**3. Computational observations**

The channel-type assembly is observed if the CDs are stacked in columns so that cavities are aligned to produce channels (**Figure 1c**). While the channel arrangement can be converted into a cage structure by water sorption/desorption cycles, with an intermediated amorphous state, the latter usually results from rapid recrystallization of CDs. After reaching sorption equilibrium, CD molecules undergo a slow rearrangement to the cage structure with defined water content [66]. Similar patterns are generally found in the crystal structures of CD inclusion complexes [66]. When the entire guest molecule is small enough to be included inside a single CD cavity, cage-type structures are formed. On the other hand, a channel-type structure is observed in the presence of long-chain molecules as guests (e.g., polymers). Rusa and co-workers [2, 67] have reported the encapsulation of poly(ε-caprolactone) and poly(l-lactic acid) into α- and γ-CDs. The inclusion of a polymeric structure inside the CD cavity induces the formation of channel-like structures, being those with α-CD more stable due to the increase of hydrophobic CD-polymer interactions. By using an appropriate experimental procedure, the authors were able to produce a solid-state channel packing of CDs containing only water molecules inside the cavities [68]. The same group has also observed the inclusion of poly(vinyl alcohol) (PVA) into CD by taking advantage of the freezing–thawing process for PVA gelation [69]. In this process, the gelation of PVA-containing composites occurs, taking into account two different types of cross-linking: (i) the hydrogel-bonding naturally observed during the freezing-thawing process

and (ii) the CD-CD aggregation resulting from channel-type arrangements [69].

As already mentioned in previous sections, a variety of CD-based aggregates can be formed under different conditions (e.g., concentration, solvent medium, and temperature). These include native and modified CDs, inclusion complexes and the respective aggregates and also rotaxanes and polyrotaxanes, nanotubes, and other high-order structures, such as nanospheres and network aggregates [70]. The potential uses of these self-assembled nanomaterials have been explored for advanced applications, ranging from drug solubilization and drug delivery [71], selective binding [72], and controlled adsorption [72]. In pharmaceutical and biomedical fields, it is expected that such applications may include (i) the nanoencapsulation of drugs in the hydrophobic interchain volumes and nanocavities of modified CDs, which can be used as drug carriers or pharmaceutical excipients, (ii) anticancer phototherapy, (iii) gene delivery, and (iv) protection of unstable active components through the formation of inclusion complexes [70]. Several interesting examples of these potential applications have been focused on amphiphilic CDs, which allow to easily modulate both hydrophobic/hydrophilic and self-assembly properties, by grafting different substituents on the portals of native CDs [70, 73]. For instance, supramolecular assemblies based on CD/porphyrin nanoassemblies have been studied *in vitro* [74] as potential nanotherapeutics in A375 human melanoma cells. Other micellar structures and spherical vesicles based on CD-perylene conjugates have been designed to be included in fluorescence sensory and photoresponsive materials, photoinduced electron transfer systems, and organic electronic devices [75]. The self-aggregation of amphiphilic CDs has also been explored for drug delivery applications, as they are able to capture selectively drug molecules, displaying enhanced solubilization capacity [71]. The affinity of amphiphilic CDs for incorporation in model and biological membranes has

**2.3. Applications of CD aggregates**

52 Cyclodextrin - A Versatile Ingredient

Irrespective of the disparate observations, the self-aggregation capability must be affected by the type of CD present in the aqueous solution. While the aggregates of α-CD and γ-CD can be completely removed by standard filtering procedures, the formation of β-CD aggregates (at least as dimers or possibly larger aggregates) persists in solution, displaying fast aggregation kinetics. This suggests that the hydrophilic CD portals play a definite role in the aggregation process [29]. The disruption of hydrogen bond networks by ionization (or functionalization) increases solubility and may suppress aggregation.

The presence of aggregates in solutions containing structure-breaking solutes, in which the solubility of β-CD is enhanced, has provided new insights into this unusual behavior. The low solubility of β-CD (see **Table 1**) has been explained by the presence of aggregates and the respective unfavorable interaction with the hydrogen bond network of bulk water [46]. Note that aspects pertaining to the binding energy in the solid state cannot be disregarded. The relevance of understanding the mechanistic details of the CD aggregation phenomena encompasses either controlling/preventing the formation of aggregates (that preclude the development of specific formulations and the product development) or designing novel formulation strategies.

Computer simulations have been used to rationalize the experimental findings concerning recognition [77], inclusion [36, 77–79], and aggregation [34, 35, 37, 39, 80]. The cooperative binding of at least two CD monomers to a guest molecule has been considered the driving force responsible for self-assembly processes in the construction of CD-based nanoarchitectures [78]. For aggregation processes without using guests, the assembly is usually driven by the hydrophilic portals (in native CDs) and by interactions between substituent chains of CD derivatives with the neighboring cavities of other CDs [78].

The orientational patterns of inter-glucopyranose hydrogen bonds at the secondary portal of β-CD and the respective effect on the CD structure and dimer binding/stability in polar and nonpolar solvents have been explored by van der Spoel et al. [77] in the presence of various guest molecules. It was demonstrated, based on MD simulations and free energy calculations, that polar solvents with stronger hydrogen bond accepting abilities can easily disrupt intermolecular hydrogen bonds, resulting in less stable dimers. Also, the guest models included in the channel-type cavity increase the binding affinity between CD monomers, particularly in polar solvents [77]. Using a similar computational approach, the authors have explored the effect of three different dimerization modes of β-CD molecules and the presence of isoflavone drug analogues in the construction of CD-based nanostructured materials. It was demonstrated that the cooperative binding of CD cavities to guest molecules favors the dimerization process and, consequently, the overall stability and assembly of the CD nanostructures. It was also proved that the desolvation of CD dimers and entropy changes upon complexation cooperatively contributes to the binding process [78].

allows evaluating the conformational prevalence of each CD-CD structure, by determining dominant clusters based on the root mean square deviation of the atom positions between all pairs of structures. For each CD-CD arrangement, the number of neighboring structures is calculated for RMSD values of 0.35 nm. **Figure 3** presents the behavior of CD-CD structures in different simulation runs, each corresponding to a different initial arrangement. For each CD backbone, the center of mass (COM) of the oxygen atoms at the secondary portal (S) was defined as the reference point for evaluating aggregated and nonaggregated structures and

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For PS and PP as initial arrangements, a significant evolution is observed in the relative positioning of the two molecules. The PS and PP initial arrangements display an almost complete rotation or a tilt of one molecule with respect to the other, leading to most favorable SS and PS arrangements, respectively. The "intermediate" PS arrangement increases the CD-CD interactions through partial inclusion of some P groups in the hydrophobic cavity of the other CD molecule. The initial SS arrangement prevails over the course of the simulation with a typical COM distance of 0.46 nm. In addition to intramolecular hydrogen bonds, the two CD molecules can form additional intermolecular hydrogen bonds, optimizing the CD-CD interaction. PS is an intermediate arrangement between the most (SS) and the least stable (PP) arrangements. The PP arrangement of the CD pair involves weaker interactions between P groups of the two molecules, producing a low prevalence, relatively open aggregate (COM distance of

The rotational autocorrelation functions (ACF) corresponding to the motion of each CD, free or mostly in dimer arrangement, were also inspected. Two alternatives were tested for the

**Figure 3.** Distribution of distances between the centers of mass of β-CD molecules, defined by the oxygen atoms of the secondary portals. Right panels illustrate the final conformations for the imposed PS, PP, and SS initial arrangements of β-CD molecules, in aqueous solution, sampled during the MD simulations at 300 K and identified by geometric cluster analysis. The color codes for CD molecules are as in **Figure 1**, while the initial arrangements are represented in black,

0.8 nm), suggesting a relatively poor clustering of this dimeric aggregate.

the possible rotation or tilt of the CD molecules.

green, and red, for PS, PP, and SS, respectively.

Another study [37] focused on the spontaneous adsorption of native CDs and the respective aggregates and the related dependence on temperature. It was found that the adsorption of both individual CDs and small CD aggregates (ca. 20 molecules) to the solution/air interface is negligible. The solute-solute interactions were significantly larger for β-CD than for α-CD at 298 K, and the dependence of these interactions on temperature was more relevant for the smaller CD, which displayed a more favorable aggregation at 283 K than at 298 K. The dynamic exchange of hydrogen bonds between the CD hydroxyl groups and the neighboring water molecules indicated a much larger occupancy for individual intramolecular H-bonds in β-CD.

In what follows, the CD-CD interactions [57], for deuterium labeled CDs, in aqueous solutions are further explored by atomistic simulations. Two types of systems are defined, one in which the β-CD is free in water and three others in which two β-CDs are present and may form dimers. In what concerns the latter, these include initial arrangements with proximity of one primary portal and one secondary portal (PS), two primary portals (PP), and two secondary portals (SS), as shown in **Figure 2**.

The molecular dynamics simulations were performed with Gromacs (version 4.6.5), using the all-atom amber99sb [81] force field and the TIP3P water model. The initial coordinates of the β-CD were extracted from the RCSB protein data bank (PDB code: 1DMB), and partial charges were generated using the R.E.D.D. Server [82].

In each system, the molecules were accommodated in a cubic box (7.5 nm edge-length) containing approximately 13,000 explicit TIP3P water molecules. To obtain a starting configuration, each system was firstly subjected to an energy minimization step. All the calculations were carried out in NPT ensemble with periodic boundary conditions at a constant temperature of 300 K and a pressure coupling of 1.0 bar, respectively, to V-rescale and Berendsen external baths. A standard time step of 2 fs was used for both equilibration and production runs. A cut-off of 0.9 nm was used for calculating the Lennard-Jones interactions. Electrostatic interactions were evaluated using the particle mesh Ewald method [83]. Constraints were applied for bond lengths with the LINCS algorithm [84].

Equilibrium properties, structure, and dynamics of β-CD systems were calculated for the simulation runs of 50 ns after the systems were equilibrated for 2 ns. Geometric clustering was performed to identify dominant CD-CD structures, sampled during the MD simulations. The algorithm for cluster analysis is based on the hierarchical (top-down) approach [85] and

**Figure 2.** Schematic illustration of the pairwise initial arrangements of β-CDs, with facing primary and secondary portals (PS), two primary portals (PP), and two secondary portals (SS), with the colors used to distinguish β-CD molecules.

allows evaluating the conformational prevalence of each CD-CD structure, by determining dominant clusters based on the root mean square deviation of the atom positions between all pairs of structures. For each CD-CD arrangement, the number of neighboring structures is calculated for RMSD values of 0.35 nm. **Figure 3** presents the behavior of CD-CD structures in different simulation runs, each corresponding to a different initial arrangement. For each CD backbone, the center of mass (COM) of the oxygen atoms at the secondary portal (S) was defined as the reference point for evaluating aggregated and nonaggregated structures and the possible rotation or tilt of the CD molecules.

was also proved that the desolvation of CD dimers and entropy changes upon complexation

Another study [37] focused on the spontaneous adsorption of native CDs and the respective aggregates and the related dependence on temperature. It was found that the adsorption of both individual CDs and small CD aggregates (ca. 20 molecules) to the solution/air interface is negligible. The solute-solute interactions were significantly larger for β-CD than for α-CD at 298 K, and the dependence of these interactions on temperature was more relevant for the smaller CD, which displayed a more favorable aggregation at 283 K than at 298 K. The dynamic exchange of hydrogen bonds between the CD hydroxyl groups and the neighboring water molecules indicated a much larger occupancy for individual intramolecular H-bonds in β-CD. In what follows, the CD-CD interactions [57], for deuterium labeled CDs, in aqueous solutions are further explored by atomistic simulations. Two types of systems are defined, one in which the β-CD is free in water and three others in which two β-CDs are present and may form dimers. In what concerns the latter, these include initial arrangements with proximity of one primary portal and one secondary portal (PS), two primary portals (PP), and two second-

The molecular dynamics simulations were performed with Gromacs (version 4.6.5), using the all-atom amber99sb [81] force field and the TIP3P water model. The initial coordinates of the β-CD were extracted from the RCSB protein data bank (PDB code: 1DMB), and partial charges

In each system, the molecules were accommodated in a cubic box (7.5 nm edge-length) containing approximately 13,000 explicit TIP3P water molecules. To obtain a starting configuration, each system was firstly subjected to an energy minimization step. All the calculations were carried out in NPT ensemble with periodic boundary conditions at a constant temperature of 300 K and a pressure coupling of 1.0 bar, respectively, to V-rescale and Berendsen external baths. A standard time step of 2 fs was used for both equilibration and production runs. A cut-off of 0.9 nm was used for calculating the Lennard-Jones interactions. Electrostatic interactions were evaluated using the particle mesh Ewald method [83]. Constraints were

Equilibrium properties, structure, and dynamics of β-CD systems were calculated for the simulation runs of 50 ns after the systems were equilibrated for 2 ns. Geometric clustering was performed to identify dominant CD-CD structures, sampled during the MD simulations. The algorithm for cluster analysis is based on the hierarchical (top-down) approach [85] and

**Figure 2.** Schematic illustration of the pairwise initial arrangements of β-CDs, with facing primary and secondary portals (PS), two primary portals (PP), and two secondary portals (SS), with the colors used to distinguish β-CD molecules.

cooperatively contributes to the binding process [78].

54 Cyclodextrin - A Versatile Ingredient

ary portals (SS), as shown in **Figure 2**.

were generated using the R.E.D.D. Server [82].

applied for bond lengths with the LINCS algorithm [84].

For PS and PP as initial arrangements, a significant evolution is observed in the relative positioning of the two molecules. The PS and PP initial arrangements display an almost complete rotation or a tilt of one molecule with respect to the other, leading to most favorable SS and PS arrangements, respectively. The "intermediate" PS arrangement increases the CD-CD interactions through partial inclusion of some P groups in the hydrophobic cavity of the other CD molecule. The initial SS arrangement prevails over the course of the simulation with a typical COM distance of 0.46 nm. In addition to intramolecular hydrogen bonds, the two CD molecules can form additional intermolecular hydrogen bonds, optimizing the CD-CD interaction. PS is an intermediate arrangement between the most (SS) and the least stable (PP) arrangements. The PP arrangement of the CD pair involves weaker interactions between P groups of the two molecules, producing a low prevalence, relatively open aggregate (COM distance of 0.8 nm), suggesting a relatively poor clustering of this dimeric aggregate.

The rotational autocorrelation functions (ACF) corresponding to the motion of each CD, free or mostly in dimer arrangement, were also inspected. Two alternatives were tested for the

**Figure 3.** Distribution of distances between the centers of mass of β-CD molecules, defined by the oxygen atoms of the secondary portals. Right panels illustrate the final conformations for the imposed PS, PP, and SS initial arrangements of β-CD molecules, in aqueous solution, sampled during the MD simulations at 300 K and identified by geometric cluster analysis. The color codes for CD molecules are as in **Figure 1**, while the initial arrangements are represented in black, green, and red, for PS, PP, and SS, respectively.

definition of the molecule fixed rotating vector defined by the C2-D (see **Figure 4**) bond (vector) and resulting from the use of three atoms (triplet), those of the C2-D bond and the adjacent carbon C3, and defined as the cross product of vectors C3-C2 and C2-D.

(denoted as A and B) molecules with 1 PVA, 2 PVA (A and B), and 10 PVA (A to J) oligomers,

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CDs are able to form aggregates at early stages of the simulations, and PVA seems to promote the formation of CD dimers (DmAB). Indeed, PVA contains both hydrophilic and hydrophobic groups that may interact either with the outside part of the CDs or form inclusion complexes; the latter is shown by the snapshot in **Figure 6(b)**, while the former appears for simulations of

**Figure 6.** Summary of the MD simulations between β-CD and PVA molecules. Left panels present the measured distances between the center of mass of the groups formed by (i) each β-CD in the dimer (DmAB), (ii) the secondary-secondary portals (SS), the primary-primary portals (DmAB/PP), the secondary-primary portals (PS), DmAB-PVA, DmAB-PVB, CDA-PVA, CDA-PVB, CDB-PVA, CDB-PVB, DmAB-PVA aggregate (Ag(4PVA)), CDA-Ag(4PVA), CDB-Ag(4PVA), and Ag(4PVA)—6 separated PVA molecules (Sg(6PVA)). Right panels illustrate the 3 dominant conformations (accounting for more than 50%, panel a, and 90%, panels b and c, of the occurrences) sampled during the equilibrated parts of the production runs, at 300 K, in aqueous solution. The force field F-85 [90] was used for the CDs. The electrostatic charges of PVA were calculated using

the R.E.D. server and the remaining terms generated by ACPYPE [91].

respectively. The main results are illustrated in **Figure 6**.

The ACF curves are similar for these two cases and are represented in **Figure 5**. The curves were fitted from 0 up to 500.0 ps to a one-parameter exponential and reflect the slower decay for the dimer situation, τ<sup>0</sup> = 1250 ps, much larger than for the free CD, τ<sup>0</sup> = 448 ps. These values are of order of magnitude of those experimentally obtained.

The organization of CD molecules in aggregates when in the presence of guest-entities clearly deserves further attention. As an example of the behavior found for more complex systems, simulations were performed to study the inclusion complex of β-CD and poly(vinyl alcohol) (PVA) molecules in water. The importance of this polymer is related to the ability to form hydrogels exhibiting a high degree of swelling in water that has demonstrated a great potential to act as a matrix for many applications, including drug delivery [86], wound dressing [87], and sensors [88]. More recently, it has been found that such broad applications of PVA result from its ability to behave as an amphiphilic polymer [89]. This latter feature is relevant for studying the ability of CDs for forming host-guest or aggregate complexes. In this example, three molecular dynamics simulations were performed in systems containing two β-CD

**Figure 4.** Cyclodextrin structures (α-CD, n = 6; β-CD, n = 7; and γ-CD, n = 8).

**Figure 5.** Average autocorrelation function of C2-D bond for CD molecules in the monomeric and dimeric states, in water at 300 K (black and orange curves, respectively).

(denoted as A and B) molecules with 1 PVA, 2 PVA (A and B), and 10 PVA (A to J) oligomers, respectively. The main results are illustrated in **Figure 6**.

definition of the molecule fixed rotating vector defined by the C2-D (see **Figure 4**) bond (vector) and resulting from the use of three atoms (triplet), those of the C2-D bond and the adja-

The ACF curves are similar for these two cases and are represented in **Figure 5**. The curves were fitted from 0 up to 500.0 ps to a one-parameter exponential and reflect the slower decay for the dimer situation, τ<sup>0</sup> = 1250 ps, much larger than for the free CD, τ<sup>0</sup> = 448 ps. These values

The organization of CD molecules in aggregates when in the presence of guest-entities clearly deserves further attention. As an example of the behavior found for more complex systems, simulations were performed to study the inclusion complex of β-CD and poly(vinyl alcohol) (PVA) molecules in water. The importance of this polymer is related to the ability to form hydrogels exhibiting a high degree of swelling in water that has demonstrated a great potential to act as a matrix for many applications, including drug delivery [86], wound dressing [87], and sensors [88]. More recently, it has been found that such broad applications of PVA result from its ability to behave as an amphiphilic polymer [89]. This latter feature is relevant for studying the ability of CDs for forming host-guest or aggregate complexes. In this example, three molecular dynamics simulations were performed in systems containing two β-CD

**Figure 5.** Average autocorrelation function of C2-D bond for CD molecules in the monomeric and dimeric states, in

water at 300 K (black and orange curves, respectively).

cent carbon C3, and defined as the cross product of vectors C3-C2 and C2-D.

are of order of magnitude of those experimentally obtained.

56 Cyclodextrin - A Versatile Ingredient

**Figure 4.** Cyclodextrin structures (α-CD, n = 6; β-CD, n = 7; and γ-CD, n = 8).

CDs are able to form aggregates at early stages of the simulations, and PVA seems to promote the formation of CD dimers (DmAB). Indeed, PVA contains both hydrophilic and hydrophobic groups that may interact either with the outside part of the CDs or form inclusion complexes; the latter is shown by the snapshot in **Figure 6(b)**, while the former appears for simulations of

**Figure 6.** Summary of the MD simulations between β-CD and PVA molecules. Left panels present the measured distances between the center of mass of the groups formed by (i) each β-CD in the dimer (DmAB), (ii) the secondary-secondary portals (SS), the primary-primary portals (DmAB/PP), the secondary-primary portals (PS), DmAB-PVA, DmAB-PVB, CDA-PVA, CDA-PVB, CDB-PVA, CDB-PVB, DmAB-PVA aggregate (Ag(4PVA)), CDA-Ag(4PVA), CDB-Ag(4PVA), and Ag(4PVA)—6 separated PVA molecules (Sg(6PVA)). Right panels illustrate the 3 dominant conformations (accounting for more than 50%, panel a, and 90%, panels b and c, of the occurrences) sampled during the equilibrated parts of the production runs, at 300 K, in aqueous solution. The force field F-85 [90] was used for the CDs. The electrostatic charges of PVA were calculated using the R.E.D. server and the remaining terms generated by ACPYPE [91].

2 CDs with 1 PVA (**Figure 6(a)**) and 2 CDs with 10 PVAs (**Figure 6(c)**). It is also noted that the prevalence of the type of configurations in **Figure 6(b)** and **Figure 6(c)** across the simulation is very high (above 95%), which is a strong indication that such complexes are stable; for 2 CDs with 1 PVA, even though the prevalence of the typical configuration represented in **Figure 6(a)** is above 50%, it is much less than the other two cases. Nonetheless, it is apparent from the distance versus time plot in **Figure 6(b)** that the PVA is able to exit the CD pocket in some instances and, then, reform the inclusion complex. In turn, it is particularly interesting to notice from the simulation of 2 CDs with 10 PVAs that the concomitant aggregation of the CDs with various molecules of PVA appears to be relatively stable complex and likely to delay or even prevent the formation of inclusion complexes (not observed during the course of the simulation).

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