dissociation constants of host–guest complexes of alkyl-bearing compounds with β-cyclodextrin and...

Oswald S. Tee, Timothy A. Gadosy, and Javier B. Giorgi

Dissociation constants of host-guest complexes of alkyl-bearing compounds with P-cyclodextrin and "hydroxypropyl-P- cyclodextrin"

Abstract: Dissociation constants (Kd) of host-guest complexes formed from P-cyclodextrin or "hydroxypropyl-P-cyclodextrin" (P-CD and Hp-P-CD) and several types of aliphatic guests (alcohols, alkanesulfonate ions, alkylamines, and a-amino acids), with up to eight carbons in a chain, are reported. These constants were determined by inhibition kinetics and by a spectrofluorometric displacement method based on competition with 1-anilino-8-naphthalenesulfonate ion as a fluorescent probe. The value of Kd for a particular amine is close to that for the corresponding alcohol. For linear alkyl derivatives, there are strong correlations between pK, (= -log Kd) and the chain length of the guest, with slopes around 0.5, complementing trends that were noted earlier. Furthermore, the strengths of binding of various aliphatic derivatives to P-CD and to Hp-P-CD are close, with Kd values for the two CDs usually being within a factor of 2 of each other. Overall, for the binding of over 50 alkyl-bearing derivatives, there is a good correlation of pKd for Hp-P-CD with that for P-CD, with unit slope. These observations imply that the binding of simple aliphatic guests to Hp-P-CD is not greatly influenced by the modification of the hydroxyl groups on the primary side of the P-CD cavity but this may not be true for longer aliphatic derivatives (>Cx) or for aromatics that penetrate farther into the CD cavity.

Key words: cyclodextrins, host-guest complexes, dissociation constants.

Resume : On a mesurC les constantes de dissociation (Kd) de complexes hBte-invitC form& h partir de P-cyclodextrines ou d'<<hydroxypropyl-P-cyclodextrinex (P-CD et Hp-P-CD) et plusieurs types d'invitCs aliphatiques (alcools, ions alcanesulfonates, alkylamines et acides a-aminis) comportantjusqu'h huit atomes de carbone. On a dCterminC ces constantes par l'inhibitionde la cinCtique et par une mCthode de dkplacement spectrofluoromttrique qui est basCe sur une compCtition avec I'ion I-anilino-8- naphtalknesulfonate comme sonde fluorescente. La valeur du K, pour une amine donnte est trks proche de la valeur pour l'alcool correspondant. Pour les dtrivCs alkyles IinCaires, il existe une forte corrClation entre le pK, (= -log K,) et la longueur de la chaine de I'invitC; les pentes de 0,5 sont un complement aux tendances notCes anterieurement. De plus, les forces de liaison de divers dCrivts aliphatiques h la P-CD et h la Hp-P-CD sont trks semblables; les valeurs de K, pour les deux CD sont gCnCralement h l'intirieur d'un facteur de deux I'une par rapport h l'autre. Dans l'ensemble, pour la liaison de plus de 50 dCrivCs portant des groupes alkyles, il existe une bonne corrClation entre le pK, de la Hp-P-CD et celui de la P-CD et la pente est Cgale h I'unitC. Ces observations impliquent que la liaison d'invitCs aliphatiques simples 2 la Hp-P-CD n'est pas beaucoup influencCe par la modification des groupes hydroxyles sur le cBtC primaire de la cavitC de la P-CD; ceci n'est toutefois pas vrai avec les dCrivCs comportant des chaines aliphatiques plus longues (>C8) ou pour les derives aromatiques qui pCnktrent plus dans IacavitCde la CD.

Mors elks : cyclodextrines, complexes hbte-invitk, constantes de dissociation.

[Traduit par la rkdaction]

Introduction Moreover, non-covalent assembly of carefully chosen pre- cursors is easier and faster than conventional synthesis as a

A feature of Su~ramolecu la r is non-covalent means of developing novel catalytic systems and new mate- binding between the constituents of supermolecules (1, 2). rials (3), Better of the interactions responsi-

Received January 3 I , 1995.'

O.S. ~ e e ? T.A. Gadosy? and J.B. GiorgL4 Department of Chemistry and Biochemistry, Concordia University, MontrCal, QC H3G 1 M8, Canada.

' Revision received January 29, 1996. ' Author to whom correspondence may be addressed.

Telephone: (514) 848-3348. Fax: (514) 848-2868. Holder of an NSERC post-graduate scholarship (1991-1995). Holder of NSERC summer student awards (1993, 1994).

ble for non-covalent binding, and their relative importance to molecular recognition, requires knowledge of complexation constants and how they vary with host-guest structure and the medium (2, 4). The present paper reports dissociation constants of complexes formed between two cyclodextrins (CDs) (5) and some aliphatic derivatives in water. Most of the values were specifically required for ongoing studies of the effects of cyclodextrins on reactivity (6-8), while others were obtained for comparative purposes or for future use.

Can. J . Chem. 74: 736-744 (1996). Printed in Canada / Imprim6 au Canada

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Tee et al.

There are many ways of estimating dissocation constants (Kd) or formation constants (Kf = l/Kd), based on the alteration of some chemical or physical property that is brought about by complexation (eq. [I]) (9). However, for any particular equi- librium the choice between different methods may not be easy since each one has its own specific requirements and limita- tions. For example, direct spectrophotometric methods require that either A or B or the complex A.B has a suitable absorption, and that there is a well-behaved, measureable spectral change that accompanies complexation. Likewise, the use of inhibition kinetics (10) requires a probe reaction that is not interfered with by the "inhibitor," except by competitive inhibition (1 1). A further requirement is that the site on the host occupied by the inhibitorlguest is basically the same as that involved in the probe reaction; otherwise the inhibition is not truly "competitive" and misleading results will be obtained (8, 1 I).

A different type of limitation, one that is common to many analytical methods, is due to the requirement or assumption of very unequal host and guest concentrations ([A], >> [B], or [B], >> [A],). This inequality allows for a mathematical sim- plification inherent to various "graphical" treatments (e.g., Benesi-Hildebrand, Eadie, and Scatchard plots (9)) but often it is a condition that is difficult or even impossible to fulfil. One improvement in the present work results from removal of this constraint. The other main improvement results from nonlinear fitting of saturation data to an appropriate hyperbolic function, rather than the traditional use of a double-reciprocal plots, with their statistical deficiencies (12), or of other methods based on linearization of the data (9).

Methods and results

Using inhibition kinetics, we have determined dissociation constants for complexes of various aliphatic alcohols with P- cyclodextrin (P-CD) and "hydroxypropyl-P-cyclodextrin" (Hp-P-CD) (5). The method is based on the retarding effect of a CD-binding species on the rate of basic cleavage of rri-nitrophenyl acetate (mNPA) by a CD (8c, 10).

Given that there is hydrolysis of the ester (S) in the basic medium, eq. [2], and cleavage through an ester-CD complex, eq. [3], the dependence of the rate constant for ester cleavage on [CD] is as given by eq. [4]. From experiments over a range of CD concentration, [CD], one finds values of k,, kc, and Ks, preferably by nonlinear fitting of eq. [4] (6).5

k [2] S 2 products

Note that a usual condition of the experiments to characterize the saturation kinetics is that [S], > [SCD] << [CD], so that one can set [CD] equal to [CD], in eq. [4]. Likewise, for the inhibition experiments, [S], is kept low, so that it does not significantly affect [CD] compared to the effect of the added inhibitor. See last paragraph of the Experimental.

Rearrangement of eq. [4] leads to an expression for [CD] in terms of kObs (eq. [5]), from which one can estimate [CD], as long as kobc is determined under the same conditions as k, and kc. In the presence of an inhibitor (I) that also binds to the CD (eq. [6]) the concentration of unbound CD is reduced and kobs is decreased in accord with eq. [4], if kc > k,, as in the present case. Traditionally (9, lo), experiments are carried out with high [I], >> [CD], so that the approximation [CD] = [CD]oKdI (Kd + [I],) is reasonably valid. Between this expression and eq. [5], [CD] can be eliminated to give an equation relating kobs and [I], that is suitable for the graphical estimation of Kd.

A major problem with the above approach is that it is not always convenient or even possible to maintain the condition that [I], >> [CD],, particularly when the inhibitor has a low solubility in water, which is usually the case with species that bind strongly to CDs. Our approach removes requirement of the inequality by calculating Kd values at various [I:],, directly. Using eq. [5], we estimate [CD] for a given [I],, and then calcu- late [CD.I] = [CD], - [CDI, and [I] = [I], - [CD.I] = [I], - ([CD], - [CD]), taking account of mass balance. Substitution of these concentrations into Kd = [CD][I]/[CD.I] leads to an estimate of the desired dissociation constant (eq. [7]). This pro- cedure is carried out for several different [I], and the estimates are averaged. The calculations are conveniently carried out using commercial spreadsheet software (see Experimental).

Table 1 contains Kd values for 18 alcohols and 5 alkanesulfonate ions binding to P-CD and Hp-P-CD, most of which were determined by the inhibition method just outlined. It also contains values taken from the literature, particularly those for P-CD, that were obtained in other ways (13-15).

The inhibition of mNPA cleavage also works well for the binding of aliphatic k e t ~ n e s , ~ but we did not use it for complexes formed by CDs and alkylamines because amines react with esters in basic solution.' To circumvent this problem, we developed a methodology based on competition for the CD between a guest and a fluorescent probe, which in the present case is the 1-anilino-8-naphthalenesulfonate anion (ANS). Mathematically, it is similar to the inhibition method, but with specific particularities.

In aqueous solution, the fluorescence of ANS is very weak but in nonpolar media it is much stronger. Likewise, when ANS is bound to CDs (eq. [8]) its fluorescence intensity is enhanced (16) and for 1: 1 binding8 the relative fluorescence F,,, (= IobslIo) varies with [CD] in accord with eq. [9] (9).

O.S. Tee, A.A. Fedortchenko, P.G. Loncke, and T.A. Gadosy. J. Chem. Soc. Perkin Trans. 2. In press.

' In fact, it was studies of the effects of CDs on ester aminolysis (cf. 7g, 7h) that required us to determine Kd values for {amine.CD] complexes. Since we were primarily concerned with the quantitation of 1 : 1 binding, we have avoided conditions (long alkyl chains, very high [CD]) that tend to give rise to 2: 1 (CD:guest) binding.

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Can. J . Chem. Vol. 74, 1996

Table 1. Dissocation constants of guest-cyclodextrin complexes, determined by the inhibition kinetics method."

Guest Hp-P-CD P-CD""

(a) Alcoholsb EtOH n-PrOH 12-BuOH n-PentOH n-HexOH n-HeptOH iso-PrOH iso-BuOH iso-PentOH 2-BuOH 2-PentOH 2-HexOH 3-PentOH tert-BuOH neo-PentOH cycloPentOH cycloHexOH

(b) Alkanesulfonate BuS0,- 105 f 1.1 PentS0,- 26.6 f 1.1, 67 HexS0,- 9.54 f 0.23, 8.9 HeptS0,- 3.38 f 0.27, 1.8 OctS0,- 1.07 f 0.13, 0.9 1

"At 25"C, in aqueous solution. All of the values for Hp-P-CD were determined, in this work, in a phosphate buffer of pH 11.6.

bMost of the values for alcohols and P-CD were determined by Matsui et al., using a spectral displacement method (13). The remaining values (those given with errors) were determined earlier in this laboratory, by the inhibition method (8c).

'All but one of the values for RS0,- and P-CD are taken from Satake et al. who used a conductimetric method (14a,b). Very similar results were obtained by Park and Song, using an ANS fluorescence probe method (14c). Earlier experiments in this laboratory on the binding of these ions to a-CD, using the inhibition method (8c), gave results in reasonable agreement with those from conductimetry (14n,B).

"Reinsborough and co-workers (15) found similar values of K, for RS0,- binding to Hp-P-CD. using fluorescent probe displacement and conductimetry.

[81 ANS + C D + ANS.CD KANS

Figure 1 shows observed data and calculated curves for the effects of P-CD, y-CD, and Hp-P-CD on the relative fluorescence of ANS in aqueous solution and Table 2 contains the appropriate constants derived from nonlinear fitting of eq. [9] to the data. As seen in Fig. I, binding ANS to P-CD and y-CD causes substantial increases in its fluorescence and these may be used as the basis of competition experiments (14c, 17-23).

Fig. 1. Effects of added cyclodextrins on the fluorescence of ANS in aqueous solution at pH 11.60: P-CD, v; Hp-P-CD, H; y-CD, 0. Note that the vertical scale on the left is for Hp-P-CD and that it is 16 times greater than that on the right for the others two CDs. The actual data for Hp-P-CD extend to [Hp-P-CD] = 20 mM.

Table 2. Effects of cyclodextrins on the fluorescence of the 1-anilino-8-naphthalenesulfonate ion (ANS) due to complexation."

CD Fc This work Literature values (ref.)

P-CD 46.7 f 1.7 26.8 f 1.3 9.1-90h Hp-P-CD 430 f 2 1.7 1 f 0.04 y-CD 34.5 f 0.4 7.81 f 0.17 0.79(22), 3.6(19)

"At 25"C, in an aqueous phosphate buffer (0.2 M) of pH 11.6. Values of F, and Kc\,, were obtained from nonlinear fitting of eq. [9] to relative fluorescence data (F,,, = 1,,,/1,), with F,, = I (see Fig. 1).

"~iterature values of K,\,, (in mM) are: 9.1 ( 2 0 , 11 (20, 23). 12 ( 1 4 ~ ) . 13 (17b). 15 (22). 16 (18), 17 (17r1), 90 (19).

On the other hand, ANS binding to a-CD is much weaker and the resulting fluorescence increase is small (1 6), making it less suitable as a probe, in our experience.6 By contrast, the binding of ANS to Hp-P-CD is stronger than that to P-CD and it brings about a very large enhancement in fluorescence (Fig. 1).

The literature contains several values of KANs for the complexation by P-CD (Table 2, footnote b), ranging from 9 to 90 mM, but most fall within 13% 4 mM. We have settled on a value of 27 mM as being appropriate for our conditions (pH 11.6, 0.2 M phosphate buffer), whereas colleagues have obtained more "normal" values of 10.5 i 1.3 and 16.4' 1.5 mM at lower pH and lower ionic strength.9 ANS binding under our conditions is discussed further in the experimental section.

When another guest is added to a solution of ANS and a CD, the amount of free CD is reduced, so that some of the CD- bound ANS dissociates, and the ANS fluorescence dimin- ishes, as shown in the examples in Fig. 2. From such decreases, the free [CD] can be estimated from eq. [lo], obtained by rearrangement of eq. [9]. Substitution of these CD

Q.R. Mikkelsen, S. Rubio and Q. Tan, unpublished results.

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Fig. 2. Examples of the effects of amines on the ANS fluorescence in the presence of Hp-P-CD, in aqueous solution at pH 11.6: tz-propylamine, a; n-butylamine, 0; cyclopentylamine, B; cyclohexylamine, +.

[amine], mM

Table 3. Estimation of a dissociation constant by displacement of the fluorescent probe, ANS. Guest = tz-butylamine; [ANSI, = 0.075 mM; for 13-cyclodextrin, with [CD], = 10.0 mM."

[Guest],, [CD], [ C D y e s t ] , [guest], K,, mM l o b s F,I mM mM mM mM

Average: 35.6 Standard deviation: f 1.2

"At 25OC, in aqueous solution at pH 11.60. Individual K, values were obtained from eq. [7] (with [fl, = [guest],), using [CD] values estimated

. , from eq. [I01 and F,, in column 3. See the Experimental for more details. "Less than [CD], = 10.00 mM due to depletion of CD by binding to

ANS. For [CD] = 9.98 mM, a reference tluorescence F,,, (= 13.40) was calculated from eq. [9] and the observed intensities were scaled to this. giving F,,, in column 3.

concentrations into eq. [7], for each of several [guestlo, leads to estimates of K, for the guest and these estimates are averaged. Again, the calculations can be most easily carried out in a spreadsheet, an example of which is given in Table 3.

As a test of the above fluorescent probe method under our conditions, we looked first at the effects of some alcohols on ANS fluorescence in the presence of P-CD and Hp-P-CD and found values of Kd that are in reasonable to good agreement with those determined in other ways (Table 4 (a)). We then applied the method to the binding of several alkylamines and related derivatives, and obtained the K, values presented in Table 4 (b). For the purposes of comparison, Table 4 also contains values that were found in the literature (13, 17, 23-25).

We have also used the fluorescence method to find Kd values for the binding of a-amino acids to P-CD, for the purposes of studies of the reaction of these nucleophiles with esters in the presence of CDs (cf. ref. 26). Our attempts were only par- tially successful in that smaller derivatives appear to bind weakly, if at all. However, derivatives with larger alkyl or aryl substitutents at the a-carbon of the amino acid bind strongly enough to cause significant decreases in ANSvCD fluorescence, analysis of which afforded the dissociation constants given in Table 4 (c).

We have had only limited success using the fluorescent probe method for the binding of ketones to C D S . ~ In general, we have found inhibition kinetics easier to use and to give more reproducible results, perhaps because it is less suscepti- ble to trace impurities (which may quench fluorescence) and to instrumental fluctuations.

Discussion

In earlier work (6, 7c, 14c) it was noted that the strength of binding of several n-alkyl derivatives to CDs, expressed by pKd = -log K,, increases monotonically with alkyl chain length, for up to about eight carbons.1° Similar correlations are found in the present results for both (3-CD and Hp-P-CD, and these are summarized in Table 5, along with some others for comparison. The data for P-CD are plotted in Fig. 3.

For reasons given earlier (7c), correlations of pKd with chain length (N) may be treated as linear free energy relation- ships (LFERs) whose slopes are measures of the sensitivity of binding to structural change in the guests. In the present case, the slopes are in the range 0.4-0.6 (Table 5, Fig. 3), corresponding to free energy increments of 0.55-0.82 kcaYmol for each CH, group that is sequestered by the CD. These increments are close to those (0.7-0.9 kcallmol) found for the trans- fer of simple aliphatics from water to organic solvents (27). Given this observation, one might infer that hydrophobic interactions (27) largely determine the binding of aliphatics to CDs in aqueous solution but one must recognize that the size and surface area of alkyl chains also increase linearly with N, so that van der Waals interactions (4) may contribute to the chain length dependence, as well. Consistent with this latter view, we have found that the binding of nitrophenyl alkanoate esters to both a-CD and P-CD shows a significant, but reduced, dependence on chain length in 60% aqueous DMSO, even though hydrophobic effects are largely absent in this medium (28).

We now compare the binding of aliphatics to Hp-P-CD and P-CD, to see the effects of hydroxypropylation nf the primary hydroxy groups of P-CD. For a given n-alkylamine, the strength of binding to the two CDs is very similar, being mar- ginally greater for P-CD (Table 4). Both CDs show good linear correlations of pK, with the chain length of the alkylamines, with similar slopes of -0.5 (Table 5), and so the pK, values for binding to P-CD and to Hp-P-CD are strongly correlated (I; = 0.997), with near unit slope (0.95 ? 0.05). In

"' At greater chain lengths, complications set in. First, the chain length dependence of pK, levels off (6,7c, 7f, 14, 15), presumably because of the finite depths of the CD cavities. Second, the intrusion of 2: 1 (CD:guest) binding becomes increasingly significant, even at fairly low [CD] (e.g., 7b, 7d, 7e, 14c).

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Table 4. Dissociation constants of guest-cyclodextrin complexes determined by the displacement of a fluorescent probe."

K,, m M

P-CD Hp-P-CD

Guest This work Lit" This work Litc

(a) Alcoholsd tz-PrOH n-PentOH n-HexOH iso-PrOH cycloHexOH

(b) Amines' n-Propylamine n-Butylarnine tz-Pentylamine n-Hexylamine n-Heptylamine n-Octylamine n-HexNMe, Cyclopentylamine Cyclohexylamine

HO(CH2)3NH2 Morpholine N-Methy lrnorpholine N-Ethylmorpholine Piperidine

(c) a-Amino acidsk L-Alanine L-Valine L-Leucine L-Cysteine L-Tryptophan L-Tyrosine L-Pheny lalanine DL-Norvaline DL-Norleucine

v. large 255 f 15 107 f 5

> l o o 0 45.1 f 1.6 55.8 f 10.0 19.8 f 2.1 -2500 158 f 3 0

"At 25'C, in aqueous buffers, as noted below. q h e literature values for alcohols and P-CD were obtained by a dye

displacement method (13). 'From inhibition kinetics, canied out at pH 11.6, taken from Table 1.

a 0.2 M phosphate buffer of pH 11.6. 'Earlier workers (17, 20, 23) obtained values of 2.0, 1.4, and 2.2 mM, using

similar methods based on the displacement of the ANS. /Five of the amines (n-propyl, n-butyl, n-pentyl, cyclopentyl, cyclohexyl) were

studied in their own buffers, adjusted to pH 11.6. The other amines were determined in the phosphate buffer of pH 1 1.6.

gObtained by Kano et al. (24) using the dye displacement method (130). "Determined by an indicator displacement method, using p-nitroaniline (25). 'Forms a complex that precipitates from solution. 'From an experiment with [amine], = 0-33.4 mM. Since the cited value did not

lead to acceptable analysis in an aminolysis experiment. a second experiment, with [amine], = 0-28.6 mM, was canied out, but it gave the same value: K, = 5.21 f 0.59 mM.

'In a buffer of the amino acid, adjusted to pH = 9.88.

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Table 5. Chain length dependence of the binding of aliphatic guests to cyclodextrins. Correlations between pK, and the alkyl chain length, N."

Guests C D N Slope f s.d. r Note

R O H P-CD Hp-P-CD

R C H ( 0 H ) M e P-CD Hp-P-CD

RCO; P-CD RS0,- P-CD

Hp-P-CD RNH? P-CD

Hp-P-CD R C O M e P-CD

Hp-P-CD

"In aqueous solution at 25°C. The slope, standard deviation (s.d.), and correlation coefficient (r) are taken from linear least-squares analysis of pK, against N.

hBased on results given by Matsui et al. (13). For the I-alkanols, the points for methanol and ethanol were not included because we suspect that their K, values are distorted due to the binding of more than one guest molecule, since this is evident at high [guest].9

'From K, values determined in this work (Table I or Table 4). "From K, values determined in earlier studies in this laboratory (8). 'Based on data given in Table 1, taken largely from Satake et al. (14). Qesults submitted for publication."

Fig. 3. Correlations of the binding o f linear aliphatics to P - C D with alkyl chain length, N. The points are R-OH, A; RCH(OH)Me, .; R-C0,- , 0; RS0,- , A; R-NH,, e; R-COMe, 0 . There are similar correlations for Hp-P-CD (see Table 5).

fact, similar correlations are found for other alkyl derivatives, and in a communication (29) we noted a strong correlation between the pK, values for a collection of 28 aliphatics binding to P-CD and H p - P - C D , with unit slope. With the addition of new results, this correlation can now be extended to 54 derivatives, comprising 18 alcohols, 10 aryl alkanoates, 5 alkanesulfonate ions, 8 amines, and 13 ketone^,^ for which the slope = 1.01 t 0.03, intercept = -0.11 t 0.14, and r = 0.983 (Fig. 4). The collection of guests includes some branched and cyclic compounds (e.g., Tables 1 and 4) and without these the

Fig. 4. Correlation between the binding of aliphatics to Hp-P- C D and to P-CD. The solid diagonal line is for pK, (Hp-P-CD) = pKd (P-CD); the adjacent broken line is the actual correlation line (see text). T h e points are a s follows: nitrophenyl alkanoates, 0 ; alcohols, *; RS0,- , A; arnines, .; ketones, 0.

correlation is decidedly better (r = 0.991, 42 points), but the slope is essentially unchanged (1.04 5 0.02). Thus, to a very good approximation, the strength of binding of simple aliphatics to P-CD and Hp-P-CD is the same, and the closeness of the K, values for the two CDs implies that the guests enter from the wider opening of the CD cavity that is rimmed by second- ary hydroxy groups ( 3 , and that the guests do not penetrate far enough into the cavity to interact strongly with the groups on the other side.

Apparently, a similar situation exists for other types of guests binding to Hp-P-CD. For example, 4-(2-pyridy1azo)- N,N-dimethylaniline binds equally well to Hp-P-CD and P- CD (30), as do the tetraphenylborate ion and BF,- (15). For two naphthalene derivatives, 1- and 2-naphthyl acetate, binding to Hp-P-CD is about twice as strong as that to P-CD (3 1). By contrast, we note that ANS binds to Hp-P-CD 16 times more strongly than to P-CD (Table 2) but for a related fluorescent probe, 2-p-toluidino-6-naphthlenesulfonate ion, binding by Hp-P-CD is only slightly (about 15%) stronger (15b).

Recently, Hamasaki et al. (32) prepared substituted CDs that are functionalized with a p-dimethylaminobenzamido group in place of one of the primary hydroxyls. These derivatives exhibit TICT fluorescence, which can be altered by the binding of guests in the CD cavities. Of relevance to the present discussion, we note their P-CD derivative binds aliphatic alcohols 1.4 to 4 times stronger than unfunctionalized P-CD. So, as with H p - P - C D , the modification on the primary side of P-CD does not cause a large positive or negative effect on the inclusion of guests, even though it is envisaged that inclusion of the guest forces the fluorophoric group out of the cavity and into the bulk medium (32). The effects of "cap- ping" of the primary side of the P-CD cavity are more variable, depending on the nature of the "cap" and the type of guest that is included, but in many cases the effects on the strength of binding are relatively small (33).

In addition to the correlations discussed above, other fea-

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Table 6. Example of estimation of a dissociation constant by inhibition kinetics. Inhibitor = n-BuOH; [Hp-P-CD], = 2.00 mM; ester = rnNPA; k, = 0.0502 s-I; kc = 0.956 s-'; Ks = 6.98 mM."

[ ~ I o , kobs, krca~l LCD], [PI], K*, rnM S-' s-l rnM rnM rnM

Average: 64.0" Standard deviation k1.0

"At 25"C, in 0.2 M aqueous phosphate buffer of pH 11.6. For this [CD],, the expected k <,,,, = 0.252 s-' and so k,,,, is scaled to this, as follows: k,,, = k,,,(0.252)/(0.237). I t should be understood that the actual spreadsheet carried more significant figures.

"For t h ~ s set of data the graphical method also works very well, glvlng K, = 64.7 + 0.8 mM.

tures of the present results are noteworthy. For example, K, for n-HexNMe, binding to Hp-P-CD is virtually the same as that for n-HexNH, and Hp-P-CD. In fact, this type of situation is common since the K, values for alcohols (ROH), alkanoate ions (RC0,-), and alkanesulfonate ions (RS0,-) having the same alkyl groups are comparable (Fig. 3), and the binding of the analogous amines (RNH,) is only slightly stronger (Tables 1 and 4, Fig. 3). Also, all the alkyl derivatives show very similar sensitivities to changes in chain length (Table 5). Taken together, these similarities must mean that the binding of such aliphatic guests is almost solely due to inclusion of their alkyl groups and that the hydrophilic end groups of the bound guests are sufficiently outside the CD cavity that they do not interact strongly with its rim. These are useful observations that may be utilized to estimate K, values prior to their determination.

Conclusions

In this work, and in earlier studies (6,7c-f), we have noted various correlations of pK, with alkyl chain length, as well as the strong correlation between the pK, values for the binding of alkyl-bearing compounds to Hp-P-CD and P-CD, with unit slope (Fig. 4). Such correlations have great predictive value for the purposes of planning experiments and for estimating K, values that may be difficult to determine. At the same time, in combination with other types of studies (4), they may provide information about modes of binding and contribute to our understanding of the factors involved in host-guest complexation in aqueous solution.

Experimental

The cyclodextrins were purchased from Aldrich and from Wacker Chemie, and were used as received. The "hydroxypropyl-P-cyclodextrin" had an average molecular weight of 1500, corresponding to alkylation of six of the seven primary OH groups of P-CD by 2-hydroxypropyl groups. We found no

appreciable difference in the behaviour of Hp-P-CD from the two suppliers. Most of the other reagents were purchased from Aldrich and used as supplied.

For the inhibition method of determining K,, the kinetics of the cleavage of mNPA in the presence of several concentrations of inhibitor ([inhibitor]) were followed by monitoring the first-order appearance of the nitrophenolate ion at 390 nm, in a stopped-flow spectrophotometer with the temperature of the cell kept at 25.050.l0C, as previously (8c). The rate constants for various [inhibitor], were analyzed as outlined in the main text, using a spreadsheet to do the calculations, as shown by the example given in Table 6.

To determine dissociation constants of amineCD complexes we used competition between the amines and the fluorescent probe ANS for the CD (17-23). First, dissociation constants (KANS) for the CD.ANS complexes were determined in a basic solution, the same as that to be used with the amines. A solution containing a CD (0-20 mM for P-CD or y-CD; 0-40 mM for Hp-P-CD) in a 0.4 M sodium phosphate - NaOH buffer of pH 11.60, and a solution containing 200 p,M ANS were mixed (1: 1) in a stopped-flow apparatus, yielding final concentrations half of the foregoing. The observation cell was irradiated at 383 nm, and the fluorescence was measured at either 474 nm (P-CD), 468 nm (Hp-P-CD), or473 nm (y-CD). These wavelengths may not correspond to the actual fluorescence maxima of the CD-ANS complexes, but they were found to be the best for our apparatus, an Applied Photophys- ics SX17MV spectrofluorimeter. Uncorrected fluorescence values, obtained as the averages of several scans, were then converted into relative fluorescence, using F,,, = IobslIo, where I, is the fluorescence intensity at zero [CD]. Analysis of the F,,, values at several [CD] (Fig. 1) were carried out by nonlinear regression of eq. [9] (34), giving the fitted constants F, and KANs in Table 2.

Several experiments were carried out on the binding of ANS to P-CD, with variable results. Depending on the range of [P-CD] used, we obtained KANs values ranging from 12 to 50 mM, but most were between 20 and 35 mM, with the high- est values coming from experiments where [P-CD] was taken up to 30 m ~ . " In general, we found that eq. [9] gave good fits to the fluorescence data only when [P-CD] < 15 mM, probably because of the intrusion of 2: 1 binding at high [CD]. Accord- ingly, we have used the value of 26.8 + 1.3 mM, obtained from the data with LCD] in the range 0-10 mM, as shown in Fig. 1, and we restricted all further experiments to the same [P-CD] range. By contrast, ANS with Hp-P-CD gave well- behaved fluoresecence data for [CD] up to 20 mM (Fig. 1).

Dissociation constants for the amines complexing with P- CD or Hp-P-CD were obtained as follows. Solution 1 contained the amine and, where necessary, 10 mM P-CD. For most of the amines, this solution was prepared in a 0.4 M phosphate buffer, and adjusted to pH 11.60. In the case of 11-propylamine, n-butylamine, n-pentylamine, cyclopentylamine, and cyclohexylamine, the solutions were prepared in water and set to pH 11.60, using the amine as the buffering species. Solution 2 contained CD (P-CD, 10 mM or Hp-P-CD, 5.0 mM) and ANS in water. Both solutions were then mixed to

" The normal solubility of P-CD in water is about 16 rnM (5), but higher concentrations are attainable in a strong phosphate buffer ofpH 11.6.

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give final concentrations of 10 mM P-CD + 50-100 p M ANS or 2.5 mM Hp-P-CD + 25 pM ANS. Amine concentrations, which were governed primarily by solubility, varied between 0 and 250 mM (3-amino-1-propanol) and 0 and 5.2 mM (n-octylamine). The mixed solution in the observation cell of the spectrofluorimeter, maintained at 25.0 2 0. l0C, was irradiated at 383 nm, and the fluorescence intensity (I,,,) was taken as the average of several scans at 474 nm (P-CD) or 468 nm (Hp-P-CD) for each [aminel,.

For estimation of K, values (e.g., Table 3), the observed fluorescence intensities, lob, (column 2, Table 3), must first be scaled to bring them into line with the previous ANSICD "cal- ibration" curves described by eq. [9] with the parameters in Table 2. From the initial [ANSI, and [CD],, the actual [ANSI was calculated by solving the quadratic that is obtained by expansion of:

- [ANSI)

Using this [ANSI, [CD] was then found from [CD], - ([ANSI, - [ANSI) and a reference fluorescence (Fref) was evaluated from eq. [9]. This Frtf was set equivalent to the observed fluorescence intensity with no guest present (Ing), and the other lobs were converted to relative fluorescence values using FreI = Iob,.Fref 11, (column 3, Table 3). These values of Frel were then used to cafculate values of [CD] from eq. [lo] for the various [guest], (column 4, Table 3), from which estimates of K, were obtained using eq. [7] (column 7, Table 3). All of these manipulations were carried out in a spreadsheet designed for the purpose.

Dissociation constants for complexation of the amino acids by P-CD were also determined as above, with minor differ- ences. The solutions were set to pH 9.88, to correspond to other experiments (26), using the amino acid as the buffering species. The concentration ranges of the a-amino acids varied between 0 and 200 mM (L-valine, L-cysteine, and DL-norvaline) and 0 and 5.0 mM (L-tyrosine).

Prompted by a referee's comment, we have referred to a paper by Selvidge and Eftink (9a) in which they point out some of the same problems that we do and they present an analysis of the use of various concentrations, [guest], and [probe],, in relation to the strengths of guest and probe binding. When they estimate guest binding constants, using their equations [lo]-[12], they correct for [probe-CD]. So do we in the fluorescence method, but it only makes a difference of 1 % a t most, for the lowest [guest], of the strongest binding guest that was studied. When using the inhibition method, developed earlier (8a,b), we did not make this correction, but even there it would only make a difference of 2% in the worst case. The major difference between our approach and that of Selvidge and Eftink (9a) is that they used double-reciprocal plots to find the binding constants of their spectroscopic probes, whereas we prefer to use nonlinear fitting.

Acknowledgement We thank the Natural Sciences and Engineering Research Council of Canada for an operating grant, a post-graduate scholarship, summer student awards, and an equipment grant.

We also thank Professor Susan Mikkelsen for several helpful discussions.

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dissociation constants of host–guest complexes of alkyl-bearing compounds with β-cyclodextrin and...

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