NMR diffusion as a novel tool for measuring the association constant between cyclodextrin and guest molecules

doi:10.1016/S0008-6215(02)00066-6

Carbohydrate Research

Volume 337, Issue 9, 30 April 2002, Pages 841-849

https://doi.org/10.1016/S0008-6215(02)00066-6 Get rights and content

Abstract

In this paper we introduce the use of diffusion measurements by nuclear magnetic resonance (NMR) spectroscopy for determining association constants of weak and very weak interactions between cyclodextrin and guest molecules, as long as both the free and complexed guest molecules are soluble to an extent that allows good sensitivity in the NMR experiment. The experimental setup and data analysis is discussed for three different guest molecules: l-phenylalanine, l-leucine and l-valine, representing different strengths of interaction. The underlying assumptions are discussed and the scope of the method (range of K_a values, requirements to the guest molecule) are discussed. The method's main advantage is its general applicability independent of chromogenic or electrochemical properties of the guest molecule. Whereas calorimetric methods that exhibit a similar generality, are applicable mainly to strong interactions, NMR diffusion measurements are applicable to weaker interactions down to the theoretical limit of 1 M⁻¹, the upper limit for K_a values to be determined by it is approximately 200. A further advantage of the method is the low amount of sample needed. The method is in principle applicable to any case of molecular recognition between a host and guest molecule leading to weak interactions.

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Introduction

Cyclodextrins are cyclic oligosaccharides composed of α-(1→4)-linked α-d-glycosyl residues, of which α, β- and γ-cyclodextrin, consisting of 6, 7 and 8 glycosyl-units, respectively, are the most studied.1., 2., 3., 4. These cyclodextrins can be described as toroidal, hollow, truncated cones with a hydrophilic exterior and a hydrophobic interior. This unique structure allows molecules (guests) with hydrophobic groups to at least partly enter the cavity and be bound by the cyclodextrin (host) by non-covalent forces only. The resulting entity is known as a guest–host complex or inclusion complex. The inclusion of a guest molecule in a cyclodextrin often alters its chromogenic (e.g., absorbance and fluorescence behaviour) and electrochemical properties. Furthermore, these complexes display very different properties compared to the free guest and host, such as altered solubility, reduced volatility, reduced or enhanced stability, modified chemical reactivity and altered bioavailability. These properties are utilised in many applications in the pharmaceutical, agro-chemical, food and chemical industries, e.g., as a vehicle for drug-delivery of poorly water-soluble drugs, for increasing stability of labile molecules, masking of unpleasant taste or odour and stabilisation of protein solutions against aggregation.1., 2., 3. Moreover, cyclodextrins have gained a position as the most widely used eluent modifier for the separation of structural similar molecules (e.g., enantiomeres) by chromatography and electrophoresis. Additionally, cyclodextrins have gained considerable attention as enzyme models based on their ability to accelerate chemical reactions, e.g., hydrolysis of certain molecules. For the study of non-covalent molecular interactions between molecules, cyclodextrins have been and still are a popular choice. Within the field of supramolecular macrocyclic chemistry, the cyclodextrins have gained a unique position as the most studied and commercially successful class of compounds.⁴

Of central importance for the understanding and evaluation of the phenomena of molecular interaction (host–guest complex formation) is the knowledge of the association constants (K_a) and even more important are the thermodynamic parameters, enthalpy, entropy and Gibbs free energy in combination with structural data on the supramolecule formed. The association constant (K_a) between a cyclodextrin and a guest molecule is expressed by: $n CD +m G ⥂ G_{m} : CD_{n}$ $K_{a} = [G_{m} : CD_{n}] [CD]^{n} ·[G]^{m}$ where [CD] is the concentration of cyclodextrin, [G] is the concentration of the guest molecule and [G_m:CD_n] is the concentration of the inclusion complex. In this paper, however, we will only discuss 1:1 complex stoichiometries.

Thermodynamic parameters can be obtained directly by use of calorimetric techniques (e.g., isothermal titration calorimetry). However, these techniques are limited by the enthalpy of complexation and very weak interactions most often yield unreliable thermodynamic parameters. Alternatively, thermodynamic parameters can be obtained by careful measurement of the association constant at various experimental temperatures. The thermodynamic parameters can be derived from such a dataset by use of the van't Hoff equation in the most simple cases (assuming constant heat capacity, c_p). Thus, new methods for reliable measurement of especially weak association constants are of high importance.

Numerous methods have been used for the determination of association constants in host–guest chemistry including: NMR, calorimetry, spectroscopy, chromatography, capillary electrophoresis, solubility isotherms, potentiometry5., 6., 7., 8. and diffusion measurements by Gouey interferometry.⁹ All methods used for the quantification of binding affinity are in one way or the other limited in their use and are varying in accuracy. Several parameters have to be considered, when choosing the most appropriate method for a given set of guest and host molecules. Often, measurement of association constants requires a change of an intrinsic property of the guest molecule or in special cases the host. This includes changes in the chromogenic- and electrochemical properties, retention behaviour, changes in chemical shifts or nuclear magnetic relaxation times, solubility and enthalpy of complexation and is thus highly dependent on the molecules in question. This limits the various techniques to a limited class of molecules with the appropriate physico-chemical properties. Additionally, the choice of solvent and amount and purity requirements for the materials can pose limitations to the methods.⁸

In this paper, we present a method for the determination of association constants between guest and host species based on NMR diffusion measurements.

Nuclear magnetic resonance (NMR) has been used widely to determine association constants from chemical shift changes and relaxation time measurements.¹⁰ These methods are, however, not universally applicable since the chemical shift changes are not often significant, especially with aliphatic guests or when association constants are low. Here we investigate the use of nuclear magnetic resonance to quantify the ratio of bound to unbound ligand directly by NMR diffusion measurements. The use of NMR diffusion measurements to determine association constants has been reported for micelle–peptide association and other associations of small molecule with micelles, where there is a large difference in diffusion constant of the binding partners.¹¹

In the case of cyclodextrin–guest interaction, this difference is not necessarily that big, but the method can nevertheless be applied.

These measurements, which are described in the next section and shown in Fig. 1, consist of a diffusion delay, flanked by two pulsed-field gradients, where the fraction of magnetisation that the second pulse rephases, is described by: $A G =A 0 · e^{−Rt−γ^{2}G^{2}Dδ^{2}Δ−δ/3}$ where A(G) is the signal strength at gradient strength G, R(t) the relaxation attenuation, γ the gyromagnetic ratio (rad T⁻¹ s⁻¹), G the gradient strength (T m⁻¹), D the diffusion coefficient (m² s⁻¹), δ the gradient duration (s) and Δ the time between the start of the two gradient pulses (s).

The diffusion constant depends on the size of the molecule: $D= kT 6πηr$ where k is the Boltzmann constant (1.380662×10⁻²³ J K⁻¹), T the absolute temperature (K), η the dynamic viscosity (Pa s) and r the radius of the molecule (m). In the case of non-spherical molecules, r is replaced by R_h, the hydrodynamic radius.¹²

If the exchange between free and bound guest is fast on the diffusion time scale (∼100 ms), the diffusion constant observed in the NMR experiment is a weighted average of the diffusion constant of bound and unbound guest: $D_{obs} =ρ×D_{complex} + 1−ρ D_{free}$ In the case of fast exchange, the fraction of bound guest can be determined by: $ρ= D_{obs} −D_{guest} D_{complex} −D_{guest}$ where D_obs is the apparent (weighted average) diffusion constant of the guest, D_complex is the diffusion constant of cyclodextrin and D_guest is the diffusion constant of the guest molecule. In the practical application, D_complex is not known and cannot be determined. Since our guest molecules are small compared to cyclodextrin, we assume that D_complex≈D_CD, which will lead to a slight overestimation of the determined value for ρ. The method can be applied to guest molecules of any size—in the case that the size of the guest molecule is of the same order or even bigger than that of cyclodextrin, suitable approximations have to be made.

Furthermore, we assume that the diffusion of one component of the mixture is independent from the others. According to Fick's first law, the flux of solute molecules through a unit area in a system consisting of dissolved guest molecules, dissolved cyclodextrin and dissolved inclusion complex is given by: $− J_{CD} J_{G} J_{G:CD} = D_{CD,CD} D_{CD,G} D_{CD,G:CD} D_{G,CD} D_{G,G} D_{G,G:CD} D_{G:CD,CD} D_{G:CD,G} D_{G:CD,G:CD} · Δ C_{CD} Δ C_{G} Δ C_{G:CD}$ where J (mol m⁻² s⁻¹) denotes the flux of solute molecules through a unit area per unit time, ΔC (mol m⁻⁴) denotes the concentration gradient and D denotes the diffusion constants: D_CD,CD, D_g,g and D_G:CD,G:CD denote the self-diffusion constants of cyclodextrin, guest molecules and complex, respectively, while the off-diagonal cross-diffusion coefficients denote the diffusion of one component under the concentration gradient of the other.⁹ In the absence of any interaction between the molecules and in dilute solutions, the cross-diffusion constants can be assumed to be zero. Both requirements are not fulfilled in our case. Based on the results of Paduano,⁹ we nevertheless assume that the cross-diffusion constants are negligible, which is justified by the good agreement between our results and previously published results (see Table 1).

The fraction of guest molecules (ρ) bound to cyclodextrin is defined as: $ρ= [G : CD] [G]+[G : CD]$ Combining , gives: $ρ= K_{a} [G][CD] [G]+[G]K_{a} [CD]$ $ρ= K_{a} [CD] 1+K_{a} [CD]$ By measuring the apparent diffusion constant of guest molecules and calculating the fraction of bound guest molecules at different concentrations of cyclodextrin and plotting ρ versus [CD], K_a can be determined from fitting the data to Eq. (8).

Section snippets

Results

We have applied the method to different guest molecules: the interaction of l-phenylalanine (Phe) and α-cyclodextrin, which is well-studied9., 13., 14., 15., 16. to prove the validity of the method. Furthermore we wished to demonstrate the ability to detect even weaker interactions and therefore chose l-leucine (Leu) and l-valine (Val) and α-cyclodextrin. The complex formation between Phe, Leu and Val with α-cyclodextrin was studied with a 2D-ROESY experiment. In contrast to Phe and Leu, no

Discussion

We have shown that NMR diffusion measurements are a valuable tool for determining—especially weak—association constants for cyclodextrin–guest complexes. Association constants down to the theoretical limit can be measured. Thus NMR diffusion measurements complement the existing methods which are mainly applicable for strong association constants.

NMR diffusion measurements also complement the “classical” NMR method for stability constant determination, which is based on chemical shift changes.

Experimental

99% pure l-phenylalanine, l-valine and l-leucine were purchased from Sigma–Aldrich. Pharmaceutical grade α-cyclodextrin was purchased from Wacker Chemie Burghausen, Germany. 99% D₂O was purchased from Larodan Fine Chemicals AB, Malmö, Sweden.

Prior to its use in NMR experiments, the cyclodextrins were completely dissolved in D₂O and the solvent was evaporated at 95 °C.

The viscosity of solutions of 0, 25, 50, 75 and 100 mM α-cyclodextrin in 100 mM phosphate buffer at pH 7.28 were measured at rt

Note added in proof

After acceptance of this article, we became aware of a previous publication utilizing pulsed field gradient NMR to demonstrate the binding of alcohols to cyclodextrins.²⁸ However, “the purpose of this investigation was to explore the applicability of this technique […] and not to make precision measurements of binding constants”. In the present paper, precision measurements of binding constants with elimination of possible sources of error is emphasized and a thorough treatment of scope and

Acknowledgements

We wish to thank Novo Nordisk A/S for a Novo Scholarship to F.L.A. Charlotte Pedersen, Liese Giehm, Anders Sloth, Anne Lentz, Thomas Lundgaard and Jannie Kristensen are thanked for enthusiastic participation.

References (28)

L. Paduano et al.
Thermochim. Acta
(1990)
G. Castronuovo et al.
Carbohydr. Res.
(1995)
L. Szente et al.
J. Pharm. Sci.
(1998)
J. Szejtli
J. Szejtli
K. Frömming et al.
Cyclodextrins in Pharmacy
(1994)
J.W. Steed et al.
K. Connors
Binding Constants: The Measurement of Molecular Complex Stability
(1987)
K.A. Connors
Chem. Rev.
(1997)
K. Connors
Measurement of Cyclodexyrin Complex Stability Constants

H. Schneider et al.

Principles and Methods in Supramolecular Chemistry

(2000)

H.-J. Schneider et al.

Chem. Rev.

(1998)

K. Deaton et al.

Magn. Reson. Chem.

(2001)

P. Schurtenberger et al.

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^†: Present address: Department of Biotechnology, Norwegian University of Science and Technology, N-7491, Trondheim, Norway.

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NMR diffusion as a novel tool for measuring the association constant between cyclodextrin and guest molecules

Abstract

Introduction

Section snippets

Results

Discussion

Experimental

Note added in proof

Acknowledgements

Thermochim. Acta

Carbohydr. Res.

J. Pharm. Sci.

Cyclodextrins in Pharmacy

Binding Constants: The Measurement of Molecular Complex Stability

Chem. Rev.

Measurement of Cyclodexyrin Complex Stability Constants

Principles and Methods in Supramolecular Chemistry

Chem. Rev.

Magn. Reson. Chem.