Determination of the Association Constant of Alpha and Beta Cyclodextrins Using Methyl Orange

Abstract

This work describes a method for determination of the association constants of cyclodextrins (CDs) using methyl orange (MO) dye and complexation theory. The best operational conditions were complexation between the dye and the CDs at pH 3.0, using disodium citrate-phosphate buffer, a detection wavelength of 500 nm, and a maximum dye concentration of 0.045 × 10⁻³ mol/L. Under these conditions, the constants obtained were 2527/M for the complex formed between the α-CD and MO, and 952/M for the complex formed between the β-CD and MO. In both cases, the molar absorptivity of the complexes diminished by almost a third after complexation with the CDs. These values can be used with complexation theory to model the values of the constants for association between CDs and other substances.

Introduction

Cyclodextrins (CDs) are cyclic oligosaccharides consisting of 6 (α-cyclodextrin), 7 (β-cyclodextrin), 8 (γ-cyclodextrin) or more glucopyranose units linked by α-(1–4) bonds. They are produced in intramolecular transglycolization reactions, following degradation of amide by the CGTase enzyme.^1,2 One of the main uses of CDs is related to their capacity to form inclusion complexes with different substances, modifying their properties; for this reason they are widely used in the separation and solubilization of various biomolecules.^3,4

After inclusion in the CD cavity, the complexed molecule undergoes changes in its physicochemical characteristics, which allows complexation to be detected.^5,6 In solution, there is an equilibrium between the complexed molecules; following complexation, changes occur in the ultraviolet (UV)/visible absorption spectrum—namely, shifts or increases/decreases in the maximum absorption peak—that are often similar to the effects caused by solvents with different polarities. This reflects transfer of the guest molecule from a polar medium to the apolar CD cavity. These changes can be due to electronic perturbations in the complexed molecule caused by direct interaction with the CD, by the exclusion of water molecules from the cavity, or by a combination of these two effects. Despite the difficulty in detecting these spectral alterations (when observed in the UV region), this method is still widely used.^7,8

Knowledge of the equilibrium or dissociation constants of the guest-CD complex is very important, because these parameters can be used to characterize changes in the physico-chemical properties of the guest molecule as a function of the inclusion. Most of the methods used to determine the values of K are based on titrating certain physical or chemical properties of the guest molecule with CD and analyzing their concentration dependence.^9
–11

Determining the inclusion constant of the complex of methyl orange (MO) in CDs is important because in determining the constant value and the measurement of absorbance of a MO sample solution, it is possible to calculate the concentration with accuracy. Furthermore, the spectrophotometric method based on the equilibrium theoretical equation from complex formation can be extended, to cases where a third colorless substance is present that competes with the MO to form a complex. Thus it becomes possible to also establish the equilibrium formation constant of the inclusion of colorless substance complex.

Complexation theory was used by Hamon and Moraes for assaying mixtures of CDs, and Tardioli used the technique to determine the concentration of β-CD, employing colorimetric assaying with phenolphthalein.^12,13 The method was based on formation of a complex between the dye and the β-CD molecule, which reduced the absorbance of the solution at a wavelength of 550 nm. A value of approximately 2.0 × 10⁴/M was obtained for the formation constant of the complex between the dye and the CD, showing that phenolphthalein had a high affinity for the β-CD.

The present work sought to identify a dye that would provide a lower value for the formation constant of the complex with CDs, so that in the colorimetric determination of the constants of the complexes with CDs and other compounds, there would be greater separation between the absorbance curves obtained in the presence and absence of the compounds. This would provide better precision in the results for the constants.

One of the other advantages to determining the association constant of a substance using dye in competition with another that also forms a complex is that this method is relatively easy to apply and produces reliable results. Within appropriate concentrations ranges, there is a good agreement between the theory of complexation and the experimental results. It is based on the absorption spectra of some organic molecules, in particular some dyes, which undergo a change upon complexation with CDs. This change can be used to determine the concentration of these molecules using calibration curves constructed from samples of known concentrations.⁸

The dye selected for this purpose was MO, which is widely used in titrations due to its obvious color change, although other types of dyes could also be used. Since MO changes color in a moderately acidic pH range, it is normally used in titrations of acids. Unlike a universal indicator, MO does not have a broad spectrum of color changes, but rather has a well-defined final point. In the form of the sodium salt, its chemical formula is C₁₄H₁₄N₃O₃SNa and its molar mass is 327.33 g/mol.

MO is widely utilized in α-CD assays, although its affinity for β-CD is lower than that shown by phenolphthalein.¹⁴ Yeuxican et al. reported K values ranging from around 550 to 850/M when the dye was complexed with α-CD, with higher values at lower temperatures.¹⁵ In terms of stoichiometry, it has been found that the dye forms 1:1 complexes with β-CD and 2:1 complexes with γ-CD, and that, according to the K values, MO has much greater affinity for β-CD than for γ-CD. This can be explained by the small size of the dye structure, compared to the large cavity of γ-CD.¹⁶

Calculation of the equilibrium constant between MO and the CDs employed the equation reported by Moriwaki and Fregadolli, based on complexation theory.¹⁷ The same equation was used by Souza and Moraes, who developed a more efficient method for determination of the equilibrium constant.¹⁸

This method allows work with a wider range of concentration sample, and could provide accurate results, because in the calculation of the theoretical equation method is not made any approach. However, the method used by Benesi-Hildebrand is only valid for very dilute solutions.¹⁹ Another available method, from Higuchi-Connors, requires high concentrations—very close to the guest molecule solubility limit in the complex.²⁰ This favors the formation of complexes with other molar ratios of guest:host.

Materials and Methods

Influence of pH on the Absorption Spectra, and Determination of the Maximum Absorbance Wavelengths for Solutions of free and Complexed MO

Absorption spectra in the presence and absence of α-CD and β-CD (2.0 × 10⁻³ mol/L) were obtained at pH 3 and pH 10.5, using different buffers, in order to observe changes in the amplitudes of the peaks and identify peaks or valleys that were most influenced by the presence of the CDs. 1 mL of the MO working solution (0.20 × 10⁻³ mol/L) was added to a cuvette, followed by 2 mL of the solution containing the buffer and either 1 mL of the CD solution or 1 mL of water.

Determination of the Linearity Limit for Absorption by the Pure MO Solution

Experiments were performed to determine the concentration at which the absorbance data departed from the fitted straight line. The disodium citrate–phosphate buffer at pH 3.0 was used to prepare a solution of MO at a concentration of 0.1 × 10⁻³ mol/L, which was then diluted to concentrations in the range from 0 to 0.10 × 10⁻³ mol/L (using the same buffer solution). The absorbances of these solutions were measured at 500 nm.

CD Concentration assays and Determination of the Constants for Complexation between MO and the CDS

Investigation of the complexes formed between MO and the CDs employed the citric acid-sodium citrate (CA/SC) buffer solution at pH 3.0 and concentration of 0.05 mol/L.

Preparation of the buffer solutions

CA/CS buffer solutions at pH 3.0 were prepared at concentrations of 0.1 and 0.05 mol/L.

Preparation of stock solutions of α-CD, β-CD, and MO in CA/SC buffer solution (0.05 mol/L, pH 3.0)

Solutions of α-CD (0.75 × 10⁻³ mol/L), β-CD (6.0 × 10⁻³ mol/L), and MO (0.27 × 10⁻³ mol/L) were prepared using 0.1 mol/L CA/SC buffer solution.

Dilution of the CD stock solutions

Volumes of between 0 and 4 mL of CD (α-CD or β- CD) stock solutions, in steps of 0.2 mL, were transferred to 21 vials. 0.05 mol/L CA/SC buffer solution was added until volumes equaled 4 mL.

Construction of the standard curve for complexation between MO and the CDs, and determination of the MO:CD complexation constants

Volumes of 0.5 mL of the MO working solution and 2.5 mL of the different concentrations of the CDs (as described above) were placed in 21 test tubes, resulting in final concentrations of 0.045 × 10⁻³ mol/L of MO and between 0 and 0.625 × 10⁻³ mol/L of α-CD, or between 0 and 5.0 × 10⁻³ mol/L of β-CD. The tubes were agitated using a vortex mixer and the absorbances were measured at 500 nm, with zeroing against distilled water.

Results and Discussion

Theory of Complexation of MO with CDS

Determination of α-CD and β-CD concentrations using the colorimetric assay method with MO was based on the formation of a complex between the dye and CD molecules, resulting in a decrease in the absorbance of the solution at a wavelength of 500 nm. The absorbances of the MO -CD complexes were different to that of free MO, which enabled quantification of the CD present in the sample. However, the relationship between the absorbance and the CD concentration only showed linearity at low concentrations. Therefore, at higher concentrations, complexation theory was used to describe the nonlinear relationship between absorbance and CD concentration, as reported by Hamon and Moraes.¹² At lower concentrations, it was also possible to use complexation theory to improve the precision of the CD assay, above that obtained using the linear relationship.

Influence of pH on the Absorption Spectra and Determination of the Maximum Absorbance Wavelength for Solutions of MO (free, or Complexed with the CDS)

The results of the tests described above are shown in Fig. 1 for the α-CD and in Fig. 2 for the β-CD. The only pH that resulted in a significant difference after complexation was pH 3.0 (for both CDs). This pH was therefore selected in the subsequent experiments. As the pH was increased, the peaks became superimposed, so in the case of this dye, the use of high pH values was inappropriate.

Fig. 1.

Spectra obtained for a solution of MO (0.05 × 10⁻³ mol L⁻¹) in the (a) absence and (b) presence of α-CD (0.5 × 10⁻³ mol/L), using disodium citrate-phosphate buffer at 25°C and pH 3.0.

Fig. 2.

Spectra obtained for a solution of MO (0.05 × 10⁻³ mol/L) in the (a) absence and (b) presence of β-CD (0.5 × 10⁻³ mol/L), using disodium citrate-phosphate buffer at 25°C and pH 3.0.

Figures 3 and 4 show that the behavior was very similar for both CDs. The use of pH 3.0, with disodium citrate-phosphate buffer and a wavelength of 500 nm, resulted in the greatest differences between the absorbance peaks obtained in the presence and absence of the CDs, hence providing greater sensitivity of the colorimetric method for detection of the CD. The differences were around 31% and 18.6% for the α-CD and β-CD, respectively, from which it can be concluded that there was greater affinity between MO and the α-CD and demonstrating the suitability of MO for assays of α-CD.¹⁴ A possible explanation for the reduced absorbance of MO following complexation could be the decrease in coplanarity of the dye caused by the spatially restricted conformation of the dye molecules within the CD cavities.¹⁵

Fig. 3.

Linearity limit for absorption by the solution of MO at a wavelength of 500 nm.

Fig. 4.

Second order polynomial fitting used to obtain a linear approximation for the assay of α-CD with MO.

The spectra shown in Figs. 1 and 2 revealed two absorbance peaks—one at 460–500 nm and another at 270–275 nm. The first could be attributed to the tautomeric form of the azo group, and the second to the tautomeric form of the ammonia group.²¹

The spectra also showed that there was a shift in the MO peak wavelength after complexation with the CDs, which was more accentuated for the α-CD than for the β-CD. Changes in the electronic spectra of guest molecules after inclusion in CDs can usually be explained by the effect of the environment around the guest molecule, known as the solvent effect. However, the changes that occurred with MO could have been caused by completely different effects, notably the superimposition of two bands corresponding to the monomeric and dimeric forms of MO.¹⁷

Determination of the Linearity Limit for Absorption by the Pure MO Solution

Figure 3 shows the linearity limit of the pure solution of MO prepared using the proposed methodology. The absorbance remained linear up to a concentration of 0.045 × 10⁻³ mol/L, so in order to avoid measurement errors, this was the maximum MO concentration used in the subsequent experiments.

Assays of CD Concentrations and Determination of the Constants of Complexation Between MO and the CDS

α-CD

The data for absorbance as a function of the α-CD concentration and Equation S29 (Supplementary Data are available online at www.liebertpub.com/ind), were used for the assays of α-CD and determination of the parameters for calculation of the equilibrium constant using Equation S31.

The maximum α-CD concentration considered was 0.75 × 10⁻³ mol/L, because scatter of the data was observed at higher concentrations, which could have led to erroneous results.

Equation S29 was fitted to the experimental data using the complexation theory procedure.¹⁸

Firstly, the linear fit through the origin (DABS = 0, [α-CD] = 0) was estimated using a second order polynomial and could be described by: C_α-CD (mmol L⁻¹) = −0.515 DABS (Fig. 4), corresponding to α = −0.515 × 10⁻³ mol_α-CD/L units of ABS⁻¹ cm.

The second step of the fitting process provided the upper limit of Δ, the difference between the specific molar absorptions of the free and complexed dye. The value obtained was Δ < −2330.1. In the third step, a value of Δ < −13667 was calculated as described by Souza and Moraes.¹⁸

In the fourth step, fitting was performed using Equation S29, with the lowest upper limit of Δ (Δ < −13667), determined in the third step, as the starting point of the fitting procedure. The fitted value of Δ was −22820.07.

Substituting the values of a, Δ, and α in Equation S29 then gave the equation of the fitted MO:α-_CD standard curve: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ C_ { \alpha - CD } } = - { \frac { DABS ( 0.052584 \cdot DABS + 0.52887 ) } { DABS + 1.0269 } } \qquad { \rm R } = 0.9994 \end{align*} \end{document}

In step 6 of the Supplementary Data, Equation S29 was used to calculate the specific molar absorption (σ) of complexed MO, under the test conditions, and the equilibrium constant for formation of the MO:α-CD complex (K_α-CD), with ABS₀ = 1.474, K_α-CD = 2527 M⁻¹, and σ = 9934.86 ABS units/cm/mol_{MO complexed}, while σ₀ = 32775.56 ABS units/cm/mol⁻¹ _MO.

From this, it was found that the molar absorptivity of the MO dye decreased by more than a third after complexation.

Equation S29 provided an excellent fit to the experimental data for the concentration of α-CD as a function of absorbance (Fig. 5), and the value of the equilibrium constant for formation of the MO:α-CD complex, K_α-CD = 4557.2 M⁻¹, was much higher than the value of 850 M⁻¹ reported by Yeuxican et al.¹⁵ The high value obtained in the present work could be explained by the use of the citric acid buffer, which has been found to assist in stabilizing complexes formed with CDs.²²

Fig. 5.

Standard curve for assay of α-CD with MO dye, obtained using the complexation theory method (dye concentration 0.045 mM; α-CD concentrations 0–0.75 mM; pH 3.0; citrate buffer (0.05 mol/L); ambient temperature.

β-CD

The data for absorbance as a function of the β-CD concentration were used with Equation S29 for the assay of β-CD and determination of the parameters for calculation of the equilibrium constant for formation of the MO:β-CD complex.

In the case of the β-CD, the maximum concentration of β-CD considered was 6.0 × 10⁻³ mol/L, because, similar to α-CD, tests using higher concentrations (up to the solubility limit) revealed scatter of the data, which could compromise calculation of the constants.

The same steps described for the α-CD were employed for the fitting of Equation S29 to the experimental data. In the first step, the linear fitting used the first four points, up to C_β-CD = 0.90 × 10⁻³ mol/L (Fig. 6), for fitting of the second order polynomial, resulting in α = −1.4353 mmol_β-CD/L/ABS cm.

Fig. 6.

Fitting of the second order polynomial to obtain the linear approximation passing through the origin (DABS = 0, [β-CD] = 0), in the first step of the procedure to obtain the standard curve for assay of the β-CD with the MO dye.

The second and third steps of the fitting procedure provided upper limits of Δ < −836.1 and Δ < −16844, respectively.

In the fourth step, fitting with Equation S31 employed the lower upper limit, Δ < −16844, determined in the third step, as the starting point of the fitting process. The fitted value of Δ was −20351.55.

Substituting the values of a , Δ, and α in Equation S29 resulted in the equation of the fitted MO:β-CD standard curve: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ C_ { \beta - CD } } = - { \frac { DABS ( 0.058 \cdot DABS + 1.314 ) } { DABS + 0.916 } } \qquad { \rm R } = 0.9996 \end{align*} \end{document}

In step 6, Equation S31 was used to calculate σ and the equilibrium constant for formation of the MO:β-CD complex, K_β-CD, where ABS₀ = 1.485, K_β-CD = 952.0 M⁻¹, and σ = 12648.5 ABS units/cm/mol_{MO complexed}, while σ₀ = 33000 ABS units/cm/mol_MO.

It could be seen that, as with the α-CD, the molar absorptivity of the MO dye decreased by almost a third after complexation.

Figure 7 shows the fitted experimental data for absorbance as a function of the β-CD concentration.

Fig. 7.

Standard curve for assay of β-CD with MO dye, obtained using the complexation theory method (dye concentration 0.045 mM; β-CD concentrations 0–6.0 mM; pH 3.0; citrate buffer (0.05 mol/L); ambient temperature.

An excellent fit was obtained by applying Equation S29 to the complexation of the β-CD. The value of the equilibrium constant for formation of the MO:β-CD complex (K_β-CD = 952 M⁻¹) was considerably smaller than the value obtained for the α-CD (K_α-CD = 2527 M⁻¹). The MO dye therefore had greater affinity for the α-CD, as already found in the tests for determination of the optimum pH for complexation. This finding can be explained by the smaller size of the cavity of the α-CD, which provided better accommodation of the dye molecule, compared to the larger cavity of the β-CD.

In other work, an equilibrium constant value of 26 mol/L was reported for a 1:1 complex of MO and β-CD, using the Benesi-Hildebrand equation. A value of 850 M⁻¹ was obtained by Yuexian et al. for a complex between MO and α-CD, using a concentration of 0.1 mol/L at acidic pH, and it was found that the equilibrium constant value decreased at higher temperatures.¹⁵ Elsewhere, a value of 7,690 M⁻¹ was found for a complex between MO and α-CD at low temperature (16°C) and pH 1.2.²³ The complex obtained between rosmarinic acid (RA) and β-CD was characterized in aqueous solution by 1H NMR (1D- and 2D-ROESY), completed with studies by capillary electrophoresis. From the 1H NMR data, the stoichiometry of the complex was determined by a Job's plot and the binding constant was estimated from a linear regression. At pH 2.9, the results showed that RA binds CD with a 1:1 stoichiometry and a binding constant of 445 (±53) M⁻¹ or 465 (±81) M⁻¹, depending on the CD protons (H-5 or H-3) selected for the evaluation.²⁴

Conclusion

The data obtained here were consistent, and demonstrated the capacity of complexation theory to provide high quality fitting, with higher correlation coefficients and the ability to work with wider ranges of concentrations.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

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