Article pubs.acs.org/molecularpharmaceutics
Insights into Pharmaceutical Nanocrystal Dissolution: A Molecular Dynamics Simulation Study on Aspirin Maximilian Greiner, Ekaterina Elts, and Heiko Briesen* Chair for Process Systems Engineering, Technische Universität München, Freising 85354, Germany ABSTRACT: The presented molecular dynamics simulations are the first simulations to reveal dynamic dissolution of a pharmaceutical crystal in its experimentally determined shape. Continuous dissolution at constant undersaturation of the surrounding medium is ensured by introducing a plane of sticky dummy atoms into the water slab. These atoms have a strong interaction potential with dissolved aspirin molecules, but interactions with water are excluded from the calculations. Thus, the number of aspirin molecules diffusing freely in solution is kept at a low value and continuous dissolution of the aspirin crystal is monitored. Further insight into face-specific dissolution is drawn. The dissolution mechanism of receding edges is found for the (001) plane. These findings are in good agreement with experimental results. While the proposed dissolution mechanism for the (100) plane is terrace sinking on a rough surface, no pronounced dissolution of the perfectly flat face is seen in the present work. Molecular simulations of pharmaceuticals in their experimentally obtained structure therefore have shown to be especially suited for the investigation of dissolving faces, where the edges have a pronounced effect. In contrast to previous studies a propagation of the dissolution front into the crystal face is reported, and the crystal bulk is stable over the whole simulation time of 150 ns. KEYWORDS: molecular dynamics simulation, nanocrystal, dissolution
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INTRODUCTION The dissolution properties of active pharmaceutical ingredients (APIs) have been an extensively studied topic in the last decades and still are. After synthesis, APIs are crystallized at a high purity. After orally administering the drug to a human, these crystal compounds need to be dissolved to make the APIs available for absorption. Thus, characterizing dissolution properties is a critical step in the design of new products just as it is in the improvement of existing ones. Many approaches are available to increase the bioavailability of APIs, such as synthesis of cocrystals or salt-forms, liquid dosage forms, or solid dispersions to mention just a few besides formulation design.1 As the variety of APIs exhibiting poor pharmacokinetics, either due to poor solubility or permeability, is long,2 aspirin was chosen as a model system for this study. Aspirin is an experimentally very well-known substance and exhibits a higher degree of freedom when compared to many systems previously studied in dissolution or growth simulations. As an overview of such an intensively studied substance can never be exhaustive, only a short review is given in the following. Atomic force microscopy (AFM) is an important technique to evaluate surface structures with a subnanometer resolution and is widely applied for crystal characterization.3 Masaki et al. studied the (100), (001), and the (011) faces of aspirin using AFM, revealing the (100) face being most rigidly sustained, when compared to XRD structures, and the (011) face did not give reasonable images.4 Another study investigated the hydrophobicity of different aspirin crystal faces. Using different AFM tips, the (001) crystal plane was found to be more hydrophobic than the (100) face.5 Another application of AFM is the evaluation of etching patterns. The etching of crystal © 2014 American Chemical Society
surfaces allows to reveal dissolution kinetics, mechanisms, and surface morphologies.6,7 These findings have a significant impact in understanding and characterizing molecular crystal surface structures and properties, important in crystal dissolution. The application of atomic force microscopy is an imaging technique that is of great importance also for the investigation of nanoscale drug delivery systems.8,9 In recent years, simulation techniques became increasingly important in crystallization and pharmaceutical research. Providing an atomistic resolution, molecular simulation techniques are a promising tool to further understand the underlying properties. Recent work on aspirin includes the influence of hydrogen bonds for aspirin in the liquid state,10 the calculation of surface energies,11 the interaction of aspirin molecules with specific surfaces,12 and aspirin crystal structure prediction.13,14 Especially the knowledge of surface or lattice energies are crucial, e.g., to predict correct crystal shape and morphology. For novel substances, predicted crystal structures are of crucial importance. For well-studied substances, such as aspirin, the structure is known from experiment,13,15 and crystallographic crystal structure has been determined.16 A recent publication, however, reports on false crystal face determination of aspirin. The identification of the (100) and (001) faces is reported to be wrongly characterized in much of the existing literature.17 There is experimental knowledge of crystal structures for known systems, and there are theoretical Received: Revised: Accepted: Published: 3009
February 21, 2014 July 22, 2014 August 4, 2014 August 4, 2014 dx.doi.org/10.1021/mp500148q | Mol. Pharmaceutics 2014, 11, 3009−3016
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Figure 1. Structure of aspirin crystals as proposed in the literature (a), as seen in our experiment (b), and as implemented in the MD simulation (c).
group interactions between dummy atoms and water molecules were excluded in the calculations. The aspirin nanocrystal was prepared in VMD29 from a periodic crystal, built from a pre-equilibrated structure of the experimental unit cell,16 after relaxing the periodic supercell at a temperature of 310 K and ambient pressure. The size of the final crystal was around 10 × 15 × 8 nm3 and consisted of a total number of 4079 molecules. The crystal was then placed in a triclinic simulation box with a minimum spacing of 1.6 nm between the crystal and the simulation box boundaries. Next, the structure was enlarged in the x-direction by 3 nm. A slab of 100 dummy atoms was added in the center of the additional space (see Figure 1c). As solvent, pure TIP3P water was added to the system, and water molecules accidentally placed into the crystal lattice were removed. Finally, the simulation box contained 84160 molecules of water. The resulting structure, containing a total of 338239 atoms, was then subject to temperature and volume equilibration in subsequent simulations. During production simulation a unit cell in the center of the nanocrystal was position-restrained to avoid rotation of the crystal. Aspirin was modeled in its protonated state representing a simulation at low pH. The impact of the dummy atoms on the molecules in solution (aspirin and water) was evaluated in a separate simulation setup. In an 8 × 8 × 8 nm3 sized cubic box, containing 25 dummy atoms centered along the z-axis and uniformly distributed along the x- and y-axes. Sixty-four aspirin molecules were added randomly, and the free space was filled with water. Simulations with and without the dummy atoms were run for 1.5 ns. Liquid, adsorbed, and crystal molecules were identified by counting the nearest neighbor crystal molecules with correct orientation according to the relaxed unit cell. Further details can be found in a previous publication.30 Experimental Techniques. Three grams of aspirin (purity 99%) was dissolved in a mixture of 50 mL of ethanol and 50 mL of water. Aspirin single crystals were grown by recrystallization from the filtered solution in a crystallization dish of 95 mm diameter. Crystals were harvested at a size of 5 mm. For the dissolution experiments a single aspirin crystal was placed into a cylindrical sample holder (diameter 10 mm, height 3 mm) with wax. The cylinder was filled with water to start dissolution. Microscopy images of the (001) face of the crystals were taken using an Olympus BX51 system before dissolution and after significant erosion of the edges became visible. Validation of Sticky Dummy Atoms. Sticky dummy atoms were added to the simulation setup to ensure a high undersaturation within the system while keeping the total
methods to predict crystal structures for unknown substances; thus, there is everything needed for an investigation of the dissolution of API crystals on an atomistic level. There have been theoretical studies on the dissolution or growth of crystal faces and edges18 on a molecular level in recent years. A method increasingly applied for the investigation of interface properties of APIs is molecular dynamics (MD) simulations.19 Current studies on crystal growth or dissolution mainly focus on small molecules, such as glycine,20 urea,21 and even on Lennard-Jones particles.22 Of outstanding importance are works from Piana and Gale,21 where they model urea crystal growth using an approach combining MD and kinetic Monte Carlo techniques, or the work by Salvalaglio et al.,23 where the influence of additives on urea crystal growth is investigated. The approach used in the studies mentioned is to investigate dissolution or growth on periodic and thus infinitely large interfaces. To model dissolution of API molecules, the time scales accessible in molecular simulations may not always be sufficient to resolve dissolution from these perfectly shaped interfaces.24 Gao et al.25 have shown for paracetamol that there is a significant impact of corners and edges on the dissolution of APIs. Their work, however, misses to represent the experimental crystal morphology and the nanocrystal quickly gets dissolved due to the limited size of the crystal bulk. In this article, aspirin is used as a model substance to demonstrate how crystal dissolution of API molecules can be investigated combining molecular dynamics simulations and experimental crystal morphology information. Therefore, in the first section a suitable representation for simulating continuous dissolution of a three-dimensional aspirin crystal is introduced, and the influence of the dummy atoms is validated. Finally, the resulting crystal morphology for the (001) face, erosion of its corners and edges, and details on the (100) face are reported.
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MATERIAL AND METHODS Simulation Techniques. For all simulations the GROMACS software package was used,26 applying the CHARMM force field parameter.27,28 In short, the cutoff applied for van der Waals forces and the neighbor list was 1.2 nm and the particle-mesh Ewald method was applied for electrostatic interactions. The LINCS algorithm was used to constrain bonds, and a 2 fs time step was chosen. The production simulation was run at 310 K by applying the Nosé−Hoover thermostat. In equilibration simulations temperature and pressure were adjusted using the Berendsen algorithm. The depth of the potential well for the dummy atoms was 999 kJ mol−1 with all other parameters identical to carbon atom representations. To avoid spurious results for water, energy 3010
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Figure 2. Number density of aspirin as a function of the z-coordinate at different time steps with dummy atoms switched off (a) and on (b).
diffuse freely, and finally, the molecules are permanently removed from the system as the number density of molecules near the sticky dummy atoms increases continuously. In the following simulation setup a distance of at least 3 nm between the bulk crystal and its periodic image as well as between the crystal and the sticky dummy atoms are introduced. This is more than twice the cutoff and should therefore be sufficient to ensure for no significant impact of the sticky dummy atoms on the dissolution behavior of aspirin.
system size at a minimum. Familiar concepts are known, e.g., from virtual sites in water models31 or to generally improve structural stability26 of more complex molecules, whereas the dummy atoms used in this study are evenly distributed, single atoms to irreversibly trap dissolved aspirin molecules. Alternatively, molecules could be removed during the simulation, leading to noncontinuous potentials and an online determination of appropriate molecules to delete. Further, the size of the water slab could be increased; however, the computational cost would largely increase due to the comparably low solubility of aspirin. Thus, adding sticky dummy atoms enable to simulate continuous dissolution at comparably low computational cost. The requested properties of these virtual atoms are, first, not to interfere with the crystal bulk; second, to irreversibly trap dissolved aspirin molecules; and third, they should allow for free diffusion in the solvent. To investigate these features a validation of the sticky dummy atoms in a separate simulation setup is presented, where 64 aspirin molecules, placed randomly in the simulation box, are diffusing in the liquid. Optionally, a layer of sticky dummy atoms is present in the center of the z-axis of the simulation box. The number density of aspirin molecules without the presence of sticky dummy atoms is presented in Figure 2a, and besides natural fluctuations due to the limited amount of molecules present (64 aspirin molecules), no changes over time can be seen. The molecular number density is as low as 7 nm−3 also because only aspirin molecules were considered. In contrast, in Figure 2b the sticky dummy atoms were introduced as a slab in the center of the z-axis of the simulation box. While the interactions between dummy atoms and water were removed by excluding energy group interactions, the depth of the potential well almost immediately catches aspirin molecules within the cutoff radius of 1.2 nm. The increase in number density over time comes from more and more aspirin molecules diffusing into the cutoff radius of the sticky dummy atoms, where they are adsorbed. After a simulation time of 1.5 ns, the area within 1.2 nm of the dummy atoms is depleted. In the regions from 0 to 2 nm and from 6 to 8 nm, the number density of aspirin remains almost unchanged until 3.5 ns, when the number density also decreases in the surrounding liquid. These findings show that aspirin molecules within the cutoff radius (1.2 nm) of the sticky dummy atoms get trapped immediately. Aspirin molecules outside of the cutoff radius
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RESULTS AND DISCUSSION Structure Building and Validation. The aspirin crystal morphology as grown in experiment from ethanol−water solution is sketched in Figure 1a, accordingly to the literature.13,15,17 Representations of typical crystal structures obtained from experiment in this work are presented in Figure 1b, and the crystal structure of aspirin as investigated in the simulations is given in Figure 1c. The crystals grown in experiment agree well with the structures reported in the literature, exhibiting prominent (100) and (001) faces and the typical structure of the (110) and (011) faces. Applying this crystal structure in the simulations ensures an efficient setup to monitor continuous dissolution when exposed to undersaturated aqueous solution. In the final structure each edge of the crystal has a length of around 3 nm. This not only corresponds to a size well above the critical diameter for stable nuclei reported by Hammond et al.11 but also allows for the simulation of a significant dissolution on the aspirin crystal surface without losing crystal bulk stability, which has not been possible in previous studies.25 Building the crystal with all faces as present in the experimental morphology, the etching of different edges and corners is assumed to be related to experimental findings in dissolution. Molecular Dissolution Analysis. To monitor the dissolution of aspirin from the crystal, the molecules were classified into solid-like, liquid-like, and adsorbed molecules. The full details of this procedure can be found in the literature.30 In short: the molecular orientation and number of nearest neighbors of each aspirin molecule was compared to molecules from a reference unit cell. Molecules with the correct orientation and nonzero number of neighbors were classified as solid-like. Molecules with wrong orientation or zero number of neighbors were classified as liquid-like. Liquid-like molecules 3011
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until a significant amount of liquid molecules can be found is realistic due to the absence of convective flow in the simulation system, the tendency of the uncharged benzene ring to stay attached to the crystal surface, and the strong hydrogen bonds formed in the crystal, which prevent molecules with wrong orientation from disintegrating immediately. Further, the continuous increase in liquid molecules is strongly affected by the dummy atoms, which successfully ensure for constant undersaturation, as the majority of aspirin molecules, detected as liquid, are bound to the dummy atoms. Finally, the number of adsorbed molecules seems to change only slightly toward the end of the simulation but still the number of crystal molecules decreases significantly. Liquid molecules either return to the crystal, where they adsorb and might reintegrate into the crystal lattice, or they reach within the cutoff of the dummy atoms and are irreversibly caught. After 150 ns of simulation the resulting number of liquid molecules is 202, and out of these liquid molecules, 188 are bound to the sticky dummy atoms. For an analysis frame of 100 ps, the cumulative sum (without double counting) of molecules found to be in the liquid is 362. Thus, almost exactly half of the molecules, which have been in the liquid once, have returned to the crystal and the other half has been caught by the sticky dummy atoms. This agrees nicely with the random walk expected for free diffusion. A final snapshot of the resulting crystal configuration can be seen in Figure 4a. While most adsorbed molecules are on the (001) faces of the crystal, there are also a significant number of adsorbed molecules on the (100) face as well as on the (110)/ (011) faces. Figure 4b shows the accumulated density of aspirin over the whole simulation time. Dark black regions are the bulk crystal and the trapped aspirin molecules near the sticky dummy atoms. In good agreement with the visual impression, erosion is most pronounced on the left and right ((001) faces). The distribution of aspirin molecules in the liquid is symmetric toward the top and bottom of the simulation box, due to the periodic boundary conditions applied. Further, the equal density in the surrounding liquid shows that free diffusion is possible within the presented system setup. Neither the crystal bulk nor the adsorbed molecules on faces near the sticky dummy atoms are destabilized by the interaction potential implemented. The dissolution mechanism on the (001) and (100) faces will be discussed in the following section. Dissolution Details on the (001) Crystal Plane. As seen in the previous section, a considerable amount of molecules has
that are near the surface within the length of one unit cell are considered as adsorbed. The evolution of molecule classes over time can be seen in Figure 3. Within the first nanoseconds of the simulation, a
Figure 3. Number of solid, liquid, and adsorbed molecules during a 150 ns simulation of an aspirin nanocrystal.
quick decline of crystal molecules can be seen, increasing the number of adsorbed molecules but without a change in the number of liquid molecules. It takes about 25 ns until the number of liquid molecules also increases significantly. After around 50 ns, the slope with which the number of liquid molecules increases remains constant until the end of the simulation. While also the slope with which the number of crystal molecules declines stays almost constant over time, the number of adsorbed molecules seems to level out toward the end of the simulation, or at least the slope in the last 50 ns of the simulation decreases continuously. From the constant decline of crystal molecules it can be stated that a continuous process of dissolution can be seen in the simulations. This is of particular importance, as dissolution simulations of three-dimensional pharmaceutical crystals in their experimentally observed morphology are not known to the authors. Further, the quick initial decline of crystal molecules, or the initial steep increase of adsorbed molecules, respectively, results from a significant amount of aspirin molecules, which are only loosely integrated into the crystal lattice at the start of the simulation. The observed leak time
Figure 4. Final snapshot after 150 ns plotted as gray surface: liquid molecules in blue and adsorbed molecules in red (a). Density of aspirin molecules accumulated over the whole trajectory, where black denotes high density and white is low density (b). 3012
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Figure 5. Results of the (001) faces with crystal molecules plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red. Initial crystal structure (a) and final snapshots from the front (b) and back (c) after 150 ns with liquid and adsorbed molecules in their initial positions.
of molecular orientation may be important for future investigations in aspirin crystal simulations; the influence on dissolution pattern at longer times and bigger size, however, would have to be evaluated by other methods. Dissolution Details on the (100) Crystal Plane. Results for dissolution of the (100) crystal plane are presented in Figure 6. The nonsymmetrical dissolution of the edges between
dissolved during the 150 ns of the simulation. Figure 5 shows that almost all these molecules were initially located on the (001) face or on its edges. While at the beginning of the simulation the crystal edges were sharp and defined (Figure 5a), the erosion of molecules can be seen in Figure 5b,c, where molecules with an atomistic representation are located at their initial position but disintegrated from the crystal lattice at some point during the simulation. The reported dissolution mechanism in experimental literature for the (001) face of aspirin is receding step edges.6 In their study, Danesh et al. investigated the erosion of the (001) crystal plane, when subjected to acid (0.05 M HCl) solution.6 An acid solution was chosen because dissolution in pure water was too slow to be imaged with atomic force microscopy. The simulations have revealed strong erosion especially on the edges between the (001) and the (100) crystal planes. Further, the propagation of the erosion into the crystal plane is clearly present in Figure 5c and a whole molecular layer of aspirin has dissolved. Also in Figure 5b, a row of molecules has dissolved from the crystal face on the top and the bottom. This dissolution pattern may be well explained by the molecular structure of the aspirin molecules on the surface. As the hydrogen bonds are formed parallel to the (001) crystal plane there is only minor interaction between the molecular layers. Within one layer, however, always two molecules are connected with hydrogen bonds. Therefore, if one of the H-bond binding partners is disintegrated from the lattice, the second is incorporated only loosely and will follow shortly after. Thus, the simulations reveal the importance of hydrogen bonding for the molecular dissolution of aspirin. The molecular orientation of the aspirin molecules on the (001) crystal plane also plays a significant role in the asymmetric dissolution pattern present in both Figure 5b,c. Erosion is more pronounced for the left edge, than for the right edge, even though both are intersections of the (001) and the (100) planes. On the left, the aromatic ring is exposed to the surrounding liquid and the ester group stretches into the crystal plane. On the right, however, the aromatic ring is oriented into the crystal plane, whereas the ester group is exposed to the liquid. This meets the expected stability as the hydrophobic groups are not accessible for the water, which is interacting with the hydrogen-bonding groups. These findings on the influence
Figure 6. Final snapshot of the (100) face after 150 ns with crystal molecules plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red.
the (001) and (100) faces can also be seen from this representation. A linear dissolution pattern potentially leading to a novel (101) crystal plane is present on the right side of Figure 6, and on the opposing side, especially the vertices are subject to pronounced erosion. The asymmetric dissolution of the aspirin crystal reported above can also clearly be seen from Figure 7. Here the representation of the aspirin crystal is rotated by 90°, indicating the (001) planes on the left and right and the (100) faces on the top and bottom. This view also reveals the formation of new (101) faces (top left and bottom right in Figure 7). Molecular dynamics simulations revealing whether this would be a stable face also for longer times and larger systems are not feasible with current computational resources. It is interesting that related findings can also be seen from experimental dissolution of macroscopic 3013
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The most obvious reason why there is no dissolution of the (100) aspirin crystal face in the simulations is that simulation times were too short. While this is necessarily true, a second reason for the stability of the (100) plane might be the surface structure as found in experiment and as modeled in the simulations. Danesh et al.6 have shown that the (100) faces of aspirin are very rough, which is in good agreement with etching patterns obtained by Wen et al.7 for pure water as etching medium. The roughness of the (100) crystal face is expected to be of major importance for crystal dissolution. In contrast, the simulation setup presented here consists of a perfectly flat (100) crystal face. The feasible simulation cell size does not allow for the construction of proper, rough surfaces.
Figure 7. Snapshot of the (110) and (011) aspirin faces at 0 ns. Molecules are colored according to their state definition at 150 ns. Crystal molecules are plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red.
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CONCLUSIONS A three-dimensional crystal representation, as presented in this article, revealed being suited to monitor dissolution, while a common simulation setup with a periodic two-dimensional crystal interface is not.24 A strong influence of the edges and vertices within the system is revealed, as proposed by Gao and Olsen.25 Including the morphology of the aspirin crystal and monitoring dissolution from a stable crystal bulk is an essential step toward predicting dissolution properties of novel substances, where no other information but the molecular structure is needed, as methods to predict the underlying configuration in the unit cell33 or the morphology of the crystal13 already exist. The asymmetric dissolution pattern between different faces and the propagation of the dissolution front into the crystal face is additionally revealed in the present study. For nanocrystals these findings are of particular importance, as the surface-tovolume and edge-to-face ratios considerably increase with diminishing crystal size. Further, by building the crystal morphology according to experimental findings, conclusions from AFM measurements of etching patterns and dissolution mechanisms are drawn. A similar dissolution mechanism as found in the literature is found for the (001) face. Even though a comparison of absolute dissolution kinetics from molecular dynamics alone is not feasible, it can be well explained from experimental findings that the receding step edges dissolution mechanism leads to dissolution in the presented simulation setup, whereas the perfectly flat (100) face in the simulation misses the surface roughness present in experimental aspirin etching pattern.
crystals, as presented in Figure 8. Here, the dissolution on the edges between the (001) and the (100) face leads to significant rounding. The images, however, also show a smaller height of the aspirin crystal after dissolution. Thus, dissolution of the (100) face must have been present in experiment, while no dissolution was observed in the simulations. Whether dissolution on the (100) face of aspirin can be expected in molecular simulations, when considerable dissolution of the (001) face was seen, cannot clearly be answered from literature. Experimental results on dissolution kinetics of the (100) face of aspirin are ambiguous. Danesh et al. report the dissolution of the (100) face to be approximately six times faster than the (001) face, when etched by a 0.5 M HCl solution. In their paper they, however, state that this is largely due to the reactive nature of the dissolution process, where the acid catalyzes the hydrolysis of the ester group.6 For pure water as dissolution medium, Kim et al. found the (100) face dissolving roughly twice as fast as the (001) face,32 but their face indexing is not consistent with more recent literature,6,11 a problem just recently communicated.17 Concluding from the morphology of the crystal, the (001) face shows significantly faster dissolution. These findings indicate that it is reasonable that longer simulation times might be needed to see dissolution at the (100) face compared to the (001) face. As it is not possible to evaluate quantitative dissolution kinetics from molecular simulations, it should be noted here that significant changes in the height of the experimental crystal was seen in the experiments shown in Figure 8.
Figure 8. Microscopic images of the aspirin single crystal before (a) and after (b) dissolution in aqueous media. 3014
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(8) Sitterberg, J.; Oezcetin, A.; Ehrhardt, C.; Bakowsky, U. Utilising atomic force microscopy for the characterisation of nanoscale drug delivery systems. Eur. J. Pharm. Biopharm. 2010, 74, 2−13. (9) Shegokar, R.; Mueller, R. H. Nanocrystals: Industrially feasible multifunctional formulation technology for poorly soluble actives. Int. J. Pharm. 2010, 399, 129−139. (10) Cristina Donnamaria, M.; de Xammar Oro, J. R. The role of hydrogen bonds in an aqueous solution of acetylsalicylic acid: a molecular dynamics simulation study. J. Mol. Model. 2011, 17, 2485− 2490. (11) Hammond, R. B.; Pencheva, K.; Roberts, K. J. A structuralkinetic approach to model face-specific solution/crystal surface energy associated with the crystallization of acetyl salicylic acid from supersaturated aqueous/ethanol solution. Cryst. Growth Des. 2006, 6, 1324−1334. (12) Li, T.; Li, B.; Tomassone, M. S. Surface characterization of aspirin crystal planes using molecular dynamics simulations. Chem. Eng. Sci. 2006, 61, 5159−5169. (13) Hammond, R. B.; Pencheva, K.; Ramachandran, V.; Roberts, K. J. Application of grid-based molecular methods for modeling solventdependent crystal growth morphology: Aspirin crystallized from aqueous ethanolic solution. Cryst. Growth Des. 2007, 7, 1571−1574. (14) Price, S. L. Computed crystal energy landscapes for understanding and predicting organic crystal structures and polymorphism. Acc. Chem. Res. 2009, 42, 117−126. (15) Longuemard, P.; Jbilou, M.; Guyot-Hermann, A. M.; Guyot, J. C. Ground and native crystals: comparison of compression capacity and dissolution rate. Int. J. Pharm. 1998, 170, 51−61. (16) Wilson, C. C. Interesting proton behaviour in molecular structures. Variable temperature neutron diffraction and ab initio study of acetylsalicylic acid: characterising librational motions and comparing protons in different hydrogen bonding potentials. New J. Chem. 2002, 26, 1733−1739. (17) Aubrey-Medendorp, C.; Parkin, S.; Li, T. The confusion of indexing aspirin crystals. J. Pharm. Sci. 2008, 97, 1361−1367. (18) Snyder, R. C.; Doherty, M. F. Faceted crystal shape evolution during dissolution or growth. AIChE J. 2007, 53, 1337−1348. (19) Cui, Y. Using molecular simulations to probe pharmaceutical materials. J. Pharm. Sci. 2011, 100, 2000−2019. (20) Cheong, D. W.; Di Boon, Y. Comparative study of force fields for molecular dynamics simulations of alpha-glycine crystal growth from solution. Cryst. Growth Des. 2010, 10, 5146−5158. (21) Piana, S.; Gale, J. D. Understanding the barriers to crystal growth: Dynamical simulation of the dissolution and growth of urea from aqueous solution. J. Am. Chem. Soc. 2005, 127, 1975−1982. (22) Reilly, A. M.; Briesen, H. Modeling crystal growth from solution with molecular dynamics simulations: Approaches to transition rate constants. J. Chem. Phys. 2012, 136, 034704. (23) Salvalaglio, M.; Vetter, T.; Giberti, F.; Mazzotti, M.; Parrinello, M. Uncovering molecular details of urea crystal growth in the presence of additives. J. Am. Chem. Soc. 2012, 134, 17221−17233. (24) Greiner, M.; Elts, E.; Briesen, H. Dissolution study of active pharmaceutical ingredients using molecular dynamics simulations with classical force fields. J. Cryst. Growth, accepted. DOI: 10.1016/ j.jcrysgro.2014.07.046. (25) Gao, Y.; Olsen, K. W. Molecular dynamics of drug crystal dissolution: Simulation of acetaminophen form I in water. Mol. Pharmacol. 2013, 10, 905−917. (26) Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701−1718. (27) Bjelkmar, P.; Larsson, P.; Cuendet, M. A.; Hess, B.; Lindahl, E. Implementation of the CHARMM Force Field in GROMACS: Analysis of protein stability effects from correction maps, virtual interaction sites, and water models. J. Chem. Theory Comput. 2010, 6, 459−466. (28) Aliev, A. E.; Courtier-Murias, D. Experimental verification of force fields for molecular dynamics simulations using Gly-Pro-Gly-Gly. J. Phys. Chem. B 2010, 114, 12358−12375.
These insights into the dissolution of crystals come at a high cost. The simulations are, due to the system size and time scale investigated, expensive and require considerable computational resources. Despite this, the size of the crystal investigated was still too small and the time simulated too short to draw quantitative conclusions. Also it cannot be taken for granted that on larger scales of time and size the findings presented here still persist. For example, the (101) plane, which seems to evolve, might not be as pronounced, when dissolution of the (001) faces becomes crucial. Piana and Gale21 have revealed considerable differences in surface dissolution between small-scale molecular dynamics simulations and more coarse grained kinetic Monte Carlo simulations. We will propose a kinetic Monte Carlo model for the dissolution of a three-dimensional aspirin crystal with experimental morphology and realistic size in future work to reveal if similar differences also arise for aspirin dissolution. For the (001) face, the dissolution rates needed in a kinetic Monte Carlo simulation can be gained from the simulations presented here, whereas a periodic, two-dimensional simulation setup might be more suited to further investigate the dissolution of structured and rough surfaces, such as the (100) face of aspirin.
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AUTHOR INFORMATION
Corresponding Author
*(H.B.) E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through grants BR 2035/4-1 and BR 2035/ 8-1. Julian Schneider is thankfully acknowledged for the fruitful discussions as well as Alexander Reinhold and Tijana Kovac̆ević for the crystal shape images. We made use of the computer resources provided by the Leibniz Supercomputing Centre under the grant pr58la.
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(29) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics Model. 1996, 14, 33−38. (30) Elts, E.; Greiner, M. M.; Briesen, H. Data filtering for effective analysis of crystal-solution interface molecular dynamics simulations. J. Chem. Theory Comput. 2014, 10, 1686−1697. (31) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926−935. (32) Kim, Y.; Matsumoto, M.; Machida, K. Specific surface energies and dissolution behavior of aspirin crystal. Chem. Pharm. Bull. 1985, 33, 4125−4131. (33) Ouvrard, C.; Price, S. L. Toward crystal structure prediction for conformationally flexible molecules: The headaches illustrated by aspirin. Cryst. Growth Des. 2004, 4, 1119−1127.
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Insights into Pharmaceutical Nanocrystal Dissolution: A Molecular Dynamics Simulation Study on Aspirin Maximilian Greiner, Ekaterina Elts, and Heiko Briesen* Chair for Process Systems Engineering, Technische Universität München, Freising 85354, Germany ABSTRACT: The presented molecular dynamics simulations are the first simulations to reveal dynamic dissolution of a pharmaceutical crystal in its experimentally determined shape. Continuous dissolution at constant undersaturation of the surrounding medium is ensured by introducing a plane of sticky dummy atoms into the water slab. These atoms have a strong interaction potential with dissolved aspirin molecules, but interactions with water are excluded from the calculations. Thus, the number of aspirin molecules diffusing freely in solution is kept at a low value and continuous dissolution of the aspirin crystal is monitored. Further insight into face-specific dissolution is drawn. The dissolution mechanism of receding edges is found for the (001) plane. These findings are in good agreement with experimental results. While the proposed dissolution mechanism for the (100) plane is terrace sinking on a rough surface, no pronounced dissolution of the perfectly flat face is seen in the present work. Molecular simulations of pharmaceuticals in their experimentally obtained structure therefore have shown to be especially suited for the investigation of dissolving faces, where the edges have a pronounced effect. In contrast to previous studies a propagation of the dissolution front into the crystal face is reported, and the crystal bulk is stable over the whole simulation time of 150 ns. KEYWORDS: molecular dynamics simulation, nanocrystal, dissolution
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INTRODUCTION The dissolution properties of active pharmaceutical ingredients (APIs) have been an extensively studied topic in the last decades and still are. After synthesis, APIs are crystallized at a high purity. After orally administering the drug to a human, these crystal compounds need to be dissolved to make the APIs available for absorption. Thus, characterizing dissolution properties is a critical step in the design of new products just as it is in the improvement of existing ones. Many approaches are available to increase the bioavailability of APIs, such as synthesis of cocrystals or salt-forms, liquid dosage forms, or solid dispersions to mention just a few besides formulation design.1 As the variety of APIs exhibiting poor pharmacokinetics, either due to poor solubility or permeability, is long,2 aspirin was chosen as a model system for this study. Aspirin is an experimentally very well-known substance and exhibits a higher degree of freedom when compared to many systems previously studied in dissolution or growth simulations. As an overview of such an intensively studied substance can never be exhaustive, only a short review is given in the following. Atomic force microscopy (AFM) is an important technique to evaluate surface structures with a subnanometer resolution and is widely applied for crystal characterization.3 Masaki et al. studied the (100), (001), and the (011) faces of aspirin using AFM, revealing the (100) face being most rigidly sustained, when compared to XRD structures, and the (011) face did not give reasonable images.4 Another study investigated the hydrophobicity of different aspirin crystal faces. Using different AFM tips, the (001) crystal plane was found to be more hydrophobic than the (100) face.5 Another application of AFM is the evaluation of etching patterns. The etching of crystal © 2014 American Chemical Society
surfaces allows to reveal dissolution kinetics, mechanisms, and surface morphologies.6,7 These findings have a significant impact in understanding and characterizing molecular crystal surface structures and properties, important in crystal dissolution. The application of atomic force microscopy is an imaging technique that is of great importance also for the investigation of nanoscale drug delivery systems.8,9 In recent years, simulation techniques became increasingly important in crystallization and pharmaceutical research. Providing an atomistic resolution, molecular simulation techniques are a promising tool to further understand the underlying properties. Recent work on aspirin includes the influence of hydrogen bonds for aspirin in the liquid state,10 the calculation of surface energies,11 the interaction of aspirin molecules with specific surfaces,12 and aspirin crystal structure prediction.13,14 Especially the knowledge of surface or lattice energies are crucial, e.g., to predict correct crystal shape and morphology. For novel substances, predicted crystal structures are of crucial importance. For well-studied substances, such as aspirin, the structure is known from experiment,13,15 and crystallographic crystal structure has been determined.16 A recent publication, however, reports on false crystal face determination of aspirin. The identification of the (100) and (001) faces is reported to be wrongly characterized in much of the existing literature.17 There is experimental knowledge of crystal structures for known systems, and there are theoretical Received: Revised: Accepted: Published: 3009
February 21, 2014 July 22, 2014 August 4, 2014 August 4, 2014 dx.doi.org/10.1021/mp500148q | Mol. Pharmaceutics 2014, 11, 3009−3016
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Figure 1. Structure of aspirin crystals as proposed in the literature (a), as seen in our experiment (b), and as implemented in the MD simulation (c).
group interactions between dummy atoms and water molecules were excluded in the calculations. The aspirin nanocrystal was prepared in VMD29 from a periodic crystal, built from a pre-equilibrated structure of the experimental unit cell,16 after relaxing the periodic supercell at a temperature of 310 K and ambient pressure. The size of the final crystal was around 10 × 15 × 8 nm3 and consisted of a total number of 4079 molecules. The crystal was then placed in a triclinic simulation box with a minimum spacing of 1.6 nm between the crystal and the simulation box boundaries. Next, the structure was enlarged in the x-direction by 3 nm. A slab of 100 dummy atoms was added in the center of the additional space (see Figure 1c). As solvent, pure TIP3P water was added to the system, and water molecules accidentally placed into the crystal lattice were removed. Finally, the simulation box contained 84160 molecules of water. The resulting structure, containing a total of 338239 atoms, was then subject to temperature and volume equilibration in subsequent simulations. During production simulation a unit cell in the center of the nanocrystal was position-restrained to avoid rotation of the crystal. Aspirin was modeled in its protonated state representing a simulation at low pH. The impact of the dummy atoms on the molecules in solution (aspirin and water) was evaluated in a separate simulation setup. In an 8 × 8 × 8 nm3 sized cubic box, containing 25 dummy atoms centered along the z-axis and uniformly distributed along the x- and y-axes. Sixty-four aspirin molecules were added randomly, and the free space was filled with water. Simulations with and without the dummy atoms were run for 1.5 ns. Liquid, adsorbed, and crystal molecules were identified by counting the nearest neighbor crystal molecules with correct orientation according to the relaxed unit cell. Further details can be found in a previous publication.30 Experimental Techniques. Three grams of aspirin (purity 99%) was dissolved in a mixture of 50 mL of ethanol and 50 mL of water. Aspirin single crystals were grown by recrystallization from the filtered solution in a crystallization dish of 95 mm diameter. Crystals were harvested at a size of 5 mm. For the dissolution experiments a single aspirin crystal was placed into a cylindrical sample holder (diameter 10 mm, height 3 mm) with wax. The cylinder was filled with water to start dissolution. Microscopy images of the (001) face of the crystals were taken using an Olympus BX51 system before dissolution and after significant erosion of the edges became visible. Validation of Sticky Dummy Atoms. Sticky dummy atoms were added to the simulation setup to ensure a high undersaturation within the system while keeping the total
methods to predict crystal structures for unknown substances; thus, there is everything needed for an investigation of the dissolution of API crystals on an atomistic level. There have been theoretical studies on the dissolution or growth of crystal faces and edges18 on a molecular level in recent years. A method increasingly applied for the investigation of interface properties of APIs is molecular dynamics (MD) simulations.19 Current studies on crystal growth or dissolution mainly focus on small molecules, such as glycine,20 urea,21 and even on Lennard-Jones particles.22 Of outstanding importance are works from Piana and Gale,21 where they model urea crystal growth using an approach combining MD and kinetic Monte Carlo techniques, or the work by Salvalaglio et al.,23 where the influence of additives on urea crystal growth is investigated. The approach used in the studies mentioned is to investigate dissolution or growth on periodic and thus infinitely large interfaces. To model dissolution of API molecules, the time scales accessible in molecular simulations may not always be sufficient to resolve dissolution from these perfectly shaped interfaces.24 Gao et al.25 have shown for paracetamol that there is a significant impact of corners and edges on the dissolution of APIs. Their work, however, misses to represent the experimental crystal morphology and the nanocrystal quickly gets dissolved due to the limited size of the crystal bulk. In this article, aspirin is used as a model substance to demonstrate how crystal dissolution of API molecules can be investigated combining molecular dynamics simulations and experimental crystal morphology information. Therefore, in the first section a suitable representation for simulating continuous dissolution of a three-dimensional aspirin crystal is introduced, and the influence of the dummy atoms is validated. Finally, the resulting crystal morphology for the (001) face, erosion of its corners and edges, and details on the (100) face are reported.
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MATERIAL AND METHODS Simulation Techniques. For all simulations the GROMACS software package was used,26 applying the CHARMM force field parameter.27,28 In short, the cutoff applied for van der Waals forces and the neighbor list was 1.2 nm and the particle-mesh Ewald method was applied for electrostatic interactions. The LINCS algorithm was used to constrain bonds, and a 2 fs time step was chosen. The production simulation was run at 310 K by applying the Nosé−Hoover thermostat. In equilibration simulations temperature and pressure were adjusted using the Berendsen algorithm. The depth of the potential well for the dummy atoms was 999 kJ mol−1 with all other parameters identical to carbon atom representations. To avoid spurious results for water, energy 3010
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Figure 2. Number density of aspirin as a function of the z-coordinate at different time steps with dummy atoms switched off (a) and on (b).
diffuse freely, and finally, the molecules are permanently removed from the system as the number density of molecules near the sticky dummy atoms increases continuously. In the following simulation setup a distance of at least 3 nm between the bulk crystal and its periodic image as well as between the crystal and the sticky dummy atoms are introduced. This is more than twice the cutoff and should therefore be sufficient to ensure for no significant impact of the sticky dummy atoms on the dissolution behavior of aspirin.
system size at a minimum. Familiar concepts are known, e.g., from virtual sites in water models31 or to generally improve structural stability26 of more complex molecules, whereas the dummy atoms used in this study are evenly distributed, single atoms to irreversibly trap dissolved aspirin molecules. Alternatively, molecules could be removed during the simulation, leading to noncontinuous potentials and an online determination of appropriate molecules to delete. Further, the size of the water slab could be increased; however, the computational cost would largely increase due to the comparably low solubility of aspirin. Thus, adding sticky dummy atoms enable to simulate continuous dissolution at comparably low computational cost. The requested properties of these virtual atoms are, first, not to interfere with the crystal bulk; second, to irreversibly trap dissolved aspirin molecules; and third, they should allow for free diffusion in the solvent. To investigate these features a validation of the sticky dummy atoms in a separate simulation setup is presented, where 64 aspirin molecules, placed randomly in the simulation box, are diffusing in the liquid. Optionally, a layer of sticky dummy atoms is present in the center of the z-axis of the simulation box. The number density of aspirin molecules without the presence of sticky dummy atoms is presented in Figure 2a, and besides natural fluctuations due to the limited amount of molecules present (64 aspirin molecules), no changes over time can be seen. The molecular number density is as low as 7 nm−3 also because only aspirin molecules were considered. In contrast, in Figure 2b the sticky dummy atoms were introduced as a slab in the center of the z-axis of the simulation box. While the interactions between dummy atoms and water were removed by excluding energy group interactions, the depth of the potential well almost immediately catches aspirin molecules within the cutoff radius of 1.2 nm. The increase in number density over time comes from more and more aspirin molecules diffusing into the cutoff radius of the sticky dummy atoms, where they are adsorbed. After a simulation time of 1.5 ns, the area within 1.2 nm of the dummy atoms is depleted. In the regions from 0 to 2 nm and from 6 to 8 nm, the number density of aspirin remains almost unchanged until 3.5 ns, when the number density also decreases in the surrounding liquid. These findings show that aspirin molecules within the cutoff radius (1.2 nm) of the sticky dummy atoms get trapped immediately. Aspirin molecules outside of the cutoff radius
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RESULTS AND DISCUSSION Structure Building and Validation. The aspirin crystal morphology as grown in experiment from ethanol−water solution is sketched in Figure 1a, accordingly to the literature.13,15,17 Representations of typical crystal structures obtained from experiment in this work are presented in Figure 1b, and the crystal structure of aspirin as investigated in the simulations is given in Figure 1c. The crystals grown in experiment agree well with the structures reported in the literature, exhibiting prominent (100) and (001) faces and the typical structure of the (110) and (011) faces. Applying this crystal structure in the simulations ensures an efficient setup to monitor continuous dissolution when exposed to undersaturated aqueous solution. In the final structure each edge of the crystal has a length of around 3 nm. This not only corresponds to a size well above the critical diameter for stable nuclei reported by Hammond et al.11 but also allows for the simulation of a significant dissolution on the aspirin crystal surface without losing crystal bulk stability, which has not been possible in previous studies.25 Building the crystal with all faces as present in the experimental morphology, the etching of different edges and corners is assumed to be related to experimental findings in dissolution. Molecular Dissolution Analysis. To monitor the dissolution of aspirin from the crystal, the molecules were classified into solid-like, liquid-like, and adsorbed molecules. The full details of this procedure can be found in the literature.30 In short: the molecular orientation and number of nearest neighbors of each aspirin molecule was compared to molecules from a reference unit cell. Molecules with the correct orientation and nonzero number of neighbors were classified as solid-like. Molecules with wrong orientation or zero number of neighbors were classified as liquid-like. Liquid-like molecules 3011
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until a significant amount of liquid molecules can be found is realistic due to the absence of convective flow in the simulation system, the tendency of the uncharged benzene ring to stay attached to the crystal surface, and the strong hydrogen bonds formed in the crystal, which prevent molecules with wrong orientation from disintegrating immediately. Further, the continuous increase in liquid molecules is strongly affected by the dummy atoms, which successfully ensure for constant undersaturation, as the majority of aspirin molecules, detected as liquid, are bound to the dummy atoms. Finally, the number of adsorbed molecules seems to change only slightly toward the end of the simulation but still the number of crystal molecules decreases significantly. Liquid molecules either return to the crystal, where they adsorb and might reintegrate into the crystal lattice, or they reach within the cutoff of the dummy atoms and are irreversibly caught. After 150 ns of simulation the resulting number of liquid molecules is 202, and out of these liquid molecules, 188 are bound to the sticky dummy atoms. For an analysis frame of 100 ps, the cumulative sum (without double counting) of molecules found to be in the liquid is 362. Thus, almost exactly half of the molecules, which have been in the liquid once, have returned to the crystal and the other half has been caught by the sticky dummy atoms. This agrees nicely with the random walk expected for free diffusion. A final snapshot of the resulting crystal configuration can be seen in Figure 4a. While most adsorbed molecules are on the (001) faces of the crystal, there are also a significant number of adsorbed molecules on the (100) face as well as on the (110)/ (011) faces. Figure 4b shows the accumulated density of aspirin over the whole simulation time. Dark black regions are the bulk crystal and the trapped aspirin molecules near the sticky dummy atoms. In good agreement with the visual impression, erosion is most pronounced on the left and right ((001) faces). The distribution of aspirin molecules in the liquid is symmetric toward the top and bottom of the simulation box, due to the periodic boundary conditions applied. Further, the equal density in the surrounding liquid shows that free diffusion is possible within the presented system setup. Neither the crystal bulk nor the adsorbed molecules on faces near the sticky dummy atoms are destabilized by the interaction potential implemented. The dissolution mechanism on the (001) and (100) faces will be discussed in the following section. Dissolution Details on the (001) Crystal Plane. As seen in the previous section, a considerable amount of molecules has
that are near the surface within the length of one unit cell are considered as adsorbed. The evolution of molecule classes over time can be seen in Figure 3. Within the first nanoseconds of the simulation, a
Figure 3. Number of solid, liquid, and adsorbed molecules during a 150 ns simulation of an aspirin nanocrystal.
quick decline of crystal molecules can be seen, increasing the number of adsorbed molecules but without a change in the number of liquid molecules. It takes about 25 ns until the number of liquid molecules also increases significantly. After around 50 ns, the slope with which the number of liquid molecules increases remains constant until the end of the simulation. While also the slope with which the number of crystal molecules declines stays almost constant over time, the number of adsorbed molecules seems to level out toward the end of the simulation, or at least the slope in the last 50 ns of the simulation decreases continuously. From the constant decline of crystal molecules it can be stated that a continuous process of dissolution can be seen in the simulations. This is of particular importance, as dissolution simulations of three-dimensional pharmaceutical crystals in their experimentally observed morphology are not known to the authors. Further, the quick initial decline of crystal molecules, or the initial steep increase of adsorbed molecules, respectively, results from a significant amount of aspirin molecules, which are only loosely integrated into the crystal lattice at the start of the simulation. The observed leak time
Figure 4. Final snapshot after 150 ns plotted as gray surface: liquid molecules in blue and adsorbed molecules in red (a). Density of aspirin molecules accumulated over the whole trajectory, where black denotes high density and white is low density (b). 3012
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Figure 5. Results of the (001) faces with crystal molecules plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red. Initial crystal structure (a) and final snapshots from the front (b) and back (c) after 150 ns with liquid and adsorbed molecules in their initial positions.
of molecular orientation may be important for future investigations in aspirin crystal simulations; the influence on dissolution pattern at longer times and bigger size, however, would have to be evaluated by other methods. Dissolution Details on the (100) Crystal Plane. Results for dissolution of the (100) crystal plane are presented in Figure 6. The nonsymmetrical dissolution of the edges between
dissolved during the 150 ns of the simulation. Figure 5 shows that almost all these molecules were initially located on the (001) face or on its edges. While at the beginning of the simulation the crystal edges were sharp and defined (Figure 5a), the erosion of molecules can be seen in Figure 5b,c, where molecules with an atomistic representation are located at their initial position but disintegrated from the crystal lattice at some point during the simulation. The reported dissolution mechanism in experimental literature for the (001) face of aspirin is receding step edges.6 In their study, Danesh et al. investigated the erosion of the (001) crystal plane, when subjected to acid (0.05 M HCl) solution.6 An acid solution was chosen because dissolution in pure water was too slow to be imaged with atomic force microscopy. The simulations have revealed strong erosion especially on the edges between the (001) and the (100) crystal planes. Further, the propagation of the erosion into the crystal plane is clearly present in Figure 5c and a whole molecular layer of aspirin has dissolved. Also in Figure 5b, a row of molecules has dissolved from the crystal face on the top and the bottom. This dissolution pattern may be well explained by the molecular structure of the aspirin molecules on the surface. As the hydrogen bonds are formed parallel to the (001) crystal plane there is only minor interaction between the molecular layers. Within one layer, however, always two molecules are connected with hydrogen bonds. Therefore, if one of the H-bond binding partners is disintegrated from the lattice, the second is incorporated only loosely and will follow shortly after. Thus, the simulations reveal the importance of hydrogen bonding for the molecular dissolution of aspirin. The molecular orientation of the aspirin molecules on the (001) crystal plane also plays a significant role in the asymmetric dissolution pattern present in both Figure 5b,c. Erosion is more pronounced for the left edge, than for the right edge, even though both are intersections of the (001) and the (100) planes. On the left, the aromatic ring is exposed to the surrounding liquid and the ester group stretches into the crystal plane. On the right, however, the aromatic ring is oriented into the crystal plane, whereas the ester group is exposed to the liquid. This meets the expected stability as the hydrophobic groups are not accessible for the water, which is interacting with the hydrogen-bonding groups. These findings on the influence
Figure 6. Final snapshot of the (100) face after 150 ns with crystal molecules plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red.
the (001) and (100) faces can also be seen from this representation. A linear dissolution pattern potentially leading to a novel (101) crystal plane is present on the right side of Figure 6, and on the opposing side, especially the vertices are subject to pronounced erosion. The asymmetric dissolution of the aspirin crystal reported above can also clearly be seen from Figure 7. Here the representation of the aspirin crystal is rotated by 90°, indicating the (001) planes on the left and right and the (100) faces on the top and bottom. This view also reveals the formation of new (101) faces (top left and bottom right in Figure 7). Molecular dynamics simulations revealing whether this would be a stable face also for longer times and larger systems are not feasible with current computational resources. It is interesting that related findings can also be seen from experimental dissolution of macroscopic 3013
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The most obvious reason why there is no dissolution of the (100) aspirin crystal face in the simulations is that simulation times were too short. While this is necessarily true, a second reason for the stability of the (100) plane might be the surface structure as found in experiment and as modeled in the simulations. Danesh et al.6 have shown that the (100) faces of aspirin are very rough, which is in good agreement with etching patterns obtained by Wen et al.7 for pure water as etching medium. The roughness of the (100) crystal face is expected to be of major importance for crystal dissolution. In contrast, the simulation setup presented here consists of a perfectly flat (100) crystal face. The feasible simulation cell size does not allow for the construction of proper, rough surfaces.
Figure 7. Snapshot of the (110) and (011) aspirin faces at 0 ns. Molecules are colored according to their state definition at 150 ns. Crystal molecules are plotted as gray surface, liquid molecules in blue, and adsorbed molecules in red.
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CONCLUSIONS A three-dimensional crystal representation, as presented in this article, revealed being suited to monitor dissolution, while a common simulation setup with a periodic two-dimensional crystal interface is not.24 A strong influence of the edges and vertices within the system is revealed, as proposed by Gao and Olsen.25 Including the morphology of the aspirin crystal and monitoring dissolution from a stable crystal bulk is an essential step toward predicting dissolution properties of novel substances, where no other information but the molecular structure is needed, as methods to predict the underlying configuration in the unit cell33 or the morphology of the crystal13 already exist. The asymmetric dissolution pattern between different faces and the propagation of the dissolution front into the crystal face is additionally revealed in the present study. For nanocrystals these findings are of particular importance, as the surface-tovolume and edge-to-face ratios considerably increase with diminishing crystal size. Further, by building the crystal morphology according to experimental findings, conclusions from AFM measurements of etching patterns and dissolution mechanisms are drawn. A similar dissolution mechanism as found in the literature is found for the (001) face. Even though a comparison of absolute dissolution kinetics from molecular dynamics alone is not feasible, it can be well explained from experimental findings that the receding step edges dissolution mechanism leads to dissolution in the presented simulation setup, whereas the perfectly flat (100) face in the simulation misses the surface roughness present in experimental aspirin etching pattern.
crystals, as presented in Figure 8. Here, the dissolution on the edges between the (001) and the (100) face leads to significant rounding. The images, however, also show a smaller height of the aspirin crystal after dissolution. Thus, dissolution of the (100) face must have been present in experiment, while no dissolution was observed in the simulations. Whether dissolution on the (100) face of aspirin can be expected in molecular simulations, when considerable dissolution of the (001) face was seen, cannot clearly be answered from literature. Experimental results on dissolution kinetics of the (100) face of aspirin are ambiguous. Danesh et al. report the dissolution of the (100) face to be approximately six times faster than the (001) face, when etched by a 0.5 M HCl solution. In their paper they, however, state that this is largely due to the reactive nature of the dissolution process, where the acid catalyzes the hydrolysis of the ester group.6 For pure water as dissolution medium, Kim et al. found the (100) face dissolving roughly twice as fast as the (001) face,32 but their face indexing is not consistent with more recent literature,6,11 a problem just recently communicated.17 Concluding from the morphology of the crystal, the (001) face shows significantly faster dissolution. These findings indicate that it is reasonable that longer simulation times might be needed to see dissolution at the (100) face compared to the (001) face. As it is not possible to evaluate quantitative dissolution kinetics from molecular simulations, it should be noted here that significant changes in the height of the experimental crystal was seen in the experiments shown in Figure 8.
Figure 8. Microscopic images of the aspirin single crystal before (a) and after (b) dissolution in aqueous media. 3014
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(8) Sitterberg, J.; Oezcetin, A.; Ehrhardt, C.; Bakowsky, U. Utilising atomic force microscopy for the characterisation of nanoscale drug delivery systems. Eur. J. Pharm. Biopharm. 2010, 74, 2−13. (9) Shegokar, R.; Mueller, R. H. Nanocrystals: Industrially feasible multifunctional formulation technology for poorly soluble actives. Int. J. Pharm. 2010, 399, 129−139. (10) Cristina Donnamaria, M.; de Xammar Oro, J. R. The role of hydrogen bonds in an aqueous solution of acetylsalicylic acid: a molecular dynamics simulation study. J. Mol. Model. 2011, 17, 2485− 2490. (11) Hammond, R. B.; Pencheva, K.; Roberts, K. J. A structuralkinetic approach to model face-specific solution/crystal surface energy associated with the crystallization of acetyl salicylic acid from supersaturated aqueous/ethanol solution. Cryst. Growth Des. 2006, 6, 1324−1334. (12) Li, T.; Li, B.; Tomassone, M. S. Surface characterization of aspirin crystal planes using molecular dynamics simulations. Chem. Eng. Sci. 2006, 61, 5159−5169. (13) Hammond, R. B.; Pencheva, K.; Ramachandran, V.; Roberts, K. J. Application of grid-based molecular methods for modeling solventdependent crystal growth morphology: Aspirin crystallized from aqueous ethanolic solution. Cryst. Growth Des. 2007, 7, 1571−1574. (14) Price, S. L. Computed crystal energy landscapes for understanding and predicting organic crystal structures and polymorphism. Acc. Chem. Res. 2009, 42, 117−126. (15) Longuemard, P.; Jbilou, M.; Guyot-Hermann, A. M.; Guyot, J. C. Ground and native crystals: comparison of compression capacity and dissolution rate. Int. J. Pharm. 1998, 170, 51−61. (16) Wilson, C. C. Interesting proton behaviour in molecular structures. Variable temperature neutron diffraction and ab initio study of acetylsalicylic acid: characterising librational motions and comparing protons in different hydrogen bonding potentials. New J. Chem. 2002, 26, 1733−1739. (17) Aubrey-Medendorp, C.; Parkin, S.; Li, T. The confusion of indexing aspirin crystals. J. Pharm. Sci. 2008, 97, 1361−1367. (18) Snyder, R. C.; Doherty, M. F. Faceted crystal shape evolution during dissolution or growth. AIChE J. 2007, 53, 1337−1348. (19) Cui, Y. Using molecular simulations to probe pharmaceutical materials. J. Pharm. Sci. 2011, 100, 2000−2019. (20) Cheong, D. W.; Di Boon, Y. Comparative study of force fields for molecular dynamics simulations of alpha-glycine crystal growth from solution. Cryst. Growth Des. 2010, 10, 5146−5158. (21) Piana, S.; Gale, J. D. Understanding the barriers to crystal growth: Dynamical simulation of the dissolution and growth of urea from aqueous solution. J. Am. Chem. Soc. 2005, 127, 1975−1982. (22) Reilly, A. M.; Briesen, H. Modeling crystal growth from solution with molecular dynamics simulations: Approaches to transition rate constants. J. Chem. Phys. 2012, 136, 034704. (23) Salvalaglio, M.; Vetter, T.; Giberti, F.; Mazzotti, M.; Parrinello, M. Uncovering molecular details of urea crystal growth in the presence of additives. J. Am. Chem. Soc. 2012, 134, 17221−17233. (24) Greiner, M.; Elts, E.; Briesen, H. Dissolution study of active pharmaceutical ingredients using molecular dynamics simulations with classical force fields. J. Cryst. Growth, accepted. DOI: 10.1016/ j.jcrysgro.2014.07.046. (25) Gao, Y.; Olsen, K. W. Molecular dynamics of drug crystal dissolution: Simulation of acetaminophen form I in water. Mol. Pharmacol. 2013, 10, 905−917. (26) Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701−1718. (27) Bjelkmar, P.; Larsson, P.; Cuendet, M. A.; Hess, B.; Lindahl, E. Implementation of the CHARMM Force Field in GROMACS: Analysis of protein stability effects from correction maps, virtual interaction sites, and water models. J. Chem. Theory Comput. 2010, 6, 459−466. (28) Aliev, A. E.; Courtier-Murias, D. Experimental verification of force fields for molecular dynamics simulations using Gly-Pro-Gly-Gly. J. Phys. Chem. B 2010, 114, 12358−12375.
These insights into the dissolution of crystals come at a high cost. The simulations are, due to the system size and time scale investigated, expensive and require considerable computational resources. Despite this, the size of the crystal investigated was still too small and the time simulated too short to draw quantitative conclusions. Also it cannot be taken for granted that on larger scales of time and size the findings presented here still persist. For example, the (101) plane, which seems to evolve, might not be as pronounced, when dissolution of the (001) faces becomes crucial. Piana and Gale21 have revealed considerable differences in surface dissolution between small-scale molecular dynamics simulations and more coarse grained kinetic Monte Carlo simulations. We will propose a kinetic Monte Carlo model for the dissolution of a three-dimensional aspirin crystal with experimental morphology and realistic size in future work to reveal if similar differences also arise for aspirin dissolution. For the (001) face, the dissolution rates needed in a kinetic Monte Carlo simulation can be gained from the simulations presented here, whereas a periodic, two-dimensional simulation setup might be more suited to further investigate the dissolution of structured and rough surfaces, such as the (100) face of aspirin.
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AUTHOR INFORMATION
Corresponding Author
*(H.B.) E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) through grants BR 2035/4-1 and BR 2035/ 8-1. Julian Schneider is thankfully acknowledged for the fruitful discussions as well as Alexander Reinhold and Tijana Kovac̆ević for the crystal shape images. We made use of the computer resources provided by the Leibniz Supercomputing Centre under the grant pr58la.
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