by 1H–1H dipolar couplings in the CLIP, which leads to a rather large error margin for some of the coupling constants. For the isotropic sample the methylene group problem remains, but in the anisotropic sample at least one of the central lines is sharp enough to lead to a reliably extractable coupling constant. As can be seen from the columns in Fig. 3c and d, there are some artefacts present in the spectra. These have already been observed in the initial publication [18] and are due to a mismatch in the BIRD element (variation of 1J/1T coupling). As was already observed by Feher et al. these artefacts appear in the center of the multiplet and can thus be identified easily and in our case did not impede the extraction of coupling constants. As above we investigated, whether it is not only possible to save time with NUS, but also to increase resolution. Thus we recorded spectra with 25% out of 16k complex data points (25%/16k/4k, same experimental time as the traditionally sampled one). When doing so we obtained spectra with astonishing resolution and extremely sharp lines, thus leading to very precise and accurate coupling constants (compare column 1 and 5 of Tables 1 and 2). After we had seen, that 30% of 4k complex points lead to excellent spectra with much higher S/N than in the x1-coupled HSQC, we realized that for this sequence it might be possible to reduce the number of points further. We found out, that even for 5% sparseness (out of 4k, 5%/4k/204) excellent spectra with more than sufficient S/N are obtained, thus reducing the experimental time from 10 h 40 min to 31 min without any significant loss in spectral quality. Piqued by this observation, we then investigated, whether it is possible to also increase the sparseness in the highly resolved spectra (16k complex points). Down to 1.25% out of 16k (1.25%/
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(a)
(b)
BIRD HSQC(b) trad.
J-scaled BIRD HSQC(c) trad., =8 512 1h20
4k 10h40 (1JCH1 + 1JCH2 )
[ppm]
40.5
(c)
40.0
39.5
39.0
38.5
38.0
[ppm]
J-scaled BIRD HSQC(c) NUS, =8
(d)
48 46 44 42 40 38 36 34 32 30 28
J-scaled BIRD HSQC(c) NUS, =8 25%/2k 1h20
30%/512 23min
[ppm]
48 46 44 42 40 38 36 34 32 30 28
[ppm]
48 46 44 42 40 38 36 34 32 30 28
(13C) Fig. 5. Columns of the CH2 group at C4 of the isotropic (+)-IPC sample extracted from (a) the traditionally sampled BIRD-HSQC (sequence b, 4k complex points), (b) the traditionally sampled J-scaled BIRD-HSQC (sequence c, j = 8, 512 complex points), (c) J-scaled BIRD-HSQC with NUS (sequence c, j = 8, 30% (30%/512/153), (d) J-scaled BIRDHSQC with NUS (sequence c, j = 8, 25% (25%/2k/512). The relative intensities of lines (resulting from the INEPT transfer) are opposite when going from the BIRD-HSQC to the BIRD-HSQC with scaling. This is due to the different number of p-pulses (see Fig. 2b and c) and could be corrected for if necessary.
16k/204, 31 min) no difference in the spectra is discernible. Below that, artefacts start disappearing again. Thus for this sequence it is not only possible to reduce experimental time by NUS, or increase resolution; it is also possible to do both at the same time: increase resolution to 16k complex points and reduce experimental time to 31 min. This is of course only true as long as relaxation and sensitivity are not an issue, neither was critical here. At first glance this large difference between the minimum number of sampled data points in x1-coupled HSQC and its BIRD variant is surprising. It can, however, be nicely explained by the large difference in numbers of frequencies observed in the two spectra. During the work with NUS we got the impression that the following rule of thumb can be proposed: The number of complex points sampled should be higher than the number of signals expected (see also Ref. [49]). For the measurement of coupling constants the same is essentially true with two restrictions: (a) the number of frequencies (including all splitting by long-range couplings) and not just the number of signals expected needs to be taken into account; (b) if one wants to make sure not to loose any information also the additional frequencies resulting from artefacts (like COSY cross peaks in HSQC) need to be considered. As splittings resulting from long-range couplings are efficiently removed by the BIRD module, the number of frequencies and thus demand on sampled data points is drastically reduced in x1-coupled HSQCs with BIRD. It has to be highlighted at this point that using 1.25% out of 16k data points in the x1-coupled HSQC leads to couplings as accurate and precise as from the CLIP-HSQC in as little as 31 min !
3.3. x1-Coupled HSQC with G-BIRD(r)-element and scaling Already from the very beginning of the measurement of RDCs in
x1-coupled HSQCs it was recognized, that the number of increments can be significantly reduced if J-scaling is used. We have combined this idea with the BIRD-HSQC. The resulting pulse sequence is shown in Fig. 2c. We investigated whether this pulse sequence also allows a significant time saving and whether this time saving can even be increased by using NUS. To have comparability with pulse sequence b (BIRD-HSQC) we used a scaling factor of j = 8. As can be seen in Figs. 4 and 5a and b, the high spectral quality of the BIRD-HSQC is retained, while the splitting is multiplied by 8. This leads already to a significant time saving (1 h 20 min vs. 10 h 40 min) at the same resolution for J. Of course, in cases of less welldispersed signals, overlap can occur. The couplings extracted for the isotropic and anisotropic sample can be found in Table 3. As can be seen the couplings for the isotropic and for the anisotropic sample (with exception of the same coupling constant as above) match perfectly to the ones extracted from CLIP HSQC. The same investigation concerning NUS as above was also conducted using this pulse sequence. In Fig. 5 columns for C4 are extracted for the isotropic sample and again the two concepts: (a) reduction of measurement time by NUS (30%/512/153, Fig. 5c and b) increase of resolution by NUS (25%/2k/512, Fig. 5d) are compared to the traditionally sampled J-scaled BIRD-HSQC (1k, Fig. 5b). As can be seen both approaches lead to spectra of excellent quality.
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(a)
(b)
BIRD HSQC(b) trad.
J-scaled BIRD HSQC with MQ-evolution (d) trad., =8
4k 10h40
512 1h20
CH1
[ppm] 40.5 40.0
(c)
39.5
39.0
38.5
38.0
48 46 44 42 40 38 36 34 32 30 28
[ppm]
J-scaled BIRD HSQC with MQ-evolution (d) NUS, =8
(d)
JCH2
1
J-scaled BIRD HSQC with MQ-evolution (d) NUS, =8
30%/512 23min
[ppm]
25%/2k 1h20
48 46 44 42 40 38 36 34 32 30 28
48 46 44 42 40 38 36 34 32 30 28
[ppm]
(13C) Fig. 6. Columns of the CH2 group at C4/H4a = H1 of the isotropic (+)-IPC sample extracted from (a) the traditionally sampled BIRD-HSQC (sequence b, 4k complex points), (b) the traditionally sampled J-scaled BIRD-HSQC with DQ-evolution (sequence d, j = 8, 512 complex points), (c) J-scaled BIRD-HSQC with DQ-evolution with NUS (sequence d, j = 8, 30%/512/153), (d) J-scaled BIRD-HSQC with DQ-evolution with NUS (sequence d, j = 8, 25%/2k/512). In b, c and d only the passive C–H (1JC–H2=H4s) coupling together with the geminal H–H coupling is observed.
Table 1 Comparison of 1JC–H coupling constants extracted from CLIP-HSQC (column 1), x1-coupled HSQC (column 2, 3) and x1-coupled HSQC with G-BIRD(r) (column 4, 5) using traditional sampling (column 2, 4) and NUS (25%/16k/4k, column 3, 5) for the isotropic sample of (+)-IPC. Pulse sequence (# in Fig. 2)
CLIP HSQC
x1-Coupled HSQC (a)
Sampl. scheme/# of data points
8k (in x2)
Traditional 4ka,b 1
13
Coupling C1 C2 C3 C4 C5 C7 C8 C9 C10
H1 H2 H3 H4s H4a H5 H7s H7a H8 H9 H10
d( C)
d( H)
1
47.83 47.69 71.59
1.79 1.93 4.06 2.5 1.71 1.93 2.37 1.04 1.21 0.91 1.13 FIDres:
140.87 ± 0.2 126.54 ± 0.1 141.98 ± 0.1 126.54 ± 0.2 126.95 ± 0.1 141.14 ± 0.1 135.12 ± 0.1 136.95 ± 0.1 124.63 ± 0.1 123.65 ± 0.1 124.86 ± 0.1 0.4
39 41.77 34.37 27.68 23.7 20.74
1
JC–H (Hz)
JC–H (Hz)
BIRD-HSQC (b) NUS (25%/16k/4k)b 1
JC–H (Hz)
Traditional 4ka,b
NUS (25%/16k/4k)b
1
1
JC–H (Hz)
JC–H (Hz)
144.76 ± 0.5 128.01 ± 1 144.25 ± 1
144.92 ± 0.5 128.21 ± 0.5 144.52 ± 2
140.92 ± 0.5 126.6 ± 0.2 142.04 ± 0.2
140.91 ± 0.2 126.58 ± 0.1 141.99 ± 0.1
253.6 ± 0.5
253.48 ± 0.5
253.44 ± 0.2
253.45 ± 0.1
143.56 ± 1
143.77 ± 2
141.24 ± 0.2
141.2 ± 0.1
272.52 ± 0.5
272.14 ± 0.3
272.03 ± 0.2
272.07 ± 0.1
124.55 ± 0.5 123.61 ± 0.5 124.76 ± 0.5 1.52
124.65 ± 0.2 123.69 ± 0.2 124.74 ± 0.2 0.38
124.58 ± 0.2 123.58 ± 0.2 124.8 ± 0.2 1.52
124.62 ± 0.1 123.65 ± 0.1 124.83 ± 0.1 0.38
a Spectra recorded under traditional conditions and using 30% NUS (30%/4k/1228) are identical; thus coupling constants are also identical to the ones from traditionally sampled spectra and are not listed. b Only the sum of couplings to methylene protons can be extracted from these spectra as the difference in couplings is too small to lead to observable/evaluable anti-phase patterns.
When we tried to increase the sparseness further (as above), we realized that 30% (30%/512/153, 23 min) is the minimum, for the higher resolution 20% (20%/2k/408, 64 min) is the lower limit of the data we recorded. We believe that 15% would also have led to satisfactory results. As this sparseness was not recorded, we chose to report the conservative values.
3.4. x1-Coupled HSQC with G-BIRD(r)-element, scaling and double quantum J-evolution As can be nicely seen in Fig. 5, again individual coupling constants for CH2 groups are not accessible for the isotropic sample from the J-scaled BIRD-HSQC as was the case for all other x1-coupled HSQC
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Table 2 Comparison of 1TC–H couplings extracted from CLIP-HSQC (column 1), x1-coupled HSQC (column 2,3) and x1-coupled HSQC with G-BIRD(r) (column 4,5) using traditional sampling (column 2, 4) and NUS (25%/16k/4k, column 3, 5) for the anisotropic sample of (+)-IPC. Pulse sequence (Fig. 2)
CLIP HSQC
x1-Coupled HSQC (a)
Sampl. scheme/# of data points Coupling
8k (in x2) 1 TC–H (Hz)
Traditional 4ka,b 1 TC–H (Hz)
NUS (25%/16k/4k) 1 TC–H (Hz)
1
Traditional 4ka,b TC–H (Hz)
NUS (25%/16k/4k) 1 TC–H (Hz)
C1 C2 C3
166.37 ± 3 115.07 ± 1 162.22 ± 0.5 148.99 ± 0.4 117.99 ± 0.4 130.97 ± 0.3 141.86 ± 0.5 104.48 ± 0.5 130.57 ± 0.4 118.14 ± 0.2 124.1 ± 0.2 0.4
168.3 ± 1 117.7 ± 1 165 ± 1 151.48 ± 2 117 ± 3 134.9 ± 1 139 ± 5d 105 ± 5d 130.62 ± 1 117.58 ± 1 123.71 ± 1 1.52
168.25 ± 0.5 117.14 ± 0.5 164.46 ± 0.5 148.97 ± 1 117.78 ± 1 134.38 ± 1 137 ± 5d 110 ± 5d 130.2 ± 0.5 118.17 ± 0.5 123.89 ± 0.5 0.38
165.04 ± 0.2 115.4 ± 0.2 162.79 ± 0.2 149.48 ± 0.2 117.55 ± 0.2 131.55 ± 0.2 142 ± 2 103.8 ± 2 130.78 ± 0.2 117.69 ± 0.2 123.79 ± 0.2 1.52
164.75 ± 0.2 115.02 ± 0.2 161.83 ± 0.1 148.4 ± 0.1 118.05 ± 0.1 130.98 ± 0.2 142.3 ± 0.2 104.94 ± 0.2 130.22 ± 0.1 118.15 ± 0.2 123.92 ± 0.1 0.38
H1 H2 H3 H4s H4a H5 H7sc H7ac H8 H9 H10 FIDres:
C4 C5 C7 C8 C9 C10
BIRD-HSQC (b)
a Spectra recorded under traditional conditions and using 30% NUS (30%/4k/1228) are identical; thus couplings are also identical to the ones from traditionally sampled spectra and are not listed. b Couplings were extracted from spectra with different D1 (and D2 in the case of the BIRD-HSQC). Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts in BIRD-HSQC, see text), such that for the 25% NUS (25%/16k/4k) spectra we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. c The H–H total coupling constant is ca. 40 Hz, which makes extraction from CLIP error prone. d The center peaks (anti-phase) are not completely base line separated. Thus the error given is a conservative estimate.
Table 3 Comparison of 1JC–H and 1TC–H couplings extracted from CLIP HSQC (column 1, 4) and J-scaled HSQC-BIRD (sequence c) using traditional sampling (512, j = 8, column 2, 5) and NUS (25%/2k/512, j = 8, column 3, 6) for the isotropic (columns 1, 2, 3) and anisotropic sample (columns 4, 5, 6) of (+)-IPC. Sample
Isotropic
Pulse sequence (Fig. 2)
CLIP HSQC
J-scaled HSQC-BIRD
Sampl. scheme/# of points
8k (in x2)
Traditional 512a,b
NUS (25%/2k/512)b
8k (in x2)
Traditional 512c
NUS (25%/2k/512)
1
1
1
1
1
140.97 ± 0.25 126.57 ± 0.25 142.01 ± 0.25
140.89 ± 0.1 126.56 ± 0.1 142.01 ± 0.1
166.37 ± 3 115.07 ± 1 162.22 ± 0.5 148.99 ± 0.4 117.99 ± 0.4 130.97 ± 0.3 141.86 ± 0.5 104.48 ± 0.5 130.57 ± 0.4 118.14 ± 0.2 124.1 ± 0.2 0.4
165.18 ± 0.5 115.05 ± 0.5 161.28 ± 0.5 149.13 ± 0.5 117.94 ± 0.5 131.28 ± 0.5 142.19 ± 0.5 104.6 ± 0.5 130.49 ± 0.5 118.15 ± 0.5 124.03 ± 0.5 1.52
165.21 ± 0.1 114.90 ± 0.1 161.80 ± 0.1 148.36 ± 1d 118.03 ± 1d 131.00 ± 0.1 142.39 ± 1d 104.92 ± 1d 130.18 ± 0.1 118.22 ± 0.1 123.95 ± 0.1 0.38
13
Coupling C1 C2 C3 C4 C5 C7 C8 C9 C10
H1 H2 H3 H4s H4a H5 H7se H7ae H8 H9 H10
d( C)
d( H)
1
47.83 47.69 71.59
1.79 1.93 4.06 2.5 1.71 1.93 2.37 1.04 1.21 0.91 1.13 FIDres:
140.87 ± 0.2 126.54 ± 0.1 141.98 ± 0.1 126.54 ± 0.2 126.95 ± 0.1 141.14 ± 0.1 135.12 ± 0.1 136.95 ± 0.1 124.63 ± 0.1 123.65 ± 0.1 124.86 ± 0.1 0.4
39 41.77 34.37 27.68 23.7 20.74
1
JC–H (Hz)
Anisotropic
JC–H (Hz)
CLIP HSQC
JC–H (Hz)
253.45 ± 0.25
253.40 ± 0.1
141.29 ± 0.25
141.19 ± 0.1
272.07 ± 0.25
272.09 ± 0.1
124.56 ± 0.25 123.72 ± 0.25 124.87 ± 0.25 1.52
124.60 ± 0.1 123.65 ± 0.1 124.84 ± 0.1 0.38
TC–H (Hz)
J-scaled HSQC-BIRD
TC–H (Hz)
TC–H (Hz)
a Spectra recorded under traditional conditions and using 30% NUS (30%/512/153) are identical; thus couplings are also identical to the ones from traditionally sampled spectra and are not listed. b Only the sum of couplings to methylene protons can be extracted from the isotropic spectra as the difference in couplings is too small to lead to observable/evaluable anti-phase patterns. c Couplings were extracted from spectra with different D1 and D2. Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts due to J mismatch in the BIRD), such that for the 25% NUS (25%/2k/512) spectra we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. d The center peaks (anti-phase) are not completely base line separated. Thus the error given is a conservative estimate. e The H–H total coupling constant (in the anisotropic sample) is ca. 40 Hz, which makes extraction from CLIP error prone.
spectra investigated here. Among many other solutions [11–14,50], one clever solution to this problem uses the evolution of DQ magnetization, BIRD and J-scaling [20]. For a detailed description of the pulse sequence (Fig. 2d) the reader is referred to the original literature, here it should suffice to say, that one special property of multi quantum coherences (MQC) is used, namely that they are not modulated by the coupling between the active spins involved in them, but only evolve under the coupling of passive spins. Thus signals for CH2 groups are observed, in which the cross peak (of one geminal proton H1) carries the JC–H2 coupling constant of the (other geminal) passive spin (H2). An additional splitting by the geminal H1–H2 coupling constant is observed.
Using this pulse sequence we again performed the same tasks: recording a traditionally sampled spectrum (again using the scaling factor j = 8 to provide comparability), the fast NUS (30%/512/ 153) and the highly resolved NUS (25%/2k/512) ones (see Fig. 6). As can be seen in Fig. 6, the passive coupling (1JC–H2) can be obtained from the signal of the active spin (C–H1), together with the geminal 1H–1H coupling 2JH1–H2. When considering the line-shape observed in Fig. 6, which originate from 1H–1H coupling evolution of geminal protons during the BIRD module, it is quite surprising that a comparison of the values extracted from these spectra with those obtained from CLIP reveals almost perfectly accurate and precise coupling constants (see Table 4).
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Table 4 Comparison of 1JC–H and 1TC–H couplings extracted from CLIP HSQC (column 1, 4) and J-scaled HSQC-BIRD with DQ-evolution (sequence d) using traditional sampling (512, j = 8, column 2, 5) and NUS (25%/2k/512, j = 8, column 3, 6) for the isotropic (columns 1, 2, 3) and anisotropic sample (columns 4, 5, 6) of (+)-IPC. For completeness 2JH–H protons are also given. Sample
Isotropic
Pulse sequence (Fig. 2)
CLIP HSQC
J-scaled HSQC-BIRD, with DQ (d)
CLIP HSQC
Sampl. scheme/# of points
8k (in x2)
Traditional 512a
NUS (25%/2k/512)
8k (in x2)
Traditional 512b
NUS (25%/2k/512)
1
1
1
1
1
148.99 ± 0.4 117.99 ± 0.4
149.28 ± 1 118.03 ± 1 13.4 ± 2 142.28 ± 1 104.33 ± 1 36.5 ± 2 1.52
148.48 ± 1 117.85 ± 1 13.4 ± 1.25 142.14 ± 0.25 105.23 ± 0.25 35.6 ± 1.25 0.38
13
Coupling C4 H4s C7 H7s
H4s H4a H4a H7sc H7ac H7a
1
d( C)
d( H)
1
39
2.5 1.71
126.54 ± 0.2 126.95 ± 0.1
34.37
2.37 1.04
135.12 ± 0.1 136.95 ± 0.1
FIDres:
0.4
JC–H (Hz)
Anisotropic
JC–H (Hz)
126.56 ± 0.25 126.95 ± 0.25 14.3 ± 0.25 134.96 ± 0.25 137.15 ± 0.25 9.6 ± 0.25 1.52
JC–H (Hz)
126.53 ± 0.25 126.94 ± 0.13 14.0 ± 0.25 135.14 ± 0.13 136.98 ± 0.13 9.7 ± 0.25 0.38
TC–H (Hz
141.86 ± 0.5 104.48 ± 0.5 0.4
J-scaled HSQC-BIRD, with DQ (d)
TC–H (Hz)
TC–H (Hz)
a
Couplings from 30% NUS (30%/512/153) are essentially identical to the ones from traditionally sampled spectra (±0.2 Hz) and are not listed. Couplings were extracted from spectra with different D1 and D2. Values for 1J/1T between 105 Hz and 165 Hz were chosen and couplings were extracted from the two spectra closest to the actual coupling constant and were essentially identical. The main difference between the spectra with different D1 (and D2) was the intensity of the cross peak (and the appearance of artefacts due to J-mismatch in the BIRD), such that for the 25% NUS spectra /25%/2k/512) we restricted ourselves to one value corresponding to 1J/1T = 145 Hz. c The H–H total coupling constant (in the anisotropic sample) is ca. 40 Hz, which makes extraction from CLIP error prone. b
The investigation concerning reduction of measurement time by NUS and increasing resolution by NUS was also conducted using this pulse sequence. In Fig. 6 columns for H4–H4a are extracted for the isotropic sample and for the NUS spectra: 30% (30%/512/153), Fig. 6c and 25% (25%/2k/512), Fig. 6d, which are compared to the traditionally sampled J-scaled BIRD-HSQC with DQ evolution (512 complex points, Fig. 6b). When we tried to increase the sparseness further, we saw that 30% (30%/512/153, 23 min) is the minimum, for the higher resolution 20% (20%/2k/408, 1 h) is the lower limit. 4. Conclusion We have investigated whether non-uniform sampling (NUS) in combination with the recently proposed compressed sensing (CS) algorithm for processing allows improving the measurement of one-bond scalar and total/residual dipolar couplings from different kinds of x1-coupled HSQCs. Two main points were investigated: Speeding up the measurement by reducing the number of sampled data points at the same digital resolution (time saving). Improving the resolution by sampling the same amount of data points as in traditionally sampled spectra but at a much higher digital resolution (resolution improvement). Both approaches yielded – in our eyes – spectacular improvements without any loss in spectral quality as long as the minimum requirements with respect to sparseness of the data was respected (number of sampled points > number of expected frequencies). When care was taken to remove long-range couplings by using the BIRD-HSQC and/or its J-scaled variants even a combination of the two upper approaches was possible (reduction of number of sampled data points at the same time as increasing resolution) making the measurement of couplings in x1 equally fast as in x2, while conserving accuracy and precision. This way an alternative for problems occurring in cases of large 1H–1H dipolar couplings (as is frequently observed in methylene groups) is offered. While we investigated these methods with a focus on small organic molecules in organic solvents, the extension to other cases should be straight forward. Acknowledgments C.M.T thanks the European Research Council (ERC, Starting Grant RDC@catalysis) for financial support. The authors thank To-
bias Montag for the preparation of the isotropic and anisotropic sample used in this study.
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