Predicting the Complex Phase Behavior of Self-Assembling Drug

Article pubs.acs.org/molecularpharmaceutics

Predicting the Complex Phase Behavior of Self-Assembling Drug Delivery Nanoparticles Tu C. Le,† Xavier Mulet,†,‡ Frank R. Burden,†,‡ and David A. Winkler*,†,‡ †

CSIRO Materials Science and Engineering, Bag 10, Clayton South MDC 3169, Australia Monash Institute of Pharmaceutical Sciences, 381 Royal Parade, Parkville 3052, Australia

‡

S Supporting Information *

ABSTRACT: Amphiphilic lyotropic liquid crystalline selfassembled nanomaterials have important applications in the delivery of therapeutic and imaging agents. However, little is known about the effect of the incorporated drug on the structure of nanoparticles. Predicting these properties is widely considered intractable. We present computational models for three drug delivery carriers, loaded with 10 drugs at six concentrations and two temperatures. These models predicted phase behavior for 11 new drugs. Subsequent synchrotron small-angle X-ray scattering experiments validated the predictions. KEYWORDS: cubosomes, drug delivery, self-assembly, computational modeling, nanophase prediction, experimental validation, SAXS

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INTRODUCTION Increasing numbers of drug candidates have significant lipophilic or amphiphilic character1 associated with serious solubility issues. In such cases, drug delivery vehicles are frequently used in the drug development process. Lyotropic liquid crystalline phases offer significant advantages as advanced drug delivery vehicles.2 Liquid crystals (LCs) are in a state of matter with properties between those of a conventional liquid and those of a solid crystal. LC materials are often amphiphilic (having both water loving and fat loving properties) and lyotropic (form liquid crystals upon addition of solvent). The amphiphilic nature of these materials makes them ideal matrices for the encapsulation of bioactive molecules, and they can be individually tailored to deliver specific types of drugs. Liposomes, dispersed lyotropic liquid crystalline lamellar phases made of phospholipids, are one the most commonly used and studied classes of drug delivery vehicles.3 Liposomes vary in size from tens of nanometers to tens of micrometers. However, other liquid crystalline phases have also demonstrated significant drug delivery potential. The self-assembled systems presented herein, based on amphiphilic lipid materials, offer an elegant solution to the problem of solubilizing, or tissue-specific delivery of problematic drugs.4 These materials have additional advantages over liposomes in that they have an ordered internal structure, potentially allowing higher drug loading, and can be dispersed into a nanoparticulate form that improves their pharmacokinetic properties.5 The various LC phases (called mesophases) are characterized by the nature of their long-range order. However, higher-order nanoparticles based on two- and three-dimensional symmetry [e.g., hexagonal phases (hexosomes) and cubic phases (cubosomes), respectively] are of particular interest because of their larger amphiphilic volumes Published 2013 by the American Chemical Society

and surface areas. We employ block copolymer sterically stabilized lyotropic LC particles, typically of inverse-bicontinuous cubic or inverse-hexagonal symmetry. Bicontinuous cubic phases consist of a curved lipid bilayer considered to be draped over an infinite periodic minimal surface that subdivides space into two interpenetrating, but not connected, water networks. Inverse phases, in which water is solubilized in a continuous hydrophobic medium, have a polar−apolar interface with a negative mean curvature. There are three main types known as the gyroid (G, with space group Ia3d), diamond (D, with space group Pn3m), and primitive (P, with space group Im3m) bicontinuous cubic phases6−9 whose structures are shown in Figure 1. The inverse hexagonal phase (HII) consists of cylindrical inverse micellar-like structures packed in a hexagonal configuration.10 The phase behaviors of the three excipients used here, phytantriol, monoolein, and Myverol (a commercially available lipid mixture with monoolein as the main component), are well-known.11,12 However, the presence of the incorporated bioactive small organic drug molecule will affect the internal structure, and thus the resulting nanostructure, of the delivery nanoparticles. As recently reviewed by Mulet et al., a wide range of drugs have been loaded into a different lipidic phases, many of which have an effect on the phase behavior of these systems.13 For example, Engström and co-workers demonstrated that addition of lidocaine base to glycerol monooleate drove the formation of mesophases with higher negative Received: Revised: Accepted: Published: 1368

November 9, 2012 February 12, 2013 March 6, 2013 March 6, 2013 dx.doi.org/10.1021/mp3006402 | Mol. Pharmaceutics 2013, 10, 1368−1377

Molecular Pharmaceutics

Article

Figure 1. Structures of the inverse-bicontinuous diamond QIID (Pn3m), gyroid QIIG (Ia3d), and primitive QIIP (Im3m) cubic phases.

curvatures while lidocaine hydrochloride tended to form flatter interfaces.14 Changes to the inherent nanostructure of these phases have been shown to affect both the drug release kinetics in the bulk phase and may affect long-term particle stability in aqueous dispersions.15 In addition, the maximal drug dose that can be incorporated in a system is critical for the development of therapeutic carrier nanoparticles. The incorporation capacities of different nanophases and how different loadings change the nanostructure are very important information for drug delivery applications. Currently, the main method for characterizing nanoparticle structure is small-angle X-ray scattering (SAXS), which provides information about the symmetry and the lattice parameter (unit cell size) of the internal structure. Successful application of lyotropic LC nanoparticles to drug delivery therefore requires models that can predict more quickly and efficiently than synchrotron experiments the bioactive compatibility, phase behavior, and maximal loadings for lyotropic LC-based drug delivery nanoparticles. Hitherto, predicting this complex phase behavior computationally has been considered intractable.16 We report here a computational method for reliably predicting the effect of incorporation of drug molecules on the phase behavior of LC nanoparticle drug delivery vehicles. To the best of our knowledge, this is the first time a machine learning approach has been used to predict the phase behavior of LC nanoparticles as a function of drug type, drug loading, and temperature. It is also the first report of an effective, potentially general method for predicting the phase behavior of amphiphilic nanoparticulate drug delivery carriers by any computational means. As different phases exhibit different surface properties, drug loadings, and release behavior and knowledge of the complex interplay between the nanoparticle components is very limited, such predictive computational methods are potentially valuable.

and the second sample set used DSM-sourced phytantriol (manufactured February 2009). A steric stabilizer solution of Pluronic F127 (7.5 mg/mL) was prepared using Milli-Q deionized water. Drug-Loaded Nanoparticle Preparation Method. The LC dispersions were prepared in 2 mL 96-deep square well collection plates (Supelco) using an automated synthesis platform, Chemspeed Accelerator TM SLT2 (Chemspeed), as described by Mulet et al.4 Briefly, 50 mg of lipid (to provide 100 mg/mL in the final dispersion; 10 wt % of the total sample mass) was dispensed in a chloroform solution per sample well as well as the appropriate quantity of drug dissolved in a suitable solvent, typically chloroform or methanol. The solvent was removed in a vacuum centrifuge (Atlas Evaporator, Genevac, England), at 2 mb, heated to 40 °C for at least 4 h, and placed under vacuum overnight to remove all traces of solvent. Subsequently, 500 μL of stabilizer solution was added. Each sample was probe-sonicated (Chemspeed model SLT2 sonicator) at amplitude 5 for a total time of 5 min at a 1 Hz on−off cycle to minimize heating. Characterization of Internal Structure and Particle Morphology. The internal liquid crystalline structure of the dispersed particles was determined by using SAXS. Data were collected using the SAXS/WAXS beamline at the Australian Synchrotron using a beam with a wavelength (λ) of 1.033 Å (12.0 keV) with a typical flux of 1013 photons/s. Twodimensional diffraction patterns were recorded on a DecrisPilatus 1 M detector of 10 modules. The detector was offset to access a greater q range. A silver behenate standard (λ = 58.38 Å) was used to calibrate the reciprocal space vector. The samples were loaded in special glass 1.5 mm capillaries (Hampton Research) and positioned in a custom-designed semi-high-throughput capillary holder capable of holding 40 capillaries with the temperature controlled to ±0.1 °C between 20 and 75 °C. The temperature was maintained via a recirculating water bath. The exposure time for each sample was 1 s. Representative SAXS data are shown in Figure 1 of the Supporting Information. Computational Methods. Quantitative structure−property relationship (QSPR) modeling methods were employed to model the phase behavior data of amphiphilic nanostructured nanoparticle drug delivery vehicles.17 The model inputs are numerical parameters (descriptors) that describe the molecular properties of drug molecules or experimental conditions such as the temperature, drug loading, or existence of other phases. The relationship between these input descriptors and the phase

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MATERIALS AND METHODS Materials. The following compounds were used without further purification: monoolein, hydrocortisone, transretinol, diazepam, prednisolone, dexamethasone, progesterone, haloperidol, levofloxacin, indometacin, Pluronic F127, chlorambucil, cimetidine, β-estradiol, androsterone, nifedipine, ibuprofen, curcumin, histamine, dopamine calcein (Sigma-Aldrich), atropine (TCI), Myverol 18-99K (Bronson & Jacobs). Solvents used were at least HPLC grade from Merck. Phytantriol was obtained from two different batches as generous donations from DSM (manufactured March 2005) for first sample set 1, 1369

dx.doi.org/10.1021/mp3006402 | Mol. Pharmaceutics 2013, 10, 1368−1377


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one output layer. Sigmoidal transfer functions were employed in the hidden and output layers and linear transfer functions in the input layer. The number of nodes in the input layer was equal to the number of descriptors, and the output layer had only one node corresponding to the existence of a given phase. Separate models were built for each phase, and all individual phase prediction models combined to predict the complex phase diagram. Two or three hidden layer nodes were found to be sufficient to build good models, and increasing the number is unnecessary as the Bayesian regularization automatically controls the complexity of the models to optimize predictivity.26 The number of effective weights in the neural network models tended to a constant value as the number of hidden layer nodes increased. Details of the Bayesian regularization applied to back-propagation neural networks are found elsewhere.19,27 The training set and BFGS method were used to train the models until a maximum was attained in the Bayesian evidence (maximum likelihood method). This avoids the need to use a validation set to determine when training should be stopped to prevent overtraining of the network. The number of effective weights in the neural network models ranged from 8 to 32; hence, the models were not overfitted. Data sets were separated into a training set (80%) and a test set (20%) using K-means clustering. The prediction power of the models was tested by performing an a priori blind prediction of the complex phase behavior of 11 new drugs. These additional validation experiments used BRANN models derived from all of the phase behavior data for phytantriol (batch 2) and monoolein. The descriptors for 11 new drugs were used to predict the phases adopted by the nanoparticles for these drugs at the same range of loadings and temperatures as the drugs used to develop the models. These predictions were tested by a subsequent round of experiments. The accuracy of the phase predictions for these new drugs was assessed by SAXS measurements.

behavior of the drug delivery nanoparticles was derived using a novel nonlinear Bayesian regularized artificial neural network (see below). Descriptors are mathematical descriptions of molecular properties of the drug molecules that are used in developing QSPR models. Examples of simple descriptors include the numbers of atoms of a specific elemental type with specific numbers of connections (atomistic descriptors), the number of rings of varying sizes, the dipole moment, the molecular weight, the molecular size, etc. Although some descriptors are simple, they have been shown to encode not only physicochemical parameters (e.g., hydrophobicity and molar refractivity) but also biological activity (e.g., dihydrofolate reductase inhibition).18 The Burden index (B), which encodes the connectivity of the molecules and nature of the valence electrons,19 was also calculated. These eigenvalue descriptors are obtained by diagonalizing the adjacency matrices derived from the molecular graphs. These matrices describe how atoms in a molecule are connected. Off-diagonal elements of the matrices are square roots of the number of bonds between two atoms if these atoms are chemically bonded and zero if not. The binned charge (BC) indices20 describe the charge properties of molecules (and indirectly the dipolar and hydrogen bonding properties). Atom charges were computed using electronegativity equalization methods for each drug structure and the charges for each element type used to populate bins representing different ranges of atomic charge. The vector of bin occupancies for all element types represented the charge fingerprint. Functional group representations were also used to account for molecular contributions to the phase behavior of the drug delivery carriers. Although there is some overlap with the atomistic representation, functional group counts such as the number of primary, secondary, or tertiary hydroxyl groups (nOHp, nOHs, or nOHt, respectively), the number of donor or acceptor atoms for hydrogen bonds (nHDon or nHAcc, respectively), and the number of esters, aliphatic and aromatic (nRCOOR and nArCOOR, respectively), are relatively informative. The functional group counts for drugs included in this study were calculated using DRAGON.21 We used DRAGON to calculate other molecular descriptors,22 including the unsaturation index Ui, hydrophilic factor Hy,22 molar refractivity,23 AMR, topological polar surface areas24 using N, O polar contributions TPSA(NO) or using N, O, S, P polar contributions TPSA(Tot), and different octanol− water partition coefficients,23,25 MLOGP or ALOGP. Experimental parameters were also employed as input descriptors of the models. These include the temperature (25 or 37 °C), drug loadings (percent), and the measured logarithm of water−octanol partition coefficients (log Ko/w) obtained from the online database of the Sangster Research Laboratories (http://logkow.cisti.nrc.ca/logkow/). The dependent variables in the models were the presence or absence of each phase at each specific experimental point. These were encoded using indicator variables that take a value of 1 if the phase is present and 0 if the phase is absent. Bayesian Regularized Neural Networks. The Bayesian regularized artificial neural network (BRANN) method was employed to discover the relationship between the descriptors described in the previous section and the existence of phases of the amphiphilic nanostructured nanoparticulate drug delivery carriers. The network consisted of one input, one hidden, and

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RESULTS AND DISCUSSION Modeling the Effect of Drug Incorporation on Nanophases. We constructed QSPR models using data from drug encapsulation experiments using four different types or batches of lipids. Two experiments used phytantriol from different batches to assess effects of batch-to-batch variability; another used monoolein, and the last used Myverol, the commercial product containing monoolein. Boyd et al. recently reported that impurities in commercial amphiphilic lipids could very significantly alter the liquid crystalline phase behaviorm, so we investigated this by comparing Myverol and pure monoolein.28 These amphiphilic materials were used to prepare inverse-bicontinuous cubic and inverse-hexagonal liquid-crystalline nanoparticles loaded with 10 commonly used drugs. These drugs had a wide range of structures and lipophilicities and were loaded at six concentrations (0, 1, 2, 5, 10, and 15 mol %) and at two temperatures (25 and 37 °C). It should be noted that at the higher drug loading levels there may be some unbound or unassociated drug. As these would not affect the phase behavior of the lipid, they would not affect the modeling data obtained herein. Some of the data were quarantined into a test set used to assess the predictive power of the models. Two of the four data sets were reported previously, so a full description of the experimental methods can be found elsewhere.4 The phase behavior of these systems 1370



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Figure 2. Individual phases, including inverse-bicontinuous diamond QIID (Pn3m) cubic (blue), hexagonal HII (yellow), gyroid QIIG (Ia3d) cubic (red), crystalline Lc (green), and fluid isotropic FI (brown), predicted by the best BRANN models for (A) batch 1 and (B) batch 2 phytantriol nanoparticles loaded with drugs at 25 and 37 °C. Circled samples indicate the mismatch between modeled and experimental results.

was quite complex, depending on the temperature, concentration, and identity of the incorporated drug. In addition, the coexistence of two or more phases was often observed. The coexistence of the gyroid phase in some of these fully hydrated dispersions (see Figure 2) is notable as this phase is normally observed under only limited hydration conditions for pure lipid systems. However, in this case, the gyroid phase (Ia3d space group) was observed only in presence of drugs molecules. Separate models were built for each phase, and the individual phase prediction models combined by “stacking” the individual phase diagrams on top of each other to generate the complex phase diagram of the complete system containing multiple

coexisting phases at many of the drug, concentration, and temperature data points. Multiple linear regression was initially employed to derive a relationship between descriptors (mathematical descriptions of molecular properties of the drug molecules and lipids), experimental conditions (drug concentration and temperature), and the observed phase behavior of nanophase drug delivery systems. However, these models made poor predictions for the complex phase behavior of all the drug delivery vehicles compared to nonlinear models. This strongly suggested that the relationship between the types of phases observed and the descriptors is nonlinear. Bayesian regularized artificial neural 1371



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Figure 3. Individual phases, including inverse-bicontinuous diamond QIID (Pn3m) cubic (blue), hexagonal HII (yellow), and primitive QIIP (Im3m) cubic (purple), predicted by the best BRANN models for monoolein nanoparticles loaded with drugs at 25 and 37 °C. The lack of circled data points (mismatches between model prediction and experimental observation) shows that the model made zero prediction errors for this phase.

network (BRANN)19,27 nonlinear modeling methods were therefore used to model the phases in the four experiments. Data from the two phytantriol experiments were modeled using BRANNs. Figure 2 shows the phase diagram for both batches of phytantriol predicted by the BRANN models. The LC phase behavior of both batches of phytantriol was similar, but differences in impurities altered the behavior of the minor phases, confirming that these are relatively sensitive to the purity of the lipid.28 For the inverse-bicontinuous diamond QIID (Pn3m) cubic phase, the models generated only one prediction error for both training and test sets for both batches of phytantriol. For the inverse-hexagonal HII phase, the models also gave high accuracy with only one training set and one test set prediction error for the first batch of phytantriol. For the second batch of phytantriol, the model generated three prediction errors for the training set and no errors for the test set. For the inversebicontinuous gyroid QIIG (Ia3d) cubic phase, the models generated no prediction errors for either batch of phytantriol. The crystalline Lc phase for phytantriol in batch 1 and the fluid isotropic FI phase in phytantriol batch 2 were also predicted with high accuracy (only one prediction error). Combining these individual phase prediction results shows that of 480 individual phase predictions, there were only two and five prediction errors for the first and second batches of phytantriol, respectively. This approach predicted the complex phases shown in Figure 2 for phytantriol with an accuracy of >99% (478 and 475 of 480 data points for the two phytantriol batches, respectively).

The performance of the nonlinear BRANN model for the individual phases generated by monoolein is summarized in Figure 3. The models generated no prediction errors in either the training or test sets. Myverol is the most common commercial form of monoolein and contains a complex mixture of amphiphilic substances varying in chain length and level of purity, which leads to difficulties in characterizing and controlling its LC behavior.29 We anticipated that these impurities would change the observed phase behavior considerably, as was reported by Boyd et al.28 We were interested in how much the phase behavior of Myverol differed from that of pure monoolein and how well our modeling method could capture relatively complex phase behavior. As Figure 4 shows, the phase behavior is clearly different from that of pure monoolein (Figure 3), with Myverol adopting significantly more hexagonal and diamond cubic phases and less primitive cubic phase. This provided a clear indication of the somewhat dramatic effect that impurities in the lipids can have on phase behavior. Nonetheless, robust machine learning methods were also able to model and predict the phase behavior even in this complex case, as the relatively small number of prediction errors in Figure 4 shows. For the inverse-bicontinuous diamond QIID (Pn3m) cubic phase, the BRANN model gave high prediction accuracy with no errors for the training set and four errors for the test set. For the inverse-hexagonal (HII) phase, the model generated 10 prediction errors for the training set and four errors for the test set. However, for the inverse-bicontinuous primitive QIIP (Im3m) cubic phase, none of the models could predict that 1372



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Figure 4. Individual phases, including inverse-bicontinuous diamond QIID (Pn3m) cubic (blue), hexagonal HII (yellow), and primitive QIIP (Im3m) cubic (purple), predicted by the best BRANN models for Myverol nanoparticles loaded with drugs at 25 and 37 °C. Circled samples indicate the mismatch between modeled and experimental results.

such a level of prediction accuracy is noteworthy. The linear and nonlinear feature selection methods found relevant descriptors that were largely similar. Relevance of the Model Descriptors. The phase prediction models were sparse, employing just 18−32 network weights and a small number of molecular descriptors, depending on the phase. The pruning of the least informative descriptors and selection of the most relevant descriptors may provide useful insight into the factors that drive the formation of different phases of the lipid materials. Both MLREM (linear) and BRANNLP (nonlinear) sparse neural network modeling approaches were used to identify the most relevant subset of descriptors that affect the existence of each phase. There was substantial overlap in the descriptors chosen by the two methods as Figure 5 shows. This suggests that the linear and nonlinear models are using similar information from descriptors but that the nonlinear model developed from these is more accurate. Figure 6 summarizes the descriptors suggested by the MLREM methods to play important roles in phase formation. In all cases, the concentration of drug affects the formation of each phase, although in most cases this is positive with QIID in phytantriol and QIIP in monoolein having a negative effect. The number of carbonyl and ether oxygen atoms (A14 and A15) is significant in phytantriol phase models, reflecting the importance of hydrogen bond acceptors in the phase. This is also suggested by the importance of the two partial oxygen charge descriptors, BCGM10 and BCGM11, and the number of ketones, nRCO and nArCO. Hydrogen bond donors and acceptors are featured more prominently in monoolein through

this phase would exist under any of the experimental conditions. This resulted in a relatively high number of prediction errors overall, so an additional computational strategy was devised. It has been recognized that the existence or coexistence of phases in these types of systems obeys specific rules. The three bicontinuous cubic phases are inter-related by the Bonnet transformation30 that performs a one-to-one mapping between equivalent surface patches on the three phases and predicts the ratio of lattice parameters of two coexisting cubic phases. Consequently, we attempted to improve the rather poor primitive cubic phase prediction ability for Myverol by incorporating information about the existence of other phases when generating models for a specific phase. We used two indicator variables denoting the presence (1) or absence (0) of the other two phases in the models for the third (Im3m) phase. Given that these two phases could be predicted well by their respective models, we could use calculated values for the existence of these phases to assist with the prediction of the primitive cubic phase. This substantially reduced the prediction errors for the QIIP (Im3m) phase, resulting in only two prediction errors for the training set and four for the test set. Combining the individual phase prediction results shows that of 360 individual phase predictions, there were 24 incorrect phase predictions (a prediction accuracy of >93%). This improvement suggested that the inverse-bicontinuous primitive QIIP (Im3m) cubic phase is dependent on the presence of the diamond QIID (Pn3m) cubic and hexagonal (HII) phases. Given that there were many data points in which two or more phases coexisted, 1373



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Figure 5. Significant descriptors19−25 selected by the best BRANNLP and MLREM models for (A) phytantriol and (B) monoolein.

encapsulating all new drugs (Figure 7A). The prediction accuracy of the model was 82% (correctly predicted 108 of 132 phases). The prediction accuracies for the inverse-hexagonal HII, gyroid cubic QIIG (Ia3d), and fluid isotropic FI minor phases of phytantriol were 89, 99, and 92% (correctly predicted 117, 131, and 122, respectively, of 132 phases), respectively. Our models for these phases used the indicator variables for the existence of major phase QIID (Pn3m) as descriptors to predict the existence of the FI phase. Combining the individual phase prediction results shows that of 528 individual phase predictions, there were 50 incorrect predictions (91% accuracy). For monoolein, the inverse-continuous primitive Q IIP (Im3m) cubic phase was the major phase formed for all new drugs, as shown in Figure 7B. The model correctly predicted the phase with 73% accuracy (96 of 132 data points). The

the descriptors nRCOOR, nOHt, and RNR2. Temperature plays a more important role in phase formation for phytantriol than for monoolein, at least at the temperature points sampled in these experiments. Experimental Validation of Model Predictions for New Drugs. The phase prediction models have the greatest value when they can predict the effect of completely new drugs on the delivery system phases. To this end, we predicted the effect of 11 different drugs on the complex phase behavior of lyotropic LC nanoparticles using the BRANN models derived form the original set of drugs. Experiments were then conducted to test the accuracy of the phase predictions using the SAXS beamline of the Australian Synchrotron as described by Mulet et al.4 For phytantriol, the inverse-bicontinuous diamond QIID (Pn3m) cubic phase was the major phase formed when 1374



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Figure 6. Significant descriptors selected by the best MLREM models. The coefficients show the importance of the factor to the existence of the phase (positive) or lack of the phase (negative) for (A) phytantriol and (B) monoolein.

prediction accuracies for the minor inverse diamond cubic QIID (Pn3m) and hexagonal HII phases were 93 and 92%, respectively. For multiple coexisting phases, there were 55 errors in the prediction of any phase from 360 phase predictions (an accuracy of 85%). The phase behavior of amphiphilic, multicomponent systems like those studied here is clearly very complex. Consequently, predicting the phase behavior of “real world” drug delivery systems by other computational methods such as molecular dynamics is widely considered unfeasible. The approach we have adopted is able to find relationships between the molecular properties of the systems components, temperature, and loading that accurately predicts the phase behavior for new drugs. Our modeling approach will also facilitate the design of nanophases with applications such as templates for the generation of more rigid, high-surface area nanometer-scale

structures, nanophases to support membrane-bound proteins for structural biology, and delivery of proteins such as insulin.

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CONCLUSION

Our work demonstrates that the complex phase behavior of amphiphilic nanostructured nanoparticle drug delivery vehicles can be predicted with very useful accuracy. This modeling technique is relatively simple to apply and is currently the only method capable of predicting how different drugs, drug loadings, and temperatures affect nanoparticle mesophase behavior. These phase prediction models are capable of making true predictions of changes in nanophase behavior as validated by subsequent synchrotron experiments. 1375



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Figure 7. Individual phases, including inverse-bicontinuous diamond QIID (Pn3m) cubic (blue), hexagonal HII (yellow), gyroid QIIG (Ia3d) cubic (red), primitive QIIP (Im3m) cubic (purple), and fluid isotropic FI (brown), predicted by the best BRANN models for (A) phytantriol and (B) monoolein nanoparticles loaded with new drugs at 25 and 37 °C. Circled samples indicate the mismatch between modeled and experimental results.

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Author Contributions

ASSOCIATED CONTENT

S Supporting Information *

T.C.L. conducted the modeling and jointly wrote the manuscript. D.A.W. jointly wrote the paper, conceived the project, and provided intellectual input to the modeling. X.M. conducted the experiments and contributed to the paper. F.R.B. provided intellectual input to the modeling and wrote the software used.

Representative SAXS data for dispersions of phytantriol and monoolein. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

Notes

*E-mail: [email protected].

The authors declare no competing financial interest. 1376



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(21) TALETE srl Dragon for Windows (Software for Molecular Descriptor Calculations), version 2.2, Talete srl: Milano, Italy, 2007. (22) Todeschini, R.; Consonni, V. Handbook of Molecular Descriptors; Wiley-VCH: Weinheim, Germany, 2000. (23) Viswanadhan, V. N.; Ghose, A. K.; Revankar, G. R.; Robins, R. K. Atomic Physicochemical Parameters for 3 Dimensional Structure Directed Quantitative Structure-Activity Relationships. 4. Additional Parameters for Hydrophobic and Dispersive Interactions and Their Application for an Automated Superposition of Certain NaturallyOccurring Nucleoside Antibiotics. J. Chem. Inf. Comput. Sci. 1989, 29, 163−172. (24) Ertl, P.; Rohde, B.; Selzer, P. Fast calculation of molecular polar surface area as a sum of fragment-based contributions and its application to the prediction of drug transport properties. J. Med. Chem. 2000, 43, 3714−3717. (25) Moriguchi, I.; Hirono, S.; Liu, Q.; Nakagome, I.; Matsushita, Y. Simple Method of Calculating Octanol Water Partition-Coefficient. Chem. Pharm. Bull. 1992, 40, 127−130. (26) Tarasova, A.; Burden, F.; Gasteiger, J.; Winkler, D. A. Robust modelling of solubility in supercritical carbon dioxide using Bayesian methods. J. Mol. Graphics Modell. 2010, 28, 593−597. (27) Burden, F. R.; Winkler, D. A. Robust QSAR models using Bayesian regularized neural networks. J. Med. Chem. 1999, 42, 3183− 3187. (28) Boyd, B. J.; Dong, Y. D.; Dong, A. W.; Larson, I.; Rappolt, M.; Amenitsch, H.; Hanley, T. Impurities in commercial phytantriol significantly alter its lyotropic liquid-crystalline phase behavior. Langmuir 2008, 24, 6998−7003. (29) Dong, Y. D.; Larson, I.; Hanley, T.; Boyd, B. J. Bulk and dispersed aqueous phase behavior of phytantriol: Effect of vitamin E acetate and F127 polymer on liquid crystal nanostructure. Langmuir 2006, 22, 9512−9518. (30) Hyde, S. T.; Andersson, S.; Ericsson, B.; Larsson, K. A Cubic Structure Consisting of a Lipid Bilayer Forming an Infinite Periodic Minimum Surface of the Gyroid Type in the GlycerolmonooleateWater System. Z. Kristallogr. 1984, 168, 213−219.

ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the CSIRO Advanced Materials Transformational Platform. T.C.L. acknowledges support from The Chemical Structure Association Trust Jacques-Émile Dubois Award.

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