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Computational Investigation of Enthalpy−Entropy Compensation in Complexation of Glycoconjugated Bile Salts with β‑Cyclodextrin and Analogs Kasper D. Tidemand,† Christian Schönbeck,‡,§ René Holm,*,§ Peter Westh,‡ and Günther H. Peters*,† †

Department of Chemistry, Technical University of Denmark, Building 207, DK-2800 Kongens Lyngby, Denmark 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 ‡

ABSTRACT: The inclusion complexes of glycoconjugated bile salts with β-cyclodextrin (β-CD) and 2-hydroxypropyl-β-cyclodextrins (HP-β-CD) in aqueous solution were investigated by molecular dynamics simulations to provide a molecular explanation of the experimentally observed destabilizing effect of the HP substituents. Good agreement with experimental data was found with respect to penetration depths of CDs. An increased degree of HP substitution (DS) resulted in an increased probability of blocking the cavity opening, thereby hindering the bile salt from entering CD. Further, the residence time of water molecules in the cavity increased with the DS. Release of water from the cavity resulted in a positive enthalpy change, which correlates qualitatively with the experimentally determined increase in complexation enthalpy and contributes to the enthalpy−entropy compensation. The positive change in complexation entropy with DS was not able to compensate for this unfavorable change in enthalpy induced by the HP substituents, resulting in a destabilizing effect. This was found to originate from fixation of the HP substituents and decreased free rotation of the bile salts within the CD cavities.

1. INTRODUCTION Newly developed drugs have become increasingly more hydrophobic in nature, so their water solubility becomes a major challenge for formulation scientists. Orally administered drugs that show poor water solubility are allied with slow drug absorption, resulting in variable bioavailability and potential gastrointestinal mucosal toxicity.1 One approach to ensure sufficient bioavailability of poorly water-soluble drugs is to formulate the compound with solubilizing agents, where one commonly used strategy is the molecular encapsulation of the compound with cyclodextrins (CDs) to form inclusion complexes.2 CDs are cyclic oligosaccharides and most commonly marketed as complexing agents composed of six (α-CD), seven (β-CD), or eight (γ-CD) α-1,4-linked glucose units, which have the shape of a truncated cone or torus.3 CDs with a larger number of glucose units are also available, but they are commonly not sufficient as solubilizers for drugs with a molar mass below 1 kDa.4 CDs have a unique chemical structure with a hydrophobic cavity accessible for a great variety of compounds and a relatively large number of hydroxyl groups on the faces of the structure that provides their water solubility.5 Thus, complexation with CDs increases the aqueous solubility and stability of hydrophobic drugs. This application of CDs is not new, and they have been extensively applied in industry,6,7 separation methodologies,8,9 and the pharmaceutical field.4,10−12 To date, there are more than 30 drugs available worldwide where the solubility and stabilization of the active pharmaceutical ingredient has been improved either by CDs or © 2014 American Chemical Society

derivatives with random or site-specific chemical functionalization.13,14 The physicochemical properties of CDs are different; for instance, the water solubility varies among α-CD 13% (w/w), β-CD (2%), and γ-CD (26%) under ambient conditions.3 The lower solubility of β-CD is thought to be caused by the formation of an intramolecular hydrogen bond network between the secondary hydroxyl groups.15 Chemical functionalization of any of the hydrogen-bond-forming hydroxyl groups, even by hydrophobic moieties such as methoxy, ethoxy, and 2hydroxypropyl groups, will increase water solubility.10,16 Comparing these CD analogs, 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) is the preferred cyclodextrin, since HP-β-CD has a relatively higher aqueous solubility of ∼60% (w/w),10 in comparison to ∼25% w/v for methyl-β-cyclodextrin, and the safety profile of HP-β-CD is considered much safer than that of methyl-β-cyclodextrin. A vast amount of experimental data exists on the complexation with CDs, and advances have been made in the thermodynamic understanding of the complexation process.17−20 As no explicit relationship can be derived from fundamental thermodynamics to describe the complexation process, the molecular mechanism behind this inclusion has been extensively discussed,21−35 and the general consensus is Received: July 5, 2014 Revised: August 22, 2014 Published: August 26, 2014 10889

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approximately 34 × 34 × 34 Å3. BSs are negatively charged, and to neutralize the systems, one sodium ion was added as a counterion to the simulation cell. Initial coordinates for the CDs were taken from the CHARMM package, and coordinates for BSs were based on crystal structures of glycodeoxycholate and glycochenodeoxycholate.50 Structures of HP-β-CDs were derived from the β-CD structure by replacing hydrogen atoms of relevant hydroxyl groups with 2-hydroxypropyl groups. Along the native β-CD, we investigated four different CD analogs, where the HP groups were attached to hydroxyl groups on the top (oxygen O2 or O3) or bottom (O6) rim of the parent β-CD (Figure 1).

that the driving force is due to hydrophobic interaction.5,36 Empirically, an enthalpy−entropy compensation has been observed in a large variety of CD inclusion complexes,17,37,38 including complexation of glycoconjugated bile salts (BSs) with β-CD and β-CD decorated with HP substituents.39 In these studies, it has been found that TΔS° and ΔH° upon complexation between HP-substituted β-CD and BSs increase with increased degree of substitution (DS). It has been estimated that this is caused by the increase in dehydration of the hydrophobic surface area as a consequence of increased DS.39,40 However, a molecular understanding of the complexation process remains elusive, since release of water molecules from the cavity of CDs, the inclusion depth of the BS, and the partially blocking of the cavity by HP substituents may also contribute to the observed compensation. This is difficult to probe by experiments; hence, computational methods can establish the link between experimental observations and events on the molecular level.41 In particular, molecular dynamics simulations can provide information in time and space, thereby mapping the structural and energetic aspects that control the complexation mechanisms. In fact, computational techniques, such as molecular mechanics, molecular dynamics simulations, ab initio quantum chemistry, or even hybrid quantum mechanics/molecular mechanics methods have been used to study the structural and dynamic behavior of CDs and their inclusion complexes at the molecular level.40,42−47 In the present study the focus was on HP-β-CDs, and on a molecular level, it was investigated how the affinity for hydrophobic compounds such as bile salts was affected by the type, number, and position of the substituents on the CD molecule using MD simulations. Bile salts were investigated upon the basis of their biological importance in the gastrointestinal tract, where they are important for the displacement after oral administration of drugs formulated with cyclodextrins.48 Understanding the complexation between bile salts and cyclodextrins is therefore of general importance for cyclodextrins’ oral use, and this knowledge may forward help in the rational use of cyclodextrins as excipients. The DS does not unambiguously characterize HP-β-CD. When produced under different conditions, the physicochemical properties of HP-β-CDs with the same DS may not be identical due to occupancy of 2-hydroxylpropyl groups at different positions on the parent CD molecule. In the present study, a detailed analysis of previously conducted MD simulations40 on HP-βCDs with different degrees of 2-hydroxylpropyl substitution in their free state and in complex with two different glycoconjugated BSs, glycodeoxycholate and glycochenodeoxycholate, are presented. The parent β-CD was decorated with five or seven HP substituents. In these complexes, the contributions from release of restrained water molecules from the cavity, removal of the HP substituents from the entry of the cavity, and inclusion depth of the guest were investigated to shed light on the experimentally observed entropy−enthalpy compensation.

Figure 1. Schematic structure of the modified β-CD and a table presenting the position and number of HP substituents. The oxygen atoms O2, O3, O4, O5, and O6 are indicated. Five or seven HP substituents are attached to β-CD, as summarized in the table. On the bottom are structural representations of CDs from left to right: HP060a, HP060b, HP060c, and HP100c.

For simplicity, a short name for CDs that has previously been introduced is used throughout the text: HP followed by the degree of substitution.39 We have studied CDs with five substituents (HP060) and seven substituents (HP100). HP substituents were placed on O2, O3, and O6. For instance, extension “a” in HP060a refers to three HP groups placed on O2, two HP groups on O3, and no HP groups on O6. The CDs investigated are HP060a (O2, 3; O3, 2; O6, 0), HP060b (3, 0, 2), HP060c (3, 1, 1) and HP100c (4, 2, 1) (Figure 1). HP060x indicates an average of HP060a, HP060b, and HP060c. The two investigated BSs were glycodeoxycholate (GDC) and glycochenodeoxycholate (GCDC); the chemical structures are shown in Figure 2. MD simulations were conducted using NAMD version 2.751 with optimized parameters for the natural β-CD and the CHARMM27 force field52 for BSs and TIP3P waters. Parameters for the HP substituents were taken from the CHARMM22 force field52 and CHARMM32 ether force field.53 The velocity Verlet algorithm with a time step of 2 fs was used to solve Newton’s equations of motion. Simulations were carried out in the NPT ensemble, i.e. at constant number of atoms (N), pressure (P = 1.013 bar), and temperature (T = 298 K). Periodic boundary conditions were applied in x, y, and z directions. Isotropic pressure regulation was applied in the simulations, and the pressure was held constant using a Langevin piston method.54 The piston damping coefficient, piston period, and piston decay were set respectively to 5 ps−1,

2. THEORETICAL METHODS Molecular dynamics (MD) simulations were carried out on free, native β-CD, free CDs decorated with 2-hydroxypropyl substituents, free bile salts, and complexes thereof with explicit water molecules. Solvation was performed using VMD,49 resulting in simulation cell dimensions of approximately 40 × 40 × 40 Å3, except for free BSs, where the box dimensions were 10890

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Comparing the isothermal titration calorimetry data of the different CD:BS complexes presented in Table 1, it appears that increasing the DS of HP substituents renders the enthalpy change less negative; i.e., interactions between BS and CDs became less energetically favorable. The same tendency was observed for the change in entropy, which increases upon increased DS. This increase is, however, not big enough to compensate for the positive change in enthalpy upon increased DS. As a result, the addition of HP substituents seems to destabilize the CD:BS complex. The question arises of how the increased DS of HP substituents, on a molecular level, destabilizes the complex. To shed light on the underlying thermodynamics of the interactions between CDs and the BSs, a series of molecular dynamics (MD) simulations were analyzed, and their results are presented in the following sections. 3.1. Inclusion of Bile Salts into Cyclodextrins. The MD simulation system was initiated with BSs positioned with the glycine side chain inserted into the investigated CD cavity. BSs diffuse relatively quickly into the cavity of CDs. As an example, the trajectory of the complexation of GCDC into HP060a is presented in Figure 3. The distance was measured between the center of mass of GCDC and HP060a. The inclusion was monitored by measuring the distance between the center of mass of BS and CD throughout the trajectory. The distance starts at 6.50 Å and an equilibrium position with a distance of 1.70 ± 0.6 Å was reached after approximately 1 ns. Similar results were observed for the other complexes. Therefore, the first few nanoseconds were discarded from the analysis discussed below. The penetration depths of GDC and GCDC into the CDs were quantified. For easier comparison, the positions of the CDs were defined by the average position of oxygen atoms (O4) in the sugar units at the lower rim (Figure 1). For BSs, carbon atom 17 (Figure 2) was used as a reference point. Snapshots displaying an example of the HP060c:GDC and HP060c:GCDC systems are shown in Figure 4. The numerical values of the penetration depths are given in Table 2. Clearly, GCDC diffuses deeper into β-CD and HP060x than GDC (p < 0.05, unpaired t test), with an average distance of ∼2 Å between the two reference points. This distance was increased for GDC having an average value of ∼3 Å. This trend was, however, not observed for HP100c. It appears that the arrangement of six HP substituents located at the top rim (Figure 1) hinders inclusion, resulting in the same penetration depth for GDC and GCDC. The observation that GCDC penetrates deeper into β-CD and HP060a−c than seen for GDC is in good agreement with NMR results.62 3.2. Degree of Rotation of Bile Salts within the Cavity of Cyclodextrins. To ensure that CD:BS complexes were not biased by the predefined orientation of BS molecule within the cavity of CD, rotation of BSs within the cavity was also investigated. The rotation was determined by monitoring the variation in a dihedral angle spanned by three atoms in BS and one atom from CD (Figure 5) along the trajectory. Representative time evolution of the dihedral angle is displayed in Figure 6 and shows free rotation of BS at the equilibrium inclusion depth. The rotation was, however, restricted by an increasing number of HP substituents, and the rotation rate changed in the following order: βCD > HP060a−c > HP100c.

Figure 2. Chemical structures of the bile salts glycoldeoxycholate (GDC) and glycochenodeoxycholate (GCDC): GDC, R1 = H, R2 = OH; GCDC, R1 = OH, R2 = H. For both GDC and GCDC, R3 = NHCH2COO−.

100, and 50 fs. The long-ranged electrostatic forces were calculated using the particle mesh Ewald method55,56 with a grid spacing of approximately 1 Å and a fourth-order spline for the interpolation. Electrostatic forces were updated every 2 fs. van der Waals interactions were cut off at 12 Å in combination with a switching function starting at 10 Å. Coordinates for analysis were saved every 500 fs. Simulations of the free CDs and BSs were carried out for 10 ns. Initial structures of the complexes were based on the coordinates of the free CDs and BSs after 10 ns equilibration of the noncomplexed molecules. Simulations on the complexes were performed for 20 ns. The BS was placed with the glycine side chain inside the cavity of the CD and the rest of BS protruding from the wider rim of the CD. This orientation of the BS was chosen on the basis of experimental observations.39,57−61

3. RESULTS AND DISCUSSION In the present study, five different CDs in complex with two different glycoconjugated BSs (Figure 2) were investigated. The CDs were β-CD and four modified β-CDs, which were decorated with HP substituents at different degrees and positions, as indicated in Figure 1. Addition of HP substituents has been demonstrated to increase the hydrophobic surface area that is dehydrated upon complexation with 12−16 Å2 per HP substituent.40 Although these HP substituents extend the CD cavity and thereby increase the hydrophobic interactions with the included BS, the substituents are found to destabilize the complex (Table 1). Table 1. Experimentally Determined Thermodynamic Data Obtained from Isothermal Calorimetry Titration at 25 °Ca CD/BS β-CD62

HP06339

HP10239

a

ΔG° (kJ/mol) ΔH° (kJ/mol) ΔS° (J/mol/K) K (M−1) ΔG° (kJ/mol) ΔH° (kJ/mol) ΔS° (J/mol/K) K (M−1) ΔG° (kJ/mol) ΔH° (kJ/mol) ΔS° (J/mol/K) K (M−1)

GDC

GCDC

−21.4 −28.5 −23.8 5673 −20.62 −13.61 23.15 4099 −19.77 −4.33 51.78 2916

−29.6 −30.9 −4.4 156226 −28.13 −22.40 19.21 65768 −25.61 −13.41 40.94 30703

Data are means calculated from three independent experiments.39,62 10891

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Figure 3. Graphical representation of the inclusion of GCDC into the cavity of HP060a. The BS (colored gray, displayed in licorice):CD (colored orange, displayed in licorice) complex on the left illustrates the initial position and the complex on the right illustrates the inclusion at equilibrium.

Figure 4. Snapshots displaying cyclodextrin (colored dark gray)/bile salt (colored orange) complexes. The distance between CD and bile salt is defined as the average position of oxygen atoms O4 (van der Waals presentation, colored red) in the sugar units at the lower rim and carbon atom 17 (van der Waals presentation, colored green) in the bile salt (see Figure 2). Left, HP060c:GDC; right, HP060c:GCDC.

Table 2. Distance (Å) between CDs and BSsa CD/bile salt

GDC

GCDC

β-CD HP060a HP060b HP060c HP100c

3.2 3.2 3.1 3.3 2.7

2.0 2.3 1.7 2.0 2.9

3.3. HP Substituents Blocking the Cavity. Experimental data indicate that the binding constant, K, changes in the following order: HP102 < HP063 < β-CD (Table 1). This might partly be explained by blocking of the CD cavity opening by the HP substituents, preventing the BSs from entering. This process was not included in the MD simulations, as the BS was initially placed with the glycine side chain included in the cavity. From visual inspection of conformations along the trajectory, it was estimated that a HP substituent was blocking the entrance if the angle between the HP substituents and a plane spanned by the O3 oxygen atoms (Figure 1) was ≤60°, as shown in Figure 7. In Figure 7C, the measured angle is illustrated, while in Figure 7A,B, top and side views of a conformation are shown where the HP substituent has an angle of 45°. The cone illustrating the area for which the HP substituent was within 60° is also presented. The HP substituent orientation was defined by a vector from the oxygen atom of the glucose unit (O3; Figure 1) and the methyl carbon atom of the HP substituent. The percentage of time a HP substituent was blocking the entrance of the various CDs shows that the HP substituents at the upper rim in HP100c blocks the entrance ∼25% of the time, while blockage of the cavity for HP060x only occurs ∼10% of the time. Hence, with increasing DS on the top rim of the cavity, the probability of BS entering CD decreases; i.e., the opening becomes less available for BS to enter.

a

Reference points are as follows: CD, average position of oxygen atoms in the sugar units at the lower rim (O4, Figure 1); bile salt: carbon atom 17 (Figure 2).

Hence, the initial orientation of BS did not bias the results discussed in the following sections, since free rotation, despite different rotation rates, was observed for all complexes. In Figure 6, it is seen that the orientation of GDC within the cavity of β-CD was not fixed at a certain orientation and could freely rotate. This was probably due to the uniform rims of this CD causing no preferable orientation of the BS. Constant orientation of varying time periods were, however, observed for HP060c:GDC (red, Figure 6) and especially for HP100c (green, Figure 6). These constant orientations were most likely caused by interchanging interaction between the HP substituents of CD and BS. Consequently, an increased DS seems to hamper the free rotation and lead to a decrease in the orientational entropy of BSs. 10892

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Figure 5. Illustration of the dihedral angle in GCDC (licorice presentation, colored orange):HP060c (licorice presentation, colored gray) spanned by the carbon atoms C18, C13, and C17 in BS (van der Waals presentation, colored red) and an O4 oxygen atom in CD (van der Waals presentation, colored red). Location of the atoms in CD and BS are shown in Figures 1 and 2, respectively. Left, side view; right, top view.

Figure 6. Time evolution of the rotation of GDC within β-CD (blue squares), HP060c (red squares), and HP100c (green triangles) is shown as a representative example. The rotation was determined by monitoring the dihedral angle between GDC and CDs as a function of simulation time; see caption of Figure 5 and main text for more details.

3.4. Residence Time of Cavity Water. It is discussed in the literature whether the release of cavity water molecules results in an increase or decrease in entropy.5,63 To gain further insight and to elucidate the influence of HP substituents on the mobility of water molecules, the relative residence time of cavity-bound water molecules was estimated for the different CDs. The free CDs were found to accommodate around nine water molecules within their hydrophobic cavity. The mean residence times of water molecules within the cavity of CDs were determined by the occupation time within a sphere with radii 5 Å placed within the center for the CD (Figure 8). The center of the CD was defined as the geometric center of the O4 oxygen atoms of the glucose units (Figure 1). As a reference, a simulation on water molecules was performed for 10 ns, and a sphere, identical to the one placed within the CD, was placed in bulk solution to estimate the residence time of free water molecules. The residence time of water molecules in bulk solution and within the cavity of β-CD, HP060c, and HP100c is summarized in Table 3. Counting water molecules exiting the cavity and later reentering the cavity as a new water molecule, 185, 280, 247, and 242 water molecules were included in the calculation of the residence time in bulk, β-CD, HP060c, and HP100c, respectively. From Table 3, it is evident that water molecules were trapped within the hydrophobic cavity of the CDs (p < 0.05, unpaired t-test). Addition of HP substituents to the β-CD

Figure 7. Top (A) and side (B) view of a snapshot demonstrating how the HP substituents block the opening of the CD cavity. CD is displayed in licorice and colored dark gray. HP substituents are displayed in licorice and colored orange. Blue cones illustrate the position in space in which the angle between the HP substituent and the O3 plane was ≤60°. (C) Schematic presentation of the measured angle illustrating the area in which the HP substituent is within 60° is presented.

10893

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Figure 8. Top (left) and side (right) view of a snapshot displaying the region (sphere, colored light blue) used to identify water molecules within the cyclodextrin cavity. Cyclodextrin is displayed in licorice and colored according to atom type (carbon, green; oxygen, red; hydrogen, white).

It is noteworthy that increasing the number of substituents on the top rim of β-CD (Table 4 and Figure 1) seems to shift the interactions from W−W to W−CD. The W−CD interactions were found to increase as β-CD < HP060b < HP060c < HP060a < HP100c, which correlates with the increasing number of HP substituents on the top rim. Water−water interactions of bulk water were found to be −55.2 kJ/mol. Release of water molecules from the cavity of the various CDs was therefore found to be enthalpically unfavorable, and an increased DS seems to induce more unfavorable enthalpic contribution upon water release (see ΔE in Table 4), which correlates well with experimental data.39,62 The HP substituents were engaged in favorable interactions, with the cavity-bound water molecules resulting in more unfavorable complexation enthalpy when compared to β-CD. 3.6. Entropy Contribution of the HP Substituents. Extending the cavity with HP substituents has previously been reported to increase the hydrophobic surface area that is dehydrated upon complexation, resulting in a positive change in entropy.39,40 The positive change in entropy was insufficient to compensate for the observed positive change in enthalpy resulting in increased ΔG° with increasing DS. This might be caused by a decrease in conformational freedom upon complexation. This was investigated by comparing the rootmean-square deviations (RMSDs) of the free CDs and the CDs in complex with GCDC and GDC, respectively. RMSD was measured by comparing the structure of the CDs throughout the last 10 ns of the trajectories with the structure at the beginning of the time interval, and the data are provided in Table 5. It is evident that ΔRMSD increased with increased DS (p < 0.05, unpaired t-test). The negative values presented in Table 5 were a result of lowered RMSD for CDs in complex with either GCDC or GDC. Increased DS therefore seems to result in a loss of conformational freedom of the CDs upon complexation and was not dependent on the penetration depth of the bile salt, since similar ΔRMSD values were found for hydroxypropylated CD:bile salt complexes.

Table 3. Mean Residence Time of Water Molecules within a Sphere of 5 Å Given for the Bulk Solution, β-CD, HP060c, and HP100ca location of sphere

average (ps)

bulk solution β-CD HP060c HP100c

2.53 7.81 15.62 17.51

The residence time within β-CD is significantly greater (p < 0.05, unpaired t-test) than that within bulk, while the residence time within HP060c is significantly greater than that within β-CD (p < 0.05, unpaired t-test). a

results in an increased residence time of the water molecules; this means that water molecules in the cavity of the modified CDs were more constrained than observed for the native β-CD. Hence, the presence of HP substituents resulted in a greater entropy gain upon CD:BS complexation. This agrees well with the experimental data (Table 1) and suggests that there are three contributions to the entropy gain with increased DS: (i) dehydration of the HP substituents, (ii) dehydration of BS, and (iii) displacement of water molecules from the cavity. The latter two entropy contributions have also been suggested to be important for the complexation of guest molecules with αCD.64 3.5. Release of Water Molecules. It has previously been found that release of water molecules from the cavity of CDs is enthalpically unfavorable.65 The thermodynamic outcome of release of water molecules from the cavity of HP-substituted βCDs was therefore investigated. Water molecules located within the cavity of the CDs were identified and their interaction energy with other water molecules (Ewater−water) and CD (Ewater−CD) were determined along the trajectory. The respective contributions are listed in Table 4, and by increasing the number of HP substituents, water molecule−water molecule (W−W) interactions decreased while water molecule−CD (W−CD) interactions increased.

Table 4. Energy of Water Molecules Located within the Cavity of CDsa EW−W EW−CD Etotal ΔEbulk−complex

bulk solution

β-CD (kJ/mol)

HP060a (kJ/mol)

HP060b (kJ/mol)

HP060c (kJ/mol)

HP100c (kJ/mol)

−55.2

−79.1 −7.9 −84.5 29.3

−34.7 −55.6 −90.4 35.2

−58.6 −32.2 −90.8 35.6

−43.9 −44.4 −90.4 35.2

−13.4 −85.5 −99.2 44.0

−55.2 0

a

Two contributions to the total energy, water molecules in the cavity with other water molecules (EW−W) and water molecules in the cavity with CD (EW−CD), were determined. ΔE is defined as Ewater,bulk − Ewater,complex of water molecules within the cavity of the CDs. 10894

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Table 5. ΔRMSDa Calculated as the Difference between RMSD of the Free CDs and RMSD of CDs in Complex with GCDC and GDC, Respectively

higher than found for water molecules in bulk water, where a residence time of 2.5 ps was found. Increased DS results in more constrained cavity water molecules. Release of these constrained water molecules increases the entropy, whereas fixation of the HP substituents upon complexation and reduction of free rotation of the BSs within the CD cavities reduce the entropy. At the same time, the water molecules released from the cavity have a positive energy contribution, which increases with increasing DS and ranges from 29.3 kJ/mol (β-CD) to 35.3 kJ/mol (HP060x) to 44.0 kJ/mol (HP100c). The increase in energy correlates qualitatively with the experimentally determined positive enthalpy change upon complexation and contributes to the enthalpy−entropy compensation. In comparison to β-CD, the total complexation entropy of the analogues was reduced due to fixation of the HP substituents. This reduction of entropy and the increased enthalpy induced by release of restrained cavity water molecules as well as the blocking ability of the HP substituents result in a lowering of the binding constant (K) which can explain the observed destabilizing effect.

ΔRMSD (Å)

a

bile salt

β-CD

HP060x

HP100c

GCDC GDC

−0.08 0.28

−0.59 −0.54

−0.93 −0.99

ΔRMSD = RMSDCD,complex − RMSDCD,free.

The ΔRMSD correlates well with the number of HP substituents on the top rim of the cavity. In Figure 9, it can be seen that increasing DS on the top rim resulted in increased ΔRMSD. Although increased DS resulted in increased dehydration, it also seems to induce strain on the CD upon complexation, which lowers the complexation entropy. This lowering might cause the entropy to be unable to compensate for the positive change in enthalpy produced by release of water molecules from the hydration shell of BSs and CDs, including the cavity. Consequently, the complexation ΔG° will be more unfavorable with increasing DS. The result is also in good agreement with a previous study, where the authors studied inclusion complexes of a pharmaceutical drug with CDs showing unfavorable binding of the drug with HP-β-CD in comparison with β-CD.44

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AUTHOR INFORMATION

Corresponding Authors

*R.H. e-mail: [email protected]. *G.H.P. e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSIONS A series of molecular dynamics simulations was performed on inclusion complexes of glycoconjugated bile salts, glycodeoxycholate and glycochenodeoxycholate, with β-cyclodextrin and 2-hydroxypropyl-β-cyclodextrins. Simulations were analyzed with respect to structural and energetic properties of the complexes. In good agreement with experimental NMR data,62 the simulation results showed that GCDC penetrates deeper in β-CD and HP060a−c, than observed for GDC. The degree of HP substitution had a significant effect on complexation. With increasing DS, the probability of blocking the cavity opening increased. For HP060x and HP100c, the opening was blocked respectively for ∼10% and ∼26% of the simulation time. Complementary, the residence time of water molecules in the cavity was determined to be ∼8 ps for β-CD, ∼16 ps for HP060c and ∼18 ps for HP100c. These times are significantly

ACKNOWLEDGMENTS Simulations were performed at the Danish Center for Scientific Computing at the University of Southern Denmark and the Technical University of Denmark.

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REFERENCES

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Figure 9. ΔRMSD calculated as the difference between RMSD of the free CDs and RMSD of CDs in complex with GCDC and GDC, respectively (ΔRMSD = RMSDCD,complex − RMSDCD,free). The regression line is based on an average of change in RMSD upon complexation with GCDC and GDC. 10895

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