Complexation Thermodynamics of Modified Cyclodextrins: Extended

Article pubs.acs.org/JPCB

Complexation Thermodynamics of Modified Cyclodextrins: Extended Cavities and Distorted Structures Christian Schönbeck,†,‡,§,∥ Peter Westh,† and René Holm*,‡ †

NSM, Research Unit for Functional Biomaterials, Roskilde University, Universitetsvej 1, DK-4000 Roskilde, Denmark Biologics and Pharmaceutical Science, H. Lundbeck A/S, Ottiliavej 9, DK-2500 Valby, Denmark § Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark ∥ Sino-Danish Center for Education and Research (SDC), Niels Jensens Vej 2, DK-8000 Aarhus C, Denmark ‡

S Supporting Information *

ABSTRACT: Inclusion complexes between two bile salts and a range of differently methylated β-cyclodextrins were studied in an attempt to rationalize the complexation thermodynamics of modified cyclodextrins. Calorimetric titrations at a range of temperatures provided precise values of the enthalpies (ΔH°), entropies (ΔS°), and heat capacities (ΔCp) of complexation, while molecular dynamics simulations assisted the interpretation of the obtained thermodynamic parameters. As previously observed for several types of modified cyclodextrins, the substituents at the rims of the cyclodextrin induced large changes in ΔH° and ΔS°, but due to enthalpy−entropy compensation the changes in Gibbs free energy, and the binding constant, were much smaller. For the methylated β-cyclodextrins, the substituent-induced increments in ΔH° and ΔS° were nonmonotonic with an initial strong increase in both ΔH° and ΔS° and then a strong decrease when the degree of substitution exceeded some threshold. Exactly the same trend was observed for ΔCp. The dehydration of nonpolar surface, as quantified by the simulations, can to a large extent explain the variation in the thermodynamic parameters. The methyl substituents form additional hydrophobic contacts with the bile salt, but at high degrees of methylation they also cause significant distortion of the otherwise circular cyclodextrin structure. These two opposing contributions to the dehydration are the major causes for the observed variations in the thermodynamic functions. The structural effects are not expected to be specific for methylated cyclodextrins but should be observed for most modified cyclodextrins. An even more general conclusion is that variations in the extent of hydration are an important underlying reason for the commonly observed phenomenon termed enthalpy−entropy compensation and also for the less frequent reports of entropy convergence around 110 °C.

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INTRODUCTION

host:guest systems can be readily studied by isothermal titration calorimetry (ITC), which provides precise values of the binding constants as well as direct determination of the binding enthalpy and stoichiometry. These host:guest systems may therefore serve as good model systems from which more general knowledge about the thermodynamics of CD inclusion complexes may be obtained. One of the main hypotheses in our work so far is that the enthalpy and entropy of complexation (ΔH° and ΔS°) strongly depends on the buried hydrophobic surface area. The substituents at the rims of the modified CDs form additional hydrophobic contacts with the guest molecules and thereby increase the buried surface. Burial of hydrophobic surface leads to an increase in ΔH° and ΔS°, as exemplified by the complexes of 2-hydroxypropylated βCDs (HPβCDs) where each HP substituent on average adds around 3 kJ/mol to the enthalpy

Cyclodextrins (CDs) is a highly studied class of macrocycles whose structures consists of glucose units linked by 1,4-αglycosidic bonds (Figure 1). Like other macrocycles, they are capable of forming inclusion complexes with a large range of guest molecules, and their good aqueous solubility makes them interesting as pharmaceutical solubilizers,1,2 among other applications.3 Possible driving forces for the formation of CD inclusion complexes have been extensively discussed in the literature, and although there is some disagreement about the importance of the various contributions, there seems to be consensus that hydrophobic interaction is an important and general driving force.4,5 We have previously studied inclusion complexes between bile salts (BSs, Figure 2) and various pharmaceutically important classes of modified CDs, as well as the natural α, β-, and γCDs (Figure 1).6−12 The focus on BSs as guest molecules was initially motivated by their biological importance for the release of drugs from CD complexes when dosed orally.13 It turned out that these © 2014 American Chemical Society

Received: June 17, 2014 Revised: July 18, 2014 Published: August 5, 2014 10120

dx.doi.org/10.1021/jp506001j | J. Phys. Chem. B 2014, 118, 10120−10129

The Journal of Physical Chemistry B

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ΔS° strongly decrease with increased substitution (Figure 3). Consequently, the complexes of the per-methylated βCD are the

Figure 1. Schematic structures of the cyclodextrins whose complexes with bile salts have been investigated in the present or previous works. Cyclodextrins with 6, 7, and 8 glucose units are named α-, β-, and γcyclodextrins, respectively. Only mβCDs are investigated in the present work and their detailed structures are given Table 1.

Figure 3. Enthalpy and entropy for the complexation of mβCDs with GDC (filled circles) and GCDC (filled triangles) at 25 °C plotted as a function of the degree of substitution of the mβCDs. Previously measured data for a larger set of mβCDs7 are shown as open circles and triangles. The broken lines are theoretical values of TΔS°, predicted from the theoretically determined changes in hydrophobic surface area.

most exothermic of all, but they are severely destabilized by very unfavorable entropy changes.7 (iii) The mβCDs are better structurally characterized with respect to the pattern of substitution than the HPβCDs,7 thus allowing for a better comparison of theory (MD simulations) and experiment (ITC). The overall purpose of the present work is to gain a better understanding of the complexation thermodynamics of modified CDs. Thermodynamic data, including values of ΔCp, were generated by ITC, and MD simulations were conducted to assist the structural interpretation.

Figure 2. Chemical structures of the investigated bile salts.

of complexation with BSs.6 Thus, the complexation of BSs with the highly substituted HPβCDs is almost athermal, while the process is quite exothermic (ΔH° = −25 to −31 kJ/mol) for natural βCD.6,7 Changes of a similar magnitude are observed for TΔS°, and it follows that the Gibbs free energy of complexation (ΔG°) is almost independent of the degree of substitution (DS). Partial cancellation of changes in ΔH° by similar changes in TΔS° is called enthalpy−entropy compensation and is a widely observed, and debated, phenomenon.14,15 We have previously quantified the buried hydrophobic surface in complexes of HPβCDs by (i) an osmotic stress technique,16 (ii) complexation induced heat capacity changes (ΔCp), and (iii) molecular dynamics (MD) simulations.10 All three approaches showed that the buried hydrophobic surface area increases with the number of HP substituents, and it was estimated that each HP substituent buries around 12−16 Å2.10 As mentioned above, this increase in hydrophobic contacts only brings about small changes in ΔG°, and thorough analysis in fact showed that the stabilities of the complexes slightly decrease with increased substitution.6,10 To further explore the relations between structure and complexation thermodynamics, the present work focuses on inclusion complexes between methylated βCDs (mβCDs) and BSs. In addition to being an important class of pharmaceutical excipients,2 mβCDs are interesting for several reasons: (i) A large variety of differently substituted mβCDs are available, covering the whole range from natural βCD to the per-methylated βCD. (ii) The thermodynamics of mβCD:BS complexes exhibit an interesting trend.7 At low and intermediate degrees of substitution, ΔH° and ΔS° increase linearly with the DS, resembling the trend observed for the HPβCDs. However, a turning point is observed at a DS around 1.7 after which ΔH° and

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EXPERIMENTAL SECTION Materials. The bile salts glycodeoxycholate (GDC) and glycochenodeoxycholate (GCDC) with a purity of at least 97% were purchased as sodium salts from Sigma-Aldrich (St. Louis, MO). The natural βCD (purity ≥99%), heptakis(2,6-di-Omethyl)-βCD, and heptakis(2,3,6-tri-O-methyl)-βCD (purity ≥99%) were also purchased from Sigma-Aldrich. Two samples of randomly methylated βCDs with reported DS of 0.6 and 1.8 were acquired from Wacker Chemie (Burghausen, Germany). We have previously characterized the degree and pattern of substitution of these CDs by MALDI-TOF mass spectrometry and NMR, and the results are summarized in Table 1.7 The names of the CDs in the following reflect the total degree of substitution which is defined as the number of methyl substituents per glucose unit. Thus, mβ167 is a methylated βCD with an average of 1.67 methyl groups on each glucose unit. Milli-Q water was used for the solutions. All other chemicals were of analytical grade or higher. Isothermal Titration Calorimetry. Isothermal titrations were conducted at 10-deg intervals in the temperature range 5− 55 °C on a VP-ITC titration calorimeter from MicroCal, Northhampton, MA (now GE Healthcare Life Sciences). The solutions were made by weighing out the dried powders of BSs and CDs and dissolving in 50 mM phosphate buffer, pH 7.1. A 10121



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engage in other nonspecific interactions. The One Set of Sites model provides one value for the binding constant, K, the binding enthalpy, ΔH°, and the stoichiometry, N. It is established that GCDC forms 1:1 complexes with mβCDs while GDC may bind a second CD with weaker affinity.7 However, when we used our previously developed approach8 to test for a secondary binding site on GDC, no reliable or meaningful parameters were obtained for the secondary binding site. [The Two Sets of Independent Sites binding model, which we previously used to quantify the weak secondary binding interaction of βCD with GDC,8 is probably not very well suited for describing the interaction of mβCDs with GDC as the bulky methyl substituents inevitably will result in strong negative cooperativity between the two binding sites.] For this reason, the One Set of Sites binding model was also used to analyze the titrations of GDC. It may seem natural to keep N fixed on 1, but it often serves as a concentration correction factor and was therefore used as a floating fitting parameter.22 For each of the complexes, six titrations at six different temperatures were conducted. Instead of analyzing each of these titrations individually to obtain six different sets of K, ΔH° and N, all six titrations were simultaneously fitted by a global model that takes the theoretical temperature dependence of K ((d ln(K))/ dT = ΔH/RT2) and ΔH° ((d ΔH)/dT = ΔCp) into account.8,10 This model yields one value of K and ΔH° at a reference temperature (which for convenience is set to 25 °C), one value of ΔCp (which is assumed to be constant across the investigated temperature range), and six values of N (an individual value for each titration to accommodate concentration errors and variations in the conduction of the experiment). In other words, the global model restricts the parameter space to ensure that van’t Hoff and calorimetric enthalpies are equal. The ability of the global model to fit all of the six titrations for each complex is a strong validation of the binding model and increases the precision of the obtained thermodynamic data.8 The fit of the global model to the experimental data is shown in Figure 4 and Figures S-1 to S-6 in the Supporting Information, and the obtained thermodynamic parameters are summarized in Table 2. In most cases, good fits to the experimental data are obtained, resulting in precise values of the thermodynamic parameters and consistent values of N. Only for the GDC:mβ212 complex a systematic deviation is observed (Figure S-4 in the Supporting Information) which is attributed to a poor correction for dilution enthalpy (further discussion in the caption of Figure S-4). The measured ΔH° and TΔS° at 25 °C are plotted in Figure 3 along with previous data obtained from single titrations at 25 °C.7 The dependence of the thermodynamic data on the DS follows the already mentioned trend with an initial linear increase in both ΔH° and TΔS° and then an abrupt reversal of the trend. Interestingly, the presently reported values of ΔCp exhibit exactly the same trend, as shown in Figure 5. For complexes between HPβCDs and BSs, ΔCp also follows ΔH° and ΔS° and decreases linearly with the DS,10 but for the mβCD:BS complexes a turning point is observed, and this turning point is observed for all three thermodynamic functions. This correlation suggests that the variations in each of the thermodynamic functions share the same underlying cause. Molecular Dynamics Simulations. The simulated CDs were designed to resemble the CD samples used in the ITC experiments with respect to the degree and pattern of substitution. The number and position of the methyl substituents on the simulated CDs are given in Table 1 along with the degree and pattern of substitution of the experimental CD samples.

Table 1. Cyclodextrins Used in ITC Experiments and Modeled in MD Simulations name of CD sample used in ITCa

name of CD modeled by MDa

O2 substitution in the modeled CDs at glucose units no.b



βCD mβ067

bCD mb071

− 5 (0.14; 0.19)

− 4 (0.14; 0.10)

mβ167

mb171

mβ212

mb200 mb214 mb300

− 1, 3, 6 (0.43; 0.38) 1, 2, 4, 6 (0.57; 0.63) all (1) all (1; 1) all (1; 1)

1, 3, 6 (0.43; 0.37) − 1 (0.14; 0.12) all (1; 1)

1, 3, 4, 5, 7 (0.71; 0.67) all (1) all (1; 1) all (1; 1)

mβ300 a

The names of the CDs contain the total degree of substitution (DS) which is defined as the average number of methyl groups per glucose unit. Thus, the per-methylated βCD is named mβ300 (3.00 methyls per glucose unit). For the simulated CDs the letter “b” is used instead of the Greek letter “β”. bThe numbers in the parentheses indicate the DS on each of the three substitution sites O2, O3, and O6. Thus, 0.57 means that each glucose unit on average contains 0.57 methyl groups on that particular oxygen. To compare the site-specific DS of the simulated CDs to the experimental ones, this number is shown in italics for the latter.

solution of CD (2.5−10 mM) was injected into a solution of BS (0.25−1 mM) in 28 aliquots of which the first was 2 μL and the remaining were 10 μL. Reference titrations of CD into buffer solution were made in the same way and subtracted from the CD into BS experiment. The heat peaks were integrated using the Origin 7.0 add-on that came with the calorimeter and then copied into a data file. The first data point corresponding to the 2 μL injection was not included in the subsequent regression analysis which was conducted in Matlab (version 2007b, MathWorks). Molecular Dynamics Simulations. The simulations were carried out in water boxes as previously described in detail.10 As the simulations of free BSs and free βCD have already been carried out in our previous work,10 it was only necessary to do simulations of free mβCDs and their complexes with the BSs GDC and GCDC. Simulations were run in NAMD version 2.917 and analyzed in VMD18 which was also used to generate the psf and pdb input files. Force field parameters for the mβCDs were from the CHARMM package19 and the CHARMM32 ether force field,20 while for the BSs, sodium ions, and TIP3P waters the CHARMM27 force field21 was used. Simulations of free mβCDs were run for 30 ns and simulations of complexes were run for 20 ns. After 5 ns of equilibration, the sampling of relevant structural information started. Calculation of water accessible surface area (ASA) was done in VMD18 using a spherical probe of radius 1.4 Å. ASA was calculated every 25 ps and averaged over the sampling interval. ASA was divided into polar and nonpolar surface area (ASApol and ASAnon) by defining oxygen, nitrogen, and attached hydrogens as polar, while carbons and attached hydrogens are nonpolar.

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RESULTS Isothermal Titration Calorimetry. The One Set of Sites binding model, which assumes a single set of identical and independent binding sites on the BS, was capable of fitting all of the ITC data, except for the titrations of GDC with mβ300 which resulted in small heat signals at all temperatures. Most likely, GDC and mβ300 do not form an inclusion complex but may still 10122



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Figure 5. Heat capacity changes induced by the complexation of mβCDs with GDC (filled circles) and GCDC (filled triangles) at 25 °C plotted as a function of the degree of substitution of the mβCDs. The broken lines are theoretical values of ΔCp, predicted from the theoretically determined changes in hydrophobic surface area.

simulated mbCDs, the 180° rotation was only observed for mb200 and mb214. All of these distortions were transient, and the CDs occasionally returned to their initial circular structures, except for mb300 which became very distorted within the first nanosecond and more or less remained in this distorted conformation for the rest of the simulation. As a measure of the tilting of glucose units with respect to adjacent glucose units, the O5−C1−C4−C5 dihedral angle was monitored.23 In the undistorted CD structure this angle is close to 0°. The O5−C1−C4−C5 dihedral angles were extracted from the trajectories and plotted as histograms in Figure 6 and Figures

Figure 4. Six calorimetric titrations of GCDC with mβ067 conducted at 10 K intervals from 5 °C (top) to 55 °C (bottom). The global One Set of Sites model was fitted to the titrations to give the binding parameters shown in the table. The values of N are 0.926, 0.932, 0.927, 0.934, 0.925, and 0.935.

Table 2. Complexation Thermodynamics of the Studied Complexes BS GDC

GCDC

CD

K at 25 °C (mM−1)a

ΔH at 25 °C (kJ/mol)a

ΔCp (J/mol/K)a

βCDb mβ067 mβ167 mβ212 mβ300c βCDd mβ067 mβ167 mβ212 mβ300

5.67 ± 0.05 5.71 ± 0.08 3.88 ± 0.05 7.5 ± 0.2 NA 156 ± 2 175 ± 1 137 ± 2 136 ± 2 2.63 ± 0.04

−28.50 ± 0.06 −20.9 ± 0.1 −11.06 ± 0.07 −20.1 ± 0.2 NA −30.94 ± 0.08 −27.33 ± 0.04 −21.36 ± 0.07 −26.78 ± 0.09 −33.6 ± 0.4

−271 ± 3 −396 ± 6 −534 ± 6 −432 ± 10 NA −484 ± 4 −518 ± 2 −650 ± 3 −598 ± 4 −564 ± 20

a

Thermodynamic parameters for the formation of inclusion complexes between cyclodextrins and bile salts were obtained from the global fit of the One Set of Sites model to six calorimetric titrations in the temperature range 5−55 °C. The listed errors are the 95% confidence intervals. bData from ref 8. cmβ300 and GDC do not seem to form an inclusion complex. dData from ref 10.

Note that the names of the simulated CDs contain a “b” instead of the Greek letter “β” which is reserved for the experimental CDs. Methylation Distorts the Structure of Free CDs. During the 30 ns simulations of the free (uncomplexed) CDs, the most noticeable feature was the increased distortion of the circular CD structure with increased methylation. This was primarily manifested in the tilting of glucose units; 90° tilt angles were often observed and occasionally a 180° rotation of a single glucose unit took place such that O2 and O3 of that particular glucose unit appeared on the primary (narrow) rim and O6 at the secondary (wide) rim. While 90° tilts were observed for all of the

Figure 6. Histograms of O5−C1−C4−C5 dihedral angles calculated from the trajectory of the free mb214. Histograms for each of the seven dihedrals are shown as dashed lines and the average is shown by the thick line.

S-7 to S-14 in the Supporting Information. The figures clearly show that methylation promotes rotational mobility around the glycosidic bonds. To quantitatively compare the various CDs, the total distortion was defined as the average displacement of the O5−C1−C4−C5 dihedrals from the equilibrium value at 0°. This quantity is plotted in Figure 7. Even though increased 10123



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Figure 8. Snapshot from MD simulation of the complex between mb171 and GCDC. The carbon atoms on GCDC are black while the carbons on mb171 are in cyan. Hydrogens, oxygens, and nitrogen are colored white, red, and blue, respectively. Similar structures were observed for all of the complexes. Figure 7. Average distortion of the glycosidic bonds in the free CDs (closed squares) and in the CDs complexed with GDC (open circles) and GCDC (open triangles).

type of substituents on the CD hardly affect the location of the CD on the BS. However, analysis of the MD simulations revealed subtle but systematic differences in the binding modes of the methylated CDs. It has previously been shown that GCDC is deeper included in the CD than GDC due to the lack of a hydroxyl group on C12 of the former BS.7,31,33 Using the distance between the center of mass of the glycosidic oxygens and the center of mass of C17 and C20 on the BS as a rough measure of the inclusion depth, the above-mentioned observation was reproducedexcept for the highly methylated CDs that included GDC deeper than GCDC (Figure 9). The increased

distortion with increased methylation is the general trend, mb200 undergoes surprisingly few distortions compared to mb171 and mb214. Conversely, the structure of mb214, which differs from mb200 by a single methyl group at O3 (see Table 1), undergoes strong structural distortions. This indicates that methylation at O3 disturbs the circular CD structure much more than methylation at O2. To our knowledge, no direct experimental evidence of through-the-cavity rotation of glucose units in mβCDs has yet been obtained, but rotation of one or more glucose units has been observed in other modified βCDs.24 It is widely believed that disruption of the belt of intramolecular hydrogen bonds within the CD leads to more flexible CDs, so it seems plausible that also methylation may lead to rotating glucose units. A number of molecular dynamics studies of mβCDs have been published, and while some report increased flexibility and occasional through-the-cavity rotation of glucose units,23 others do not observe increased flexibility25 or do not mention this issue.26 On the experimental side, X-ray crystallography of mβ300 monohydrate reveals a significantly distorted structure, in which the characteristic round shape of the CD is converted into an irregular elliptical shape with a reduced cavity volume.27 Further, it has in several cases been observed that the NMR peaks of C1 and C4 in highly methylated CDs are shifted significantly downfield upon inclusion of guest molecules, while the same is not observed for natural CDs. Since these two particular carbon atoms are located next to the glycosidic bonds, this observation has been interpreted in terms of increased flexibility of the highly methylated CDs.7,28,29 An NMR study of natural and permethylated CDs in solution also concludes that mβ300 is significantly deformed.30 Structure of Complexes. Starting from the initial structures, in which the nitrogen on the BS was located at the center of mass of the CD, it took less than 1 ns for the CDs to move onto the Dring of the BS steroid structure and the innermost part of the conjugation tail (Figure 8). This position was largely maintained for the rest of the simulation time. This binding site was also observed by molecular docking calculations,31 MD simulations of BS complexes with natural βCD, HPβCDs, and sulfobutyl ether−βCD,9,10 and is in accordance with the structure deduced from different types of NMR experiments. 7,31,32 Visual inspection of the simulations suggested that the number and

Figure 9. Histogram of inclusion depths as defined by the distance between the center of mass of the glycosidic oxygens on the CD and the center of mass of C17 and C20 on the BS. Histograms for complexes with GCDC and GDC are shown with black and red lines, respectively. The inset shows the average distance as a function of the degree of substitution of the CDs; red circles denote complexes with GDC and black triangles denote complexes with GCDC.

inclusion of GDC in mb214 might explain why the complexes between GDC and mβ212 stand out as extraordinarily stable, while the corresponding complexes with GCDC do not show remarkable stability.7 The histograms of the inclusion depths (Figure 9) also reveal that the binding site on GDC is less localized than on GCDC. While the histograms for the complexes with GCDC all exhibit a narrow and relatively symmetric distribution around 0.7 Å, the histograms for the GDC complexes are broad and asymmetric. The GDC guest molecules are often as deeply included in the 10124



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CDs as the GCDC guests but are frequently pushed somewhat out of the cavity. This agrees well with the much lower stability of the GDC complexes that is observed experimentally.7 Upon complexation, the mobility of the glucose building blocks is severely restricted, and all bound CDs essentially adopted the circular structure of the natural βCD. Histograms of the O5−C1−C4−C5 dihedrals (Figures S-7 to S-14 in Supporting Information) reveal narrow and symmetric distributions around 0°, as for the noncomplexed natural βCD. The average distortion of this dihedral is plotted in Figure 7 as open symbols and is small and constant for all bound CDs, in contrast to the distorted structures of the highly methylated free CDs. Burial of Surface Area. Time-averaged values of the surface area of the free CDs, free BSs, and the complexed species were determined from the MD trajectories. The surface areas were divided into polar surface area (ASApol) and nonpolar surface area (ASAnon). Buried surface area (ΔASA) was calculated as the difference between the free and complexed species. All values appear in Tables S-1 to S-3 in the Supporting Information. The buried nonpolar surface area, ΔASAnon, is plotted against the DS of the CDs in Figure 10A and reveals a trend similar to that observed for ΔH°, ΔS°, and ΔCp (see Figures 3 and 5). First, there is a linear correlation between ΔASAnon and the DS, and then a turning point is observed at DS ≈ 2. The dissection of ΔASAnon into contributions from the burial of BS surface and CD surface (Figure 10, B and C) reveals an interesting observation. The burial of BS surface (Figure 10B) increases with the DS, as the increasing number of methyl substituents at the secondary rim of the CD form hydrophobic contacts with the parts of the BS that protrudes from the central CD cavity. The small break in the otherwise linear trend is most likely due to the lack of methyl groups at the O3 sites in mb200. In contrast to the O2 methyls, which point outward and away from the BS, the O3 methyls predominantly point inward and more effectively bury the BS surface. The plot of buried CD surface area versus DS in Figure 10C shows an initial increase in buried surface area, followed by a sudden drop upon going from mb200 (DS = 2.00) to mb214 (DS = 2.14). This surprising reversal is caused by the loss of structural rigidity of the CD, which also takes place at lower DS, but really sets in after DS ≈ 2. Increased substitution distorts the symmetric structure of the free CDs and decreases the nonpolar wateraccessible surface area. Upon complexation, the change in ASAnon is thereby reduced. To summarize, the shape of the plot of ΔASAnon in Figure 10A is the result of two opposing effects caused by methylation of the CD. On one hand, the methyl groups create additional hydrophobic contacts with the BS, but on the other hand methylation gradually cause the rigidity of the free CD to break down, resulting in a distorted structure of the free CD with a reduced nonpolar surface area.

Figure 10. Change in water-accessible nonpolar surface area, ΔASAnon, plotted against the degree of substitution of the CDs. Circles denote complexes with GDC, triangles denote complexes with GCDC. (A) Total ΔASAnon. The open symbols refer to complexes with mb200 and mb214. For the sake of comparison with the complexes of the experimental CD sample mβ212, which consists of 40% mβ200 and 40% mβ214,7 the data for these two complexes are averaged to give the solid symbols at DS 2.07. (B) Contribution to ΔASAnon from BS. (C) Contribution to ΔASAnon from CDs.

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DISCUSSION Burial of Hydrophobic Surface Dominates Differences in Complexation Thermodynamics. In aqueous solution, the burial, or dehydration, of hydrophobic surface constitutes an important contribution to the observed thermodynamics. Especially the change in heat capacity, ΔCp, seems to scale with the buried surface areaa relation which has been observed in a multitude of phenomena, from dissolution of hydrocarbons in water34 to unfolding of proteins.35 Relatively few studies of CD inclusion complexes, however, report values of ΔCp.36−43 Recently, we studied a range of complexes between HPβCDs and BSs and found that not only ΔCp but also ΔS° and ΔH° is

largely determined by differences in buried nonpolar surface area, ΔASAnon.10 For the present systems, a similar correlation was observed between ΔH°, ΔS°, ΔCp, and ΔASAnon. The plot of ΔASAnon in Figure 10A strongly resembles the plots of ΔH° and ΔS° versus DS (Figure 3) and the plot of ΔCp versus DS (Figure 10125



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On the other hand, it is merely a manifestation of the common knowledge that the reorganization of water molecules near hydrophobic surfaces is associated with large values of ΔS° and ΔCp. These large contributions tend to dominate the picture. Thermodynamics of cavity-bound water molecules is an oftenencountered topic in the CD literature.4,5,36 Due to their restricted motion and limited ability to form hydrogen bonds with other water molecules, cavity-bound water may be thermodynamically very different from “ordinary” hydrophobic surface water. Indeed, experiments suggest that the release of cavity water from αCDs contributes positively to ΔCp, in contrast to the release of hydration waters from the guest, which is associated with a negative ΔCp.36 Likewise, release of trapped water in a protein−ligand complex is expected to give a positive ΔCp.47 Methylation of the CDs gradually distorts the structure and diminishes the cavity to the extent that mb300 does not contain any waters in its (collapsed) cavity, in agreement with the crystal structure.27 Consequently, the number of released cavity waters is expected to decrease from βCD to mβ300, particularly for the CDs with a DS higher than 2. This should cause the experimental ΔCp’s for the complexes of highly substituted CDs to be more negative than what is predicted from ΔASAnon. Such deviation is indeed observed in Figure 5, but there are too many uncertainties to say anything conclusive about this. Enthalpy−Entropy Compensation and Convergence Temperatures. The strong correlation between the experimentally determined thermodynamic functions, ΔH°, ΔS°, and ΔCp, results in two interesting phenomena. First, the linear relation between ΔH° and ΔS°, where a change in ΔH° is accompanied by a similar change in TΔS° (see Figure 3 and Figure S-15 in the Supporting Information), is called enthalpy− entropy (H−S) compensation and is a widely observed phenomenon.14,48,49 There is no consensus, however, on its underlying physical cause(s).15,49−52 The second, and much less frequently reported phenomenon, is the appearance of convergence temperatures.53−55 For a series of similar compounds, the enthalpies and/or entropies of dissolution in water may intersect at a certain temperature. These convergence temperatures are sometimes found outside the experimental temperature range but can be obtained by extrapolation of ΔH° and ΔS° using ΔCp. For example, enthalpy and entropy convergence temperatures (TH* and TS*) for the unfolding of a small group of proteins are both found around 110 °C.53 It seems to be a universal feature that TS* lies around 110 °C, but no common value is found for TH* whose values range from room temperature56 to 110 °C.53 In our study of complexes between HPβCDs and BSs, values of TH* and TS* were found in the vicinity of 110 °C, when the complexes with each BS were treated as an individual series.10 Convergence temperatures occur when ΔH° and/or ΔS° are linearly related to ΔCp and are often illustrated by the use of MPG plots (named after Murphy, Privalov, and Gill), in which ΔH° or ΔS° is plotted against ΔCp.53 The slopes of the plots are determined by the convergence temperatures as seen from eqs 1 and 2, where ΔH*/ΔS* and ΔH/ΔS are the enthalpies and entropies at the convergence temperatures and at the reference temperature, T, respectively.

5). In accordance with our previous conclusions on the complexation thermodynamics of modified βCDs,6,7,9,10 this suggests that the large variations in ΔH°, ΔS°, and ΔCp, observed for the complexation of BSs with various CDs, is primarily due to differences in buried surface area. Increased burial of hydrophobic surface leads to significant increase in ΔH° and ΔS° and more negative values of ΔCp. For the complexes with HPβCDs, this resulted in linear correlations between the degree of substitution and these three thermodynamic functions,7 but for the mβCDs investigated here, the effect of the substituents is more complex due to the larger range in the DS of the investigated CDs. The methyl substituents still cause an increased dehydration of the BS leading to the above-mentioned changes in ΔH°, ΔS°, and ΔCp, but they also distort the structure of the free CD and thereby reduce its hydration and hence the dehydration of hydrophobic surface upon complexation. Consequently, the thermodynamic functions, ΔH°, ΔS°, and ΔCp, which seem to be closely related to ΔASAnon, exhibit an initial linear increase/decrease but then encounter a turning point around DS = 2 where the increase/decrease is reversed. The theoretically obtained values of ΔASAnon are in qualitative agreement with the experimental data and reproduce the turning points observed for ΔH°, ΔS°, and ΔCp. To test if the values of ΔASA non are also in quantitative agreement with the experimental data, it is necessary to use literature values that link dehydrated surface area to the thermodynamic functions. We have previously collected experimental values of ΔCp for different processes that involve hydration of hydrophobic surfaces and compared these to the buried hydrophobic surface area.10 When averaged, one obtains that each Å2 of hydrated ASAnon contributes 1.8 ± 0.4 (SD) J/mol/K to ΔCp. Similarly, the contribution of ΔASAnon to the entropy of complexation may be obtained by comparing the hydration entropies of linear alkanes (ethane to hexane)44 to their water-accessible surface areas.45 From the slope of the resulting linear plot, one finds that hydration of each Å2 adds −0.120 kJ/mol to TΔS° at 298.15 K. These two literature values may be used to predict the experimentally determined values of ΔS° and ΔCp and thereby test whether dehydration of hydrophobic surface is the main reason for the large differences in complexation thermodynamics observed in the present study. Using the complexes with natural βCD as reference points, ΔS° and ΔCp were calculated for the complexes with the other CDs, based on the increments in ΔASAnon. The results are shown as the broken lines in Figures 3 and 5. For the complexes with GCDC, the agreement with the experimental data is pretty good, considering the simplicity of the model. The only data point data that is really badly accounted for is ΔS° for the GCDC:mβ300 complex. This is probably related to the severely distorted structure of the free CD, as discussed below. For the complexes with GDC, the theoretical increments in ΔS° and ΔCp are all underestimated. Interestingly, the same was the case for the complexes with HPβCDs.10 It is maybe not so surprising that it is the complexes with GDC, rather than the GCDC complexes, that exhibit this apparent systematic discrepancy between theory and experiment. After all, GDC possess a secondary weak binding site for βCD,7,8,32,46 but this was ignored in the analysis of the calorimetric data and in the MD simulations. At first sight, it is surprising that this simple model, which is solely based on ΔASAnon and treats all hydrophobic surfaces as equivalent, ignores contributions from the differences in ΔASApol, and ignores all other contributions to ΔS° and ΔCp, to such an extent can account for the observed thermodynamics.

ΔS = ΔS* + ΔCp ln(T /TS*)

(1)

ΔH = ΔH * + ΔCp(T − TH*)

(2)

As seen on the MPG plots in Figure 11, some of the complexes with mβCDs lie very close to the straight lines spanned by the 10126



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related to the increased distortion of the free CDs, more specifically the release of fewer cavity waters and the increased difficulty of the BS to penetrate a distorted CD structure. If the above interpretation of MPG plots is correct, it means that they can be used to analyze the thermodynamics of aqueous solution processes in a new way and discriminate between contributions from ordinary dehydration and other contributions. If a series of similar compounds lie on a straight line in the MPG plot, with a slope that corresponds to the universal TS*, the thermodynamics only differ due to hydration differences. The strong correlation between ΔH°, ΔS°, and ΔASAnon also suggests that the H−S compensation observed for the present system (Figure S-15) is related to differences in the extent of dehydration upon complexation. As we have previously noted,6,7 the least dehydrated complexes are found in the lower left corner of the H−S compensation plot, while the most dehydrated complexes are found in the upper right corner. Although other factors may give rise to H−S compensation, it seems likely that hydration difference is a major cause for this often-observed phenomenon. Influence of Substituents on Binding Constant. As we observed in our previous study of complexes with HPβCDs,10 the additional hydrophobic contacts between the substituents and the BSs apparently do not stabilize the complexes, as would otherwise be expected. In the case of mβCDs, the number and position of the methyl substituents seem to be a more important factor; methyl groups at O2 stabilize the complexes while methylation at O3 destabilizes the complexes.7 The destabilizing effect of the O3 methyls was speculated to arise from steric repulsion between the inward-pointing methyl groups and the BS. The present data, however, support another explanation, previously outlined by Botsi et al.30 Methylation, and especially methylation at O3, distorts the open structure of the free CD and reduces the chance that an approaching BS enters the cavity, thereby shifting the equilibrium toward the uncomplexed species. This is especially pronounced for mβ300 which is highly distorted. The natural bCD always adopt a circular and open conformation, but this conformation is less visited as the DS increases. This limited availability of an open guest-accommodating structure is expected to show up in the complexation thermodynamics as an entropic destabilization. Indeed, the complexation entropy of the weakly binding mβ300 is much more negative than what is expected from ΔASAnon (Figure 3) and deviates significantly from the straight line in the entropy MGP plot (Figure 11B). The binding constants in Table 2 reveal that the mβ300:GCDC complex is destabilized by 10 kJ/mol compared to the complexes of the other CDs. In Figure 3, the vertical distance between the expected and the measured TΔS° suggests an entropic destabilization of mβ300:GCDC by roughly 15 kJ/mol. The extraordinarily low binding constant of mβ300 may therefore to a large extent be ascribed to the strong tendency of mβ300 to adopt distorted conformations that are incapable of including the guest. The poor ability of mβ300 to form inclusion complexes, as compared to the natural βCD and other mβCDs, has been observed in several other cases with other types of guest molecules,14,57,58 although there is also a single example of the opposite.29 Nevertheless, in all cases where the complexation entropy has been determined, the complexes with mβ300 were characterized by having the lowest values of ΔS°,14,29,58 as observed in the present study. This supports the above interpretation that complexes of mβ300 are disfavored by

Figure 11. Enthalpy and entropy MPG plots. Closed symbols denote complexes with mβCDs (and natural βCD) and the arrow points in the direction of increased degree of methylation. Open symbols denote complexes with HPβCDs and the straight lines are based on linear regression to these data and βCD.10 Complexes with GDC and GCDC are shown with circles and triangles, respectively.

HPβCD:BS complexes. However, the complexes of the highly methylated βCDs, especially mβ300, tend to deviate from these lines. There seems to be general consensus in the literature that the occurrence of convergence temperatures is related to the properties of water, and this is also the basis for the present interpretation. It is not unreasonable to assume that dehydration of hydrophobic surface is associated with characteristic values of ΔS° and ΔCp. This assumption proved relatively successful in accounting for the observed values of ΔS° and ΔCp in the present study, as shown in Figures 3 and 5. The employed empirical relations between ΔASAnon and TΔS° and ΔCp, −0.120 kJ/mol/ Å2 and 1.8 J/mol/K/Å2, respectively, give a slope in the entropy MPG plot of −0.22, which translates into an entropy convergence temperature of 100 °C, close to the “universal” TS* of 110 °C. This leads to the interpretation that the complexation thermodynamics for all complexes that lie on the straight lines in the MPG plots in Figure 11 only differ due to differences in ΔASAnon. For complexes outside the straight lines there are other significant contributions to the complexation thermodynamics. Since the deviations occur for the highly substituted complexes, such other contributions are probably 10127



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(4) Connors, K. A. The Stability of Cyclodextrin Complexes in Solution. Chem. Rev. 1997, 97, 1325−1357. (5) Liu, L.; Guo, Q.-X. The Driving Force in the Inclusion Complexation of Cyclodextrins. J. Inclusion Phenom. Macrocycl. Chem. 2002, 42, 1−14. (6) Schönbeck, C.; Westh, P.; Madsen, J. C.; Larsen, K. L.; Städe, L. W.; Holm, R. Hydroxypropyl Substituted β-Cyclodextrins: Influence of Degree of Substitution on the Thermodynamics of Complexation with Tauro- and Glyco-Conjugated Bile Salts. Langmuir 2010, 26, 17949− 17957. (7) Schönbeck, C.; Westh, P.; Madsen, J. C.; Larsen, K. L.; Stade, L. W.; Holm, R. Methylated β-Cyclodextrins: Influence of Degree and Pattern of Substitution on the Thermodynamics of Complexation with Tauroand Glyco-Conjugated Bile Salts. Langmuir 2011, 27, 5832−5841. (8) Schönbeck, C.; Holm, R.; Westh, P. Higher Order Inclusion Complexes and Secondary Interactions Studied by Global Analysis of Calorimetric Titrations. Anal. Chem. 2012, 84, 2305−2312. (9) Holm, R.; Østergaard, J.; Schönbeck, C.; Jensen, H.; Shi, W.; Peters, G. H.; Westh, P. Determination of Stability Constants of Tauroand Glyco-Conjugated Bile Salts with the Negatively Charged Sulfobutylether-β-Cyclodextrin: Comparison of Affinity Capillary Electrophoresis and Isothermal Titration Calorimetry and Thermodynamic Analysis of the Interaction. J. Inclusion Phenom. Macrocycl. Chem. 2014, 78, 185−194. (10) Schönbeck, C.; Holm, R.; Westh, P.; Peters, G. H. Extending the Hydrophobic Cavity of β-Cyclodextrin Results in More Negative Heat Capacity Changes but Reduced Binding Affinities. J. Inclusion Phenom. Macrocycl. Chem. 2014, 78, 351−361. (11) Holm, R.; Schönbeck, C.; Askjær, S.; Westh, P. Thermodynamics of the Interaction of γ-Cyclodextrin and Tauro- and Glyco-Conjugated Bile Salts. J. Inclusion Phenom. Macrocycl. Chem. 2013, 75, 223−233. (12) Holm, R.; Schönbeck, C.; Askjær, S.; Jensen, H.; Westh, P.; Østergaard, J. Complexation of Tauro- and Glyco-Conjugated Bile Salts with α-Cyclodextrin and Hydroxypropyl-α -Cyclodextrin Studied by Affinity Capillary Electrophoresis and Molecular Modelling. J. Sep. Sci. 2011, 34, 3221−3230. (13) Holm, R.; Müllertz, A.; Mu, H. Bile Salts and Their Importance for Drug Absorption. Int. J. Pharm. 2013, 453, 44−55. (14) Rekharsky, M. V.; Inoue, Y. Complexation Thermodynamics of Cyclodextrins. Chem. Rev. 1998, 98, 1875−1917. (15) Cooper, A.; Johnson, C. M.; Lakey, J. H.; Nöllmann, M. Heat Does Not Come in Different Colours: Entropy-Enthalpy Compensation, Free Energy Windows, Quantum Confinement, Pressure Perturbation Calorimetry, Solvation and the Multiple Causes of Heat Capacity Effects in Biomolecular Interactions. Biophys. Chem. 2001, 93, 215−230. (16) Holm, R.; Schönbeck, C.; Somprasirt, P.; Westh, P.; Mu, H. A Study of Salt Effects on the Complexation between β-Cyclodextrins and Bile Salts Based on the Hofmeister Series. J. Inclusion Phenom. Macrocycl. Chem. 2014, DOI: 10.1007/s10847-014-0383-9. (17) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781− 1802. (18) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (19) bcdtest.inp file in the CHARMM package: Chemistry at HARvard Macromolecular Mechanics (CHARMM) - Developmental Version 31b2, February 15, 2005. (http://www.charmm.org/package/releases. html). (20) Vorobyov, I.; Anisimov, V. M.; Greene, S.; Venable, R. M.; Moser, A.; Pastor, R. W.; MacKerell, A. D. Additive and Classical Drude Polarizable Force Fields for Linear and Cyclic Ethers. J. Chem. Theory Comput. 2007, 3, 1120−1133. (21) MacKerell, A. D.; Bashford, D.; Bellott; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; et al. AllAtom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. J. Phys. Chem. B 1998, 102, 3586−3616.

entropy due to the distorted structure of the uncomplexed mβ300.

■

CONCLUSION The changes in enthalpy, entropy, and heat capacity for the complexation of various methylated βCDs with bile salts strongly depend on the number of methyl substituents at the rims of the cyclodextrin, as previously observed for other modified cyclodextrins. Initially, ΔH° and ΔS° increase monotonously with increased methylation, while ΔCp becomes more negative. Then, at a degree of substitution close to 2, the trend is reversed, and ΔH° and ΔS° decrease while ΔCp increases. These variations in the thermodynamic functions seem to be closely related to the burial of hydrophobic surface area which exhibits the same trend. The measured variations in ΔS° and ΔCp can even be quantitatively accounted for by the changes in the wateraccessible surface area. The methyl substituents extend the cavity of the cyclodextrin and create hydrophobic contacts with the guest molecule, thereby increasing the burial of hydrophobic surface. However, at higher degrees of methylation, another effect sets in; the circular structures of the noncomplexed cyclodextrins are destabilized, presumably due to the disruption of the intramolecular hydrogen bond belt, resulting in increasingly distorted cyclodextrin structures with diminished hydrophobic surface areas. These are the underlying causes for the peculiar trends observed for ΔH°, ΔS°, and ΔCp. Interestingly, these trends are expected to be general for modified cyclodextrins, since most substituents will disrupt the hydrogen bond belt and form hydrophobic contacts with the guest molecule. It is concluded that the observed increments in ΔH°, ΔS°, and ΔCp are dominated by contributions from dehydration of hydrophobic surface. Then, the observed enthalpy−entropy compensation and the convergence temperatures around 110 °C, both of which are also observed for hydroxypropylated βCDs, must also be the result of dehydration of hydrophobic surface. It turns out that a plot of ΔS° vs ΔCp for a homologous series of experimental data is a convenient way of evaluating whether or not the thermodynamics are dominated by hydration differences.

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ASSOCIATED CONTENT

S Supporting Information *

ITC enthalpograms and regression results. Histograms of dihedral angles. Tables of water-accessible surface areas. Enthalpy−entropy compensation plot. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (+45) 3630 1311. Fax: (+45) 3643 8242. Notes

The authors declare no competing financial interest.

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REFERENCES

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