NMR Diffusion Measurements in Complex Mixtures Using Constant

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Anal. Chem. 2006, 78, 5601-5606

NMR Diffusion Measurements in Complex Mixtures Using Constant-Time-HSQC-IDOSY and Computer-Optimized Spectral Aliasing for High Resolution in the Carbon Dimension Bruno Vitorge and Damien Jeanneat*

Department of Organic Chemistry, University of Geneva, 30 Quai E. Ansermet, CH-1211 Geneva 4

A new 3D pulse sequence for NMR diffusion measurements in complex mixtures is presented. It is based on the constant-time (CT) HSQC experiment and combines diffusion delay with the carbon evolution time. This combination has great potential to obtain high resolution in the carbon dimension. When using classical sampling of the carbon dimension, maximal resolution would require a large number of time increments, leading to unrealistically long acquisition times. The application of computer-optimized spectral aliasing allows one to reduce the number of time increments and the total acquisition time by 1-2 orders of magnitude by taking advantage of the information content of 1D carbon spectra, HSQC experiments, or both. With the new CT-HSQC-IDOSY experiment, the diffusion rates of the six anomers present in a 0.1 M D2O solution of glucose, maltose, and maltotriose could be obtained at natural abundance in 8 h with standard deviations below 5%. Measuring diffusion coefficients in solution is important in many fields of chemistry and biochemistry. Applications include estimations of molecular size,1-8 association constants,9 and identification of ion pairing phenomena.10 Although NMR has long been used for diffusion studies,11 it became truly practical only after recent developments in hardware,12 pulse sequences,13,14 and * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +41 22 379 6084. Fax: +41 22 379 3215. (1) Simpson, A. J. Magn. Reson. Chem. 2002, 40, S72-S82. (2) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson., A 1996, 123, 215218. (3) Tomati, U.; Belardinelli, M.; Galli, E.; Iori, V.; Capitani, D.; Mannina, L.; Viel, S.; Segre, A. Carbohydr. Res. 2004, 339, 1129-1134. (4) Viel, S.; Capitani, D.; Mannina, L.; Segre, A. Biomacromolecules 2003, 4, 1843-1847. (5) Schraml, J.; Blechta, V.; Soukupova´, L.; Petra´kova´, E. J. Carbohydr. Chem. 2001, 20, 87-91. (6) Dı´az, M. D.; Berger, S. Carbohydr. Res. 2000, 329, 1-5. (7) Groves, P.; Rasmussen, M. O.; Molero, M. D.; Samain, E.; Can ˜ada, F. J.; Driguez, H.; Jime´nez-Barbero, J. Glycobiology 2004, 14, 451-456. (8) Kapur, G. S.; Findeisen, M.; Berger, S. Fuel 2000, 79, 1347-1351. (9) Fielding, L. Tetrahedron 2000, 56, 6151-6170. (10) Martı`nez-Viviente, E.; Pregosin, P. S.; Vial, L.; Herse, C.; Lacour, J. Chem.Eur. J. 2004, 10, 2912-2918. (11) Tanner, J. E. J. Chem. Phys. 1970, 52, 2523-2526. (12) Wider, G.; Do ¨tsch, V.; Wu ¨ thrich, K. J. Magn. Reson., A 1994, 108, 255258. (13) Gibbs, S. J.; Johnson C. S., Jr. J. Magn. Reson. 1991, 93, 395-402. 10.1021/ac060744g CCC: $33.50 Published on Web 07/07/2006

© 2006 American Chemical Society

data processing.15,16 A milestone was the idea by Morris and Johnson16 to display the diffusion rates in a separate dimension. Recent NMR spectrometers usually include pulse-field gradient devices making diffusion measurements accessible to every researcher, as can be appreciated by the number of reviews on the principles,17,18 experimental aspects,18,19 and applications.18,20 Diffusion measurements are often taken using series of 1D 1H spectra. Difficulties may arise when measuring the diffusion coefficients in solutions containing mixtures of molecules with similar structures. Mixtures of oligomers or conformers, complexes with slowly exchanging ligands, and elements of supramolecular assemblies are just a few cases where determining the diffusion rates of the individual components would be useful. In all of these cases, overlap in the proton spectrum is likely to be very severe. Signal overlap can be treated by multivariate analysis21-26 only to a certain extent, since it is difficult to apply.20,21 However, it is preferable to resolve signals. Selective experiments such as the STEP-DOSY can be quite useful27 to select components of a mixture, but a unique entry point for the magnetization is needed. When the molecules under study have sensitive nuclei like 31P or 19F, diffusion measurements on these isotopes can be an alternative.28,29 Otherwise one has to rely on the low sensitivity of (14) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson., A 1996, 121, 88-91. (15) Barjat, H.; Morris, G. A.; Smart, S.; Swanson, A. G.; Williams, S. C. R. J. Magn. Reson., Ser. B 1995, 108, 170-172. (16) Morris, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1993, 115, 42914299. (17) Price, W. S. Concepts Magn. Reson. 1997, 9, 299-336. (18) Johnson, C. S., Jr. Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203-256. (19) Price, W. S. Concepts Magn. Reson. 1998, 10, 197-237. (20) Brand, T.; Cabrita, E. J.; Berger, S. Prog. Nucl. Magn. Reson. Spectrosc. 2005, 46, 159-196. (21) Huo, R.; Wehrens, R.; Van Duynhoven, J.; Buydens, L. M. C. Anal. Chim. Acta 2003, 490, 231-251. (22) Windig, W.; Antalek, B. Chemom. Intell. Lab. Syst. 1997, 37, 241-254. (23) Van Gorkom, L. C. M.; Hancewicz, T. M. J. Magn. Reson. 1998, 130, 125130. (24) Armstrong, G. S.; Loening, N. M.; Curtis, J. E.; Shaka, A. J.; Mandelshtam, V. A. J. Magn. Reson. 2003, 163, 139-148. (25) Stilbs, P.; Paulsen, K.; Griffiths, P. C. J. Phys. Chem. 1996, 100, 81808189. (26) Delsuc, M. A.; Malliavin, T. E. Anal. Chem. 1998, 70, 2146-2148. (27) Bradley, S. A.; Krishnamurthy, K.; Hu, H. J. Magn. Reson. 2005, 172, 110117. (28) Kapur, G. S.; Cabrita, E. J.; Berger, S. Tetrahedron Lett. 2000, 41, 71817185.

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INEPT-DOSY2,30 and DEPT-DOSY31 may be used to partially compensate for the signal-to-noise ratio problem arising from the low 13C natural abundance. However, it is advantageous to benefit from the higher sensitivity associated with protondetected 2D spectra. Two-Dimensional Diffusion Experiments. In this paper, we present a technique that combines the high resolution of 1D carbon spectra with the high sensitivity of 2D 1H-13C HSQC spectra. It allows one to measure the individual diffusion rates of any signal provided it is resolved in either the proton or the carbon spectrum. A series of 2D spectra is recorded, and as in the case of 1D spectra, the reduction of the amplitude of any 1H-13C crosspeak is fitted to an exponential decay to determine the diffusion rates of the corresponding molecule. The price of this additional signal dispersion of 2D spectra is an increase in the total experimental time because of the need to sample the indirect spectral dimension. This approach has already been successfully applied to measure diffusion rates in homonuclear experiments such as COSY,14,32 but also NOESY,33 TOCSY, and 2D J spectra.34,35 However, since the carbon dimension has a higher ability to resolve signals than the proton dimension, we decided to focus our interest on the heteronuclear experiments. The straightforward transformation of any experiment into a diffusion-sensitive variant consists of the insertion of the diffusion sequence before or after the sequence of interest. For example, gHMQC31,36 and 1H-15N HSQC37 have both been described, but as Morris pointed out,34 catenation is far from optimal. We therefore developed the CT-HSQC-IDOSY sequence (Figure 1) that increases sensitivity for two reasons. First, the sequence being more compact, less magnetization is lost due to imperfect pulse calibration. More importantly, it reduces relaxation during the sequence by combining the diffusion delay and the t1 evolution time. As a result of the need for a constant duration for the diffusion period, we took the constant-time (CT) version of the HSQC sequence38 as a starting point. The main difference from the original sequence is the addition of variable gradients to make the sequence diffusionsensitive. The sections of the INEPT during which the in-phase proton magnetization transforms into antiphase provide perfect locations to fit pairs of dipolar gradients. The constant time 2T (see Figure 1) is calculated according to the desired diffusion time ∆, typically in the range of 100-500 ms. With the τ delays being quite short, the rest of the constant time allows for long carbon evolution. This provides the conditions to obtain an excellent spectral resolution in the carbon dimension. Nevertheless, in order to take advantage of this potential, it is necessary to sample the (29) Derrick, T. S.; Lucas, L. H.; Dimicoli, J.-L.; Larive, C. K. Magn. Reson. Chem. 2002, 40, S98-S105. (30) Schlo ¨rer, N. E.; Cabrita, E. J.; Berger, S. Angew. Chem., Int. Ed. 2002, 41, 107-109. (31) Wu, D.; Chen, A.; Johnson, C. S., Jr. 37th Experimental Nuclear Magnetic Resonance Conference, 1996; p 74. (32) Nilsson, M.; Gil, A. M.; DelNilsson, M.; Morris, G. A. Chem. Commun. 2005, 1737-1739. (33) Gozansky, E. K.; Gorenstein, D. G. J. Magn. Reson., B 1996, 111, 94-96. (34) Nilsson, M.; Gil, A. M.; Delgadillo, I.; Morris, G. A. Anal. Chem. 2004, 76, 5418-5422. (35) Lucas, L. H.; Otto, W. H.; Larive, C. K. J. Magn. Reson. 2002, 156, 138145. (36) Barjat, H.; Morris, G. A.; Swanson, A. G. J. Magn. Reson. 1998, 131, 131138. (37) Buevich, A. V.; Baum, J. J. Am. Chem. Soc. 2002, 124, 7156-7162. (38) Vuister, G. W.; Bax, A. J. Magn. Reson. 1992, 98, 428-435.

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Figure 1. Pulse sequence of the 3D CT-HSQC-IDOSY experiment. Narrow and broad bars denote 90° and 180° hard power pulses, respectively. The dashed box indicates a spin-lock pulse to eliminate unwanted in-phase magnetization. Unless indicated otherwise, pulses are applied along the x axis. φ1 ) y; φ2 ) x; φ3 ) x, -x; φ4 ) 2(x), 2(-x); φ5 ) 4(x), 4(-x); receiver, 2(x, -x), 2(-x, x). Quadrature in t1 is obtained using the echo-antiecho method, inverting the phases of φ2, φ3, and the receiver in the antiecho scan. The minimum phase cycling is two, but small artifacts are eliminated using 4- or 8-step cycles. Decoupling is performed using low-power chirp pulses to reduce sample heating. The amplitude ratio of the first over the second filled gradient, γH/γC. The diffusion delay ∆ determines the constant time 2T.

t1 dimension in a manner that requires a minimal number of time increments. Different methods address this problem, among which are the Hadamar techniques39 and the use of nonlinearly acquired spectra processed using maximum entropy40,41 or more classical techniques,42,43 but as discussed below, spectral aliasing provides a more practical alternative. Spectral Width Reduction and Signal Aliasing. In 2D heteronuclear diffusion experiments, the main difficulty is to provide satisfactory resolution in the carbon dimension. When using classical acquisition techniques, fine resolution imposes a large number of time increments; unfortunately, the experiments cannot be performed within a reasonable time since one needs to repeat each set of 2D acquisitions for different gradient amplitudes. A close look at the sampling parameters will show how serious this problem can be and how it can be avoided. When studying small molecules, the spectral width in the carbon dimension can reach 200 ppm, which corresponds to a sweep width (SW) of 25 kHz on a 500-MHz proton Larmor frequency. The Nyquist condition44 gives the t1 increment time

∆t1 ) 1/2SW ) 20 µs

(1)

needed to unambiguously determine the frequency of any signal. The number of time increments N depends on the signal resolution that one needs to reach. In a normal 1D spectrum, this number is typically 64K, a number that resolves signals that are more than 0.8 Hz apart. However, a 200 ppm 2D HSQC spectrum acquired using 128 increments is not able to resolve signals that are less than 3.1 ppm apart. Increasing the number of increments improves the resolution, but also increases the experimental time. (39) Kupce, E.; Nishida, T.; Freeman, R. Prog. Nucl. Magn. Reson. Spectrosc. 2003, 42, 95. (40) Jones, J. A.; Hore, P. J. J. Magn. Reson. 1991, 92, 276-292. (41) Jones, J. A.; Hore, P. J. J. Magn. Reson. 1991, 92, 363-376. (42) Marion, D. J. Biomol. NMR 2005, 32, 141-150. (43) Dutt, A.; Rokhlin, V. Appl. Comput. Harmon. Anal. 1995, 2, 85-100. (44) Claridge, T. D. W. High-Resolution NMR Techniques in Organic Chemistry; Pergamon Press: Oxford, 1999.

Figure 2. Influence of spectral-width reduction on signal position and resolution. When the window is reduced from its full width SW0 (a) to SWa, the resulting spectrum (c) corresponds to the superposition of stripes of width SWa (b). When using TPPI as quadrature detection scheme, every other stripe is inverted. For equivalent resolutions, the aliased spectrum (c) requires SW0/SWa times fewer time increments than (a). Computer-optimized spectral aliasing provides spectral widths that avoid the superposition of signals upon aliasing.

The acquisition of a diffusion experiment using these conditions would take almost 1 day and still have no ability to resolve signals closer than ∼100 Hz. This shows that standard sampling techniques are far from reaching the resolution of a 1D carbon spectrum. Processing techniques, like linear prediction, can increase the resolution by a factor 2-4,45 but this still does not solve the problem. One way out of the situation in which the spectral proximity of pairs of carbon signals must be paid at a heavy experimental time cost is to reduce the spectral width from its full width SW0 to a smaller value SWa. Figure 2 shows the effect of spectral width reduction on signals falling outside the spectral boundaries. Such signals are called “aliased” because they appear back-folded at the other end of the spectrum at a position that does not correspond to their true chemical shifts. It may seem confusing to work with such spectra because the carbon dimension has no chemical shift scale. Nevertheless, they are easily handled because the position of any carbon in the reduced-width spectrum is perfectly predictable, when having in hand a list of carbon chemical shifts. The chemical shift scales are therefore replaced by a system designating the position of each carbon. The apparent frequency in the aliased spectrum νa, is simply given by the modulo function:

νa ) mod (ν0, SWa)

(2)

where ν0 is the Larmor frequency of the carbon measured in a normal full-width spectrum and SWa is the reduced spectral width in hertz. The benefit of spectral-width reduction is an increase in signal resolution at a constant number of time increments and total experimental time. The goal is then to choose a spectral width for which the aliased signals do not overlap. This can be done by hand using printed strips of carbon spectra, by trying to overlap as many displaced strips and looking for a displacement distance SWa for which no overlaps occur. However, it would be preferable to give this tedious task to a computer. We have developed two optimization procedures, as discussed in the following section. (45) Reynolds, W. F.; McLean, S.; Tay, L.-L.; Yu, M.; Enriquez, R. G.; Estwick, D. M.; Pascoe, K. O. Magn. Reson. Chem. 1997, 35, 455-462.

Figure 3. Example of computer-optimized spectral aliasing based on 1D carbon data. The HSQC spectrum of the two anomers of glucose in D2O was acquired using an optimized spectral width of 147.4 Hz (1.179 ppm). The improved distribution of carbon signals within the aliased spectrum allows the resolution of each with only 70 increments. The full spectrum with the same resolution would require 30 times more increments. In aliased spectra, the carbon chemical shift scales are usefully replaced by the set of lines that give the position of each carbon found in ref 1D spectra.

Computer Optimized Spectral Aliasing (COSA). The first computer optimization method46 for spectral aliasing can be accessed on-line (http:/rmn.unige.ch/simplealias). It takes a list of carbon chemical shifts and a few other parameters (Larmor and carrier frequencies) as input and proposes a spectral width SWa and a number of increments N for which all signals are resolved using a minimal acquisition time. It also gives, for each carbon, the signal position in the reduced-width spectrum. Figure 3 shows the result of the optimization of the carbon chemical shift for the two anomers of glucose. The comparison of the number of increments in a normal spectrum (2058 increments for 4422 Hz), and after optimization (70 for 147.4 Hz), shows that computeroptimized spectral aliasing reduces the number of increments by a factor of 30. The measurement of the diffusion rates for each C-H signal would take ∼3 h using the acquisition parameters of our program, as opposed to nearly 4 days using the full carbon spectrum at the same signal resolution. Note that this example only shows the power of computeroptimized aliasing. In the context of measuring the diffusion rates of the two anomers of glucose, it would not have been needed to resolve all the signals as we did here. The use of the standard 1D sequence would have been sufficient since the HR-C(1) and HβC(1) are well resolved. The second computer optimization method47 for spectral aliasing takes advantage of the proton dispersion in standard HSQC spectra to allow carbons to overlap when the protons bound to them do not. This method allows one to further reduce the number of time increments. EXPERIMENTAL SECTION Equimolar amounts (0.1 M) of glucose, maltose, and maltotriose (Fluka) were dissolved in 350 µL of D2O (Cambridge Isotope Laboratories) and placed in a 5-mm tube sealed after two dehydration cycles for H/D exchange. The sample height has to be limited to 4 cm in order to avoid convection caused by (46) Jeannerat, D.; Ronan, D.; Baudry, Y.; Pinto, A.; Saulnier, J. P.; Matile, S. Helv. Chim. Acta 2004, 87, 2190. (47) Jeannerat, D. In preparation.

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Figure 4. (a) First plane of the 3D CT-HSQC-IDOSY experiment of the mixture of glucose, maltose, and maltotriose in D2O. The spectral width and number of time increments were provided by computer optimization to obtain high resolution in the carbon dimension in minimal number of time increments. (b) Enlargement of the dotted region for comparison with the resolution obtained in the 1D DEPT spectrum with 1-Hz line broadening. (c) The same spectrum processed using linear prediction prior to FT. Note the presence of linear prediction artifacts as indicated by arrows. A cluster of unresolved signals is designated by an asterisk.

nonhomogeneous heating above the level corresponding to the top of the probe head. Our assignment is based on the spectra of the individual components and is consistent with literature data.49,50 The experiments were run on a Bruker DRX spectrometer operating at 500-MHz 1H Larmor frequency. The temperature was set to 297.4 K. The spinner of the NMR tube was modified to avoid sample vibration. Three grooves were carved, and additional weight was added in order to avoid levitation due to the air flow. A string was used to manipulate the sample in the magnet. The {1H}13C spectrum was acquired using a quadruply switchable probe optimized for direct detection of 13C. The processing used 1-Hz line broadening as window function. All proton-detected diffusion measurements were run using a room-temperature probe, optimized for proton detection. The pulse program of the CT-HSQC-IDOSY sequence (Figure 1) acquires data in an interleaved manner.51 We used bipolar pairs

of gradients12,52 to reduce eddy current artifacts18 and a 1-ms spinlock pulse to eliminate unwanted in-phase magnetization.53,54 The spectral width in the carbon dimension SWa ) 2.3724 ppm (1/16th of the full width) was calculated47 to avoid overlap and corresponds to a time increment of 1.67 ms. The diffusion delay time ∆ ) 300 ms allowed the acquisition of 178 time increments. In the proton dimension, the spectral width was set to 5 ppm and the FID acquired over 205 ms under 13C decoupling. To minimize sample heating that could jeopardize diffusion measurements by causing convection, we used adiabatic decoupling55,56 consisting of 1-ms CHIRP pulses sweeping over a 30-kHz bandwidth. The recovery delay was set at 2.5 s, a value chosen to ensure complete relaxation but also to avoid sample heating. All gradients had sine shapes truncated at 0.5% of the top amplitude. The duration of the diffusion gradient was 0.816 ms and the spoiling gradient 0.5 s. The top amplitude of the diffusion gradients ranged from 0.674 to 33.041 G/cm (2-98% of the maximal power) in 13 linear

(48) Palmer, A. G., III.; Cavanagh, J.; Wright, P. E.; Rance, M. J. Magn. Reson. 1991, 93, 151-170. (49) Fraschini, C.; Greffe, L.; Driguez, H.; Vignon, M. R. Carbohydr. Res. 2005, 340, 1893-1899. (50) Benesi, A. J.; Brant, D. A. Macromolecules 1985, 18, 1109-1116. (51) Orekhov, V. Y.; Korzhnev, D. M.; Diercks, T.; Kessler, H.; Arseniev, A. S. J. Biomol. NMR 1999, 14, 345-356.

(52) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson., A 1995, 115, 260264. (53) Otting, G.; Wu ¨ thrich, K. J. Magn. Reson. 1988, 76, 569-574. (54) Messerle, B. A.; Wider, G.; Otting, G.; Weber, C.; Wu ¨ thrich, K. J. Magn. Reson. 1989, 85, 608-613. (55) Kupcˇe, E.; Freeman, R. J. Magn. Reson., A 1995, 117, 246-256. (56) Fu, R.; Bodenhausen, G. J. Magn. Reson., A 1995, 117, 324-325.

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Table 1. Average Diffusion Rates Obtained Using the CT-HSQC-IDOSY Experiment

a

component

diffusion rate (×1010)a

error (%)b

R-glucose β-glucose R-maltose β-maltose R-maltotriose β-maltotriose

3.765 3.727 2.752 2.749 2.232 2.267

1.06 1.19 1.70 1.53 4.15 1.84

Averages over the values displayed in Figure 5. b Standard deviations.

steps. The gradients were calibrated using H2O/D2O samples.19 The number of scans was four, but the minimal phase cycling is two. The 128 preacquisition scans preceded the acquisition as another precaution to ensure thermal equilibration under the carbon-decoupling condition. The total experimental time was 7 h 58 min, which is to be compared to the nearly 5 days a full spectrum with the same signal resolution would have taken. Processing of the FIDs was performed with nmrPipe.57 Two spectra were generated. In the first, the carbon dimension was apodized using a squared shifted sine bell and zero filled to 512 points. In the second, the same extension was performed using forward linear prediction using eight coefficients. In the 1H dimension, a shifted sine bell was applied and the number of points was 1024 after zero-filling. The peak picking was made with nmrDraw.57 The height of each peak in each plan was automatically extracted with the program nlinLS.57 Diffusion coefficients D were extracted from a nonlinear least-squares fit of the signal amplitudes measured for 13 gradients strengths g with the signal attenuation function taking into account bipolar gradients12 and sine-shaped gradient profiles:58,59

I ) I0e-Dγ g δ (

2 2 2 ∆-

δ 3

-

)

τ′ 2

(3)

where I0 is the initial signal intensity, γ is the magnetogyric ratio of 1H, and the other symbols delays are shown in Figure 1. The diffusion coefficients were obtained using “cftool” based on the Matlab numerical calculation platform. RESULTS AND DISCUSSION We have applied our diffusion measurement method to an equimolar mixture of the three pairs of anomers of glucose, maltose, and maltotriose. This sample was chosen because it is very challenging. The overlap of signals is so severe in the proton spectrum that no diffusion measurement would be feasible in a 1D or any homonuclear 2D experiment. Only the 13C spectrum provided enough resolved signals to permit the measurements. The overlap was also quite severe in the carbon spectrum: out of the 72 carbons present in the mixture, about half of them are well-resolved, but 5 pairs are less than 10 Hz apart. The challenge, for our proton-detected experiment, was to resolve these signals in the indirectly detected carbon dimension. The acquisition (57) Delaglio, F.; Grzesiek, S.; Vuister, G. W.; Zhu, G.; Pfeifer, J.; Bax, A. J. Biomol. NMR 1995, 6, 277-293. (58) Merrill M. R. J. Magn. Reson., A 1993, 103, 223-225. (59) Price W. S.; Kuchel P. W. J. Magn. Reson. 1991, 94, 133-139.

Figure 5. Diffusion rates obtained by least-squares fit of the signal amplitudes of the CT-HSQC-IDOSY spectra to eq 3. The labels designate the carbon numbers, and primes and double primes correspond to the second and third sugar rings. Asterisks indicate values obtained with linear prediction. The error bars correspond to 95% confidence levels.

conditions fulfilling this requirement were obtained using computeroptimized spectral aliasing taking into account the dispersion of protons.47 A spectral width of SWa ) 296.5 Hz (2.372 ppm) avoided any overlap upon aliasing. The number of increments was set to 178, which is the maximum with a diffusion time ∆ ) 300 ms. The CT-HSQC-IDOSY sequence allowed us to distinguish clearly momomers, dimers, and trimers, but we did not expect to observe any difference between the R and β anomers. Consistent diffusion rates could be obtained for all resolved signals. Using standard processing, signals for 25 carbons were analyzed. The M3β/MT3β pair, separated by only 6 Hz, could be easily resolved (Figure 4b). For signal pairs less than 5 Hz apart, we relied on linear prediction. The increased resolution (Figure 4c) allowed us to measure eight additional diffusion rates including values for the pair MT2β/M2β, which are just 2.5 Hz apart. Many signals were impossible to resolve because the molecular environments of the relevant C-H were identical in the different components of the mixture. The ability of 2D spectra to resolve, in the proton dimension, signals that overlap in the carbon dimension was exploited to measure diffusion values for the pair MT2′β/G2R (Figure 4a). We have therefore demonstrated the ability of aliased 2D spectra to reach a resolution comparable to 1D spectra with higher sensitivity than INEPT-HSQC experiments. Aliased 2D spectra also benefit from the dispersion of signals in the proton dimension. We verified the absence of systematic artifacts by plotting the residual curves (difference between the best-fit curve and the experimental points). The few artifacts observed in the spectra obtained after linear prediction might have perturbed signal integration because they are not always present at the same locations within the series of HSQC spectra. However, Figure 5 shows that the precision and accuracy of the rates are quite similar to the values calculated using standard processing. The standard deviations of the measurements (Table 1) are slightly lower than the 5-10% commonly found in the literature. The largest deviation is found in the case of R-maltotriose, a minor isomer (∼2:1 β/R), and because trioses have more rapid relaxations. This high precision is especially good considering that the CT-HSQC-IDOSY experiment is based on natural abundance 13C. It can be explained by the amount of sample but also by the use Analytical Chemistry, Vol. 78, No. 15, August 1, 2006

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of a special sample spinner to avoid any movements in the presence of temperature control (see Experimental Section). Interleaved acquisition,51 that is, nesting the loop over the increasing gradient amplitudes into the one incrementing the time increments, limits drastically the impact of long-term instabilities. Any modification in the experimental conditions only affect the signal line shapes (with no adverse consequences) instead of influencing the signal amplitudes that would affect the precision of the measurements. The choice of the pulse sequences was made based on the following considerations. When aiming at the highest possible resolution in the carbon dimension, HSQC spectra are preferable to HMBC spectra because they show narrower signals. In the latter, the multiple-quantum evolution gives rise to a coupling structure in the carbon dimension. We therefore started with the CT-HSQC experiment38 because the sensitivity-enhanced version48

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would have complicated the decoding of the diffusion dimension and increased the number of pulses in the sequence. ACKNOWLEDGMENT This work was financed by the De´ partement de l’Instruction Publique du canton de Gene` ve. We thank Andre´ Pinto for spectrometer management and optimization, Richard Frantz and Massimiliano Valentini for pointing out the problem of vibrations due to air flow, Mia Milos for preliminary experiments, and Graham Cumming and Jonathan Nitschke for critical comments on the manuscript.

Received for review April 19, 2006. Accepted May 14, 2006. AC060744G