Theory and Application of NMR Diffusion Studies - Springer Link

135

Torsten Brand1 , Eurico J. Cabrita2 , and Stefan Berger1 1 Institut

für Analytische Chemie, Universität Leipzig, Johannisallee 29, 04103 Leipzig, Germany; and 2 REQUIMTE/CQFB, Department de Qu´ımica, Faculdade de Ciˆ encias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

Theoretical Aspects Concepts of diffusion Self-diffusion is the random translational motion of molecules driven by their internal kinetic energy [1]. Translational diffusion and rotational diffusion can be distinguished. Diffusion is related to molecular size, as becomes apparent from the Stokes–Einstein equation: D = kB T / f

(1)

where D is the diffusion coefficient, kB is the Boltzmann constant, T is the temperature, and f is the friction coefficient. If the solute is considered to be a spherical particle with an effective hydrodynamic radius (i.e. Stokes radius) rS in a solution of viscosity η, then the friction coefficient is given by: f = 6πηrS

(2)

Pulse Sequences for PFG NMR Diffusion Measurements Using the pulsed-field gradient (PFG) method, motion is measured by evaluating the attenuation of a spin echo signal [2]. The attenuation is achieved by the dephasing of nuclear spins due to the combination of the translational motion and the imposition of gradient pulses. In contrast to relaxation methods, no assumptions concerning the relaxation mechanism(s) are necessary. The PFG NMR sequence (Figure 1) is the simplest for measuring diffusion [2]. During application of the gradient, which is along the direction of the static, spectrometer field, B0 , the effective magnetic field for each spin is dependent on its position. Therefore, the precession frequency is also position dependent which leads to the development of position dependent phase angles. The 180◦ pulse changes the direction of the precession. Hence, the second gradient of equal magnitude will cancel the effects of the first and refocus all spins, provided that no change of position, with Graham A. Webb (ed.), Modern Magnetic Resonance, 135–143. C 2008 Springer.

respect to the direction of the gradient, has occurred. If there is a change of position, the refocusing will not be complete. This results in a remaining dephasing which is proportional to the displacement during the period between the two gradients. Since diffusion is a random motion, there is a distribution of gradient-induced phase angles. These random phase shifts are averaged over the ensemble of spins contributing to the observed NMR signal. Hence, this signal is not phase shifted but attenuated, with the degree of attenuation depending on the displacement. In Ref. [1], this phenomenon is explained in more detail. It is shown in Ref. [1] that the signal intensity S(2τ ) after the total echo time 2τ is given by: 2τ δ S(2τ ) = S(0) exp − exp −γ 2 g 2 Dδ 2 − T2 3 δ (3) = S(2τ )g=0 exp −γ 2 g 2 Dδ 2 − 3 where S(0) is the signal intensity immediately after the 90◦ pulse, T2 is the spin–spin relaxation time of the species, γ is the gyromagnetic ratio of the observed nucleus, g is the strength of the applied gradient, and δ and are the length of the rectangular gradient pulses and the separation between them, respectively. Typically, δ is in the range of 0–10 ms, the diffusion time is in the range of milliseconds to seconds, and g is up to 20 T/m [1]. To determine diffusion coefficients, a series of experiments is performed in which either g, δ, or is varied while keeping τ constant to achieve identical attenuation due to relaxation. Normally, the gradient strength g is incremented in subsequent experiments. Non-linear regression of the experimental data can be used for the determination of D. Nowadays, the BPPLED pulse sequence (see Figure 2) is most often used for measuring diffusion since it allows eddy currents to decay and uses bipolar gradients which enables double effective strength as well as compensation for imperfections. This sequence is not affected by spin– spin coupling since it is based on the stimulated echo sequence.

Part I

Theory and Application of NMR Diffusion Studies

136 Part I

Chemistry

Part I

τ

Fig. 1. The Stejskal and Tanner pulsedfield gradient NMR sequence. Narrow and wide filled bars correspond to 90◦ and 180◦ pulses, respectively. Open bars with horizontal stripes correspond to pulsed-field gradients whose strength is varied during the experiment. The pulse phases are φ1 = x and φ2 = y. Phase cycling can be included to remove spectrometer artifacts.

τ

φ1

φ2

g G δ

t1

The signal intensity of the BPPLED sequence is given by: τg δ S = Sg=0 exp −γ 2 g 2 Dδ 2 − − 3 2

(4)

∆−δ

δ

t2

the data obtained in PFG NMR measurements where the chemical shift is plotted in one (or two) dimension and the diffusion coefficient in the other dimension. This presentation allows the identification of signals belonging to one component (or at least to components showing the same diffusion coefficient). Because of this separation, DOSY can be considered as “non-invasive chromatography” [4].

Processing of Diffusion Data In the chemical shift dimension(s), Fourier transformation (FT) is applied as usual. For each frequency ν, the signal can (in general) have contributions from several components (1, . . . n) which individually decay with their respective diffusion coefficient: S(g,v) =

n i=1

δ Si (0,v) exp −γ 2 g 2 Di δ 2 − 3

(5)

The individual diffusion coefficients Di and the signal intensities Si (0, ν) have to be extracted in order to construct the diffusion spectra. The name DOSY (diffusion ordered spectroscopy) refers to the presentation of Fig. 2. The LED pulse sequence using bipolar gradients [3]. Narrow and wide filled bars correspond to 90◦ and 180◦ pulses, respectively. Phase cycling: φ1 = φ2 = φ5 = x; φ3 = 2(x), 2(−x), φ4 = φ7 = 4(x), 4(−x), 4(y), 4(−y); φ6 = x, −x, x, 2(−x), x, −x, x, y, −y, y, 2(−y), y, (−y), y.

φ1

φ2 τ1

Applications of Diffusion NMR In PFG spin echo NMR experiments, the interesting observable variable is the diffusion coefficient, therefore, in principle, any phenomena that affects the diffusion coefficient can be studied with this technique. The concept behind the application to the study of molecular interactions is very simple and is based on the fact that the diffusion coefficient of a molecule is altered upon addition of another molecule if there is an interaction between them. Diffusion NMR has been applied to the study of intermolecular interactions both qualitatively, to identify compounds that bind to a specific receptor in NMR screening

φ3

φ4

τ1

τ2

φ5 τ1

φ6

φ7

τ1

g

g G −g

δ/2

−g

τg

te ∆


Size and Shape Determination by Diffusion Measurements Since diffusion NMR allows spectral resolution by size or shape, and this resolution being especially visible in DOSY experiments, it is not surprising that the qualitative or semi-quantitative application of DOSY to the distinction of compounds according to their size is one of the most popular [21]. Examples of this type of application of DOSY can be found in many diverse areas such as in the characterization of polymer additives [22], hydrocarbon mixtures [23], in food chemistry [24,25], or carbohydrate mixture analysis [26,27], just to name a few examples. If some cautions are taken, the experimental diffusion coefficients can be used to obtain quantitative information about the size and shape of a molecule or a particular assembly. As was already mentioned, the connection between the diffusion coefficient (D) and structural properties arises because diffusion coefficients depend on friction factors ( f ) which are associated with the molecular size and the viscosity of the solution. The Stokes–Einstein equation [Equation (1)] relates the translational self-diffusion coefficient at infinite dilution of a spherical particle to its hydrodynamic radius rS , and in spite of the difficulty to justify this equation at a molecular level [28], its simplicity and success in relating experimental diffusion coefficients to molecular radii is the basis for its extensive use in the literature. Examples of the application of experimental diffusion coefficients and the Stokes–Einstein equation for size determination can be found in fields ranging from organometallic chemistry to biochemistry. This relation is usually also the starting point for the development of

other models that connect the diffusion coefficient with shapes different from spherical and to expressions related to the molecular weight of the diffusing species. A simple but very elucidative example is the characterization of THF solvated n-butyllithium aggregates by DOSY [29]. Diffusion ordered spectroscopy was used to distinguish the tetrasolvated dimeric and tetrasolvated tetrameric aggregates (see Figure 3) in THF solution. Theoretical diffusion values for the dimer and tetramer, calculated from the Stokes–Einstein equation, predict measurable differences in diffusion coefficients. For the calculation of the theoretical diffusion the viscosity of neat THF was used, and the hydrodynamic radii were determined from molecular volumes based on crystal structures and gas-phase minimized structures. A good agreement between experimental diffusion coefficients and theoretical values was obtained [29]. As was shown by Waldeck et al. [30], by considering the relation between the Stokes radius of a molecule (rS ), its experimentally determinable partial specific volume, V , and its molecular weight, M, a useful expression relating diffusion to molecular weight can be derived: 3 D1 = D2

3

M2 M1

(6)

This general relationship shows that for “ideal” spherical models there is a reciprocal cube dependence of the diffusion coefficient on molecular weight and this allows the calculation of a set of theoretical diffusion coefficients using a reference diffusion (experimental) value. It is therefore worth considering when accounting for the effect of molecular association on the apparent diffusion coefficient, expected to be measured in an experiment. Another impressive example of the applicability of the Stokes–Einstein equation is found in a study dealing

Fig. 3. PM3 optimized structures of [n-BuLi]4 ·THF4 and [n-BuLi]2 ·THF4 . Reprinted with permission from Ref. [29]. Copyright (2000) American Chemical Society.

Part I

or in studies related to host–guest chemistry [5–8], and quantitatively, in the determination of association constants [9–12] and complex or aggregate sizes [13–18]. For binding and screening studies it is usually sufficient to identify compounds that bind to a certain receptor from a mixture of non-binding compounds, or to establish a relative binding affinity, but the determination of association constants or size requires quantitative determination of the diffusion coefficients with precision and accuracy. A very comprehensive work about the factors that affect data quality in PFG spin echo NMR methods for chemical mixture analysis was published recently by Antalek [19], both data acquisition (including a discussion about experimental conditions and available pulse programs) and data analysis were considered in detail by the author. This chapter complements well the previous work of Price on the experimental aspects of PFG spin echo NMR [2]. After completing this article, an outstanding and comprehensive review on NMR diffusion experiments by Cohen et al. has been published [20].

Applications of Diffusion NMR 137

138 Part I

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Part I

with ubiquitin [32]. The hydrodynamic radius of this protein was calculated from its diffusion coefficient determined by DOSY-HSQC experiments using an accurately calibrated temperature and the viscosity calculated for this temperature. Using Equations (1) and (2) yielded ˚ Furthermore, the NMR structure of ubiqrS = 15.8 A. uitin [33] was used for the calculation of its size, which ˚ which is in reasonably was then converted to rS = 16.3 A, good agreement with the value found in DOSY experiments. Thus, the numerical factor 6 given in Equation (2) also holds true for complex situations such as a protein in aqueous solution. This demonstrates that the assumption of a spherical solute moving in a continuous solvent is fulfilled fairly well in this case, which can be verified by inspecting Figure 4. The field of organometallic chemistry provides several examples of the application of diffusion measurements for size determination, since this is one of the fields where the use of diffusion NMR is becoming more and more popular. Pregosin is among the leaders in the application of PFG diffusion methods in organometallic chemistry and his contributions and perspectives about the technique as well as the most important applications in this field have been the subject of several publications [34]. 13 C detected DOSY was used by Schlörer et al. to study the unstable intermediate (2) in the reaction of CO2 with [Cp2 Zr(Cl)H] (1) (see Scheme 1) which was impossible to characterize by other means [35]. 13 CO2 was used for the reaction which was observed in situ by 13 C NMR.

Fig. 4. Schematic representation of the three dimensional structure of ubiquitin. The structure presented here is taken from the data set “1D3Z” [33] in the pdb data bank [31]. (See also Plate 9 on page XXI in the Color Plate Section.)

Cl Z r H

Cl O Z r O C H

1

H H Cl C Cl Z r O O 2

1

- H2CO

H2CO

Z r

Z r

Cl H H O C H

Z r

Cl O rZ Cl

3

Scheme 1. The reaction of [Cp2 Zr(Cl)H] (1) with CO2 [35].

Following the formation of sufficient amounts of 2, the mixture has been cooled to −78◦ C, and 13 C INEPT DOSY spectra were recorded. The intermediate 2 was shown to have a smaller diffusion coefficient than the mononuclear complex 3 (see Figure 5) and was therefore proven to be binuclear. Furthermore, its hydrodynamic radius calculated from the experimental results was found to be in good agreement with an estimation based on a minimized gas-phase structure. Still in the field of ionic interactions, a very recent paper from the group of Pregosin explored the application of PGSE NMR studies within the context of chiral cation/anion recognition [36]. According to the authors, this is the first reported example that shows that the diffusion data are sensitive enough to recognize a subtle diastereomeric structural effect on ion translation. The work investigated the dependence of the diffusion value on the diastereomeric structure of the ion pair for chiral organic salts (see Scheme 2). Investigated were the pairs of diastereomers formed between two novel chiral hexacoordinate phosphate anions, known to induce efficient NMR chiral-shifts, and chiral quaternary ammonium cations. Diffusion constants were determined for the salts [6][-4], [6][-5], [6][PF6 ], [7][-4], [7][-5], and [7][PF6 ] at different concentrations and in chloroform, dichloromethane, acetone, and methanol. To facilitate the comparison of results, hydrodynamic radii derived from the Stokes–Einstein equation, using the viscosity of the non-deuterated solvents, were calculated. The methanol data were employed to estimate the size of solvated and independently moving anions and cations. For the cations in methanol, the rS values were found to be independent ˚ for 6 and 5.0 A ˚ for 7). The values of the anion (5.2–5.3 A ˚ both in [6][-5] and [7][-5], for the anion -5 are 7.0 A − ˚ ˚ whereas for PF− 6 the values are 2.7 A in [6][PF6 ] and 2.6 A − in [7][PF6 ] in agreement with previous results for other salts of PF− 6 from the same group [37,38].


2

2

Part I

3


3

slow −10.2

lgD / m2s−1 −10.0

−9.8

fast 116

115

114

103

102

101

64

63

13

d ( C) Fig. 5. 100 MHz 13 C INEPT DOSY spectrum obtained during the reaction of 1 with 13 CO2 at –78 ◦ C in [D8 ] THF. The sections show the signals of 2 (δC = 114.6 ppm (Cp) and 101.7 ppm (CH2 )) and 3 (δC = 114.9 ppm (Cp) and 63.5 ppm (OCH3 )). See Scheme 1 for the chemical structure of 1, 2, and 3. Figure taken from Ref. [35]. Reproduced with permission of John Wiley & Sons Limited.

Cl Cl

Cl

Cl

Cl

O

Cl

O

Cl

Cl Cl

Cl

O

O

O

O

P Cl

P

O Cl

TRISPHAT ∆-4

O

O O

Cl

Cl

Cl Cl

Pr N

N

O O

BINPHAT ∆-5

Cl

Cl Cl

Pr N

O O

6

Cl

7

Scheme 2. Chiral anions and cations investigated by Pregosin and coworkers [36].

140 Part I

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Part I

Internal Standards for Diffusion Measurements The direct determination of hydrodynamic radii, and thus size, through the Stokes–Einstein equation requires a knowledge of the solution viscosity at the measurement temperature. Additionally, in order to have accurate information about size in studies related to molecular interactions where the comparison of diffusion coefficients obtained in different conditions is usual, it is crucial to be able to separate contributions due to changes in viscosity and effective changes in hydrodynamic radii. In PFG NMR, two major approaches are frequently used to avoid additional experimental work to measure the viscosity of the solution. The simplest approach is to consider that the viscosity of the solution is approximately the same as the viscosity of the pure non-deuterated solvent. This approximation has been shown to be legitimate in a number of cases, especially when considering pure solvents and diluted solutions and some examples have already been mentioned above for the determination of hydrodynamic radii of, n-butyllithium aggregates [29] and solvated anions and cations [36] but many more can be found in the literature. In complex solutions it may be more difficult to obtain a value for the viscosity of the exact solvent mixture, and in these cases the interpretation of size or molecular mass derived from diffusion data has to take into account the validity of the approximations made and the possibility of under/over valuating the viscosity. The other solution to the problem is the back calculation of the solution viscosity, through the Stokes– Einstein equation, by using the diffusion measured for a non-interacting reference compound of known hydrodynamic radius. This internal probe should be of similar size with respect to the molecules of interest so that it experiences a similar microscopic environment and can act as an internal viscosity standard. The use of such a standard allows the estimation of size even in complex solution mixtures and the comparison of diffusion coefficients in series of experiments where the composition of the solution is altered, a situation that commonly arises in studies related to molecular interactions. The use of a diffusion standard allows one also to separate the contributions due to changes in viscosity and effective changes in hydrodynamic radii even if the hydrodynamic radius of the standard is not known. In fact, the ratio of the diffusion of a particular solute and the reference compound will be independent of the viscosity (D/Dref = rSref /rS ) and relative information about changes in hydrodynamic radius can be obtained when comparing ratios measured in different conditions. This procedure is well exemplified in a study by Cabrita et al. where tetramethylsilane (TMS) was used as a standard for the diffusion measurements to account for viscosity changes, and was proposed as a reference for the study of intermolecular interactions involving hydrogen bonds in organic solutions [14]. Kapur et al. [39] have shown that DOSY can be a useful technique for the quali-

tative study of the relative strengths of hydrogen bonds in solution. Since the formation of an intermolecular H-bond leads to a decrease of the diffusion coefficient of a certain molecule, the relative decrease in the diffusion coefficient of a particular molecule in a mixture of molecules, interacting by H-bond with a common H-bond acceptor or donor, was interpreted in terms of the tendency for the molecules in the mixture to be involved in association by H-bonds with the H-bond donor or acceptor. As an example, it was shown that when dimethylsulfoxide (DMSO), a strong H-bond acceptor, is added to a solution containing phenol (8) and cyclohexanol (9), two molecules with a similar shape, a higher relative decrease in the diffusion coefficient of phenol was observed. This different behavior was attributed to the greater tendency of phenol to be involved in H-bonding with DMSO, since phenol is more acidic than cyclohexanol [39]. OH

8

OH

9

Binding, Screening, and Determination of Association Constants In the previous section, we have shown examples of applications that explore the relation between size and diffusion coefficient primary as a source of information on molecular size. However, this relation can be explored in a different way in order to get information about the strength of intermolecular interactions. The majority of the reports on the application of diffusion NMR to the study of intermolecular interactions deal with the alteration of the diffusion coefficient due to binding phenomena in solution. In fact, when a small molecule binds to a large receptor, its diffusion coefficient may decrease more than one order of magnitude. This means that at least for some time the small molecule will have the diffusion coefficient of the large receptor, and if we consider the fast exchange limit, its observed diffusion coefficient (Dobs ) is described by: Dobs = f free Dfree + f bound Dbound

(7)

where f and D denote the molecular fractions and diffusion coefficients of the free and bound molecule. If the difference in size is large enough, it can be assumed that the diffusion coefficient of the receptor or host (DH ) is not greatly modified and that Dbound is the same as the DH alone. This relation is the starting point for the majority of the diffusion NMR-related binding studies.


M eO

H N

M eO

O

f HG =

M eO O OM e

10 For this reason, a model peptide containing the 12 Cterminal residues of α-tubulin (VEGEGEEEGEEY) was investigated with respect to the pH dependence of the binding to 10 [40]. Although binding studies on this system have only been computational using docking programs, it was shown in the diffusion studies that the model peptide adopts different conformations depending on the pH, this being reflected by different observed diffusion constants. In this work, NOE data have also been used, but only for determining the conformation of the single peptide. The determination of association constants (K a ) from NMR data has been recently reviewed by Fielding [9] with a section dedicated to diffusion experiments. The starting point for the determination of the association constant is Equation (7) and the mathematical treatment to get K a from Dobs is exactly the same as for any other NMR observable, such as δobs . As Fielding points out in his review, the advantage of measuring Dobs instead of δobs is that the diffusion coefficient of the host–guest complex can be assumed to be the same as that of the non-complexed host molecule, thus reducing one unknown in Equation (7). In principle, this allows one to determine K a within a single experiment and without the need of titrations, as exemplified below. The formation of a host–guest complex of stoichiometry 1:1 is described by: [HG] [H] [G]

Dobs = f G DG + f HG DHG

(8) (9)

where [HG], [H], and [G] are the equilibrium concentrations of the host–guest complex, host, and guest, respectively and f G and f HG are the molar fractions of

DG − Dobs DG − DHG

(10)

If, as it was mentioned earlier, DHG is assumed to be the same as the measurable diffusion coefficient of the host (DH ), then f HG can easily be determined. Accounting for mass balance and combining Equations (8) with (10), we arrive to the expression for the association constant: Ka =

H

Ka =

non-complexed guest and complex, respectively. From Equation (9) it follows that:

f HG (1 − f HG )([H]0 − f HG [G]0 )

(11)

where [H]0 and [G]0 represent the total concentrations of host and guest, respectively. The procedure before is straightforward and examples of its application can be found in recent literature related to host–guest chemistry studies [12,41]. Rather than exemplifying the examples in detail here, we prefer to take a closer look at the limitations of the approximation that DHG = DH . The assumption that DHG = DH is valid for the majority of studies involving small molecules binding to macromolecules (typically biological), but may not necessarily be true for smaller host molecules usually employed in host–guest chemistry studies. To test the assumption that DHG = DH for a typical medium-sized host molecule, Cameron et al. [10] have studied the β-cyclodextrin (11) complexes of cyclohexylacetic acid (12) and cholic acid (13). They have shown that caution should be taken when determining the association constant by the single experiment method, and have employed a data treatment which takes into account the diffusion of all species. With this treatment, the 1 H NMR chemical shift titration method and the diffusion coefficient method give the same results for K a . Simova and Berger presented a comparison of DOSY experiments and chemical shift titrations with respect to the determination of association constants [42]. The authors investigated camphor and cyclodextrins (CD) in D2 O. They showed that precise association constants are more easily determined by chemical shift titration. Diffusion measurements using HR-DOSY allow easy determination of the complex composition at different concentration ratios and an estimation of the binding energy if a viscosity reference, in this case tetramethylammonium bromide, is present. Linear dependence of the diffusion coefficients on the molecular mass of free and associated CD has been observed (see Figure 6). The solution structures of α- and β-CD complexes of camphor in D2 O were deduced from intermolecular cross-relaxation data obtained by using the ROESY sequence. Different preferential orientation in the 2:1 α-CD and 1:1 β−CD species have been derived in contrast to the weak 1:1 complex

Part I

In this field two main lines of application can be identified, one more qualitative, related to the screening of complex mixtures or individual molecules, usually with the aim of identifying potential new drug compounds, and another, more quantitative, concerned with the determination of association constants. A recent example of the first type of application mentioned above is the binding of cholchicine 10 to α/β tubulines, which is of large interest in cancer-related studies.


142 Part I

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Part I

OH

O OH

O

O

O

H O

O OH H O

H O

O

OH

OH

H O O H O

H O

O OH

OH O OH

OH

O

H O OH O

OH O OH

H O

O

O OH

11

OH O OH

OH O

H O

OH

H

12

13

2,8

α-CD β-CD

2,6

D (10

-10

2 -1 m .s )

3,0

γ-CD

2,4 2,2

(α-CD)2-camphor

2,0 0 9

130 0

170 0

210 0

M (g.mol-1) Fig. 6. Dependence of the diffusion coefficients of cyclodextrins and the α-CD complex of camphor on the molecular mass [42].


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22. Jayawickrama DA, Larive CK, McCord EF, Roe DC. Magn. Reson. Chem. 1998;36:755. 23. Kapur GS, Findeisen M, Berger S. Fuel. 2000;79:1347. 24. Gil AM, Duarte I, Cabrita E, Goodfellow BJ, Spraul M, Kerssebaum R. Anal. Chim. Acta. 2004;506:215. 25. Nilsson M, Duarte IF, Almeida C, Delgadillo I, Goodfellow BJ, Gil AM, Morris GA. J. Agric. Food Chem. 2004;52:3736. 26. Schraml J, Blechta V, Soukupová L, Petráková E. J. Carbohydr. Chem. 2001;20:87. 27. Diaz MD, Berger S. Carbohydr. Res. 2000;329:1. 28. Walser R, Mark AE, van Gunsteren WF. Chem. Phys. Lett. 1999;303:583. 29. Keresztes I, Williard PG. J. Am. Chem. Soc. 2000;122: 10228. 30. Waldeck AR, Kuchel PW, Lennon AJ, Capman BE. Prog. NMR Spectrosc. 1997;30:39. 31. Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE. Nucleic Acids Res. 2000;28:235. 32. Brand T, Cabrita EJ, Morris GA, Berger S. (in preparation). 33. Cornilescu G, Marquardt JL, Ottiger M, Bax A. J. Am. Chem. Soc. 1998;120:6836. 34. Valentini M, Rüegger H, Pregosin PS. Helv. Chim. Acta. 2001;84:2833; and references therein. 35. Schlörer NE, Cabrita EJ, Berger S. Angew. Chem. Int. Ed. 2002;41:107. 36. Mart´ınez-Viviente E, Pregosin PS, Vial L, Herse C, Lancour J. Chem. Eur. J. 2004;10:2912. 37. Kumar PGA, Pregosin PS, Goicoechea JM, Whittlesey MK. Organometallics. 2003;22:2956. 38. Mart´ınez-Viviente E, Pregosin PS. Inorg. Chem. 2003;42: 2209. 39. Kapur GS, Cabrita EJ, Berger S. Tetrahedron Lett. 2000;41: 7181. 40. Pal D, Mahapatra P, Manna T, Chakrabarti P, Bhattacharyya B, Banerjee A, Basu G, Roy S. Biochemistry. 2001;40:512. 41. Frish L, Sansone F, Casnati A, Ungaro R, Cohen Y. J. Org. Chem. 2000;65:5026. 42. Simova S, Berger S. Journal of Inclusion Phenomena and Macrocyclic Chemistry. J. Incl. Phenom. (in press).

Part I

with γ -CD. Proton NMR chemical shift values proved to be much more sensitive to diastereomeric complex formation than are diffusion coefficients.

References 143