DOI: 10.1002/chem.201404038
Communication
& NMR Spectroscopy
Rapid Characterization of Molecular Diffusion by NMR Spectroscopy Shivanand M. Pudakalakatti,[a, b] Kousik Chandra,[a] Ravula Thirupathi,[a, b] and Hanudatta S. Atreya*[a, b] Abstract: An NMR-based approach for rapid characterization of translational diffusion of molecules has been developed. Unlike the conventional method of acquiring a series of 2D 13C and 1H spectra, the proposed approach involves a single 2D NMR spectrum, which can be acquired in minutes. Using this method, it was possible to detect the presence of intermediate oligomeric species of diphenylalanine in solution during the process of its selfassembly to form nanotubular structures.
Diffusion-ordered spectroscopy (DOSY) is an important NMR technique to characterize translational diffusion of molecules in solution, with applications ranging from study of inter-molecular interactions to analysis of mixtures.[1] The conventional approach involves the acquisition of a series of one dimensional (1D) 1H NMR spectrum with varying linear magnetic field gradients, followed by fitting the resulting intensity of peaks to the Stejskal–Tanner equation[2] to extract the diffusion coefficients. In the case of an overlap in the 1H dimension (i.e., two different molecules with nearly the same 1H chemical shift), estimation of the diffusion coefficient becomes incorrect due to the multi-exponential decay of the intensity profiles arising from different species. Though different theoretical and experimental methods[3] have been developed to address this problem, an efficient approach involves two-dimensional (2D) NMR spectroscopy to resolve the overlapping peaks.[1] In this approach, a series of 2D NMR spectra (e.g., 2D 13C1H heteronuclear single quantum correlation (HSQC) spectrum)[4] are acquired by varying the diffusion-encoding pulsed-field gradients linearly. This becomes a “pseudo-3D” experiment and comes at the expense of increased measurement time, thereby precluding its application to fast molecular processes. Notwithstanding this fact, only a few approaches have been proposed for rapid measurement of translational diffusion.[5] Here, we present a new experiment: 2D FAST-DOSY, which fa[a] S. M. Pudakalakatti,+ K. Chandra,+ R. Thirupathi, H. S. Atreya NMR Research Centre, Indian Institute of Science Bangalore-560012 (India) E-mail: [email protected] [b] S. M. Pudakalakatti,+ R. Thirupathi, H. S. Atreya Solid State and Structural Chemistry Unit Indian Institute of Science, Bangalore-560012 (India)
cilitates rapid characterization of translational diffusion of molecules, either in a mixture or in the pure form. The method combines DOSY, accordion NMR spectroscopy[6] (with the conventional constant-time 2D 13C), and 1H–HSQC, such that the linewidths of the peaks directly encode the translational diffusion coefficient. A single 2D spectrum is sufficient to measure the diffusion rates, thereby reducing the measurement time by an order of magnitude compared to existing methods. The measurement time is reduced further by utilizing the method of non-uniform sampling,[7] facilitating the monitoring of fast molecular processes in real time. We demonstrate the application of this method to a wide range of systems from analysis of mixtures to real-time characterization of intermediates in a molecular process. Accordion spectroscopy has been used in the past for measuring translational diffusion rates.[5a] However, two drawbacks have limited its utility. First, the amplitude of the free-induction decay (FID) in the indirect dimension during t1 is modulated by both transverse relaxation (T2) of 1H and translational diffusion of the molecule (D). Thus, the resulting line shape after Fourier transformation has contributions from both T2(1H) and diffusion rates. To deconvolute the two contributions, a separate data set is acquired to estimate the intrinsic linewidth arising from T2(1H) and an elaborate line-fitting approach is carried out.[5a] Second, the experiment has been demonstrated for 2D homonuclear NOESY (Nuclear Overhauser effect spectroscopy), which is seldom used for measuring translational diffusion coefficients. The key idea in 2D FAST-DOSY is: 1) the 13C chemical-shift evolution period in the indirect dimension (t1) is co-incremented with the strength of the gradient encoding the diffusion coefficients and, 2) the chemical shift evolution is carried out in a constant-time manner,[8] which removes the contribution of T1(1H/13C) and T2(13C) to the decay of FID and only contributes to the overall signal-to-noise of the signal. Thus, the amplitude of the FID (I(t1)) is modulated as Equation (1):
Iðt 1 Þ ¼ I0 exp½ðgdgðt 1 ÞÞ2 ðDd=3ÞD expðiWt 1 Þ
ð1Þ
where g is a gyromagnetic ratio (1H), d and g are the duration and strength of the diffusion gradients, respectively, D is a diffusion delay, D is the diffusion coefficient being measured, and W represents the chemical shift. The gradient strength, g, varies with t1 as shown in Equation (2):
[+] These authors contributed equally to this work. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201404038. Chem. Eur. J. 2014, 20, 15719 – 15722
gðt 1 Þ ¼ xt 1 15719
x ¼ ðDg=NÞ
ð2Þ
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Communication where Dg is a total gradient strength varied during the experiment (g0 to gmax) and N is the number of complex points in the indirect dimension. Assuming a case of on-resonance (i.e., W = 0), Fourier transform of the FID along the F1 dimension results in Equation (3):
Iðw1 Þ ¼ Cexpðw1 2 =4ðgdxÞ2 ðDd=3ÞDÞ
ð3Þ
where C = I0(p/(gdx)2(Dd/3)D)1/2 is constant, affecting only the overall intensity/volume of the peak;[5a] w1 is the frequency. The linewidth (LW) at half height of the peak is given by Equation (4): ðLWÞ2 ¼ ðln2Þ ð4ðgdxÞ2 ðDd=3ÞDÞ=ðpÞ2
ð4Þ
Thus, from the linewidth we can directly obtain the value of the diffusion coefficient (D) without recourse to any line shape fitting and/or additional processing. The method of 2D FASTDOSY can be implemented in two different ways, as depicted in Scheme 1. In one approach, the radio frequency (r.f.) pulse scheme comprising the DOSY block can be placed before a regular 2D 13C1H HSQC sequence (as in a 3D DOSY-HSQC experiment).[9] In another approach, the recently proposed experi-
Scheme 1. a) In this approach, the radio frequency (r.f.) pulse scheme comprising the DOSY block is placed before constant-time 2D 13C1H HSQC. b) DOSY block is incorporated within a constant-time 2D 13C1H HSQC as implemented in the present study. In this case the constant time delay being equal to the diffusion delay (D).
ment: HSQC-iDOSY[3f, 4] can be used, in which the DOSY block is incorporated within a constant-time 2D 13C1H HSQC. We have utilized the second approach in the present study. The r.f. pulse sequence used is shown in Figure S1 in the Supporting Information. Various experimental parameters were optimized based on simulations (Figure S2 in the Supporting Information). A typical spectrum obtained using 2D FAST-DOSY is illustrated in Figure 1 a, which was acquired using the natural abundance of 13C for a mixture of Glycine, Alanine, and Lysine, having a concentration of 10 mm each at 298 K. All resonances belonging to a given molecule had similar linewidths (Figure S3 in the Supporting Information), which implies that 2D Chem. Eur. J. 2014, 20, 15719 – 15722
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Figure 1. a) A 2D FAST-DOSY spectrum at 298 K of a mixture of glycine, alanine, and lysine (10 mm each). The linewidths of the peaks encoding the diffusion coefficients are shown on the right for selected resonances. The spectrum was acquired at 1H resonance frequency of 400 MHz with relaxation delay of 2 s between scans, 128 complex points in indirect dimension and 16 transients, resulting in a total acquisition time of approximately 70 min. b) 2D FAST-DOSY spectrum of 13C-labeled cysteine which shows a mixture of monomer and dimer. The spectrum was acquired at 1H resonance frequency of 400 MHz with a 5 mm sample in approximately 35 min with a relaxation delay of 2 s between scans, 128 complex points, and 8 transients.
FAST-DOSY can also be used as a method for assignment of peaks to a given molecule in the mixture. A second example illustrates the ability to distinguish different oligomeric species of the same molecule. Figure 1 b shows a 2D FAST-DOSY spectrum of 13C-labeled cysteine ( 5 mm) dissolved in 100 % 2H2O. The sample contains a mixture of monomer and dimer with their 13Cb chemical shifts differing significantly.[10] The linewidth of the resonance corresponding to the dimer (96 Hz) is less than the monomer (107 Hz), which is consistent with its expected relatively slower diffusion. To further validate its accuracy, the diffusion coefficients obtained from 2D FAST-DOSY were compared (Figure 2) with the diffusion coefficients measured from a conventional 1D DOSY experiment (bipolar LED) typically used in diffusion studies.[1] Data acquisition in 2D FAST-DOSY can be significantly accelerated using non-uniform sampling (NUS) as shown recently.[5f] In our approach, certain time domain points (increments) along t1 are omitted by using an appropriate algorithm, thereby reducing the overall measurement time. The omitted points are subsequently reconstructed to yield a linearly sampled data set. The linewidths remain unchanged if the FID is sampled appropriately using a suitable sampling schedule, such as Poisson-gap sampling.[7b, 11] This was verified using NUS-2D FAST-DOSY spectra of Maltose (Figure 3). The data were acquired with different amounts of deletion of points in the indirect (13C) dimension and the time-domain points were reconstructed using the multidimensional decomposition (MDD) algorithm.[12]
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Figure 3. Comparison of the 2D FAST-DOSY spectrum of maltose reconstructed using MDD (multidimensional decomposition) with different percentages of non-uniform sampling (NUS). The uniformly sampled spectrum (indicated as 100 %) was acquired in approximately 70 min with a sample of maltose ( 40 mm) at a 1H resonance frequency of 400 MHz.
Figure 2. A correlation plot comparing the diffusion coefficients obtained from a conventional bipolar LED experiment and 2D FAST-DOSY. This was carried out at 400 MHz at 25 8C for 16 compounds in the molecular-mass range of 75–350 Da and diffusion coefficients in the range of 0.44– 1.1 109 m2 s1. The linear Pearson correlation coefficient and the rootmean-square deviation (rmsd) between the two sets of values are indicated.
solved in 2H2O (100 %) at 65 8C. At 45 8C, a linewidth of 235 Hz (corresponding to D = 0.85 109 m2 s1) was observed (Figure 4 a). A full 2D FAST-DOSY spectrum of FF at 45 8C is shown in Figure S5 in the Supporting Information. This, in turn, corresponds to a radius of hydration (Rh) of approximately 0.45 nm, calculated using the Stokes–Einstein equation, Rh = kT/6phTD (hT being the solvent viscosity at temperature T),[1b] and ignoring convection. Up to a temperature of 35 8C the radius of hydration does not change significantly, implying that oligomeric FF species are not present in significant amounts at these temperatures. As the temperature nears 25 8C an average linewidth of 155 Hz (measured by repeating the entire process three times) corresponding to D = 0.36 109 m2 s1 is observed, which gives an average Rh of 0.7 nm and a range of 0.6–0.8 nm (Figure 4 b). A slow precipitation was then observed occurring in the NMR sample tube at 25 8C. We carried out molecular dynamics (MD) simulations on a mixture of FF molecules in solu-
Up to a deletion of 75 % of points the S/N remains reasonable and linewidths do not change. Further reduction in points (and thereby measurement time) can be achieved for samples with high sensitivity. Alternatively, NUS can be employed when high resolution is needed without increasing the measurement time. This is exemplified for data acquired for a mixture of maltose and glucose at very high resolution (t1max = 127 ms) to resolve their overlapping 1H and 13C peaks using 10 % NUS in a total measurement time of 12 min (Figure S4 in the Supporting information). The above features of 2D FAST-DOSY helped us to probe systems that required rapid acquisition of spectra to monitor dynamic processes. In one study, we monitored the self-assembly of diphenylalanine (FF) into nanotubular structures. Whereas the formation of FF nanotubes has been well-studied due to its potentially important applications and its recognition as a core motif for Alzheimers’ beta-amyloid polypeptide,[13] experimental evidence for the intermediate formed during the self-assembly process has remained elusive, due to its low solubility in water at room temperature. The formation of the oligoFigure 4. a) A selected region of the 2D FAST-DOSY spectrum of diphenylalanine (FF) dissolved in 2H2O as a funcmeric forms was monitored as tion of temperature indicating the changes in linewidths as the self-assembly proceeds. b) Estimated radius of hythe temperature was lowered, dration based on the linewidths and solvent viscosity at different temperatures. c) SEM images of the nanotubular starting with FF (6 mm) dis- structures formed upon solvent evaporation. Chem. Eur. J. 2014, 20, 15719 – 15722
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Communication tion to estimate the oligomeric species of FF corresponding to Rh = 0.8 nm (see Supporting Information). Our results indicate that Rh = 0.8 nm potentially corresponds to a tetramer (4-FF) which is nearly globular in shape with Rg = 0.8 nm. The tetramer has an inner hydrophobic core, consistent with that observed in the crystal structure and MD simulations.[13a,c] The pentamers (5-FF) and beyond were estimated to have Rg > 0.9 nm and, hence, a possible Rh > 1 nm. A range of approximately 0.6–0.8 nm in the estimated Rh values (Figure 4 b) indicates that at room temperature a mixture of monomeric to tetrameric (4-FF) forms are predominantly present, as proposed recently using MD simulations.[13c] As the 4-FF oligomerizes further, insoluble higher-order oligomers precipitate out of the solution and are not observed in the NMR spectrum. Our studies thus indicate that the tetramer (4-FF) is the most soluble oligomeric FF species in aqueous solution at room temperature. This will be useful for designing inhibitors, which can either inhibit the formation of these intermediates or stabilize/ trap them to prevent further oligomerization. In another study, we monitored the translational diffusion of proline in polyacrylamide gel (15 %) as function of time. This was carried out using proline (130 mm) in a solution of acrylamide (15 %) at 298 K. The formation of the polyacrylamide gel was initiated by the addition of TEMED (N, N, N’, N’ tetramethylethylenediamine) and a series of 2D FAST-DOSY spectra were acquired with 25 % nonuniform sampling at an interval of 6 min each. Figure S6 in the Supporting Information shows representative spectra acquired at different time intervals. As the polymerization proceeds the linewidths reduce due to slower diffusion, starting with a linewidth of 212(40) Hz (at t = 0) corresponding to D 1.0(0.2) 109 m2 s1. After the polymerization is complete (at t 15 min by visual inspection), the linewidth reaches a value of 140 Hz, corresponding to D = 0.6 109 m2 s1, consistent with the value expected from the acrylamide concentration (see Figure S6 in the Supporting Information).[14] In summary, we have presented a new NMR method, 2D FAST-DOSY, for rapid characterization of translational diffusion of molecules. The method is based on the principle of accordion spectroscopy and involves co-incrementing of the chemical-shift evolution period and the gradient strengths in a constant-time 2D 13C1H HSQC for encoding the diffusion. This reduces a conventional pseudo 3D experiment to two dimensions, enabling fast data collection. Using a single 2D spectrum, the diffusion coefficients can be accurately extracted from the linewidths of cross peaks in the indirect dimension. The experimental time can be decreased further using the method of non-uniform sampling. This opens up new possibilities to monitor fast molecular processes in both chemical and biomolecular systems.
Experimental Section All NMR experiments were performed on a Bruker Avance III 400 MHz or 800 MHz NMR spectrometer (the latter equipped with
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a cryogenic probe). The r.f. pulse sequence used is shown in Figure S1 in the Supporting Information.
Acknowledgements Support for the NMR Research Centre from the Department of Science and Technology (DST), India, and the Nanoscience facility at IISc is gratefully acknowledged. K.C. acknowledges support from a DST-INSPIRE fellowship. H.S.A. acknowledges support from DAE-BRNS. Keywords: diphenylalanine · FAST-DOSY · nanotubes · NMR spectroscopy · non-uniform sampling [1] a) Y. Cohen, L. Avram, L. Frish, Angew. Chem. Int. Ed. 2005, 44, 520; Angew. Chem. 2005, 117, 524; b) A. Macchioni, G. Ciancaleoni, C. Zuccaccia, D. Zuccaccia, Diffusion Ordered NMR Spectroscopy (DOSY) in Supramolecular Chemistry, Vol.2: Techniques (Eds.: J. W. Steed, P. A. Gale), Wiley, Chichester, 2012, p. 319. [2] E. O. Stejskal, J. E. Tanner, J. Chem. Phys. 1965, 42, 288. [3] a) K. F. Morris, C. S. Johnson, Jr., J. Am. Chem. Soc. 1993, 115, 4291; b) H. Barjat, G. A. Morris, A. G. Swanson, J. Magn. Reson. 1998, 131, 131; c) C. S. Johnson, Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203; d) M. Nilsson, A. Botana, G. A. Morris, Anal. Chem. 2009, 81, 8119; e) M. Nilsson, M. Khajeh, A. Botana, M. A. Bernstein, G. A. Morris, Chem. Commun. 2009, 1252; f) A. S. McLachlan, J. J. Richards, A. R. Bilia, G. A. Morris, Magn. Reson. Chem. 2009, 47, 1081; g) J. A. Aguilar, A. A. Colbourne, J. Cassani, M. Nilsson, G. A. Morris, Angew. Chem. Int. Ed. 2012, 51, 6460; Angew. Chem. 2012, 124, 6566; h) A. A. Colbourne, S. Meier, G. A. Morris, M. Nilsson, Chem. Commun. 2013, 49, 10510; i) B. R. Martini, V. A. Mandelshtam, G. A. Morris, A. A. Colbourne, M. Nilsson, J. Magn. Reson. 2013, 234, 125; j) G. Hamdoun, M. Sebban, E. Cossoul, A. HarrisonMarchand, J. Maddaluno, H. Oulyadi, Chem. Commun. 2014, 50, 4073. [4] B. Vitorge, D. Jeannerat, Anal. Chem. 2006, 78, 7601. [5] a) O. Millet, M. Pons, J. Magn. Reson. 1998, 131, 166; b) N. M. Loening, J. Keeler, G. A. Morris, J. Magn. Reson. 2001, 153, 103; c) M. J. Thrippleton, N. M. Loening, J. Keeler, Magn. Reson. Chem. 2003, 41, 441; d) C. A. Steinbeck, B. F. Chmelka, J. Am. Chem. Soc. 2005, 127, 11624; e) Y. Shrot, L. Frydman, J. Magn. Reson. 2008, 195, 226; f) M. Urban´czyk, W. Koz´min´ski, K. Kazimierczuk, Angew. Chem. Int. Ed. 2014, 53, 6464; Angew. Chem. 2014, 126, 6582. [6] G. Bodenhausen, R. R. Ernst, J. Magn. Reson. 1981, 45, 367. [7] a) D. Rovnyak, D. P. Frueh, M. Sastry, Z. Y. J. Sun, A. S. Stern, J. C. Hoch, G. Wagner, J. Magn. Reson. 2004, 170, 15; b) S. G. Hyberts, H. Arthanari, G. Wagner, Novel Sampling Approaches in Higher Dimensional NMR, Springer-Verlag, Berlin, Heidelberg 2012; c) S. G. Hyberts, H. Arthanari, G. Wagner, Top. Curr. Chem. 2011, 316, 125. [8] J. Keeler, Understanding NMR spectroscopy, 2ednd edJohn Wiley & Sons, Chichester, 2010. [9] A. V. Buevich, J. Baum, J. Am. Chem. Soc. 2002, 124, 7156. [10] H. S. Atreya, S. C. Sahu, K. V. R. Chary, G. Govil, J. Biomol. NMR 2000, 17, 125. [11] S. Paramasivam, C. L. Suiter, G. Hou, S. Sun, M. Palmer, J. C. Hoch, D. Rovnyak, T. Polenova, J. Phys. Chem. B 2012, 116, 7416. [12] V. Y. Orekhov, V. A. Jaravine, Prog. Nucl. Magn. Reson. Spectrosc. 2011, 59, 271. [13] a) C. H. Gçrbitz, Chem. Commun. 2006, 22, 2332; b) E. Gazit, Chem. Soc. Rev. 2007, 36, 1263; c) J. Jeon, C. E. Mills, M. S. Shell, J. Phys. Chem. B 2013, 117, 3935. [14] I. H. Park, C. S. Johnson, D. A. Gabriel, Macromolecules 1990, 23, 1548. Received: June 19, 2014 Published online on October 21, 2014
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Rapid Characterization of Molecular Diffusion by NMR Spectroscopy Shivanand M. Pudakalakatti,[a, b] Kousik Chandra,[a] Ravula Thirupathi,[a, b] and Hanudatta S. Atreya*[a, b] Abstract: An NMR-based approach for rapid characterization of translational diffusion of molecules has been developed. Unlike the conventional method of acquiring a series of 2D 13C and 1H spectra, the proposed approach involves a single 2D NMR spectrum, which can be acquired in minutes. Using this method, it was possible to detect the presence of intermediate oligomeric species of diphenylalanine in solution during the process of its selfassembly to form nanotubular structures.
Diffusion-ordered spectroscopy (DOSY) is an important NMR technique to characterize translational diffusion of molecules in solution, with applications ranging from study of inter-molecular interactions to analysis of mixtures.[1] The conventional approach involves the acquisition of a series of one dimensional (1D) 1H NMR spectrum with varying linear magnetic field gradients, followed by fitting the resulting intensity of peaks to the Stejskal–Tanner equation[2] to extract the diffusion coefficients. In the case of an overlap in the 1H dimension (i.e., two different molecules with nearly the same 1H chemical shift), estimation of the diffusion coefficient becomes incorrect due to the multi-exponential decay of the intensity profiles arising from different species. Though different theoretical and experimental methods[3] have been developed to address this problem, an efficient approach involves two-dimensional (2D) NMR spectroscopy to resolve the overlapping peaks.[1] In this approach, a series of 2D NMR spectra (e.g., 2D 13C1H heteronuclear single quantum correlation (HSQC) spectrum)[4] are acquired by varying the diffusion-encoding pulsed-field gradients linearly. This becomes a “pseudo-3D” experiment and comes at the expense of increased measurement time, thereby precluding its application to fast molecular processes. Notwithstanding this fact, only a few approaches have been proposed for rapid measurement of translational diffusion.[5] Here, we present a new experiment: 2D FAST-DOSY, which fa[a] S. M. Pudakalakatti,+ K. Chandra,+ R. Thirupathi, H. S. Atreya NMR Research Centre, Indian Institute of Science Bangalore-560012 (India) E-mail: [email protected] [b] S. M. Pudakalakatti,+ R. Thirupathi, H. S. Atreya Solid State and Structural Chemistry Unit Indian Institute of Science, Bangalore-560012 (India)
cilitates rapid characterization of translational diffusion of molecules, either in a mixture or in the pure form. The method combines DOSY, accordion NMR spectroscopy[6] (with the conventional constant-time 2D 13C), and 1H–HSQC, such that the linewidths of the peaks directly encode the translational diffusion coefficient. A single 2D spectrum is sufficient to measure the diffusion rates, thereby reducing the measurement time by an order of magnitude compared to existing methods. The measurement time is reduced further by utilizing the method of non-uniform sampling,[7] facilitating the monitoring of fast molecular processes in real time. We demonstrate the application of this method to a wide range of systems from analysis of mixtures to real-time characterization of intermediates in a molecular process. Accordion spectroscopy has been used in the past for measuring translational diffusion rates.[5a] However, two drawbacks have limited its utility. First, the amplitude of the free-induction decay (FID) in the indirect dimension during t1 is modulated by both transverse relaxation (T2) of 1H and translational diffusion of the molecule (D). Thus, the resulting line shape after Fourier transformation has contributions from both T2(1H) and diffusion rates. To deconvolute the two contributions, a separate data set is acquired to estimate the intrinsic linewidth arising from T2(1H) and an elaborate line-fitting approach is carried out.[5a] Second, the experiment has been demonstrated for 2D homonuclear NOESY (Nuclear Overhauser effect spectroscopy), which is seldom used for measuring translational diffusion coefficients. The key idea in 2D FAST-DOSY is: 1) the 13C chemical-shift evolution period in the indirect dimension (t1) is co-incremented with the strength of the gradient encoding the diffusion coefficients and, 2) the chemical shift evolution is carried out in a constant-time manner,[8] which removes the contribution of T1(1H/13C) and T2(13C) to the decay of FID and only contributes to the overall signal-to-noise of the signal. Thus, the amplitude of the FID (I(t1)) is modulated as Equation (1):
Iðt 1 Þ ¼ I0 exp½ðgdgðt 1 ÞÞ2 ðDd=3ÞD expðiWt 1 Þ
ð1Þ
where g is a gyromagnetic ratio (1H), d and g are the duration and strength of the diffusion gradients, respectively, D is a diffusion delay, D is the diffusion coefficient being measured, and W represents the chemical shift. The gradient strength, g, varies with t1 as shown in Equation (2):
[+] These authors contributed equally to this work. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201404038. Chem. Eur. J. 2014, 20, 15719 – 15722
gðt 1 Þ ¼ xt 1 15719
x ¼ ðDg=NÞ
ð2Þ
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Communication where Dg is a total gradient strength varied during the experiment (g0 to gmax) and N is the number of complex points in the indirect dimension. Assuming a case of on-resonance (i.e., W = 0), Fourier transform of the FID along the F1 dimension results in Equation (3):
Iðw1 Þ ¼ Cexpðw1 2 =4ðgdxÞ2 ðDd=3ÞDÞ
ð3Þ
where C = I0(p/(gdx)2(Dd/3)D)1/2 is constant, affecting only the overall intensity/volume of the peak;[5a] w1 is the frequency. The linewidth (LW) at half height of the peak is given by Equation (4): ðLWÞ2 ¼ ðln2Þ ð4ðgdxÞ2 ðDd=3ÞDÞ=ðpÞ2
ð4Þ
Thus, from the linewidth we can directly obtain the value of the diffusion coefficient (D) without recourse to any line shape fitting and/or additional processing. The method of 2D FASTDOSY can be implemented in two different ways, as depicted in Scheme 1. In one approach, the radio frequency (r.f.) pulse scheme comprising the DOSY block can be placed before a regular 2D 13C1H HSQC sequence (as in a 3D DOSY-HSQC experiment).[9] In another approach, the recently proposed experi-
Scheme 1. a) In this approach, the radio frequency (r.f.) pulse scheme comprising the DOSY block is placed before constant-time 2D 13C1H HSQC. b) DOSY block is incorporated within a constant-time 2D 13C1H HSQC as implemented in the present study. In this case the constant time delay being equal to the diffusion delay (D).
ment: HSQC-iDOSY[3f, 4] can be used, in which the DOSY block is incorporated within a constant-time 2D 13C1H HSQC. We have utilized the second approach in the present study. The r.f. pulse sequence used is shown in Figure S1 in the Supporting Information. Various experimental parameters were optimized based on simulations (Figure S2 in the Supporting Information). A typical spectrum obtained using 2D FAST-DOSY is illustrated in Figure 1 a, which was acquired using the natural abundance of 13C for a mixture of Glycine, Alanine, and Lysine, having a concentration of 10 mm each at 298 K. All resonances belonging to a given molecule had similar linewidths (Figure S3 in the Supporting Information), which implies that 2D Chem. Eur. J. 2014, 20, 15719 – 15722
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Figure 1. a) A 2D FAST-DOSY spectrum at 298 K of a mixture of glycine, alanine, and lysine (10 mm each). The linewidths of the peaks encoding the diffusion coefficients are shown on the right for selected resonances. The spectrum was acquired at 1H resonance frequency of 400 MHz with relaxation delay of 2 s between scans, 128 complex points in indirect dimension and 16 transients, resulting in a total acquisition time of approximately 70 min. b) 2D FAST-DOSY spectrum of 13C-labeled cysteine which shows a mixture of monomer and dimer. The spectrum was acquired at 1H resonance frequency of 400 MHz with a 5 mm sample in approximately 35 min with a relaxation delay of 2 s between scans, 128 complex points, and 8 transients.
FAST-DOSY can also be used as a method for assignment of peaks to a given molecule in the mixture. A second example illustrates the ability to distinguish different oligomeric species of the same molecule. Figure 1 b shows a 2D FAST-DOSY spectrum of 13C-labeled cysteine ( 5 mm) dissolved in 100 % 2H2O. The sample contains a mixture of monomer and dimer with their 13Cb chemical shifts differing significantly.[10] The linewidth of the resonance corresponding to the dimer (96 Hz) is less than the monomer (107 Hz), which is consistent with its expected relatively slower diffusion. To further validate its accuracy, the diffusion coefficients obtained from 2D FAST-DOSY were compared (Figure 2) with the diffusion coefficients measured from a conventional 1D DOSY experiment (bipolar LED) typically used in diffusion studies.[1] Data acquisition in 2D FAST-DOSY can be significantly accelerated using non-uniform sampling (NUS) as shown recently.[5f] In our approach, certain time domain points (increments) along t1 are omitted by using an appropriate algorithm, thereby reducing the overall measurement time. The omitted points are subsequently reconstructed to yield a linearly sampled data set. The linewidths remain unchanged if the FID is sampled appropriately using a suitable sampling schedule, such as Poisson-gap sampling.[7b, 11] This was verified using NUS-2D FAST-DOSY spectra of Maltose (Figure 3). The data were acquired with different amounts of deletion of points in the indirect (13C) dimension and the time-domain points were reconstructed using the multidimensional decomposition (MDD) algorithm.[12]
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Figure 3. Comparison of the 2D FAST-DOSY spectrum of maltose reconstructed using MDD (multidimensional decomposition) with different percentages of non-uniform sampling (NUS). The uniformly sampled spectrum (indicated as 100 %) was acquired in approximately 70 min with a sample of maltose ( 40 mm) at a 1H resonance frequency of 400 MHz.
Figure 2. A correlation plot comparing the diffusion coefficients obtained from a conventional bipolar LED experiment and 2D FAST-DOSY. This was carried out at 400 MHz at 25 8C for 16 compounds in the molecular-mass range of 75–350 Da and diffusion coefficients in the range of 0.44– 1.1 109 m2 s1. The linear Pearson correlation coefficient and the rootmean-square deviation (rmsd) between the two sets of values are indicated.
solved in 2H2O (100 %) at 65 8C. At 45 8C, a linewidth of 235 Hz (corresponding to D = 0.85 109 m2 s1) was observed (Figure 4 a). A full 2D FAST-DOSY spectrum of FF at 45 8C is shown in Figure S5 in the Supporting Information. This, in turn, corresponds to a radius of hydration (Rh) of approximately 0.45 nm, calculated using the Stokes–Einstein equation, Rh = kT/6phTD (hT being the solvent viscosity at temperature T),[1b] and ignoring convection. Up to a temperature of 35 8C the radius of hydration does not change significantly, implying that oligomeric FF species are not present in significant amounts at these temperatures. As the temperature nears 25 8C an average linewidth of 155 Hz (measured by repeating the entire process three times) corresponding to D = 0.36 109 m2 s1 is observed, which gives an average Rh of 0.7 nm and a range of 0.6–0.8 nm (Figure 4 b). A slow precipitation was then observed occurring in the NMR sample tube at 25 8C. We carried out molecular dynamics (MD) simulations on a mixture of FF molecules in solu-
Up to a deletion of 75 % of points the S/N remains reasonable and linewidths do not change. Further reduction in points (and thereby measurement time) can be achieved for samples with high sensitivity. Alternatively, NUS can be employed when high resolution is needed without increasing the measurement time. This is exemplified for data acquired for a mixture of maltose and glucose at very high resolution (t1max = 127 ms) to resolve their overlapping 1H and 13C peaks using 10 % NUS in a total measurement time of 12 min (Figure S4 in the Supporting information). The above features of 2D FAST-DOSY helped us to probe systems that required rapid acquisition of spectra to monitor dynamic processes. In one study, we monitored the self-assembly of diphenylalanine (FF) into nanotubular structures. Whereas the formation of FF nanotubes has been well-studied due to its potentially important applications and its recognition as a core motif for Alzheimers’ beta-amyloid polypeptide,[13] experimental evidence for the intermediate formed during the self-assembly process has remained elusive, due to its low solubility in water at room temperature. The formation of the oligoFigure 4. a) A selected region of the 2D FAST-DOSY spectrum of diphenylalanine (FF) dissolved in 2H2O as a funcmeric forms was monitored as tion of temperature indicating the changes in linewidths as the self-assembly proceeds. b) Estimated radius of hythe temperature was lowered, dration based on the linewidths and solvent viscosity at different temperatures. c) SEM images of the nanotubular starting with FF (6 mm) dis- structures formed upon solvent evaporation. Chem. Eur. J. 2014, 20, 15719 – 15722
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Communication tion to estimate the oligomeric species of FF corresponding to Rh = 0.8 nm (see Supporting Information). Our results indicate that Rh = 0.8 nm potentially corresponds to a tetramer (4-FF) which is nearly globular in shape with Rg = 0.8 nm. The tetramer has an inner hydrophobic core, consistent with that observed in the crystal structure and MD simulations.[13a,c] The pentamers (5-FF) and beyond were estimated to have Rg > 0.9 nm and, hence, a possible Rh > 1 nm. A range of approximately 0.6–0.8 nm in the estimated Rh values (Figure 4 b) indicates that at room temperature a mixture of monomeric to tetrameric (4-FF) forms are predominantly present, as proposed recently using MD simulations.[13c] As the 4-FF oligomerizes further, insoluble higher-order oligomers precipitate out of the solution and are not observed in the NMR spectrum. Our studies thus indicate that the tetramer (4-FF) is the most soluble oligomeric FF species in aqueous solution at room temperature. This will be useful for designing inhibitors, which can either inhibit the formation of these intermediates or stabilize/ trap them to prevent further oligomerization. In another study, we monitored the translational diffusion of proline in polyacrylamide gel (15 %) as function of time. This was carried out using proline (130 mm) in a solution of acrylamide (15 %) at 298 K. The formation of the polyacrylamide gel was initiated by the addition of TEMED (N, N, N’, N’ tetramethylethylenediamine) and a series of 2D FAST-DOSY spectra were acquired with 25 % nonuniform sampling at an interval of 6 min each. Figure S6 in the Supporting Information shows representative spectra acquired at different time intervals. As the polymerization proceeds the linewidths reduce due to slower diffusion, starting with a linewidth of 212(40) Hz (at t = 0) corresponding to D 1.0(0.2) 109 m2 s1. After the polymerization is complete (at t 15 min by visual inspection), the linewidth reaches a value of 140 Hz, corresponding to D = 0.6 109 m2 s1, consistent with the value expected from the acrylamide concentration (see Figure S6 in the Supporting Information).[14] In summary, we have presented a new NMR method, 2D FAST-DOSY, for rapid characterization of translational diffusion of molecules. The method is based on the principle of accordion spectroscopy and involves co-incrementing of the chemical-shift evolution period and the gradient strengths in a constant-time 2D 13C1H HSQC for encoding the diffusion. This reduces a conventional pseudo 3D experiment to two dimensions, enabling fast data collection. Using a single 2D spectrum, the diffusion coefficients can be accurately extracted from the linewidths of cross peaks in the indirect dimension. The experimental time can be decreased further using the method of non-uniform sampling. This opens up new possibilities to monitor fast molecular processes in both chemical and biomolecular systems.
Experimental Section All NMR experiments were performed on a Bruker Avance III 400 MHz or 800 MHz NMR spectrometer (the latter equipped with
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a cryogenic probe). The r.f. pulse sequence used is shown in Figure S1 in the Supporting Information.
Acknowledgements Support for the NMR Research Centre from the Department of Science and Technology (DST), India, and the Nanoscience facility at IISc is gratefully acknowledged. K.C. acknowledges support from a DST-INSPIRE fellowship. H.S.A. acknowledges support from DAE-BRNS. Keywords: diphenylalanine · FAST-DOSY · nanotubes · NMR spectroscopy · non-uniform sampling [1] a) Y. Cohen, L. Avram, L. Frish, Angew. Chem. Int. Ed. 2005, 44, 520; Angew. Chem. 2005, 117, 524; b) A. Macchioni, G. Ciancaleoni, C. Zuccaccia, D. Zuccaccia, Diffusion Ordered NMR Spectroscopy (DOSY) in Supramolecular Chemistry, Vol.2: Techniques (Eds.: J. W. Steed, P. A. Gale), Wiley, Chichester, 2012, p. 319. [2] E. O. Stejskal, J. E. Tanner, J. Chem. Phys. 1965, 42, 288. [3] a) K. F. Morris, C. S. Johnson, Jr., J. Am. Chem. Soc. 1993, 115, 4291; b) H. Barjat, G. A. Morris, A. G. Swanson, J. Magn. Reson. 1998, 131, 131; c) C. S. Johnson, Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 203; d) M. Nilsson, A. Botana, G. A. Morris, Anal. Chem. 2009, 81, 8119; e) M. Nilsson, M. Khajeh, A. Botana, M. A. Bernstein, G. A. Morris, Chem. Commun. 2009, 1252; f) A. S. McLachlan, J. J. Richards, A. R. Bilia, G. A. Morris, Magn. Reson. Chem. 2009, 47, 1081; g) J. A. Aguilar, A. A. Colbourne, J. Cassani, M. Nilsson, G. A. Morris, Angew. Chem. Int. Ed. 2012, 51, 6460; Angew. Chem. 2012, 124, 6566; h) A. A. Colbourne, S. Meier, G. A. Morris, M. Nilsson, Chem. Commun. 2013, 49, 10510; i) B. R. Martini, V. A. Mandelshtam, G. A. Morris, A. A. Colbourne, M. Nilsson, J. Magn. Reson. 2013, 234, 125; j) G. Hamdoun, M. Sebban, E. Cossoul, A. HarrisonMarchand, J. Maddaluno, H. Oulyadi, Chem. Commun. 2014, 50, 4073. [4] B. Vitorge, D. Jeannerat, Anal. Chem. 2006, 78, 7601. [5] a) O. Millet, M. Pons, J. Magn. Reson. 1998, 131, 166; b) N. M. Loening, J. Keeler, G. A. Morris, J. Magn. Reson. 2001, 153, 103; c) M. J. Thrippleton, N. M. Loening, J. Keeler, Magn. Reson. Chem. 2003, 41, 441; d) C. A. Steinbeck, B. F. Chmelka, J. Am. Chem. Soc. 2005, 127, 11624; e) Y. Shrot, L. Frydman, J. Magn. Reson. 2008, 195, 226; f) M. Urban´czyk, W. Koz´min´ski, K. Kazimierczuk, Angew. Chem. Int. Ed. 2014, 53, 6464; Angew. Chem. 2014, 126, 6582. [6] G. Bodenhausen, R. R. Ernst, J. Magn. Reson. 1981, 45, 367. [7] a) D. Rovnyak, D. P. Frueh, M. Sastry, Z. Y. J. Sun, A. S. Stern, J. C. Hoch, G. Wagner, J. Magn. Reson. 2004, 170, 15; b) S. G. Hyberts, H. Arthanari, G. Wagner, Novel Sampling Approaches in Higher Dimensional NMR, Springer-Verlag, Berlin, Heidelberg 2012; c) S. G. Hyberts, H. Arthanari, G. Wagner, Top. Curr. Chem. 2011, 316, 125. [8] J. Keeler, Understanding NMR spectroscopy, 2ednd edJohn Wiley & Sons, Chichester, 2010. [9] A. V. Buevich, J. Baum, J. Am. Chem. Soc. 2002, 124, 7156. [10] H. S. Atreya, S. C. Sahu, K. V. R. Chary, G. Govil, J. Biomol. NMR 2000, 17, 125. [11] S. Paramasivam, C. L. Suiter, G. Hou, S. Sun, M. Palmer, J. C. Hoch, D. Rovnyak, T. Polenova, J. Phys. Chem. B 2012, 116, 7416. [12] V. Y. Orekhov, V. A. Jaravine, Prog. Nucl. Magn. Reson. Spectrosc. 2011, 59, 271. [13] a) C. H. Gçrbitz, Chem. Commun. 2006, 22, 2332; b) E. Gazit, Chem. Soc. Rev. 2007, 36, 1263; c) J. Jeon, C. E. Mills, M. S. Shell, J. Phys. Chem. B 2013, 117, 3935. [14] I. H. Park, C. S. Johnson, D. A. Gabriel, Macromolecules 1990, 23, 1548. Received: June 19, 2014 Published online on October 21, 2014
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