Surface Adsorption and Bulk Aggregation of Cyclodextrins by

Article pubs.acs.org/JPCB

Surface Adsorption and Bulk Aggregation of Cyclodextrins by Computational Molecular Dynamics Simulations as a Function of Temperature: α‑CD vs β‑CD Edgar Mixcoha,† José Campos-Terán,‡ and Á ngel Piñeiro*,† †

Soft Matter & Molecular Biophysics Group, Department of Applied Physics, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain ‡ Departamento de Procesos y Tecnología, Universidad Autónoma Metropolitana, Unidad Cuajimalpa, Av. Vasco de Quiroga 4871, Col. Santa Fe, Delegación Cuajimalpa de Morelos, 05348, D.F., México S Supporting Information *

ABSTRACT: The structural simplicity of native cyclodextrins (CDs) contrasts with their complex behavior in the bulk of aqueous solutions, mainly when they are combined with other cosolutes. Many scientific and industrial applications based on these molecules are supported only by empirical information. The lack of fundamental knowledge, which would allow one to rationally optimize many of these applications, is notable mainly at the solution/air interface. Basic information on phenomena such as the spontaneous adsorption of native CDs or on the structure of CD aggregates in the bulk solution is really scarce. In order to fill these gaps, a detailed computational study on the adsorption and aggregation of αand β-CDs as a function of temperature is presented here. Our simulations reproduce, at atomic resolution, the experimentally observed much higher ability of β-CD to aggregate compared to that of α-CD at 298 K, as well as their dependence on temperature. The adsorption of both individual CDs and small CD aggregates (up to 20 molecules) to the solution/air interface is found to be negligible. 0.8 μs long trajectories of single CD molecules in aqueous solution reveal that the main differences in the behavior of both CDs are their flexibility, higher for β-CD, and the occupancy of individual intramolecular hydrogen bonds that is significantly longer for the same cyclodextrin. The aggregation pattern of α- and β-CDs is followed at the hundreds of ns time scale, allowing both the spontaneous self-assembly of cyclodextrins and their redistribution along the aggregates to be observed. This is the first attempt to study the adsorption and aggregation of native cyclodextrins by atomistic molecular dynamics simulations.

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INTRODUCTION Natural cyclodextrins (CDs) are cyclic oligosaccharides formed by six (α), seven (β), or eight (γ) 1,4-linked α-D-glucopyranoside units (GPUs) that result from the enzymatic degradation of starch. These molecules were discovered more than a century ago, but they are still the focus of many research groups and novel industrial applications,1 as evidenced by the increasing number of articles, patents, and commercial applications based on cyclodextrins that appeared during the last years.1a,2 The enduring interest in cyclodextrins relies on their topology, which provides them with particular physicochemical properties, as well as on their high stability and low toxicity. Cyclodextrins are typically employed in a wide variety of industries that include paints, pharmacy, food, cosmetics, agrochemistry, analytical chemistry, catalysis, and chemosensor applications.1,2 They have been described as truncated cone shaped molecules with a hydrophobic cavity and a hydrophilic external surface, the latter of which makes them relatively soluble in water. The primary and secondary hydroxyl groups of © 2014 American Chemical Society

the GPUs are oriented toward the narrow (tail) and wide (head) edges of the cone, respectively. One of the most exploited features of these molecules is their ability to encapsulate hydrophobic moieties, increasing the solubility, lowering the volatility, and/or protecting the encapsulated species from potential chemical reactions. It is interesting to note the lack of a regular variation in certain properties of native CDs such as their solubility, which is 1 order of magnitude lower for β-CD than for α- and γcyclodextrins (16.3 vs 149 and 179 mM at 298 K, respectively).3 The lack of solubility exhibited by cyclodextrins at relatively high concentrations has been connected to their tendency to self-aggregate, forming different supramolecular structures. There is a clear correlation between the ability of a given compound to self-aggregate in aqueous solution and its Received: December 21, 2013 Revised: May 18, 2014 Published: June 2, 2014 6999

dx.doi.org/10.1021/jp412533b | J. Phys. Chem. B 2014, 118, 6999−7011

The Journal of Physical Chemistry B

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responsible for this organization of the neighboring solvent molecules. The flexibility of native CDs is thus an important factor to take into account when explaining the differences in their macroscopic properties. This feature has been widely discussed by Dodziuk,11 who argued that the previously accepted rigidity of these molecules is not compatible with several experimental and computational results. In agreement with Naidoo et al.,10 a more recent MD study by Cai et al.12 based on 12 ns long trajectories points out that the higher rigidity of β-CD, together with the observed intramolecular hydrogen bonds present in this molecule, induces the organization of the surrounding water molecules and so its lower solubility. They also concluded that the differences in the solvation free energy of the native cyclodextrins cannot explain their different solubilities. Furthermore, these authors analyzed the importance of the intramolecular hydrogen bonds and proposed that destroying the internal H-bond network of β-CD should improve its solubility. In contrast to these results, Jana and Bandyopadhyay, based on 10 ns long MD trajectories, recently claimed that β-CD is more flexible than α-CD.13 These authors performed a detailed analysis on the behavior of water molecules confined in the cavities of the CDs, including a description of their translational and rotational motions as well as of the kinetics of water−water and water−CD H-bonds. However, they do not provide any explanation at the molecular level for the low solubility of β-CD compared to those of α-CD and γ-CDs. The importance of the solvent on CD aggregation has also been highlighted in a recent computational study by Zhang et al.14 These authors calculated the potential of mean force for β-CD dimer dissociation in 10 different solvents of different polarity. They claim that more polar solvents lead to less stable dimers due to the competition between the solvent molecules and the hydroxyl groups of the cyclodextrins to form H-bonds with each other. The relative orientation of cyclodextrins in β-CD dimers is also discussed in the same line, with the channel-type conformation resulting in being less stable than the layer- and cage-type dimers in water solution. No comparable studies have been done for larger aggregates. Despite the significant advances described above, the relationship between the slight structural differences of αand β-CD and the serious differences in their macroscopic properties is not well understood yet. No studies at molecular level have been reported on the ability of these molecules to spontaneously adsorb and aggregate. In this work, we aim to fill this gap by a detailed computational molecular dynamics study of these two cyclodextrins at the aqueous-solution/air interface as well as in the bulk aqueous solution at 283 and 298 K. The structural and dynamic behavior of both single α- and βcyclodextrins and cyclodextrin aggregates will be characterized under these conditions.

affinity to the solution/air interface. Typically, low concentrations of amphiphilic molecules diffuse and remain stable at water/air interfaces. The aggregation and organization in nanoor microstructures begin to be evident once the surface is nearly saturated. Surfactants clearly illustrate this behavior. The dependence of the surface tension (σ) on CD concentration when native cyclodextrins are dissolved in water is small (maximum decrease of about 1 mN m−1). This indicates that CDs are not strongly surface active compounds. Taking advantage of this fact, several research groups have used σ adsorption isotherms of different amphiphilic molecules as a function of CD concentration to determine the equilibrium constants of the corresponding host−guest inclusion complexes.4 The adsorption constants of native cyclodextrins to the solution/air interface have been estimated to be 10.7, 49.4, and 14.6 L mol−1 at 298 K for α-, β-, and γ-CD, respectively,4d in agreement with the significantly lower solubility of β-CD1a and its higher persistency to form aggregates.5 Publications devoted to the study of cyclodextrins at interfaces are scarce. A representative example of this kind of studies is illustrated by the work of Ferreira et al.6 who published a detailed characterization of a large variety of modified cyclodextrins in the presence of several phosphanes. The ability of cyclodextrins and cyclodextrin-based complexes to self-aggregate or to dissociate in single monomers in the bulk of aqueous solutions is key to allow, facilitate, or optimize the development of many pharmaceutical products, new materials with singular properties, or new molecular devices based on these molecules. This encouraged a significant number of studies and publications during the last years. A variety of techniques including NMR spectroscopy, X-ray diffraction, small-angle X-ray and neutron scattering, scanning electron microscopy, (cryogenic) transmission electron microscopy, dynamic and static light scattering, atomic force microscopy, and computational calculations have been employed to characterize CD aggregates in the bulk solution as well as the cyclodextrin precipitates observed upon different sample treatments.5,7 Interestingly, it has been reported that βCDs form larger and more persistent aggregates than α-CD and γ-CD, showing that subtle topological differences at the molecular level are key to the control of physical properties of larger scale structures.5 Attempts to explain the different physicochemical properties of cyclodextrins at the molecular level have been made on the basis of both experimental and computational methods. Most of these attempts explain their results in terms of the ability of the three native CDs, and their corresponding aggregates, to interact with the surrounding water molecules or even to induce a certain degree of structure in the solvent. For instance, Coleman et al. studied the solubility of cyclodextrins using different cosolvents, including ions, able to disturb the CD−CD intermolecular H-bonds.8 They proposed that the less favorable interaction of β-CD with water molecules, compared to that of α-CD or γ-CD, explains the higher ability of that cyclodextrin to aggregate and so its lower solubility. De Brauer et al. obtained similar conclusions by heat capacity experiments of anhydrous and hydrated solid CDs.9 A computational study by Naidoo et al.10 agrees with the conclusions previously obtained by Coleman et al. and De Brauer et al.8b,9 On the basis of 5 ns long molecular dynamics (MD) simulation trajectories, these authors observed that βCD dramatically increases the structure of the surrounding water molecules. They also claim that the higher rigidity of this cyclodextrin, compared to those of α-CD and γ-CD, could be

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METHODOLOGY Setup of the Simulation Boxes. Simulations of α- and βcyclodextrins were performed at 283 and 298 K using (i) a solvent slab within a larger simulation box, with the solution/air interface accessible to the solute molecules, and (ii) fully solvated boxes, with no solution/air interface. For the former type of simulations, two trajectories were generated at each temperature and for each cyclodextrin, namely, one using a single α- or β-CD at 283 or 298 K and another using 20 α- or β-CD molecules initially located at random positions and orientations within the water slab, also at both temperatures. The thickness of the solvent slab, final box lengths in the XYZ 7000



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Figure 1. Scheme illustrating the initial (A, C) and final (B, D) configurations of the cyclodextrin solutions with slab geometry (A, B) and in fully solvated boxes (C, D). Note that box C was obtained from the combination of two copies with different orientations of box B. See the main text for details.

dimensions, and number of water molecules were 4 nm, 5 × 5 × 12 nm3, and ∼3300, respectively, for the simulations of single CDs and 5 nm, 9 × 9 × 15 nm3, and ∼12 600, respectively, for the simulations with 20 solute molecules. In all of these cases, the slab surface was parallel to the XY plane. For the second type of simulations, single cyclodextrins were placed in 4 × 4 × 4 nm3 fully solvated boxes, with no solution/air interface, containing approximately 2100−2200 water molecules. The boxes with slab geometry were minimized and simulated for 200 ns, while the simulations of the single CDs in the bulk were simulated for 800 ns. Finally, the aggregation of α- and β-CD in water was studied using rectangular boxes with 40 α- or βcyclodextrins in water. The initial configuration of these latter systems was constructed by adding a copy of the final configuration of the simulations using 20 α- or β-CD in the slab geometryrotated 180° around the X axison top of the original slab and adjusting the box size to the resulting system (Figure 1). Each of these simulations employed approximately 25 000 water molecules. The total length of each of these trajectories was 200 ns. All the simulation boxes were energy minimized using the steepest descent method prior to the calculation of the molecular dynamics trajectories. MD Simulation Parameters. All the simulations were performed using the GROMACS package15 version 4.5.1 and the GROMOS96(53a6) force field.16 The cyclodextrin topologies were the same as in previous works.17 SPC waters were employed to model the solvent in an explicit way. The simulations with slab geometry were simulated at constant volume and temperature, while the NPT ensemble was employed for the simulations in the bulk phase. The temperature was controlled at 283 or 298 K using a Nosé− Hoover thermostat18 with a coupling constant of 0.1 ps. For the simulations at constant pressure (1 bar), a Parrinello−Rahman barostat19 with a coupling constant of 0.5 ps and a compressibility of 4.5 × 10−5 bar−1 was employed. Long range electrostatic interactions were calculated using the particle mesh Ewald method20 with a real-space cutoff of 1.2 nm, a 0.15 nm spaced grid, and fourth-order B-spline interpolation. The Ewald sum in three dimensions with a correction term (EW3DC) was used to avoid artifacts due to interactions between periodic images in the z direction for the simulations with slab geometry. Random initial velocities were assigned to the systems from a Maxwell−Boltzmann distribution at 283 or 298 K, depending on the system. The equations of motion were integrated using the leapfrog method21 with a time step of 2 fs. The SETTLE22 algorithm was employed to constrain the bond lengths and angles of water molecules, while the LINCS23 algorithm was employed to constrain the bond lengths of the cyclodextrin molecules. During the MD simulations, coordinates and energies were stored every 10 ps for analysis.

Solvation Free Energy Calculations. The Bennett acceptance ratio (BAR) method24 was employed to determine the solvation free energy (ΔGsolv) of α- and β-CD at 283 and 298 K, i.e., the free energy change to introduce a mole of molecules from the gas phase to the bulk of the aqueous solution. The BAR method is based on Monte Carlo acceptance rates of transitions between neighbor states. Such states should be close enough to have a significant number of transitions, which is a requirement for the convergence of the method. The potential energy of interaction between the α- or β-CD molecule and the solvent is therefore slowly switched on by a parameter λ that goes from 0 to 1. A number of 47 λ points were employed in the present work for each ΔGsolv calculation. In order to optimize the transition rates, the λ values were unevenly distributed with Δλ = 0.001 for λ values close to 0 and 1 and Δλ = 0.05 in the middle λ region. Each of these simulations was 5 ns long. Four different structures were taken for each cyclodextrin and temperature, with the final ΔGsolv value being the average between the values obtained for each case. Electrostatic and van der Waals solute−solvent interactions were simultaneously switched on in the final calculations. The intramolecular interactions of the cyclodextrins were not perturbed in any case, since they are present in both the gas and aqueous solution phases. Each trajectory was generated using a stochastic dynamics integrator with the same scheme described above for the electrostatic interactions. To prevent the overlapping of solute−solvent atoms for low λ values, the soft-core potentials implemented in GROMACS25 with α = 0.5, σ = 0.3, and p = 1 are employed. The data were treated to get the ΔGsolv values using the GROMACS package tools.

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RESULTS AND DISCUSSION Single Cyclodextrins at the Water/Air Interface, Solvation Free Energies, and Their Connection with Solubility. The simulations of single cyclodextrins using slab geometry indicate that the adsorption of α- and β-CD monomers at the solution/air interface is not highly favorable. During the trajectories at 283 and 298 K, both α-CD and β-CD diffuse through the simulation box, occasionally reaching the interface but always going back in the bulk of the solution after a short time (see Figure S1 in the Supporting Information). The distance distributions between the center of the slab and the center of the cyclodextrin show a small shoulder close to the interface, indicating that the affinity of the CD molecules for this region is just slightly higher than that for its neighborhoods but significantly lower than that for the middle section of the slab. It is also worth noting that the maximum of the shoulder is located at approximately 1.3 nm for all of the simulations, with the surface being at ∼2 nm. This clearly indicates that, even when the CD reaches the interface, it does 7001



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Figure 2. Number of clusters (top) and number of molecules in the largest cluster (bottom) for the simulations performed with 20 α-CD (red lines) and 20 β-CD (black lines) at 283 (left) and 298 (right) K in slab geometry. The cutoff distance considered to assign two molecules to the same cluster was 0.35 nm in all cases.

the number of repeats increases. ΔGsolv values have been proposed to be distributed in several contributions: cavity formation, electrostatic and dispersion interaction, and hydrogen bond formation.28 The electrostatic and van der Waals CD−water interactions were simultaneously switched on for these calculations because preliminary tests using 20 and 30 λ values revealed that the van der Waals contribution is positive and small: about 5% of the total ΔGsolv in all cases. The simultaneous consideration of both contributions allowed us to half the simulation time for these calculations with no significant worsening in the uncertainties. The role of CD− CD and CD−water hydrogen bonds will be discussed later in this work, while the contribution of the cavity formation was not explicitly determined. Our results are similar to those previously published by Danhong Zhou et al.29 who obtained a ΔGsolv value of −367 kJ·mol−1 for α-CD at 298 K with a contribution of the nonpolar interactions (van der Waals + the free energy required to form a cavity in the solvent) of 31.46 kJ· mol−1. In contrast, Cai et al.12 have also published ΔGsolv values for α- and β-CD at 298 K that differ from the previous results by 1 order of magnitude: −36.8 and −51.5 kJ·mol−1 for α- and β-CD, respectively. Semiempirical quantum calculations using the AMSOL program30 with the PM3 Hamiltonian were performed in order to have an independent estimation of ΔGsolv for α-CD at 298 K. The obtained value (−323.03 kJ· mol−1) agrees reasonably well with our results obtained by MD simulations. It is well-known that the solubility of β-CD is much lower than that of α-CD.3 The connection between solvation free energies and solubilities is not direct, since the former property is related to the interactions with the solvent while the solubility is related to the balance between solute−solvent and solute−solute interactions. In this work, we are determining the solvation free energy as the work to transfer 1 mol of isolated solute molecules from the gas phase to the solution, without considering the solute−solute interaction. The solubility of αCD has been reported to vary significantly with temperature: 39 and 130 mM at 283 and 298 K, respectively. The dependence of the β-CD solubility on the temperature is much lower, going from 13.5 mM at 283 K to 16.7 mM at 298 K31 (values at 283 K were extrapolated).

not stick out but remains fully hydrated (note that 0.7 nm, the difference between 2 and 1.3 nm, is a reasonable value to approach the average radius of these molecules). No significant differences in this behavior were observed between both CDs or as a function of temperature. The surface tension of a solution depends on the concentration of the solute at the interface. Actually, this is the basis on which semiempirical adsorption isotherms are typically proposed.26 For significant solute concentration at interfaces, the surface tension change could be estimated by MD simulations.27 In this case, the practically negligible adsorption of CDs is compatible with the experimentally observed independence of surface tension on cyclodextrin concentration. The ability of a solute molecule to adsorb to the water/air interface in aqueous solution is expected to be related to its solvation free energy, since this thermodynamic property assesses the affinity to the solvent taking the gas phase as a reference. The ΔGsolv values of α- and β-CDs at both temperatures were calculated using the BAR method, as described above. The values obtained by using just the last conformation from each trajectory as the initial structure were −325.6 ± 1.4 and −294.06 ± 0.69 kJ·mol−1 for α-CD at 283 and 298 K, respectively, while for β-CD we obtained −342.84 ± 0.79 and −342.27 ± 0.44 kJ·mol−1 at the same temperatures. The selected distribution of the λ values was key to obtain a low uncertainty for the ΔGsolv values (see Figure S2 in the Supporting Information). Since the use of a single structure for this calculation might limit the sampling to a local minimum, three repeats of each calculation were performed by using a representative structure of each of the three dominant clusters for each trajectory (see below the description and results of the cluster analysis). The averages between the four ΔGsolv values were −322 ± 11 and −294 ± 3 kJ·mol−1 for α-CD at 283 and 298 K, respectively, and −333 ± 11 and −333 ± 13 kJ·mol−1 for β-CD at the same temperatures. As it can be seen, the differences between cyclodextrins and temperatures stand but the uncertainties (the standard deviation of the average in this case) are now significantly larger. Note that uncertainties in both cases cannot be directly compared, since they were obtained by different methods and that the statistical uncertainties estimated in the latter case should decrease as 7002



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Figure 3. Distance matrix obtained for the initial (center) and final configurations of the trajectories with 20 α-CD (top) or β-CD (bottom) in the slab geometry at 283 (left) and 298 (right) K. Distances lower than 15 Å and larger than 60 Å are represented in red and blue colors, respectively. Intermediate distances are represented by a color gradient as indicated in the figure.

α- and β-CD at 283 K. Practically all the solute molecules aggregate, leading to a unique cluster for both systems within the first 50 ns (Figure 2). Although the individual CD molecules diffuse throughout the cluster, as usually happens for relatively small molecules in larger aggregates,33 the global structure remains stable over the entire trajectories. At 298 K, the results are similar for β-CD. However, α-CD seems to be much more sensitive to the temperature, since several clusters and even free solute molecules are observed in the bulk solution for this temperature. This behavior is exactly what could be expected, at molecular level, from the solubilities of both cyclodextrins as a function of temperature.31 In order to assess this, the distance between all pairs of CD molecules was determined as a function of time. The values corresponding to the initial and final configurations for the trajectories corresponding to α-CD and β-CD at both temperatures are shown as color matrices in Figure 3. The difference between the final configurations for both CDs is evident at 283 and 298 K. The spontaneous aggregation of the cyclodextrins at both temperatures is clearly observed in these simulations, but the adsorption to the solution/air interface is again marginal, with the clusters remaining submerged in the bulk solution during all of the trajectories. This, together with our results obtained from the simulations of CD monomers in slab geometry, indicates that the spontaneous adsorption of CD molecules is unlikely both as monomers and as small aggregates. This agrees well with the expected correlation between molecular adsorption and previously published surface tension measurements. However, the simulation of significantly larger aggregates at the solution/air interface could not be tackled by our atomiclevel simulations due to their high computational cost. The adsorption of such aggregates remains a possibility, mainly considering the difficulties to solubilize cyclodextrins and that the aggregate size scales in real solutions are larger than 100 nm even after filtration.

Altogether, these results indicate that the solute−solute interactions of CDs in aqueous solutions are significantly more important for β-CD than for α-CD at both 283 and 298 K. Additionally, they suggest that the solute−solute interactions for the smaller α-CD are much more important at 283 K than at 298 K while the differences with temperature are negligible for β-CD. The information contained in this section does not provide a conclusive explanation on the different macroscopic behavior between α-CD and β-CD at the solution/air interface nor in the bulk aqueous solution, but it will contribute later to a global discussion. Cyclodextrin Aggregation at the Vicinity of the Water/Air Interface and the Potential Adsorption of the Resulting Structures. Cyclodextrin aqueous solutions do not exhibit an important surface activity between 283 and 298 K; i.e., even at high CD concentrations, the surface tension of the solution is very close to that obtained for pure water.4d,32 However, the slight change detected for this property as a function of CD concentration could be interpreted in terms of cyclodextrin adsorption. Our simulations of single CDs indicate that the affinity of these molecules to the interface is not high, but the possible adsorption of cyclodextrin aggregates should also be investigated. Classical MD simulations at the atomic level are restricted to relatively small systems because the computational cost is, at best, proportional to the number of atoms considered. In order to evaluate the potential adsorption of CD aggregates to the water/air interface, simulations of 20 α- or β-CD molecules starting from random positions and orientations in the bulk solution were performed at 283 and 298 K using the slab geometry (see the Methodology section and Figure 1). These simulations were designed to facilitate both the aggregation and the adsorption of the solute molecules by controlling the local concentration (∼89 mM) and the slab thickness (∼5 nm). Thus, both processes were simultaneously monitored from the corresponding MD trajectories. The aggregation process observed in our simulations is similar for 7003



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Figure 4. Results for the simulation of a single β-CD at 283 K in a fully solvated simulation box. Top: Angle between the perpendicular to the plane of each glucopyranoside ring and the symmetry axis of the β-CD as a function of time. Middle: Root mean square deviation of the β-CD structure (excluding the hydrogen atoms) as a function of time. Bottom: Root mean square fluctuation of the β-CD atoms (excluding the hydrogen atoms) determined from the whole trajectory. The RMSF values were obtained from the last 600 ns of the trajectory, taking the average of the most populated structural cluster (see Figure S7, Supporting Information) as a reference structure. The atom IDs are defined in Figure S3 (Supporting Information).

Table 1. Average Angle (in deg) between the Axis Perpendicular to Each Glucopyranoside Ring and the Symmetry Axis of the Cyclodextrin Throughout the Last 600 ns of Each Trajectorya A1 283 K 298 K a

α-CD β-CD α-CD β-CD

65 47 64 68

± ± ± ±

A2 8 10 9 10

122 71 64 69

± ± ± ±

A3 9 10 9 13

127 99 134 115

± ± ± ±

A4 8 14 9 14

130 130 134 124

± ± ± ±

A5 8 10 9 13

135 133 150 131

± ± ± ±

A6 9 13 6 10

152 136 149 148

± ± ± ±

A7 5 12 6 10

150 ± 7 150 ± 6

The calculations correspond to the simulations with a single cyclodextrin in a fully solvated box.

Structure and Dynamics of Single Cyclodextrins in Water Solution. As described in the Introduction section, simulations of single cyclodextrins at relatively short time scales (5−12 ns) have been previously performed.10,12,13 In the present work, 2 orders of magnitude longer trajectories (0.8 μs) of α- and β-CDs at 283 and 298 K were generated. The differences between α- and β-CDs as a function of temperature are evident from the analysis of the cyclodextrin structure as a function of time. The angle between the perpendicular to the plane of each glucopyranoside ring and the symmetry axis of the CD molecule (see Figure S3, Supporting Information) was measured throughout the trajectories (Figures 4 and S4−S6, Supporting Information). This analysis reveals that the ring angles are discrete with less available states for α-CD than for β-CD. For the smallest cyclodextrin at 283 K, the orientation of the glucopyranoside rings is not stable during the first 20 ns. For the next 100 ns of the trajectory, the six rings are distributed in three states, with two rings for each angle (at approximately 65, 125, and 150°). After ∼120 ns, two of the rings experience a rotation to remain for the rest of the trajectory (120−800 ns) with one ring at ∼150°, four rings at ∼125°, and the last ring close to 65° (Figure S4, Supporting Information, and Table 1). The

behavior of the same cyclodextrin at 298 K was similar, although the final distribution of angles was reached quicker, after the first 60 ns, and it was different with two rings at each angle state. Furthermore, the intermediate state moved to ∼134°. Even though the final angle distribution was different at 283 and 298 K, once it was reached it was stable, with almost negligible fluctuations of the ring orientations, for more than 600 ns in both cases (Figure S5, Supporting Information, and Table 1). This is reflected in the root-mean-square deviation (RMSD) of both trajectories: approximately constant at 0.2 nm upon the reorientation of the rings. The root-mean-square fluctuation (RMSF) of the different atoms reveals that the flexibility of the cyclodextrin does not change significantly with the temperature (Figures S4 and S5, Supporting Information). At both temperatures, the carbon atom attached to the primary hydroxyl group (C6) and the oxygen atoms of all the OH groups (O2, O3, and O6), especially O6, clearly exhibit larger RMSF values than the atoms of the glucopyranoside rings. Note that these RMSF values were obtained from the last 600 ns of the production trajectory upon fitting the nonheavy atoms to the average structure of the most populated structural cluster. Thus, they do not include the effect of the reorientation of the glucopyranoside rings that takes place at the beginning of 7004



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Table 2. Percentage of Structures within Each of the Clusters Represented by the Average Structures Shown in Figures 5 and S7 (Supporting Information), Percentage of Structure out of the Selected Clusters, and Number of Total Clusters Found Using a Cutoff of 1 Å 283 K 298 K

# cluster:

1

2

3

4


86 68 92 77

8.3 16 6.7 7.3

2.7 5.2 0.41 4.9

2.0 4.1 0.27 3.9

the trajectory, which would artificially change the results. Average structures obtained for the most populated clusters (see Table 2), using the g_cluster tool of the GROMACS package with the GROMOS method34 and a cutoff of 1 Å, clearly illustrate the behavior of the cyclodextrin molecules in these simulations (Figure 5). The rotation of the glucopyranoside ring as well as the deformation of the cyclodextrin cavity is evident in most of these structures, mainly at 298 K.

5 2.2 2.0

% of structures out of the clusters

no. of clusters

1.1 5.0 0.43 4.7

20 11 37 31

Nevertheless, the dominant structure of each simulation (top row in Figure 5) preserves enough space in the α-CD cavity to host aliphatic chains (a well suited guest of this cyclodextrin). The results obtained for β-CD were significantly different from those of α-CD. The distribution of angles for the glucopyranoside rings was also discrete, but the number of available states is larger (Figure 4 and S6, Supporting Information). The angles corresponding to the rings of the CD at 283 K at the end of the trajectory are 47 ± 10, 70.9 ± 9.6, and 99 ± 14° for three of the rings, and the angles for the other three rings are close to 133° with small differences between them and the last ring is at 150.0 ± 7.1°. In general, the fluctuation of the angles is more important for β-CD than for α-CD, as indicated by the standard deviations. Most of the rotations observed during the trajectory have a place for the rings orientated at approximately 133°. The behavior at 298 K is similar, but in this case, it seems that there are three angle bands: two rings are orientated at ∼70°, another three rings are at 115 ± 14, 124 ± 13, and 131.4 ± 9.6°, and the other two rings are at ∼150°. No rotations were observed after the first 50 ns of this trajectory. The RMSD is significantly noisier for βCD than for α-CD, and the average value is also larger for the wider cyclodextrin. Surprisingly, the RMSD for β-CD is larger and noisier at 283 K than at 298 K. This observation is reflected in the RMSF values that mainly for the oxygen atoms of the hydroxyl groups are significantly larger at 283 K than at 298 K. Overall, these results indicate that β-CD is more flexible than αCD, which agrees with Jana and Bandyopadhyay,13 but it is in contrast with results previously published by Naidoo et al.10 and Cai et al.12 The different results observed by these authors could be explained by the extremely short time scales of their simulations compared to our trajectories. The average structures obtained from a cluster analysis for the simulations with β-CD illustrate that the internal movements of this molecule are similar to those observed for α-CD: rotations of the glucopyranoside rings and deformation of the CD cavity. However, the number of significantly populated clusters is larger for β-CD than for α-CD, as a result of the higher flexibility of this cyclodextrin. Internal hydrogen bonds between opposite rings in the CD structure are observed upon rotation of the glucopyranoside groups, although these conformations are not dominant in the ensemble (see last row of the first column and fourth row of the second column in Figure S7, Supporting Information, and Table 2). These kinds of internal hydrogen bonds were also observed to a lesser extent for α-CD (Figure 5). It is worth pointing out that at least 50 ns were required to equilibrate the structure of α- and β-CD, and thus, long simulation time scales are necessary to describe the differences and similarities between these cyclodextrins as a function of temperature. The percentage of the trajectory represented by each average structure in Figures 5 and S6 (Supporting Information) together with the number of observed clusters using a cutoff

Figure 5. Average structures obtained from a cluster analysis of all the configurations sampled throughout the trajectories of a single fully solvated α-CD at 283 K (left) and 298 K (right). The structures are ordered by decreasing number of members per cluster from top to bottom. 7005



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hydroxyl groups, are observed. This analysis suggests that the exchange between intramolecular and CD−water hydrogen bonds is much more scarce for β-CD than for α-CD, in line with results observed in previous works.10,12 This is expected to be related to the higher ability of β-CD to self-aggregate and so connected with the lower solubility of this cyclodextrin when compared to α-CD. These intramolecular hydrogen bonds affect the structure of the CDs and thus the amount of solvent molecules within the cavity. No significant differences between CDs or between temperatures were observed for the average number of water molecules inside a sphere of radius 5 Å centered in the center of mass (c.o.m.) of the corresponding cyclodextrin (Figures S10−S12, Supporting Information, and Table 3) even though the cavity of β-CD is slightly wider than

of 1 Å and the percentage of structures out of all the selected clusters are shown in Table 2. For α-CD, the population decays faster than for β-CD, the former requiring just one or two clusters to group more than 90% of the trajectory. This is related to the flexibility of the cyclodextrins. Note that β-CD at 283 K has the lower population of the four simulations in the first cluster, in agreement with the RMSF results. The number of water−CD as well as intramolecular CD−CD hydrogen bonds (determined on the basis of a cutoff of 30° for the angle hydrogen−donor−acceptor and a cutoff of 3.5 Å for the donor−acceptor distance) was also determined for this set of simulations (Figures S8 and S9, Supporting Information). No large differences were observed as a function of the cyclodextrin size or as a function of temperature. For α-CD at 283 K, an average of 37.4 ± 2.7 H-bonds with water was observed throughout the trajectory. This value was not significantly lower at 298 K (35.1 ± 2.9). The slightly higher number of water−CD hydrogen bonds observed for β-CD (40.1 ± 3.1 at 283 K and 41.7 ± 3.2 at 298 K) was expected due to the additional glucopyranoside group of the wider cyclodextrin. The number of intramolecular CD−CD hydrogen bonds was lower than unity, with a standard deviation of approximately 100%, for the simulations with α-CD at both temperatures and for that with β-CD at 298 K. For the simulation with β-CD at 283 K, the number of intramolecular hydrogen bonds was slightly higher (2.01 ± 0.99). It is interesting to follow the dynamic behavior of these hydrogen bonds, since large differences are evident between α-CD and βCD (Figure 6). Several H-bonds are highly stable for the

Table 3. Number of Water Molecules in Different Spheres or Concentric Shells Defined as a Function of the Distance to the Center of Mass of the α-CD or β-CD (Indicated in the First Row)a 0−5 Å 283 K 298 K


6 5 5 6

± ± ± ±

1 1 1 1

5−8 Å 26 26 27 25

± ± ± ±

3 3 3 3

8−9 Å 30 26 30 24

± ± ± ±

4 4 4 4

9−10 Å 42 37 38 38

± ± ± ±

5 5 5 5

0−10 Å 103 94 100 94

± ± ± ±

4 4 4 4

a

The calculations correspond to the simulations with a single cyclodextrin in a fully solvated box.

that of α-CD. For larger distances, the differences between cyclodextrins begin to be appreciable while they remain negligible for the same CD at different temperatures. The smaller size of α-CD justifies this finding, since the bulk water is closer to the center of mass of this cyclodextrin. The average radial distribution functions (RDFs) of the water oxygen atoms around the center of mass of the O4 atoms of two representative CDs for each temperature and cyclodextrin size, calculated over different trajectories, are shown in Figure S16 (Supporting Information). The cyclodextrins buried in the aggregates are clearly drier than single cyclodextrins in solution. The RDF profile is quite different for the different simulations. While that corresponding to a single α-CD at 283 K exhibits a maximum at about 2 Å, the other three simulations of single CDs (α-CD at 298 K and β-CD at both temperatures) have the maximum in the center of mass of the O4 atoms. This is probably due to the displacement of water molecules from the very center of the α-CD, that is occupied by a hydroxyl group of a glucopyranoside unit that rotated at the beginning of that trajectory. The lack of a uniform pattern is probably due to the internal movements of the molecules, since the RDFs are averaged over the trajectories. Cyclodextrin Aggregates in Water Solution. The ability of α-CD and β-CD to form aggregates has already been assessed using the simulations of 20 solute molecules at the vicinity of the air/water interface. This was further explored by duplicating the system as explained in the Methodology section and in Figure 1. Thus, the 40 CD molecules of these simulations are initially distributed in two groups, corresponding to two copies of the final configuration of the simulations of 20 CD molecules at the water/air interface. Our analysis indicates that the aggregates of β-CD grow in size with time both at 283 and 298 K (Figure 7) due to the quick fusion of clusters once they meet each other.

Figure 6. Percentage of occupancy for the most stable intramolecular H-bonds throughout the trajectories of a single fully solvated α-CD (triangles) and β-CD (circles) at 283 K (red) and 298 K (black). The IDs of the atoms involved in each H-bond are indicated next to each point; the numbers correspond to the atom ID (see definition in Figure S3, Supporting Information) and the letters to the GPU ID (from A to F for α-CD and from A to G for β-CD).

simulations with β-CD, mainly at the lower temperature considered. The H-bond that remains stable for more than 50% of the trajectory at 283 K (Figure 6) is clearly visible in the corresponding average structures (Figure S7, left column, Supporting Information). This interaction requires the rotation of two glucopyranoside rings. For α-CD, no strong differences are observed between the simulation at 283 K and that at 298 K and no H-bond was observed to be stable for more than 6.0 or 7.5% of the trajectories at 283 and 298 K, respectively. For both cyclodextrins, H-bonds between contiguous or opposite glucopyranoside rings, both involving primary or secondary 7006



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Figure 7. Number of clusters (top) and number of molecules in the largest cluster (bottom) for the simulations performed with 40 α- (red lines) and 40 β-CD (black lines) at 283 (left) and 298 (right) K in fully solvated boxes. The cutoff distance considered to assign two molecules to the same cluster was 0.35 nm in all cases.

Figure 8. Distance matrix obtained for the initial (center) and final configurations of the trajectories with 40 α-CD (top) or β-CD (bottom) in fully solvated boxes at 283 (left) and 298 (right) K. Distances lower than 15 Å and larger than 60 Å are represented in red and blue colors, respectively. Intermediate distances are represented by a color gradient as indicated in the figure.

In contrast, for α-CD, the size of the clusters remains approximately constant at 298 K and slowly increases at 283 K. The large fluctuations observed for the curves corresponding to the simulations of α-CD in Figure 7 are due to eventual collisions between clusters throughout the trajectories. A better view of the CD aggregation is represented by the distance matrices shown in Figure 8. The differences between the behavior of both cyclodextrins and for both temperatures are evident when comparing the color matrices corresponding to the last configuration of each simulation. The two groups of cyclodextrins are clearly separated in the central matrices of Figure 8. As a result of the fusion between the two clusters consisting of β-CD, the whole matrix becomes more uniform, indicating

that the individual CDs diffuse throughout the final cluster. The ratio red/blue is lower for the simulations using α-CD, mainly at 298 K, indicating that the individual molecules are significantly more separated from each other. Figure 9 shows snapshots corresponding also to the initial and final conformations of these simulations. Note that the CD molecules that are not integrated in the final cluster (Figure 9) are represented by horizontal and vertical blue lines in the corresponding color matrix (Figure 8). Although the number of solute molecules considered in our simulations is relatively low, and so the size of the aggregates is small, from a qualitative point of view, our results are equivalent to those previously reported from several experimental methods, indicating a lower solubility and a higher tendency to aggregate for β-CD than for 7007



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Figure 9. Snapshots corresponding to the initial (center) and final configurations of the trajectories with 40 α-CD (top) or β-CD (bottom) in fully solvated boxes at 283 (left) and 298 (right) K.

Figure 10. Orientational correlation function of the solute molecules in the aggregates of 20 (black lines) and 40 (red lines) α-CD (top) and β-CD (bottom) molecules at 283 (left) and 298 (right) K.

Table 4. Average Number of Waters per CD Molecule in Different Spheres or Concentric Shells Defined as a Function of the Distance to the Center of Mass of Each α-CD or β-CD (Indicated in the First Row)a 0−5 Å 283 K 298 K a


4.1 4.3 4.6 4.1

± ± ± ±

0.2 0.2 0.3 0.3

5−8 Å 22.1 17.5 21.8 17.7

± ± ± ±

0.7 0.5 0.8 0.7

8−9 Å 23.1 17.7 23.3 17.3

± ± ± ±

0.8 0.6 0.9 0.8

9−10 Å 30 26.1 32 26

± ± ± ±

1 0.9 1 1

0−10 Å 80 66 82 65

± ± ± ±

2 1 2 2

The calculations correspond to the simulations with 40 cyclodextrins in a fully solvated box.

α-CD at 298 K as well as a significantly higher ability of α-CD to aggregate at 283 K than at 298 K.31 It is interesting to determine whether or not there is a specific order or a preferential direction of the aggregate to grow. The orientational correlation function of the CD molecules, computed as the average of unitary vectors parallel to the symmetry axis of each cyclodextrin, is negligible for both

CDs and it does not show a clear trend as a function of time at 283 or 298 K (Figure 10). This indicates that the CD orientation is nearly random in all of the obtained aggregates. This result is expected to be related to the most probable conformation of cyclodextrin dimers in layer- or cage-type more than in channel-type, as recently reported by Zhang et al.14 from potential of mean force calculations for β-CD dimer 7008



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the presence of several cosolutes which can be encapsulated and assembled following different patterns that depend on the absolute and relative concentration ratios and on the temperature, among other parameters. The dynamic behavior, structure, and physicochemical or mechanical properties of systems based on these molecules has not been widely explored by experimental or computational methods, and they represent a good opportunity to design new materials and applications. Unfortunately, our work is limited by the reachable time and size scale of atomistic MD simulations. Hopefully, the quick improvement of computational facilities and simulation methods will allow people to deal with aggregates comparable to those observed in real systems without introducing serious approaches. Meanwhile, a real possibility would be to employ multiscale simulation methods that have already been recently applied for similar systems.33 It would be interesting to extend this work by an analogous study based on native γ-cyclodextrin and on a variety of modified cyclodextrins, whose properties are also of great interest, mainly for the pharmaceutical industry. We are currently working in this direction.

dissociation, since the channel-type conformations might induce a more ordered arrangement of large scale CD aggregates. Also, the average number of water molecules around the cyclodextrins was determined (see Table 4 and Figures S13−S15, Supporting Information), showing lower values than those observed for single cyclodextrins (Table 4) for the different shells. As in the case of single CDs, the number of waters within a sphere of radius 1 nm around β-CD is slightly lower than that around α-CD. However, the difference between the number of waters for a single CD and the average number per molecule obtained from the simulations using 40 CDs for a sphere of 1 nm centered in the c.o.m. of each cyclodextrin is significantly larger for β-CD (28.8 ± 5.5 at 283 K and 28.9 ± 6.5 at 298 K) than for α-CD (23.2 ± 6.2 at 283 K and 18.8 ± 6.5 at 298 K). This is a consequence of the presence of larger and more compact aggregates spontaneously formed in the simulations with β-CD (Figures S13−S15, Supporting Information).

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CONCLUSIONS AND PERSPECTIVES Atomic level molecular dynamics simulations of single cyclodextrins as well as of 20 α- or β-cyclodextrin units exposed to the solution/air interface and of 40 CDs in the bulk solution at 283 and 298 K were performed at times scales between 0.2 and 0.8 μs. The adsorption of single cyclodextrins as well as that of spontaneously formed small aggregates was found to be negligible. Solvation free energy calculations, together with the different abilities of both CDs to aggregate, indicate that the solute−solute interactions are significantly larger for β-CD than for α-CD at 298 K and that the dependence of these interactions with temperature is much more important for the smaller cyclodextrin. This results in a more favorable aggregation at 283 K than at 298 K for α-CD, in agreement with the corresponding solubility values.31 Significant differences were observed between the dynamic behavior of both cyclodextrins, with β-CD being clearly more flexible than α-CD, in contrast with conclusions obtained from previous works based on shorter time scale MD trajectories.10,12 Another important difference between both cyclodextrins is revealed by the dynamic exchange of hydrogen bonds between the CD hydroxyl groups and the neighboring water molecules, leading to a much larger occupancy for individual intramolecular H-bonds in the wider cyclodextrin (βCD). This goes in line with previous experimental and computational results that connected the differences in solubility of both cyclodextrins to the interactions with the solvent molecules.8−10 This also matches with the fact that chemical modifications of cyclodextrins, by replacing hydroxyl groups by different residues that perturb the formation of internal hydrogen bonds, dramatically increase the solubility of cyclodextrins. These results are important not only to understand the behavior of cyclodextrins from the fundamental point of view but also because structural and dynamic information at the molecular level are the basis on which more complex systems based on these compounds can be designed in order to optimize practical applications in different areas. We are especially concerned about the adsorption and aggregation of these molecules because they can seriously affect the structure and mechanical response of interfacial films with high viscoelasticity that we have characterized in the past.17a More experimental and theoretical work should be performed on these molecules to further the understanding of CD-based complex systems. They include studies of CDs in

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ASSOCIATED CONTENT

* Supporting Information S

Figures S1−S16 including complementary analysis of the simulations at the interface and in the bulk solution. 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]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Pilar Brocos (Univ. of Santiago de Compostela), Miguel Costas (Univ. Nacional Autónoma de México), and Richard Campbell (Institut Laue-Langevin) for stimulating and useful discussions that encouraged us to perform this study, as well as for their detailed revision of this manuscript. This work was supported by the grant MAT2011-25501 (MINECO, Spain). E.M. is thankful for the support of CONACyT, Mexico, by a postdoctoral fellow (grants 186153 and 203848). We are grateful to the “Centro of Supercomputación de Galicia” (CESGA) for computing time and for their excellent services. We would like to thank the two anonymous reviewers of this manuscript for their thorough revision and helpful suggestions that contributed significantly to improve our work.

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REFERENCES

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Surface Adsorption and Bulk Aggregation of Cyclodextrins by

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