J. Phys. Chem. B 1997, 101, 4863-4866
4863
Multiple Complex Formation of Fluorescent Compounds with Cyclodextrins: Efficient Determination and Evaluation of the Binding Constant with Improved Fluorometric Studies Yannis L. Loukas† Center for Drug DeliVery Research, School of Pharmacy, UniVersity of London, 29-39 Brunswick Square, London WC1N 1AX, U.K. ReceiVed: NoVember 15, 1996; In Final Form: February 14, 1997X
Equations are derived and allow the determination of the cyclodextrin compound complex primary and secondary binding constants by using fluorometric studies (by monitoring the fluorescence intensity of the compound in the presence of cyclodextrins). The fluorescence intensity is dependent on the concentration of cyclodextrins in the solution of the compound as well as on the stoichiometry of the cyclodextrin compound complex. It was found that riboflavin (fluorescent compound) forms 1:2 inclusion complex with R-cyclodextrin and 1:1 with γ-cyclodextrin. The complex stoichiometries were calculated using the continuous variation method, and the binding constants were calculated fluorometrically and were evaluated with kinetic studies in order to compare the values from the two methods. The fact that the same compound (riboflavin) can exhibit different binding behaviors with different cyclodextrins could result in new descriptive studies for each particular case.
Introduction Cyclodextrins (CDs)1 and their derivatives are well-known to form inclusion complexes with a variety of molecules. CDs have been used widely as stabilizing2 and solubilizing systems,3 enzyme models, catalysts, stationary and mobile phase additives for chiral and isomeric separations, and so on. Because of their increased interest in them and their inherent usefulness, different studies have been done to evaluate the complexation procedures, the binding constants, and the stoichiometries of the formed complexes. Most of these studies assume a 1:1 molar ratio between cyclodextrin and the guest molecule of interest. However, there have been reported studies4 in which two or more cyclodextrins can bind to a single guest molecule and the overall model is significantly altered in multiple cyclodextrin complexes. Different methods are described in literature for the determination of the binding constant based on techniques5 such as the conductometric titrations, potentiometric and spectrophotometric methods, solubility, and competitive indicator binding. It was reported that both the primary and the secondary binding constants could be obtained using these methods. It should be mentioned also that there are cases where two guest molecules bind to a single CD host. These particular ternary complexes will not be considered in this report, however. For the determination of the binding constant in 1:1 complexes a variety of linear procedures are being used. Most of these suffer from theoretical and practical drawbacks,6 including assumed concentrations of the interacting moieties and products, poor solubility of certain compounds, a boundary condition (saturation binding) with respect to the ratio of the concentrations of the two binding partners, and the occasional formation of dimmers. On the other hand, Diederich7 suggests that nonlinear procedures are free of the above assumptions and have much broader applicability, and such procedures are likely to displace the evaluations done according to Benesi-Hildebrand and to Scott or Scatchard linear models.
Similarly, nonlinear mathematical expressions have been described for the calculation of the binding constant using, for instance, UV spectrophotometry8 during complexation. Other nonlinear expressions correlate NMR resonances of CDs, guests, and their complexes.9 Furthermore, the Gauss-Newton nonlinear optimization method has been applied for the analysis of solubility curves10 and the Marquardt algorithm with HPLC methods for the correlation of retention data of the guest molecule in the presence of CD with the binding constant.11 In the present work it is demonstrated that fluorometric studies of fluorescent compounds in the presence of CDs can be used to determine all the relevant binding constants for the CDguest system. CDs as fluorescence quenchers in guest solutions have been used previously to evaluate single binding constants by using linear models;12 however, the fluorescent behavior of CD multiple complex formation should be described in order to examine higher order inclusion complexes. Experimental Section Reagents and Methods. Riboflavin 5′-(dihydrogen phosphate) monosodium salt (R) was purchased from the Aldrich Chemical Company (Gillingham, Dorset, UK) and R-, γCD from Janssen (Beerse, Belgium). Double-distilled water was used throughout. All other reagents were of analytical grade. Fluorometric studies of the R:RCD and R:γCD were monitored in a Perkin-Elmer LS-3 fluorescence spectrophotometer (excitation and emission wavelengths of 445 and 520 nm, respectively).13 Photodegradation studies were carried out using a long-wavelength (365 nm) UV lamp with 6 W rating and 460 µW cm-2 dm-1 intensity (model UVGL-58, UVP, San Gabriel, U.S.A.). The kinetics of R photodegradation in aqueous solutions in the presence of R- and γCD were performed and monitored spectrophotometrically (at 445.5 nm) in a Compuspec UV-vis spectrophotometer (Wallac) connected to a personal computer. Continuous Variation Method (Job plot)
†
Present address: Riga Ferreou 21, Ano Ilioupolis, 163 43 Athens, Greece; E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, May 15, 1997.
S1089-5647(96)03818-7 CCC: $14.00
The inclusion complexes of R with the CDs were prepared by the freeze-drying method.14 A reliable determination of the © 1997 American Chemical Society
4864 J. Phys. Chem. B, Vol. 101, No. 24, 1997
Loukas where k0 is the proportionality constant correlating the guest concentration with the fluorescence intensity. By adding to this system the CD solution and considering that the fluorescence intensity is the sum of contributions, we write
SCHEME 1
complex stoichiometry can be provided by the continuous variation technique (Job plot),15 based on the difference in fluorescence intensity ∆F (∆F ) F0 - F) of R observed in the presence of R- and γCD. Equimolar solutions of the guest G (R) and each of the corresponding CDs were prepared and mixed to standard volume and proportions in order for the total concentration to remain constant ([G]t + [CD]t ) M). ∆F values in the preparations of R were calculated by measuring the fluorescence intensity of R in the absence (F0) and presence (F) of the corresponding concentrations of CD (R- or γCD). Also, an equimolar aqueous solution of each CD was used as blank to take into account its refractive index. Subsequently, ∆F[R]t was plotted for the corresponding CD against r (r ) [G]t/([G]t + [CD]t), where G denotes the R). The concentrations of free G and CD in a 1:n inclusion complex G:CDn can be expressed as follows:
F ) k0[G] + k1[G:CD] + 2k2[G:CD2] + kCD[CD] (2) where G is the free guest, CD is the free cyclodextrin, G:CD is the 1:1 guest:cyclodextrin complex, G:CD2 is the 1:2 complex, k1, k2, and kCD are the proportionality constants for the 1:1 and 1:2 inclusion complexes and the free cyclodextrin, respectively. As CDs do not fluoresce, their contribution in fluorescence is zero and, therefore, the factor kCD[CD] is zero. Equation 2 can be thus rewritten as
F ) k0[G] + k1[G:CD] + 2k2[G:CD2]
Also the two equilibrium (binding) constants K11 and K12 in Scheme 1 can be calculated as follows:
K11 )
[G] ) rM - [G:CD] K12 )
[CD] ) M(1 - r) - n[G:CD]
(3)
[G:CD] [G][CD]
(4)
[G:CD2] [G:CD][CD]
(5)
For a given value of r, the concentration of the complex G:CDn will reach a maximum corresponding to the point where the derivative d[G:CD]/dr ) 0. Derivation of the above two equations according to r give the following: d[G]/dr ) M and d[CD]/dr ) -M. Rearrangement of the above equations leads to a single solution: the maximal absolute complex concentration is reached for r ) (n+1)-1 and does not depend on M or the binding constant.16
The fluorescence quenching is expressed with the difference ∆F ) F0 - F which is equal, after substituting the [G:CD] with its equal from eq 4 ([G:CD] ) K11[G][CD]), to
Theory
∆F ) F0 - F ) k0[Gt] - [G](k0 + k1K11[CD] +
Fluorimetry can be used for the calculation of the binding constant in a variety of ways, including changes in fluorescence polarization,17 which reflect the relaxation time of molecules, thus providing direct evidence of complex formation. Also, reduction in fluorescence intensity (quenching) of the guest molecule on inclusion in CDs is used for the determination of the binding constant and the complex stoichiometry. This reduction probably happens because, at short intermolecular distances, as in complex formation between a guest and a CD, radiationless energy transfer from the excited state of the guest to the ground state of CD takes place, thus reducing the fluorescence intensity. In some cases, inclusion reactions may be slow in aqueous solutions, especially in the presence of interactions with other agents in the solution. In such cases (i.e., those involving fluorescent molecules) it is essential that equilibrium is reached before the measurement of fluorescence intensity. A fluorescence reading that remains unchanged in time indicates equilibrium. The linear models (like the BenesiHildebrand treatment) employed for the calculation of the binding constant by correlating changes in fluorescence intensity with the CD concentration use excess CD and make the assumption that free CD is equal to total CDt. However, appropriate expressions, which take into account multiple CD complexation, are easily formulated. Consider a 1:2 system (G:CD2) (Scheme 1) with the guest (R) and the cyclodextrin (RCD or γCD) at total concentrations of Gt and CDt, respectively. In the absence of CD the fluorescence intensity of Gt is
F0 ) k0[Gt]
(1)
Substitution of [G:CD] and [G:CD2] from eqs 4 and 5 into eq 3 gives
F ) k0[G] + k1(K11[G][CD]) + 2k2(K12[G:CD][CD]) (6)
2k2K11K12[CD]2) (7) To use eq 7, the quantities [G] and [CD] are needed. The mass balance equations for G and CD are
Gt ) [G] + [G:CD] + [G:CD2]
(8)
CDt ) [CD] + [G:CD] + 2[G:CD2]
(9)
where Gt and CDt are the (known) total concentrations of guest and cyclodextrin. The average number of cyclodextrin molecules bound per guest molecule (nj) is
nj )
Σ(CD bound to G) Σ(all G)
(10)
The quantity CDb as Σ(CD bound to G), the “total bound” cyclodextrin concentration, can be further defined by
CDb ) [G:CD] + 2[G:CD2]
(11)
The free guest concentration [G] is obtained by substituting eqs 4 and 5 into eqs 8 and 9:
[G] )
Gt(1 - nj) 1 - K11K12[CDt - njGt]2
(12)
The free cyclodextrin concentration [CD] is obtained from eqs 9 and 11:
[CD] ) [CDt] - nj[Gt]
(13)
Fluorescent Compounds with Cyclodextrins
J. Phys. Chem. B, Vol. 101, No. 24, 1997 4865
TABLE 1: Cyclodextrin to Guest Stoichiometry and Binding Constantsa compd
stoichiometry
R:γCD R:RCD
1:1 1:1 + 1:2
standard standard deviation K12 (M-1) deviation
K11 (M-1)
2850[2300]a 334[183] 1645[1125] 154[93]
345[237]
44[27]
a
Values in square brackets denote the binding constants calculated kinetically (eq 15).
Finally, substitution of [G] and [CD] from eqs 12 and 13 into eq 7 provides a quadratic equation that describes the behavior of fluorescent guest complexing two cyclodextrin molecules:
∆F ) k0[Gt] -
[Gt](1 - nj)
{k0 + k1K11[CD] +
1 - K11K12[CD]2
2k2K11K12[CD]2} (14) where [CD] ) [CDt] - nj[Gt]. Results and Discussion Determination of the Binding Constants Iteration. The binding constants for the examined complexes were calculated iteratively using eq 14. To use eq 14, the quantity nj is needed. The nj is obtained experimentally by using the continuous variation method (see above). If K12 ) 0 (for 1:1 complexes), eq 14 reduces to the usual 1:1 behavior. This same approach, described above, can be used to derive expressions for higher complexes. Equation 14 involves no approximation of the concentrations of the two compounds (CD and guest) and correlates the initial total concentrations [Gt] and [CDt] with the binding constants K11 and K12. The unknown parameters K11 and K12 can be then calculated according to eq 14 by using nonlinear least-squares regression analysis. There are several algorithms for the analysis of nonlinear mathematical expressions18 by nonlinear regression. The Levenberg-Marquardt algorithm,19 for instance, is one of the most commonly used for the analysis of these expressions. The initial values for the iterative process to start were calculated according to the following procedure: First, the k0, k1 and k2 were calculated from the fluorescence intensity of known concentrations of the free guest [Gt] and the pure complex [CDb] as follows:
F0 ) k0[Gt] Fb ) kb[CDb] ) kb([G:CD] + 2[G:CD2]) k b ) k1 + k2 In the case of 1:1 R:γCD complex k2 ) 0. On the basis of such k0, k1, and k2 for a pair of values for Gt and CDt (R- or γCD) concentrations, the K11 and K12 were calculated by substituting these values into eq 14. These values for K11 and K12, as well as the nj values (see later), were used as starting values for the iterative procedure, which finally results in the values in Table 1. For a system containing only a 1:1 (G:CD) complex, the quantity njdCDb/Gt can range from 0 to 1 (0 < nj < 1), whereas for a system capable of forming both G:CD and G:CD2, nj can range from 0 to 2 (0 < nj < 2). Thus, nj is a useful indication of the extent of the binding isotherm that has been examined. In a 1:1 system, nj is equal to f11, the fraction of guest present as the 1:1 complex, whereas in a 1:1 + 1:2 system, njdf11 + 2f12. In the present study, the stoichiometries were calculated by using the continuous variation plots and the corresponding values for nj were used in eq 14. Figure 1 is indicative of the
Figure 1. Plot of ∆F/[Rt] vs [RCDt] concentration illustrating the nonlinear behavior of 1:2 inclusion complex (R:RCD2).
behavior of guests that bind more than one cyclodextrin and represents the graphical solution of eq 14 for R:RCD2 complex. Judging from the R2 value (R2 ≈ 0.96), the model appears to fit the observed values well. Table 1 gives the stoichiometries, the calculated binding constants, and the standard deviations of the examined guest (R) with the use of the above mentioned technique. Determination of Complex Stoichiometries. To determine the stoichiometries of the complexes by the continuous variation method, fluorescence spectra were obtained for R and the corresponding CD (R- or γCD) mixtures in which the total initial concentrations of the two species were maintained constant but the ratio of initial concentrations r (see Experimental Section) varied between 0 and 1. If a physical parameter directly related to the concentration of the complex (for instance, the fluorescence intensity F) can be measured under these conditions and is then plotted as a function of r, the maximal value for this parameter will occur at r ) m/(m + n), where m and n are the guest and CDs proportions in the complex, respectively (Gm:CDn).16 This means that if the complex stoichiometry is 1:1 (m and n ) 1), the maximum value for the examined parameter will be reached at r ) 0.5; if the complex stoichiometry is 1:2 (m ) 1 and n ) 2) the maximum value will be reached at r ) 0.33. The calculated quantities ∆F[R]t are proportional to the concentration of the complexes and can be thus plotted against r. The resulting continuous variation plots demonstrate that since the maximum has an r value of almost 0.5 for the R:γCD (Figure 2a), this complex has a 1:1 stoichiometry. In the case of R:RCD complex the maximum has an r value which presents a deviation from 0.5 toward the value of 0.33 (Figure 2b) which corresponds to a 1:2 complex. Evaluation of the Binding Constants Using Different Methods. The binding constants for the examined complexes (R:RCD and R:γCD) were also determined kinetically. A known phenomenon widely used for the determination of the binding constant of unstable compounds (such as the photosensitive R) is the acceleration or deceleration of the degradation kinetic in the presence of cyclodextrins.20 In the present study, the stabilizing effect of both CDs (R and γ) was examined by monitoring the degradation rate constant of R in the presence of increasing concentrations of CDs. The reaction mechanism, involving the formation of a 1:2 inclusion complex, is illustrated in Scheme 2. where k0, k1, and k2 are the degradation rate constants for the free guest (G), the 1:1 complex (G:CD), and
4866 J. Phys. Chem. B, Vol. 101, No. 24, 1997
Loukas differences in the calculated values are commonly observed in studies where the binding constant is calculated by different methods. For example, the K11 of the p-nitrophenol complex with RCD is 126 M-1 when calculated by titration calorimetry and 250 M-1 when calculated by spectrophotometry.23 Moreover, the 1:1 inclusion complex of p-nitrophenolate with RCD has a K11 value of 1590 M-1 when calculated by optical rotation24 and a value of 3550 M-1 when calculated by gel filtration.25 Furthermore, it is becoming evident that assuming a 1:1, 1:2, or 2:1 complexes without some definitive experimental evidence can lead to erroneous results. For example, in the literature one group26 assumes 1:1 complexation of prostaglandin B1 with RCD and another group27 1:2, with significant deviation in their results. Obviously, this can significantly alter the interpretation of one’s conclusions in studies involving complexation with cyclodextrins. Also, fluorescence behavior could be altered in going from a 1:1 to a 1:2 complex in fluorometric studies, such as in the present work. In conclusion, the nonlinear curve-fitting model described can be used for the calculation of the binding constants in multiple complex formation of fluorescent compounds with fluorescence intensity being affected in the presence of cyclodextrins. As this model requires only the initial concentrations of the free species (i.e., G and CD) without any limitation, experimental and theoretical drawbacks are avoided. In addition to the model system described in the present study, similar fluorometric titration can be used also for the stoichiometric determination of strongly binding systems, such as the drug-protein, antibodyhapten, metal ion-oxine sulfonate, pyrene-protein, or the calculation of the microionization constant of tetracyclines. References and Notes
Figure 2. Continuous variation plot (Job plot) of (a) R:γCD and (b) R:RCD2.
SCHEME 2
the 1:2 complex (G:CD2), respectively. Linear models describing the kinetic behavior of 1:1 complexes are usually solved according to Lineweaver-Burk20 or Eadie21 equations. The multiple complex formation in Scheme 2 can be described with the eq 15:
kobs k0 + k1K11[CDt - nGt] + k2K11K12[CDt - njGt]2 ) 1 - nj 1 - K11K12[CDt - njGt]2 (15) If K12 ) 0 (for 1:1 complexes), eq 12 reduces to the usual equation for 1:1 behavior. Equation 15 involves also no approximation of the concentrations of the two compounds (CD and guest) and correlates the initial total concentrations [Gt] and [CDt] with the rate constants k0, k1, and k2. The unknown parameters K11 and K12 can be then calculated according to eq 15 by using nonlinear least-squares regression analysis (Table 1). The description and derivation of eq 15 and the experimental protocol are described in detail elsewhere.22 On the basis of the values in Table 1, it can be concluded that the calculated values for the binding constants are slightly different when using the two methods as described above. Such
(1) Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 19, 344. (2) Loftsson, T. Drug Stab. 1995, 1, 22. (3) Loukas, Y. L. Pharm. Sci. 1995, 1, 509. (4) Connors, K. A.; Pendergast, D. J. Am. Chem. Soc. 1984, 106, 7607. (5) Gelb, R.; Schwartz, L.; Murray, C.; Laufer, D. J. Am. Chem. Soc. 1978, 100, 3553. (6) Djedaini, F.; Perly, B. New Trends in Cyclodextrins and DeriVatiVes, 1st ed.; Edition de Sante: Paris, 1993; Chapter 6. (7) Diederich, F. Angew. Chem., Int. Ed. Engl. 1988, 27, 362. (8) Rose, N.; Drago, R. J. Am. Chem. Soc. 1959, 81, 6138. (9) Djedaini, F.; Lin, S.; Perly, B.; Wouessidjewe, D. J. Pharm. Sci. 1987, 76, 643. (10) Miyahara, M.; Takahashi, T. Chem. Pharm. Bull. 1982, 30, 288. (11) Spino, L.; Armstrong, D. Ordered Media in Chemical Separations, 1st ed.; Hinze, W. L., Ed.; ACS Symposium Series 342; American Chemical Society: Washington, DC, 1987; Chapter 1. (12) Loukas, Y. L.; Vraka, V.; Gregoriadis, G. J. Pharm. Pharmacol. 1997, 49, 127. (13) Loukas, Y. L.; Jayasekara, P.; Gregoriadis, G. J. Phys. Chem. 1995, 99, 11035. (14) Loukas, Y. L.; Jayasekara, P.; Gregoriadis, G. Int. J. Pharm. 1995, 117, 85. (15) Job, P. Ann. Chim. 1928, 9, 113. (16) Connors, K. A. Binding Constants: The Measurement of Molecular Complex Stability; John Wiley and Sons: New York, 1987. (17) Bright, V.; Keimig, L.; McGown, L. Anal. Chim. Acta 1985, 175, 189. (18) Fox, J. Linear Statistical Models and Related Methods; John Wiley and Sons: New York, 1984. (19) Marquardt, D. J. Soc. for Ind. Appl. Math. 1963, 2, 431. (20) Loukas, Y. L.; Vyza, A. E.; Valiraki, A. P. Analyst 1995, 120, 533. (21) Loukas, Y. L.; Vyza, A. E.; Valiraki, A. P. J. Agric. Food Chem. 1994, 42, 944. (22) Loukas, Y. L. Analyst 1997, 122, 377. (23) Rosanske, T.; Connors, K. J. Pharm. Sci. 1980, 69, 564. (24) Bergeron, M.; Channing, G.; Gibeily, G.; Pillor, D. J. Am. Chem. Soc. 1977, 99, 5146. (25) Korpela, K.; Himanen, P. J. Chromatogr. 1984, 290, 351. (26) Armstrong, D.; Nome, F.; Spino, L.; Golden, T. J. Am. Chem. Soc. 1986, 108, 1418. (27) Kawaguchi, Y.; Tanaka, M.; Nakae, M.; Shono, T. Anal. Chem. 1983, 55, 1852.
