*2.2. PMA* β*-CD NS Model*/*PX Interaction at Di*ff*erent Concentrations*

In this Section, the PX interaction with a nanosponge (NS) model containing β-CDs connected by a pyromellitic dianhydride PMA crosslinker [30] is investigated. The NS model was generated by linking 8 β-CDs (Model 2 in [30]) through PMA moieties (see Scheme 1 in [30]). Accordingly, each CD carries two PMA linking agents bound to a primary hydroxyl at diametrically opposite sides of the macrocycle. An increasing number of host molecules was considered, with β-CD:PX equal to 8:4, 8:8, 8:16, 8:40, therefore, with β-CD:PX in a 2:1, 1:1, 1:2, 1:5 ratio.

Since it will be relevant in the following, it is important to report that the solvent-accessible surface area calculated for the β-CD NS model reported in Figure 5 is equal to 4,315 Å<sup>2</sup> and the radius of gyration is equal to 12.5 Å. In the following, the interaction between the PMA β-CD NS model [30] and PX molecules considered at smaller and larger concentrations were studied and the results are reported and discussed.

**Figure 5.** The solvent-accessible surface area of a β-CD NS (β-cyclodextrin Nanosponge) model with a pyromellitic dianhydride (PMA) crosslinker as reported in Model 2 in [29] colored by atoms. Color codes: C atoms are grey, oxygen atoms re red, and hydrogen atoms are white.

2.2.1. NS/PX Interaction: 8 β-CDs in the NS Model and 4 PX Molecules (β-CD/Drug in a 2:1 Stoichiometry)

Using the simulation protocol proposed in the previous work [20–22], as the first step, energy minimization of the NS model and 4 PX molecules, considering the β-CD/drug in a 2:1 stoichiometry, was carried out starting from a random disposition. An MD simulation run was then performed in order to understand possible conformational changes and interactions, in particular, the possible inclusion complexes or the surface interaction with the exposed PMA β-CD NS atoms. In Figure 6, the potential energy and the van der Waals contribution calculated during the MD run are reported. After an initial energy decrease, some conformational changes of the nanosponge take place in order to maximize its interactions with the four PX molecules, increasing the surface area accessible to the drug molecules. It should be noted that hydrophobic drug/drug interactions are absent. The final optimized conformation assumed by the system is reported in Figure 7. See the animation file of the MD run in SI.

**Figure 6.** The potential energy and the van der Waals contribution calculated during the MD run for the NS model interacting with 4 piroxicam molecules.

**Figure 7.** Panel (**a**) shows the optimized geometry assumed by the NS/4 PX molecules system at the end of the MD run displaying two included molecules in a 1:1 stoichiometry (see the yellow arrows) and two PX molecules interacting on the external surface of the NS model. The NS is in green for clarity and the PX molecules are colored by atoms, see the color codes in Figure 3. Panel (**b**) shows the solvent-accessible surface area without the PX molecules for clarity (see the color codes in Figure 5).

It is interesting to note that upon removal of the PX molecules as shown in panel b) of Figure 7, the solvent-accessible surface area of the NS in the optimized final geometry is equal to 5,263 Å<sup>2</sup> , with an increase of about 20% compared to the starting geometry, while the radius of gyration increases by more than 90% to a value of 23.3 Å. It is well-known that β-CD nanosponges are able to swell in a water solution [14,30]. They are very flexible systems that can have significant conformational changes in order to maximize the favorable interactions with drugs. Significant flexibility was displayed by this β-CD crosslinked system during the MD run. The final optimized geometry reported in panel a) of Figure 7 displays an evident elongation of the NS structure interacting with PX molecules forming two different host–guest complexes (see the yellow arrows) in a 1:1 stoichiometry studied and reported in Section 2.1; one complex displays the hydrogens of the pyridyl part preferentially in the β-CD cavity and the phenyl part far from the hydrophobic cavity and the second one displays the pyridyl part far from the β-CD cavity. Interestingly, these geometries are very similar to the two inclusion complexes considering the native β-CD discussed in Section 2.1.1 and reported in Figure 3 (see geometries A and

C in Figure 3). Again, it is important to note that the other two piroxicam molecules interact with the external part of the NS, in particular, with the exposed crosslinker (see the green arrows in Figure 7).

2.2.2. NS/PX Interaction: 8 β-CDs in the NS Model and 8 PX Molecules (β-CD/Drug in a 1:1 Stoichiometry)

In this Section, the interaction between PMA β-CD NS with PX was studied considering 8 drug molecules. The NS contains 8 β-CD [30], so that the β-CD/drug in a 1:1 stoichiometry is investigated. Using the same strategy as before, after the MD run in the final optimized geometry reported in Figure 8, PX was found to interact both with the NS in the accessible hydrophobic cavities and with the NS surface. The NS shows large conformational changes in order to adsorb the PX molecules well. Interestingly, at this concentration, possible drug/drug hydrophobic interactions take place. In the final optimized geometry, again, two types of inclusion complexes are found together with the surface interaction on the exposed atoms of this flexible crosslinked system. As already found for the smaller concentration, the nanosponge maximizes the possible interaction with a drug.

**Figure 8.** In the Figure, panel (**a**) shows the optimized geometry assumed by the NS/8 PX drug molecules system at the end of the MD run displaying two types of interactions with hydrophobic cavities (see the yellow arrows) and six PX molecules interacting on the external surface of the NS. The NS is in green for clarity and the PX molecules are colored by atoms according to the color codes in Figure 3. Panel (**b**) shows the solvent-accessible surface area without the PX molecules for clarity (see the color codes in Figure 5).

The NS becomes well-elongated due to the favorable interactions with the PX drug forming two inclusion complexes (see the yellow arrows) and interacting with the crosslinkers (an example is highlighted by the green arrow). At this larger concentration, two PX molecules interact owing to the hydrophobic drug/drug interactions (see Figure 8, top left). Interestingly, the solvent-accessible surface area of the NS (see panel b) in Figure 8) is equal to 6,112 Å<sup>2</sup> with the increase of 40% with respect to the initial geometry, and the radius of gyration increases by more than 90% to a value of 25.5 Å.

2.2.3. NS/PX Interaction: 8 β-CDs in the NS Model and 16 PX Molecules (β-CD/Drug in a 1:2 Stoichiometry)

In this Section, the results concerning the β-CD NS/drug in a 1:2 stoichiometry will be presented and discussed. After the initial energy minimization of the NS and 16 PX molecules in a random disposition, an MD simulation run was performed as before in order to understand the possible inclusion complexes or surface interactions between piroxicam and the NS. Figure 9 reports the potential energy and the van der Waals components calculated during the MD run.

**Figure 9.** The Figure shows the potential energy and the van der Waals components calculated during the MD run for the NS interacting with 16 PX molecules.

After the initial energy decrease, some conformational changes of the NS take place in order to maximize the interactions with the 16 PX molecules. The final optimized conformation assumed by the system at the end of the MD run is reported in Figure 10. During the MD run at this larger PX concentration, an equilibrium between a more compact NS conformation with a PX aggregate on its surface (see panel a) in Figure 10) and a more elongated NS conformation maximizing the interactions with the PX molecules (see panel b) in Figure 10) are observed.

**Figure 10.** Panel (**a**) shows the optimized geometry assumed by the NS/16 PX drug molecules system at the end of the MD run lasting 100 ns and panel (**b**) displays the optimized geometry assumed by the system at 96 ns. In the top part of each panel the NS is in green for clarity and the PX molecules are colored according to the color codes of Figure 3, and in the bottom part, the solvent-accessible surface area without the PX molecules is reported for clarity (see the color codes in Figure 5). Panel (**c**) shows the geometry assumed by the system at 60 ns.

The solvent-accessible surface areas of the optimized system calculated at 100 ns and 96 ns are reported in Figure 10. In particular, this area is equal to 5,664 Å<sup>2</sup> with a 30% increase over the initial geometry for the conformation assumed at 100 ns, while the radius of gyration is equal to 17.0 Å, with the increase of 35%. The more compact conformation assumed by the system at 96 ns corresponds to a lower potential energy value, 2424 kcal/mol, compared to 2534 kcal/mol for the optimized geometry assumed by the system at the end of the MD run. The solvent-accessible surface area reported in Figure 10 in panel b) (bottom) without the PX molecules is equal to 5161 Å<sup>2</sup> , with the increase of 20%, while the radius of gyration is equal to 13.0 Å, with a 13% increase. It is interesting to note in Figure 10 the formation of a nanopore in the central part of the β-CD NS in the optimized conformation at 96 ns. It is more evident that during the MD run, the system maximizes the interaction with PX owing to high NS flexibility. In both cases, there are some inclusion complexes and a PX drug aggregate interacting on the external NS surface at 100 ns and 96 ns formed by 10 and 11 PX molecules, respectively, therefore, with about the same number of molecules that is stable in time.

Interestingly, during the MD run at 60 ns, a spherical aggregate formed by 6 molecules of the PX drug detaches from the NS surface as shown in Figure 10 (panel c)). For the animation file of the MD run, see SI. The potential energy of the system calculated during the simulation is the lowest one, indicating also an equilibrium during the MD run between the drug molecules still attached on the NS surface for the larger part of the MD run and the detached ones diffusing as a single cluster for some ns before the new adsorption on the NS surface. The solvent-accessible surface area of the system at 60 ns is equal to 5,026 Å<sup>2</sup> , with a 16% increase over the initial geometry, while the radius of gyration is equal to 13.0 Å, with the increase of only 4%.

2.2.4. NS/PX Interaction: 8 β-CDs in the NS and 40 PX Molecules (β-CD/Drug in a 1:5 Stoichiometry)

Finally, the results concerning the β-CD/drug in a 1:5 stoichiometry of these NS/PX systems are presented and discussed. Using the same methodology as before, the potential energy and the van der Waals components calculated during the MD run are reported in Figure 11. In this case, at the largest piroxicam concentration considered here, after the initial fast decrease of the system energy, fluctuations around average values were observed with the NS in a compact structure in contact with the PX aggregate due to drug association owing to hydrophobic π–π interactions induced by the first layer of PX molecules adsorbed on the NS surface. For the animation file of the MD run, see SI.

**Figure 11.** The figure shows the potential energy calculated during the MD run and the van der Waals components for the NS model and 40 PX molecules.

The optimized conformation assumed by the system at the end of the MD run is reported in Figure 12 (panel a)).

**Figure 12.** Panel (**a**) shows the optimized geometry assumed by the NS/40 PX drug molecules system at the end of the MD run displaying some host–guest inclusion complexes (see the arrows). All the other molecules are on the external surface of the NS. Panel (**b**) shows the solvent-accessible surface area without the PX molecules for clarity (see the color codes in Figure 5). Panel (**c**) shows the PX aggregate formed by 32 molecules adsorbed on the NS surface well-ordered in an almost spherical shape in detail.

In the optimized conformation assumed at the end of the MD run (see panel a) in Figure 12), some inclusion geometries are found, in particular, two host–guest complexes in a "type A" geometry (see the yellow arrows), the most stable one being reported in the left part of Figure 3 having the pyridyl moiety in the hydrophobic β-CD cavity, and one host–guest complex in a "type C" geometry (see the green arrow, the less stable geometry) in the right part of Figure 3 with an included phenyl. All the other drug molecules interact with the external surface of the NS. In particular, it is interesting to note the almost spherical aggregate that is nucleated on the external surface after the initial favorable interaction of the first layer of adsorbed PX molecules. β-CD acts as a surface of the nucleation process which subsequently takes place thanks to π–π interactions between the drug molecules. Considering this final optimized geometry, a self-ordered structure is clearly seen in the right part of panel a) of Figure 12, with a parallel arrangement of the aromatic rings of the drug molecules producing an almost spherical aggregate formed by 32 PX molecules represented in another orientation in panel c). The conformation of the β-CD NS having the PX aggregate adsorbed is compact and, in fact, its radius of gyration is equal to 13.5 Å, larger only by 7% with respect to the isolated NS, and the solvent-accessible surface area is equal to 4,920 Å<sup>2</sup> (see panel b) in Figure 12), larger by 14% than in the isolated NS. Interestingly, in this case, the calculated increase was smaller than in the simulations at relatively smaller PX concentrations.
