Surface Adsorption and Bulk Aggregation of Cyclodextrins byComputational Molecular Dynamics Simulations as a Function ofTemperature: α‑CD vs β‑CDEdgar Mixcoha,† Jose Campos-Teran,‡ and Angel Pineiro*,†

†Soft Matter & Molecular Biophysics Group, Department of Applied Physics, Universidade de Santiago de Compostela, Santiago deCompostela, 15782, Spain‡Departamento de Procesos y Tecnología, Universidad Autonoma Metropolitana, Unidad Cuajimalpa, Av. Vasco de Quiroga 4871,Col. Santa Fe, Delegacion Cuajimalpa de Morelos, 05348, D.F., Mexico

*S Supporting Information

ABSTRACT: The structural simplicity of native cyclodextrins(CDs) contrasts with their complex behavior in the bulk ofaqueous solutions, mainly when they are combined with othercosolutes. Many scientific and industrial applications based onthese molecules are supported only by empirical information.The lack of fundamental knowledge, which would allow one torationally optimize many of these applications, is notablemainly at the solution/air interface. Basic information onphenomena such as the spontaneous adsorption of native CDsor on the structure of CD aggregates in the bulk solution isreally scarce. In order to fill these gaps, a detailedcomputational study on the adsorption and aggregation of α-and β-CDs as a function of temperature is presented here. Oursimulations reproduce, at atomic resolution, the experimentally observed much higher ability of β-CD to aggregate compared tothat of α-CD at 298 K, as well as their dependence on temperature. The adsorption of both individual CDs and small CDaggregates (up to 20 molecules) to the solution/air interface is found to be negligible. 0.8 μs long trajectories of single CDmolecules 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. Theaggregation pattern of α- and β-CDs is followed at the hundreds of ns time scale, allowing both the spontaneous self-assembly ofcyclodextrins and their redistribution along the aggregates to be observed. This is the first attempt to study the adsorption andaggregation of native cyclodextrins by atomistic molecular dynamics simulations.

■ INTRODUCTION

Natural cyclodextrins (CDs) are cyclic oligosaccharides formedby six (α), seven (β), or eight (γ) 1,4-linked α-D-glucopyrano-side units (GPUs) that result from the enzymatic degradationof starch. These molecules were discovered more than acentury ago, but they are still the focus of many research groupsand novel industrial applications,1 as evidenced by theincreasing number of articles, patents, and commercialapplications based on cyclodextrins that appeared during thelast years.1a,2 The enduring interest in cyclodextrins relies ontheir topology, which provides them with particular phys-icochemical properties, as well as on their high stability and lowtoxicity. Cyclodextrins are typically employed in a wide varietyof industries that include paints, pharmacy, food, cosmetics,agrochemistry, analytical chemistry, catalysis, and chemosensorapplications.1,2 They have been described as truncated coneshaped molecules with a hydrophobic cavity and a hydrophilicexternal surface, the latter of which makes them relativelysoluble in water. The primary and secondary hydroxyl groups of

the GPUs are oriented toward the narrow (tail) and wide(head) edges of the cone, respectively. One of the mostexploited features of these molecules is their ability toencapsulate hydrophobic moieties, increasing the solubility,lowering the volatility, and/or protecting the encapsulatedspecies 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, whichis 1 order of magnitude lower for β-CD than for α- and γ-cyclodextrins (16.3 vs 149 and 179 mM at 298 K,respectively).3 The lack of solubility exhibited by cyclodextrinsat relatively high concentrations has been connected to theirtendency to self-aggregate, forming different supramolecularstructures. There is a clear correlation between the ability of agiven compound to self-aggregate in aqueous solution and its

Received: December 21, 2013Revised: May 18, 2014Published: June 2, 2014

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affinity to the solution/air interface. Typically, low concen-trations of amphiphilic molecules diffuse and remain stable atwater/air interfaces. The aggregation and organization in nano-or microstructures begin to be evident once the surface isnearly saturated. Surfactants clearly illustrate this behavior. Thedependence of the surface tension (σ) on CD concentrationwhen native cyclodextrins are dissolved in water is small(maximum decrease of about 1 mN m−1). This indicates thatCDs are not strongly surface active compounds. Takingadvantage of this fact, several research groups have used σadsorption isotherms of different amphiphilic molecules as afunction of CD concentration to determine the equilibriumconstants of the corresponding host−guest inclusion com-plexes.4 The adsorption constants of native cyclodextrins to thesolution/air interface have been estimated to be 10.7, 49.4, and14.6 L mol−1 at 298 K for α-, β-, and γ-CD, respectively,4d inagreement with the significantly lower solubility of β-CD1a andits higher persistency to form aggregates.5 Publications devotedto the study of cyclodextrins at interfaces are scarce. Arepresentative example of this kind of studies is illustrated bythe work of Ferreira et al.6 who published a detailedcharacterization of a large variety of modified cyclodextrins inthe presence of several phosphanes.The ability of cyclodextrins and cyclodextrin-based com-

plexes to self-aggregate or to dissociate in single monomers inthe bulk of aqueous solutions is key to allow, facilitate, oroptimize the development of many pharmaceutical products,new materials with singular properties, or new moleculardevices based on these molecules. This encouraged a significantnumber of studies and publications during the last years. Avariety of techniques including NMR spectroscopy, X-raydiffraction, small-angle X-ray and neutron scattering, scanningelectron microscopy, (cryogenic) transmission electron micros-copy, dynamic and static light scattering, atomic forcemicroscopy, and computational calculations have beenemployed to characterize CD aggregates in the bulk solutionas well as the cyclodextrin precipitates observed upon differentsample treatments.5,7 Interestingly, it has been reported that β-CDs form larger and more persistent aggregates than α-CD andγ-CD, showing that subtle topological differences at themolecular level are key to the control of physical propertiesof larger scale structures.5 Attempts to explain the differentphysicochemical properties of cyclodextrins at the molecularlevel have been made on the basis of both experimental andcomputational methods. Most of these attempts explain theirresults in terms of the ability of the three native CDs, and theircorresponding aggregates, to interact with the surroundingwater molecules or even to induce a certain degree of structurein the solvent. For instance, Coleman et al. studied thesolubility of cyclodextrins using different cosolvents, includingions, able to disturb the CD−CD intermolecular H-bonds.8

They proposed that the less favorable interaction of β-CD withwater molecules, compared to that of α-CD or γ-CD, explainsthe higher ability of that cyclodextrin to aggregate and so itslower solubility. De Brauer et al. obtained similar conclusionsby heat capacity experiments of anhydrous and hydrated solidCDs.9 A computational study by Naidoo et al.10 agrees with theconclusions previously obtained by Coleman et al. and DeBrauer et al.8b,9 On the basis of 5 ns long molecular dynamics(MD) simulation trajectories, these authors observed that β-CD dramatically increases the structure of the surroundingwater molecules. They also claim that the higher rigidity of thiscyclodextrin, compared to those of α-CD and γ-CD, could be

responsible for this organization of the neighboring solventmolecules. The flexibility of native CDs is thus an importantfactor to take into account when explaining the differences intheir macroscopic properties. This feature has been widelydiscussed by Dodziuk,11 who argued that the previouslyaccepted rigidity of these molecules is not compatible withseveral experimental and computational results. In agreementwith Naidoo et al.,10 a more recent MD study by Cai et al.12

based on 12 ns long trajectories points out that the higherrigidity of β-CD, together with the observed intramolecularhydrogen bonds present in this molecule, induces theorganization of the surrounding water molecules and so itslower solubility. They also concluded that the differences in thesolvation free energy of the native cyclodextrins cannot explaintheir different solubilities. Furthermore, these authors analyzedthe importance of the intramolecular hydrogen bonds andproposed that destroying the internal H-bond network of β-CDshould improve its solubility. In contrast to these results, Janaand Bandyopadhyay, based on 10 ns long MD trajectories,recently claimed that β-CD is more flexible than α-CD.13 Theseauthors performed a detailed analysis on the behavior of watermolecules confined in the cavities of the CDs, including adescription of their translational and rotational motions as wellas of the kinetics of water−water and water−CD H-bonds.However, they do not provide any explanation at the molecularlevel for the low solubility of β-CD compared to those of α-CDand γ-CDs. The importance of the solvent on CD aggregationhas also been highlighted in a recent computational study byZhang et al.14 These authors calculated the potential of meanforce for β-CD dimer dissociation in 10 different solvents ofdifferent polarity. They claim that more polar solvents lead toless stable dimers due to the competition between the solventmolecules and the hydroxyl groups of the cyclodextrins to formH-bonds with each other. The relative orientation of cyclo-dextrins in β-CD dimers is also discussed in the same line, withthe channel-type conformation resulting in being less stablethan the layer- and cage-type dimers in water solution. Nocomparable studies have been done for larger aggregates.Despite the significant advances described above, the

relationship between the slight structural differences of α-and β-CD and the serious differences in their macroscopicproperties is not well understood yet. No studies at molecularlevel have been reported on the ability of these molecules tospontaneously adsorb and aggregate. In this work, we aim to fillthis gap by a detailed computational molecular dynamics studyof these two cyclodextrins at the aqueous-solution/air interfaceas well as in the bulk aqueous solution at 283 and 298 K. Thestructural and dynamic behavior of both single α- and β-cyclodextrins and cyclodextrin aggregates will be characterizedunder these conditions.

■ METHODOLOGYSetup of the Simulation Boxes. Simulations of α- and β-

cyclodextrins were performed at 283 and 298 K using (i) asolvent slab within a larger simulation box, with the solution/airinterface accessible to the solute molecules, and (ii) fullysolvated boxes, with no solution/air interface. For the formertype of simulations, two trajectories were generated at eachtemperature and for each cyclodextrin, namely, one using asingle α- or β-CD at 283 or 298 K and another using 20 α- orβ-CD molecules initially located at random positions andorientations within the water slab, also at both temperatures.The thickness of the solvent slab, final box lengths in the XYZ

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dimensions, and number of water molecules were 4 nm, 5 × 5× 12 nm3, and ∼3300, respectively, for the simulations of singleCDs and 5 nm, 9 × 9 × 15 nm3, and ∼12 600, respectively, forthe simulations with 20 solute molecules. In all of these cases,the slab surface was parallel to the XY plane. For the secondtype 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. Theboxes with slab geometry were minimized and simulated for200 ns, while the simulations of the single CDs in the bulk weresimulated for 800 ns. Finally, the aggregation of α- and β-CD inwater was studied using rectangular boxes with 40 α- or β-cyclodextrins in water. The initial configuration of these lattersystems was constructed by adding a copy of the finalconfiguration of the simulations using 20 α- or β-CD in theslab geometryrotated 180° around the X axison top of theoriginal slab and adjusting the box size to the resulting system(Figure 1). Each of these simulations employed approximately25 000 water molecules. The total length of each of thesetrajectories was 200 ns. All the simulation boxes were energyminimized using the steepest descent method prior to thecalculation of the molecular dynamics trajectories.MD Simulation Parameters. All the simulations were

performed using the GROMACS package15 version 4.5.1 andthe GROMOS96(53a6) force field.16 The cyclodextrin top-ologies were the same as in previous works.17 SPC waters wereemployed to model the solvent in an explicit way. Thesimulations with slab geometry were simulated at constantvolume and temperature, while the NPT ensemble wasemployed for the simulations in the bulk phase. Thetemperature was controlled at 283 or 298 K using a Nose−Hoover thermostat18 with a coupling constant of 0.1 ps. For thesimulations at constant pressure (1 bar), a Parrinello−Rahmanbarostat19 with a coupling constant of 0.5 ps and acompressibility of 4.5 × 10−5 bar−1 was employed. Longrange electrostatic interactions were calculated using theparticle mesh Ewald method20 with a real-space cutoff of 1.2nm, a 0.15 nm spaced grid, and fourth-order B-splineinterpolation. The Ewald sum in three dimensions with acorrection term (EW3DC) was used to avoid artifacts due tointeractions between periodic images in the z direction for thesimulations with slab geometry. Random initial velocities wereassigned to the systems from a Maxwell−Boltzmann distribu-tion at 283 or 298 K, depending on the system. The equationsof motion were integrated using the leapfrog method21 with atime step of 2 fs. The SETTLE22 algorithm was employed toconstrain the bond lengths and angles of water molecules, whilethe LINCS23 algorithm was employed to constrain the bondlengths of the cyclodextrin molecules. During the MDsimulations, coordinates and energies were stored every 10 psfor analysis.

Solvation Free Energy Calculations. The Bennettacceptance ratio (BAR) method24 was employed to determinethe solvation free energy (ΔGsolv) of α- and β-CD at 283 and298 K, i.e., the free energy change to introduce a mole ofmolecules from the gas phase to the bulk of the aqueoussolution. The BAR method is based on Monte Carloacceptance rates of transitions between neighbor states. Suchstates should be close enough to have a significant number oftransitions, which is a requirement for the convergence of themethod. The potential energy of interaction between the α- orβ-CD molecule and the solvent is therefore slowly switched onby a parameter λ that goes from 0 to 1. A number of 47 λ pointswere employed in the present work for each ΔGsolv calculation.In order to optimize the transition rates, the λ values wereunevenly distributed with Δλ = 0.001 for λ values close to 0 and1 and Δλ = 0.05 in the middle λ region. Each of thesesimulations was 5 ns long. Four different structures were takenfor each cyclodextrin and temperature, with the final ΔGsolvvalue being the average between the values obtained for eachcase. Electrostatic and van der Waals solute−solventinteractions were simultaneously switched on in the finalcalculations. The intramolecular interactions of the cyclo-dextrins were not perturbed in any case, since they are presentin both the gas and aqueous solution phases. Each trajectorywas generated using a stochastic dynamics integrator with thesame scheme described above for the electrostatic interactions.To prevent the overlapping of solute−solvent atoms for low λvalues, the soft-core potentials implemented in GROMACS25

with α = 0.5, σ = 0.3, and p = 1 are employed. The data weretreated to get the ΔGsolv values using the GROMACS packagetools.

■ RESULTS AND DISCUSSIONSingle Cyclodextrins at the Water/Air Interface,

Solvation Free Energies, and Their Connection withSolubility. The simulations of single cyclodextrins using slabgeometry indicate that the adsorption of α- and β-CDmonomers at the solution/air interface is not highly favorable.During the trajectories at 283 and 298 K, both α-CD and β-CDdiffuse through the simulation box, occasionally reaching theinterface but always going back in the bulk of the solution aftera short time (see Figure S1 in the Supporting Information).The distance distributions between the center of the slab andthe center of the cyclodextrin show a small shoulder close tothe interface, indicating that the affinity of the CD moleculesfor this region is just slightly higher than that for itsneighborhoods but significantly lower than that for the middlesection of the slab. It is also worth noting that the maximum ofthe shoulder is located at approximately 1.3 nm for all of thesimulations, with the surface being at ∼2 nm. This clearlyindicates that, even when the CD reaches the interface, it does

Figure 1. Scheme illustrating the initial (A, C) and final (B, D) configurations of the cyclodextrin solutions with slab geometry (A, B) and in fullysolvated 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 fordetails.

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not stick out but remains fully hydrated (note that 0.7 nm, thedifference between 2 and 1.3 nm, is a reasonable value toapproach the average radius of these molecules). No significantdifferences in this behavior were observed between both CDsor as a function of temperature. The surface tension of asolution depends on the concentration of the solute at theinterface. Actually, this is the basis on which semiempiricaladsorption isotherms are typically proposed.26 For significantsolute concentration at interfaces, the surface tension changecould be estimated by MD simulations.27 In this case, thepractically negligible adsorption of CDs is compatible with theexperimentally observed independence of surface tension oncyclodextrin concentration.The ability of a solute molecule to adsorb to the water/air

interface in aqueous solution is expected to be related to itssolvation free energy, since this thermodynamic propertyassesses the affinity to the solvent taking the gas phase as areference. The ΔGsolv values of α- and β-CDs at bothtemperatures were calculated using the BAR method, asdescribed above. The values obtained by using just the lastconformation from each trajectory as the initial structure were−325.6 ± 1.4 and −294.06 ± 0.69 kJ·mol−1 for α-CD at 283and 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 lowuncertainty for the ΔGsolv values (see Figure S2 in theSupporting Information). Since the use of a single structure forthis calculation might limit the sampling to a local minimum,three repeats of each calculation were performed by using arepresentative structure of each of the three dominant clustersfor each trajectory (see below the description and results of thecluster analysis). The averages between the four ΔGsolv valueswere −322 ± 11 and −294 ± 3 kJ·mol−1 for α-CD at 283 and298 K, respectively, and −333 ± 11 and −333 ± 13 kJ·mol−1

for β-CD at the same temperatures. As it can be seen, thedifferences between cyclodextrins and temperatures stand butthe uncertainties (the standard deviation of the average in thiscase) are now significantly larger. Note that uncertainties inboth cases cannot be directly compared, since they wereobtained by different methods and that the statisticaluncertainties estimated in the latter case should decrease as

the number of repeats increases. ΔGsolv values have beenproposed to be distributed in several contributions: cavityformation, electrostatic and dispersion interaction, and hydro-gen bond formation.28 The electrostatic and van der WaalsCD−water interactions were simultaneously switched on forthese calculations because preliminary tests using 20 and 30 λvalues revealed that the van der Waals contribution is positiveand small: about 5% of the total ΔGsolv in all cases. Thesimultaneous consideration of both contributions allowed us tohalf the simulation time for these calculations with nosignificant worsening in the uncertainties. The role of CD−CD and CD−water hydrogen bonds will be discussed later inthis work, while the contribution of the cavity formation wasnot explicitly determined. Our results are similar to thosepreviously published by Danhong Zhou et al.29 who obtained aΔGsolv value of −367 kJ·mol−1 for α-CD at 298 K with acontribution of the nonpolar interactions (van der Waals + thefree 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 valuesfor α- and β-CD at 298 K that differ from the previous resultsby 1 order of magnitude: −36.8 and −51.5 kJ·mol−1 for α- andβ-CD, respectively. Semiempirical quantum calculations usingthe AMSOL program30 with the PM3 Hamiltonian wereperformed in order to have an independent estimation ofΔGsolv for α-CD at 298 K. The obtained value (−323.03 kJ·mol−1) agrees reasonably well with our results obtained by MDsimulations.It is well-known that the solubility of β-CD is much lower

than that of α-CD.3 The connection between solvation freeenergies and solubilities is not direct, since the former propertyis related to the interactions with the solvent while thesolubility is related to the balance between solute−solvent andsolute−solute interactions. In this work, we are determining thesolvation free energy as the work to transfer 1 mol of isolatedsolute molecules from the gas phase to the solution, withoutconsidering the solute−solute interaction. The solubility of α-CD has been reported to vary significantly with temperature: 39and 130 mM at 283 and 298 K, respectively. The dependenceof the β-CD solubility on the temperature is much lower, goingfrom 13.5 mM at 283 K to 16.7 mM at 298 K31 (values at 283K were extrapolated).

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 samecluster was 0.35 nm in all cases.

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Altogether, these results indicate that the solute−soluteinteractions of CDs in aqueous solutions are significantly moreimportant for β-CD than for α-CD at both 283 and 298 K.Additionally, they suggest that the solute−solute interactionsfor the smaller α-CD are much more important at 283 K thanat 298 K while the differences with temperature are negligiblefor β-CD. The information contained in this section does notprovide a conclusive explanation on the different macroscopicbehavior between α-CD and β-CD at the solution/air interfacenor in the bulk aqueous solution, but it will contribute later to aglobal discussion.Cyclodextrin Aggregation at the Vicinity of the

Water/Air Interface and the Potential Adsorption ofthe Resulting Structures. Cyclodextrin aqueous solutions donot exhibit an important surface activity between 283 and 298K; i.e., even at high CD concentrations, the surface tension ofthe solution is very close to that obtained for pure water.4d,32

However, the slight change detected for this property as afunction of CD concentration could be interpreted in terms ofcyclodextrin adsorption. Our simulations of single CDs indicatethat the affinity of these molecules to the interface is not high,but the possible adsorption of cyclodextrin aggregates shouldalso be investigated. Classical MD simulations at the atomiclevel are restricted to relatively small systems because thecomputational cost is, at best, proportional to the number ofatoms considered. In order to evaluate the potential adsorptionof CD aggregates to the water/air interface, simulations of 20α- or β-CD molecules starting from random positions andorientations in the bulk solution were performed at 283 and298 K using the slab geometry (see the Methodology sectionand Figure 1). These simulations were designed to facilitateboth the aggregation and the adsorption of the solute moleculesby controlling the local concentration (∼89 mM) and the slabthickness (∼5 nm). Thus, both processes were simultaneouslymonitored from the corresponding MD trajectories. Theaggregation process observed in our simulations is similar for

α- and β-CD at 283 K. Practically all the solute moleculesaggregate, leading to a unique cluster for both systems withinthe first 50 ns (Figure 2). Although the individual CDmolecules diffuse throughout the cluster, as usually happens forrelatively small molecules in larger aggregates,33 the globalstructure remains stable over the entire trajectories. At 298 K,the results are similar for β-CD. However, α-CD seems to bemuch more sensitive to the temperature, since several clustersand even free solute molecules are observed in the bulksolution for this temperature. This behavior is exactly whatcould be expected, at molecular level, from the solubilities ofboth cyclodextrins as a function of temperature.31 In order toassess this, the distance between all pairs of CD molecules wasdetermined as a function of time. The values corresponding tothe initial and final configurations for the trajectoriescorresponding to α-CD and β-CD at both temperatures areshown as color matrices in Figure 3. The difference betweenthe final configurations for both CDs is evident at 283 and 298K.The spontaneous aggregation of the cyclodextrins at both

temperatures is clearly observed in these simulations, but theadsorption to the solution/air interface is again marginal, withthe clusters remaining submerged in the bulk solution during allof the trajectories. This, together with our results obtained fromthe simulations of CD monomers in slab geometry, indicatesthat the spontaneous adsorption of CD molecules is unlikelyboth as monomers and as small aggregates. This agrees wellwith the expected correlation between molecular adsorptionand previously published surface tension measurements.However, the simulation of significantly larger aggregates atthe solution/air interface could not be tackled by our atomic-level simulations due to their high computational cost. Theadsorption of such aggregates remains a possibility, mainlyconsidering the difficulties to solubilize cyclodextrins and thatthe aggregate size scales in real solutions are larger than 100 nmeven after filtration.

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 theslab 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.

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Structure and Dynamics of Single Cyclodextrins inWater 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 thepresent work, 2 orders of magnitude longer trajectories (0.8 μs)of α- and β-CDs at 283 and 298 K were generated. Thedifferences between α- and β-CDs as a function of temperatureare evident from the analysis of the cyclodextrin structure as afunction of time. The angle between the perpendicular to theplane of each glucopyranoside ring and the symmetry axis ofthe CD molecule (see Figure S3, Supporting Information) wasmeasured 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 smallestcyclodextrin at 283 K, the orientation of the glucopyranosiderings is not stable during the first 20 ns. For the next 100 ns ofthe trajectory, the six rings are distributed in three states, withtwo rings for each angle (at approximately 65, 125, and 150°).After ∼120 ns, two of the rings experience a rotation to remainfor 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 eachangle state. Furthermore, the intermediate state moved to∼134°. Even though the final angle distribution was different at283 and 298 K, once it was reached it was stable, with almostnegligible fluctuations of the ring orientations, for more than600 ns in both cases (Figure S5, Supporting Information, andTable 1). This is reflected in the root-mean-square deviation(RMSD) of both trajectories: approximately constant at 0.2 nmupon the reorientation of the rings. The root-mean-squarefluctuation (RMSF) of the different atoms reveals that theflexibility of the cyclodextrin does not change significantly withthe temperature (Figures S4 and S5, Supporting Information).At both temperatures, the carbon atom attached to the primaryhydroxyl group (C6) and the oxygen atoms of all the OHgroups (O2, O3, and O6), especially O6, clearly exhibit largerRMSF values than the atoms of the glucopyranoside rings.Note that these RMSF values were obtained from the last 600ns of the production trajectory upon fitting the nonheavy atomsto the average structure of the most populated structuralcluster. Thus, they do not include the effect of the reorientationof the glucopyranoside rings that takes place at the beginning of

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 planeof 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 mostpopulated structural cluster (see Figure S7, Supporting Information) as a reference structure. The atom IDs are defined in Figure S3 (SupportingInformation).

Table 1. Average Angle (in deg) between the Axis Perpendicular to Each Glucopyranoside Ring and the Symmetry Axis of theCyclodextrin Throughout the Last 600 ns of Each Trajectorya

A1 A2 A3 A4 A5 A6 A7

283 K α-CD 65 ± 8 122 ± 9 127 ± 8 130 ± 8 135 ± 9 152 ± 5β-CD 47 ± 10 71 ± 10 99 ± 14 130 ± 10 133 ± 13 136 ± 12 150 ± 7

298 K α-CD 64 ± 9 64 ± 9 134 ± 9 134 ± 9 150 ± 6 149 ± 6β-CD 68 ± 10 69 ± 13 115 ± 14 124 ± 13 131 ± 10 148 ± 10 150 ± 6

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

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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 GROMACSpackage with the GROMOS method34 and a cutoff of 1 Å,clearly illustrate the behavior of the cyclodextrin molecules inthese simulations (Figure 5). The rotation of the glucopyrano-side ring as well as the deformation of the cyclodextrin cavity isevident in most of these structures, mainly at 298 K.

Nevertheless, the dominant structure of each simulation (toprow in Figure 5) preserves enough space in the α-CD cavity tohost 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 theglucopyranoside rings was also discrete, but the number ofavailable states is larger (Figure 4 and S6, SupportingInformation). The angles corresponding to the rings of theCD 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 theother three rings are close to 133° with small differencesbetween them and the last ring is at 150.0 ± 7.1°. In general,the fluctuation of the angles is more important for β-CD thanfor α-CD, as indicated by the standard deviations. Most of therotations observed during the trajectory have a place for therings orientated at approximately 133°. The behavior at 298 Kis similar, but in this case, it seems that there are three anglebands: two rings are orientated at ∼70°, another three rings areat 115 ± 14, 124 ± 13, and 131.4 ± 9.6°, and the other tworings are at ∼150°. No rotations were observed after the first 50ns of this trajectory. The RMSD is significantly noisier for β-CD than for α-CD, and the average value is also larger for thewider cyclodextrin. Surprisingly, the RMSD for β-CD is largerand noisier at 283 K than at 298 K. This observation is reflectedin the RMSF values that mainly for the oxygen atoms of thehydroxyl groups are significantly larger at 283 K than at 298 K.Overall, these results indicate that β-CD is more flexible than α-CD, which agrees with Jana and Bandyopadhyay,13 but it is incontrast with results previously published by Naidoo et al.10

and Cai et al.12 The different results observed by these authorscould be explained by the extremely short time scales of theirsimulations compared to our trajectories.The average structures obtained from a cluster analysis for

the simulations with β-CD illustrate that the internal move-ments of this molecule are similar to those observed for α-CD:rotations of the glucopyranoside rings and deformation of theCD cavity. However, the number of significantly populatedclusters is larger for β-CD than for α-CD, as a result of thehigher flexibility of this cyclodextrin. Internal hydrogen bondsbetween opposite rings in the CD structure are observed uponrotation of the glucopyranoside groups, although theseconformations are not dominant in the ensemble (see lastrow of the first column and fourth row of the second column inFigure S7, Supporting Information, and Table 2). These kindsof internal hydrogen bonds were also observed to a lesserextent for α-CD (Figure 5). It is worth pointing out that at least50 ns were required to equilibrate the structure of α- and β-CD,and thus, long simulation time scales are necessary to describethe differences and similarities between these cyclodextrins as afunction 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

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 aCutoff of 1 Å

# cluster: 1 2 3 4 5 % of structures out of the clusters no. of clusters

283 K α-CD 86 8.3 2.7 2.0 1.1 20β-CD 68 16 5.2 4.1 2.2 5.0 11

298 K α-CD 92 6.7 0.41 0.27 0.43 37β-CD 77 7.3 4.9 3.9 2.0 4.7 31

Figure 5. Average structures obtained from a cluster analysis of all theconfigurations sampled throughout the trajectories of a single fullysolvated α-CD at 283 K (left) and 298 K (right). The structures areordered by decreasing number of members per cluster from top tobottom.

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of 1 Å and the percentage of structures out of all the selectedclusters are shown in Table 2. For α-CD, the population decaysfaster than for β-CD, the former requiring just one or twoclusters to group more than 90% of the trajectory. This isrelated to the flexibility of the cyclodextrins. Note that β-CD at283 K has the lower population of the four simulations in thefirst 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° forthe angle hydrogen−donor−acceptor and a cutoff of 3.5 Å forthe donor−acceptor distance) was also determined for this setof simulations (Figures S8 and S9, Supporting Information).No large differences were observed as a function of thecyclodextrin size or as a function of temperature. For α-CD at283 K, an average of 37.4 ± 2.7 H-bonds with water wasobserved throughout the trajectory. This value was notsignificantly lower at 298 K (35.1 ± 2.9). The slightly highernumber 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 expecteddue to the additional glucopyranoside group of the widercyclodextrin. The number of intramolecular CD−CD hydrogenbonds was lower than unity, with a standard deviation ofapproximately 100%, for the simulations with α-CD at bothtemperatures and for that with β-CD at 298 K. For thesimulation with β-CD at 283 K, the number of intramolecularhydrogen bonds was slightly higher (2.01 ± 0.99). It isinteresting to follow the dynamic behavior of these hydrogenbonds, since large differences are evident between α-CD and β-CD (Figure 6). Several H-bonds are highly stable for the

simulations with β-CD, mainly at the lower temperatureconsidered. The H-bond that remains stable for more than 50%of the trajectory at 283 K (Figure 6) is clearly visible in thecorresponding average structures (Figure S7, left column,Supporting Information). This interaction requires the rotationof two glucopyranoside rings. For α-CD, no strong differencesare observed between the simulation at 283 K and that at 298 Kand no H-bond was observed to be stable for more than 6.0 or7.5% of the trajectories at 283 and 298 K, respectively. For bothcyclodextrins, H-bonds between contiguous or oppositeglucopyranoside rings, both involving primary or secondary

hydroxyl groups, are observed. This analysis suggests that theexchange between intramolecular and CD−water hydrogenbonds is much more scarce for β-CD than for α-CD, in linewith results observed in previous works.10,12 This is expected tobe related to the higher ability of β-CD to self-aggregate and soconnected with the lower solubility of this cyclodextrin whencompared to α-CD. These intramolecular hydrogen bondsaffect the structure of the CDs and thus the amount of solventmolecules within the cavity. No significant differences betweenCDs or between temperatures were observed for the averagenumber of water molecules inside a sphere of radius 5 Åcentered in the center of mass (c.o.m.) of the correspondingcyclodextrin (Figures S10−S12, Supporting Information, andTable 3) even though the cavity of β-CD is slightly wider than

that of α-CD. For larger distances, the differences betweencyclodextrins begin to be appreciable while they remainnegligible for the same CD at different temperatures. Thesmaller size of α-CD justifies this finding, since the bulk water iscloser to the center of mass of this cyclodextrin. The averageradial distribution functions (RDFs) of the water oxygen atomsaround the center of mass of the O4 atoms of tworepresentative CDs for each temperature and cyclodextrinsize, calculated over different trajectories, are shown in FigureS16 (Supporting Information). The cyclodextrins buried in theaggregates 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 amaximum at about 2 Å, the other three simulations of singleCDs (α-CD at 298 K and β-CD at both temperatures) have themaximum in the center of mass of the O4 atoms. This isprobably due to the displacement of water molecules from thevery center of the α-CD, that is occupied by a hydroxyl groupof a glucopyranoside unit that rotated at the beginning of thattrajectory. The lack of a uniform pattern is probably due to theinternal movements of the molecules, since the RDFs areaveraged over the trajectories.

Cyclodextrin Aggregates in Water Solution. The abilityof α-CD and β-CD to form aggregates has already beenassessed using the simulations of 20 solute molecules at thevicinity of the air/water interface. This was further explored byduplicating the system as explained in the Methodology sectionand in Figure 1. Thus, the 40 CD molecules of thesesimulations are initially distributed in two groups, correspond-ing to two copies of the final configuration of the simulations of20 CD molecules at the water/air interface. Our analysisindicates that the aggregates of β-CD grow in size with timeboth at 283 and 298 K (Figure 7) due to the quick fusion ofclusters once they meet each other.

Figure 6. Percentage of occupancy for the most stable intramolecularH-bonds throughout the trajectories of a single fully solvated α-CD(triangles) and β-CD (circles) at 283 K (red) and 298 K (black). TheIDs of the atoms involved in each H-bond are indicated next to eachpoint; the numbers correspond to the atom ID (see definition inFigure 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).

Table 3. Number of Water Molecules in Different Spheres orConcentric Shells Defined as a Function of the Distance tothe Center of Mass of the α-CD or β-CD (Indicated in theFirst Row)a

0−5 Å 5−8 Å 8−9 Å 9−10 Å 0−10 Å

283 K α-CD 6 ± 1 26 ± 3 30 ± 4 42 ± 5 103 ± 4β-CD 5 ± 1 26 ± 3 26 ± 4 37 ± 5 94 ± 4

298 K α-CD 5 ± 1 27 ± 3 30 ± 4 38 ± 5 100 ± 4β-CD 6 ± 1 25 ± 3 24 ± 4 38 ± 5 94 ± 4

aThe calculations correspond to the simulations with a singlecyclodextrin in a fully solvated box.

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In contrast, for α-CD, the size of the clusters remainsapproximately constant at 298 K and slowly increases at 283 K.The large fluctuations observed for the curves corresponding tothe simulations of α-CD in Figure 7 are due to eventualcollisions between clusters throughout the trajectories. A betterview of the CD aggregation is represented by the distancematrices shown in Figure 8. The differences between thebehavior of both cyclodextrins and for both temperatures areevident when comparing the color matrices corresponding tothe last configuration of each simulation. The two groups ofcyclodextrins are clearly separated in the central matrices ofFigure 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. Theratio red/blue is lower for the simulations using α-CD, mainlyat 298 K, indicating that the individual molecules aresignificantly more separated from each other. Figure 9 showssnapshots corresponding also to the initial and finalconformations of these simulations. Note that the CDmolecules that are not integrated in the final cluster (Figure9) are represented by horizontal and vertical blue lines in thecorresponding color matrix (Figure 8). Although the number ofsolute molecules considered in our simulations is relatively low,and so the size of the aggregates is small, from a qualitativepoint of view, our results are equivalent to those previouslyreported from several experimental methods, indicating a lowersolubility and a higher tendency to aggregate for β-CD than for

Figure 7. Number of clusters (top) and number of molecules in the largest cluster (bottom) for the simulations performed with 40 α- (red lines) and40 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 samecluster 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 fullysolvated 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.

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α-CD at 298 K as well as a significantly higher ability of α-CDto aggregate at 283 K than at 298 K.31

It is interesting to determine whether or not there is aspecific order or a preferential direction of the aggregate togrow. The orientational correlation function of the CDmolecules, computed as the average of unitary vectors parallelto the symmetry axis of each cyclodextrin, is negligible for both

CDs and it does not show a clear trend as a function of time at283 or 298 K (Figure 10). This indicates that the CDorientation is nearly random in all of the obtained aggregates.This result is expected to be related to the most probableconformation of cyclodextrin dimers in layer- or cage-typemore than in channel-type, as recently reported by Zhang etal.14 from potential of mean force calculations for β-CD dimer

Figure 9. Snapshots corresponding to the initial (center) and final configurations of the trajectories with 40 α-CD (top) or β-CD (bottom) in fullysolvated 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 theDistance to the Center of Mass of Each α-CD or β-CD (Indicated in the First Row)a

0−5 Å 5−8 Å 8−9 Å 9−10 Å 0−10 Å

283 K α-CD 4.1 ± 0.2 22.1 ± 0.7 23.1 ± 0.8 30 ± 1 80 ± 2β-CD 4.3 ± 0.2 17.5 ± 0.5 17.7 ± 0.6 26.1 ± 0.9 66 ± 1

298 K α-CD 4.6 ± 0.3 21.8 ± 0.8 23.3 ± 0.9 32 ± 1 82 ± 2β-CD 4.1 ± 0.3 17.7 ± 0.7 17.3 ± 0.8 26 ± 1 65 ± 2

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

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dissociation, since the channel-type conformations mightinduce a more ordered arrangement of large scale CDaggregates. Also, the average number of water moleculesaround the cyclodextrins was determined (see Table 4 andFigures S13−S15, Supporting Information), showing lowervalues than those observed for single cyclodextrins (Table 4)for the different shells. As in the case of single CDs, the numberof waters within a sphere of radius 1 nm around β-CD isslightly lower than that around α-CD. However, the differencebetween the number of waters for a single CD and the averagenumber per molecule obtained from the simulations using 40CDs for a sphere of 1 nm centered in the c.o.m. of eachcyclodextrin is significantly larger for β-CD (28.8 ± 5.5 at 283K and 28.9 ± 6.5 at 298 K) than for α-CD (23.2 ± 6.2 at 283 Kand 18.8 ± 6.5 at 298 K). This is a consequence of the presenceof larger and more compact aggregates spontaneously formedin the simulations with β-CD (Figures S13−S15, SupportingInformation).

■ CONCLUSIONS AND PERSPECTIVESAtomic level molecular dynamics simulations of singlecyclodextrins as well as of 20 α- or β-cyclodextrin unitsexposed to the solution/air interface and of 40 CDs in the bulksolution at 283 and 298 K were performed at times scalesbetween 0.2 and 0.8 μs. The adsorption of single cyclodextrinsas well as that of spontaneously formed small aggregates wasfound to be negligible. Solvation free energy calculations,together with the different abilities of both CDs to aggregate,indicate that the solute−solute interactions are significantlylarger for β-CD than for α-CD at 298 K and that thedependence of these interactions with temperature is muchmore important for the smaller cyclodextrin. This results in amore favorable aggregation at 283 K than at 298 K for α-CD, inagreement with the corresponding solubility values.31 Signifi-cant differences were observed between the dynamic behaviorof both cyclodextrins, with β-CD being clearly more flexiblethan α-CD, in contrast with conclusions obtained fromprevious works based on shorter time scale MD trajecto-ries.10,12 Another important difference between both cyclo-dextrins is revealed by the dynamic exchange of hydrogenbonds between the CD hydroxyl groups and the neighboringwater molecules, leading to a much larger occupancy forindividual intramolecular H-bonds in the wider cyclodextrin (β-CD). This goes in line with previous experimental andcomputational results that connected the differences insolubility of both cyclodextrins to the interactions with thesolvent molecules.8−10 This also matches with the fact thatchemical modifications of cyclodextrins, by replacing hydroxylgroups by different residues that perturb the formation ofinternal hydrogen bonds, dramatically increase the solubility ofcyclodextrins. These results are important not only tounderstand the behavior of cyclodextrins from the fundamentalpoint of view but also because structural and dynamicinformation at the molecular level are the basis on whichmore complex systems based on these compounds can bedesigned in order to optimize practical applications in differentareas. We are especially concerned about the adsorption andaggregation of these molecules because they can seriously affectthe structure and mechanical response of interfacial films withhigh viscoelasticity that we have characterized in the past.17a

More experimental and theoretical work should beperformed on these molecules to further the understandingof CD-based complex systems. They include studies of CDs in

the presence of several cosolutes which can be encapsulatedand assembled following different patterns that depend on theabsolute and relative concentration ratios and on thetemperature, among other parameters. The dynamic behavior,structure, and physicochemical or mechanical properties ofsystems based on these molecules has not been widely exploredby experimental or computational methods, and they representa good opportunity to design new materials and applications.Unfortunately, our work is limited by the reachable time andsize scale of atomistic MD simulations. Hopefully, the quickimprovement of computational facilities and simulationmethods will allow people to deal with aggregates comparableto those observed in real systems without introducing seriousapproaches. Meanwhile, a real possibility would be to employmultiscale simulation methods that have already been recentlyapplied for similar systems.33 It would be interesting to extendthis work by an analogous study based on native γ-cyclodextrinand on a variety of modified cyclodextrins, whose properties arealso of great interest, mainly for the pharmaceutical industry.We are currently working in this direction.

■ ASSOCIATED CONTENT*S Supporting InformationFigures S1−S16 including complementary analysis of thesimulations at the interface and in the bulk solution. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: Angel.Pineiro@usc.es.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank Pilar Brocos (Univ. of Santiago de Compostela),Miguel Costas (Univ. Nacional Autonoma de Mexico), andRichard Campbell (Institut Laue-Langevin) for stimulating anduseful discussions that encouraged us to perform this study, aswell as for their detailed revision of this manuscript. This workwas 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 aregrateful to the “Centro of Supercomputacion de Galicia”(CESGA) for computing time and for their excellent services.We would like to thank the two anonymous reviewers of thismanuscript for their thorough revision and helpful suggestionsthat contributed significantly to improve our work.

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