Peculiar Aqueous Solubility Trend in Cucurbiturils Unraveled by

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Peculiar Aqueous Solubility Trend in Cucurbiturils is Unraveled by Atomistic Simulations Thaciana Valentina Malaspina, Eudes Eterno Fileti, and Vitaly V. Chaban J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b05425 • Publication Date (Web): 13 Jul 2016 Downloaded from http://pubs.acs.org on July 16, 2016

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The Journal of Physical Chemistry

Peculiar Aqueous Solubility Trend in Cucurbiturils is Unraveled by Atomistic Simulations Thaciana Malaspina, Eudes Fileti,* and Vitaly V. Chaban Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo, 12247-014, São José dos Campos, SP, Brazil

Abstract. Cucurbiturils (CBs) compose a family of macrocycles, whose elementary unit is glycouril (GLYC). CBs are of high interest to chemistry and biology due to their versatile applications ranging from sensors to advanced drug delivery. We hereby report a systematic hydration study of all presently known CBs by classical molecular dynamics simulations to understand their different aqueous solubilities, as revealed in the experiments. Water readily penetrates CBs, including the smallest CB[5]. The number of the CB[n]–water hydrogen bonds can be assessed as 2×n. Hydration enthalpies of CBs were found to be significantly favorable thanks to a number of strong hydrogen bonds with water. However, these enthalpy gains are not enough to compensate for an even larger entropic penalty due to modifying a genuine bulk arrangement of water molecules. We found that free energy of hydration moderately but uniformly increases with the number of GLYCs. Better solubility of the oddnumbered CBs is, therefore, independent on the CB–water interactions, either enthalpic or entropic contribution. Higher solubilities of CB[n]s with n=5, 7, 9 occur exclusively due to their amorphous solid state. Our results allow to prognose aqueous solubilities of not-yetsynthesized CBs. *Corresponding author: Tel: +55 12 3924-9500; e-mail: [email protected]

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Introduction Cucurbiturils (CBs) are macrocyclic polymers, which are made of 5-10 glycouril (tetrahydroimidazo[4,5-d]imidazole-2,5(1H,3H)-dione, GLYC, Mr = 142.12 g mol−1) units.1 The GLYC units are linked by the methylene bridges. The number of GLYCs n is designated in the square brackets, CB[n]. GLYC can be considered as two fused imidazole rings, in which the C2-H positions are oxidized.2 These oxygen atoms are located along the edges of the back being tilted inwards. Such arrangement of the atoms results in a partially enclosed cavity. CBs are interesting to chemistry and biology, because they can be suitable hosts for a large number of neutral and ionic species.3-6 Furthermore, CBs have been probed for asymmetric synthesis, molecular switching, and dye tuning.1 It is widely believed that molecular guests interact with CBs through hydrophobic interactions, whereas cationic guests make use primarily of ion-dipole forces.1 The sizes of CBs are comparable with those of small fullerenes, internal cavity volume being 82 Å3 for CB[5], 164 Å3 for CB[6], 279 Å3 for CB[7], 479 Å3 for CB[8], and 870 Å3 for CB[10]. Therefore, currently accessible CBs are able to incorporate only small drug molecules. The spatial structures of CB[5], CB[6], CB[7], CB[8], and CB[10] were recently determined and the molecules were isolated. Enigmatically, CB[9] has not been reported yet. CBs are excellent hosts for insoluble species or for those with a generally hydrophobic behavior.4, 7-8 Unlike many other nanoscale cavities,9 CBs possess hydrophilic sites, which are responsible for a strong electrostatic binding of both polar guests and surrounding water molecules.10 Nevertheless, the experimentally measured aqueous solubilities of CBs are modest. Wheate and coworkers11 mention ca. (3-4)×10-3 M for CB[5] and CB[7]. In turn, CB[6] and CB[8] are only sparingly soluble, as suggested by Kim and coworkers.12 Interestingly, these authors suppose an order of magnitude different aqueous solubility for

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CB[7], (2-3)×10-2 M. This value was characterized as moderate, although, in our opinion, it is more appropriate to reference it as quite significant. Despite obvious disagreements in the recent sources, the experimental solubilities can be grossly explained by a significant size of CBs, as compared to water molecules, and, thus, an energetically unfavorable disturbance of the water’s hydrogen bonded network. Solid-state investigations of CBs have also recently appeared and revealed different symmetries resulting in different energetics and aggregation behaviors.13 Due to their relatively small size (Figure 1), available CBs are only suitable for small guest molecules.3 They can unlikely do much for delivery of gene fragments, oligopeptides, and even large drug particles.14-15 In this context, obtaining larger CBs may be practically important. If such can be synthesized in the future, it is crucial to generate knowledge on their hydration regularities and aqueous solubility. Predictions of this sort can be made by analyzing a range of lower homologues in the CB family.

Figure 1. Optimized atomically-precise structures (in scale) of the CB[n], n = 5...10. The superimposed structures allow for comparison of diameters of all investigated CBs. Covalent bonds are depicted as sticks. 3 ACS Paragon Plus Environment


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In the present work, we report a systematic hydration study of CB[5], CB[6], CB[7], CB[8], CB[9], and CB[10]. Structure patterns of water inside and outside these CBs were characterized. Thermodynamic potentials of hydration, such as enthalpy, entropy, and Gibbs free energy, were obtained through a series of step-wise alchemical transformations. Although CB[9] is not yet available in the experiments,4 we considered its hydration for generality and to bridge properties of CB[8] and CB[10].

Methodology Solubilization of the cucurbituril family of macrocycles, represented in our study by CB[5], CB[6], CB[7], CB[8], CB[9], and CB[10], was characterized in terms of hydration free energy obtained from classical molecular dynamics (MD) simulations of a step-wise alchemical transformations. The Bennett Acceptance Rate method16 was employed to postprocess the MD results. Thirty-one one independent simulation windows – 0 < λ < 1, ∆λ = 0.05 (λ is coupling parameter) – were used to gradually and sequentially decouple CBs from an equilibrated aqueous environment, i. e. the first 10 windows were used to decouple the interactions of Coulomb and the other 21 to decouple the interactions of van der Waal. In every window, the MD system was equilibrated during 1.0 ns using stochastic dynamics. The average value of each 〈

〉 was obtained from the 10 ns long MD trajectory. Therefore,

every MD system was sampling during 341 ns to derive Gibbs free energy of hydration. The soft-core repulsive potential was applied to prevent unphysical behavior of the atomic nuclei at higher degrees of decoupling. All MD simulations were conducted in the constant temperature constant pressure ensemble. The constant temperature, 300 K, was maintained by the velocity rescaling 4 ACS Paragon Plus Environment

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thermostat17 with a relaxation time of 0.5 ps. The constant pressure, 1×105 Pa, was maintained by the Parrinello-Rahman barostat,18 the relaxation time being 2.0 ps and the compressibility constant being 4.5×10-5 bar-1. Therefore, simulated are standard ambient temperature and pressure and the resulting thermodynamic potentials do not require any corrections for comparison with tabulated values. The lengths of all covalent bonds were kept fixed, while angles and dihedrals were allowed to fluctuate upon MD. The electrostatic interactions were simulated directly for interatomic distances below 1.2 nm and by the Particle-Ewald-Mesh method for larger interatomic distances.19 The Lennard-Jones (12,6) energy was smoothly brought to zero in the range 1.1-1.2 nm by the switch method. A single CB molecule was surrounded by 2500 molecules of water in a cubic box with periodic boundary conditions and the minimum-image convention. The equations-of-motion were integrated with a time-step of 2.0 fs. The immediate coordinates and thermodynamic quantities were recorded every 0.1 ps. The model Hamiltonian CHARMM36,20 included bonded and non-bonded terms without an explicit electronic polarization. The TIP3P threesites model of water of compatible with the CHARMM36 all-atom parameters.20 MD simulations and subsequent analysis were performed in the GROMACS 5.0 program.21-22 PACKMOL was used to generate Cartesian coordinates for initial molecular configurations.23 VMD was used to visualize results and prepare molecular graphics.24

Results and Discussion Subnanometer-sized spatial confinements introduced by CBs are expected to significantly modify local structure of the solvent molecules and, possibly, intramolecular geometries of guests. The inner cavity of CBs is supposed to be moderately hydrophobic



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despite possessing electron rich oxygen atoms of the carbonyl groups. The room-temperature simulations reveal that water spontaneously penetrates inside the CB cavity. Binding energy between the solute and the solvent depends crucially on the confined water structure and ultimately determines the solvation behavior of CBs. Thermodynamics of the guest molecules depends on the degree of the CB solvation.25 Radial distribution functions (RDFs) for the centers-of-mass of CB and water molecules (Figure 2) characterize hydration of CBs in the absence of guest molecules. The location of the first peak clearly depends on the number of GLYCs in CBs. The heights of the first peaks are inversely proportional to n in CB[n]. The maximum density of water is observed at the center of CBs in the cases of 5, 9, and 10 GLYCs. No repetitive solvent layers exist inside CBs, even inside the largest ones. Interestingly, peaks are also present outside CBs indicating that certain hydration shell exists around them. Formation of the solvation shell reflects rather favorable CB–water interactions, which contribute to the enthalpy of CB hydration.

Figure 2. RDFs computed for centers-of-mass of CB and water molecules. See legend for line designation.

RDFs for selected sites of CBs and water molecules are provided in Figures 3-4. The oxygen atom of water does not exhibit any peculiar interactions with any of the heavy atoms of CBs. The first RDF peak is located at the sum of the van der Waals radii (carbon-oxygen,


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3.8 Ǻ, oxygen-oxygen, 2.8 Ǻ) or farther (nitrogen-oxygen, 4.8 Ǻ). An effect of the number of GLYCs is negligible. In turn, a strong hydrogen bond, 1.9 Ǻ, emerges from the hydrogenoxygen interaction. This sort of hydrogen bond exists in all systems, including the smallest one, CB[5]. Formation of hydrogen bonds must be accounted for when defining CBs as hydrophobic hosts. Although an aqueous solubility of CBs is experimentally known to be mediocre, they are much less hydrophobic as compared to nanoscale carbonaceous entities, lipids, etc.26-29 Indeed, (2-3)×10-2 M, mentioned in literature for CB[7], correspond to 23-35 g L-1.

Figure 3. RDFs computed for the oxygen atoms of water and the selected atoms of CBs: (left) carbon and (right) nitrogen. See legend for line designation.



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Figure 4. RDFs computed for the oxygen atoms of CB and the atoms of water: (left) hydrogen, (right) oxygen. See legend for line designation. All RDFs converge to unity and have been truncated for clarity in visualization of the first peak. Density maps and spatial probability distributions for water molecules around CBs are provided in Figure 5. The outer region of water is nearly the same for all CBs. We can see from the density maps the distribution of water molecules in the outer region the CB[n] showed almost the same pattern for all members in with water hydrophobically interacting at distances around ~0.30 nm from macrocycle. In turn, the structure of the confined region is determined by the diameter of each CB. Tiny amount of water fits inside CB[5] and CB[6], whose inner cavities are scarcely accessible to relevant drug molecules. Noteworthy, CB[7] and CB[8] are almost empty at their geometric centers, whereas all water molecules approach inner sidewalls. This observation is in line with hydrogen bonds, which were revealed using RDFs. Therefore, CBs should be called hydrophobic with caution. We further develop this idea upon discussing Gibbs free energy of hydration. CB[9], which was not obtained synthetically thus far, and CB[10] contain maximum amounts of water molecules without a dry or low-density region at their centers. An ability of water molecules to penetrate CB cavities fosters their solubilities, since this process effectively decreases perturbation of the solvent structure caused by a dissolved nanoscale object.


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Figure 5. Density maps: (left) side-view, (center) frontal view for CB[n], n = 5...10. (Right) Spatial probability distributions. Red regions are hydrophobic, dark regions designate water bulk density. Blue and white regions are intermediate.

Densities of the confined water are systematically smaller than in the bulk solvent at the same conditions. The simulated density increases as the CB diameter decreases. Although these results are physically meaningful, they must be treated attentively, since the definition of the confined density is somewhat arbitrary. If all three atoms of the water molecule do not belong to the inner cavity of CB, the molecule is considered to be outside, according to our 9 ACS Paragon Plus Environment


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methodology. An imaginary line connecting opposite oxygen atoms of CBs, was used to limit the inner cavity volume in the axial direction. As a result, underestimation of the confined density must be expected, especially inside the smallest macrocycles. While CB[5] incorporates only two water molecules, CB[9] and CB[10] are much larger, 19 and 25 molecules, respectively. The larger CBs can be considered properly hydrated from their insides. Number of the confined water molecules is proportional to the size of CB and to the number of the CB-water hydrogen bonds (Table 1). Hydrogen bonds are formed and destructed in the course of a single MD simulation, whereas their mean number in CB[n] equals to 2×n with a relatively large uncertainty. Check, CB[5] maintains 10 hydrogen bonds with both inside and outside water, CB[7] maintains 14 hydrogen bonds, and CB[10] maintains 21 hydrogen bonds. No difference was found between even- and odd-numbered CBs based on this structure descriptor. Since hydrogen bonding results in a significant potential energy gain, it is able to adjust solvation regularities drastically. Importantly, the number of confined water molecules does not influence the number of hydrogen bonds, which depends rather on the number of oxygen atoms within each CB. Our present results are in good agreement with recent literature25 considering that we applied a more rigorous criterion to assign water molecules to the confined region.

Table 1. Geometries of CBs and structural data characterizing their hydration: diameter (R) of CB cavity, volume (V) of CB cavity, average number of inner water molecules, n (H2O), density of confined water, and number of hydrogen bonds between CB and water (both inside and outside), n (H-bonds). Solute dCB, nm VCB, nm3 n (H2O) Density, kg m-3 n (H-bonds) CB[5] 0.86 0.31 1.9 ± 0.2 183 10 ± 2 CB[6] 0.94 0.37 2.5 ± 0.5 202 12 ± 2 CB[7] 1.16 0.58 5.8 ± 0.9 299 14 ± 2 CB[8] 1.26 0.71 9.7 ± 1.2 408 17 ± 2 CB[9] 1.44 0.92 19.4 ± 2.0 630 19 ± 3 CB[10] 1.58 1.11 24.9 ± 2.3 670 21 ± 3 10 ACS Paragon Plus Environment

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Enthalpy, entropy, and Gibbs free energy of hydration (Figures 6-7) are fundamental measures of hydrophobility / hydrophilicity of CBs. In addition, they provide an assessment of their aqueous solubilities. Useful representations of the thermodynamic potentials are per one gram of CBs (Figure 7) and per one GLYC (Table 2). Hydration of CBs is favored enthalpically. Larger CBs exhibit larger hydration enthalpies. While ∆H upon hydration of CB[5] is -385 kJ mol-1, ∆H upon hydration of CB[10] is nearly twice larger, -760 kJ mol-1. These numbers are in concordance with the numbers of hydrogen bonds between CBs and water molecules, which were discussed above. Hydration of CBs is, however, strongly prohibited entropically. The entropic factor, -T∆S, uniformly increases with the size of CB. CBs partially ruin a network of hydrogen bonds, which connect water molecules in the bulk phase. This process results in the energetic penalty, which can only partially be compensated by the formation of hydrogen bonds between CBs and water (Table 1). According to ∆G = f (n), solubilization of the larger CB[n]s is systematically worse.



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Figure 6. Enthalpic factor (∆H), entropic factor (-T∆S), and Gibbs free energy (∆G) at standard conditions as a function of the number of the glycouril units.

If the thermodynamic potentials are normalized with respect to the mass unit, the difference between CBs disappears for enthalpy (ca. -0.5 kJ g-1), but still persists for entropy increasing twice from CB[5] to CB[10] (Figure 7). Since enthalpy is independent on the number of GLYCs, interaction of CB with water per GLYC is energetically the same (Table 2). The entropic penalty increase per GLYC, (-T∆S)/n, is also constant. Our present results are helpful to predict aqueous solubilization of larger CBs, provided that they will be synthesized at some point. From the thermodynamic trend, it is evident that smaller CBs, e.g. with four GLYCs, are more soluble. However, it is unclear whether such macrocycles will be stable, because they must exhibit a large surface curvature.

Figure 7. Hydration enthalpy (red solid line), and hydration entropic factor (green dashed line), and hydration Gibbs free energy (blue dash-dotted line) per gram of CB[n], n=5...10.

Table 2. Thermodynamic potentials of hydration per GLYC: enthalpy (∆H), entropy multiplied by temperature (-T∆S), Gibbs free energy (∆G). The block-averaged errors upon calculation of the thermodynamic potentials are below 3 kJ mol-1. Solute ∆H/n, kJ mol-1 (-T∆S)/n, kJ mol-1 ∆G/n, kJ mol-1 CB[5] -77 +126 +49 CB[6] -79 +129 +50 CB[7] -82 +133 +51 CB[8] -80 +130 +50 12 ACS Paragon Plus Environment

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CB[9] CB[10]

-78 -76

+128 +124

+50 +48

Our MD simulations explain the experimental observations only partially. While an aqueous solubility of CBs (experimental data) generally decreases from n=5 to n=8, CB[7] is known to exhibit a higher solubility than CB[6].12 To reveal the origin of this behavior, one needs to consider an entire thermodynamic process occurring upon solubilization. First, the solute molecule must be removed from its solid state and placed in vacuum. Second, the solute molecule must be transferred from vacuum to bulk solvent. The conducted free energy simulations consider only the second process. Since the results suggest a uniform decrease of the aqueous solubility, the difference of CBs must be within the solid states of CBs. Indeed, the recent experimental work of Bardelang and coworkers13 reveals that CBs with the even symmetry (6 and 8 units) are crystalline, whereas CBs with the odd symmetry (5 and 7 units) are amorphous. According to these authors, the difference in the solid state occurs due to the different degrees of weak CH···O interactions between the macrocycles. Intermolecular interactions in the crystalline structures are stronger than in the amorphous state. Combining our free energy data and experimental data of Bardelang and coworkers,13 an explanation of the solubility maximum at CB[7] can be elaborated. While the favorability of transfer of CBs into water decreases uniformly with the increase of their size, CB[5], CB[7], and CB[9] undergo more favorable changes of enthalpy upon ruination of their solid states. CB[6], CB[8], and CB[10] obey the entropy trend suggested by our free energy calculations. In terms of aqueous solubility: CB[6] > CB[8] > CB[10]. In terms of ∆G: CB[6] < CB[8] < CB[10]. Destruction of the solid state in the case of the amorphous CBs, n = 5, 7, 9, is somewhat energetically cheaper than in the case of crystalline CBs, n = 6, 8, 10. Thus, a higher solubility of the odd-numbered CBs depends only on their crystalline 13 ACS Paragon Plus Environment


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symmetry and does not depend on CB–water interactions. This knowledge is important for selecting different CBs for applications. If significant concentrations of CBs are desirable, application of the odd-symmetry CBs as hosts for drugs is preferable, as aqueous solubility is important for successful drug delivery.

Conclusions Free energies of hydration were obtained for six representatives of the cucurbituril family: CB[5], CB[6], CB[7], CB[8], CB[9], CB[10] at standard conditions using classical MD simulations. Solubilization of CBs is favored by enthalpy, which uniformly decreases as the number of GLYCs increases. However, solubilization is prohibited by entropy, the entropic factor being larger for larger CBs. Immersed in water, CBs ruin a genuine hydrogenbonded network significantly. Hydrogen bonding constitutes a major source of potential energy in liquid water. CBs foster thermodynamically unfavorable rearrangement of them. This entropic penalty is insufficiently compensated by the solute-solvent hydrogen bonds, which, however, make CB much more soluble, as compared to most other particles of the nanoscale dimensions. Temperature decrease is favorable for hydration of CBs, since it linearly decreases the entropic factor, while enthalpy is expected to undergo a negligible change. Larger CBs, n > 10, should they be synthesized in the future, are expected to be even less soluble. Having combined our results and previous experimental data, we provided an explanation of the solubility maximum occurring at CB[7] in the row of CB homologues. We also predict another extremum at CB[9], whose solubility is anticipated to exceed that of CB[8]. The reported results are important for understanding of the experimentally observed


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solubilization trend and to predict behaviors of larger CBs. Larger CBs may be of a significant practical interest, since they may be able to encapsulate large drug molecules, fragments of genes, oligopeptides. In contrast to hydrophobic drug vectors, CBs foster significantly strong host-guest interactions.

Acknowledgments Some financial assistance was obtained from CNPq, CAPES, and FAPESP.

References

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Peculiar Aqueous Solubility Trend in Cucurbiturils Unraveled by

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