Modeling the Influence of Fatty Acid Incorporation on Mesophase

Article pubs.acs.org/molecularpharmaceutics

Modeling the Influence of Fatty Acid Incorporation on Mesophase Formation in Amphiphilic Therapeutic Delivery Systems By Tu C. Le,† Nhiem Tran,†,‡,# Xavier Mulet,† and David A. Winkler*,†,§,∥,⊥ †

CSIRO Manufacturing, Clayton 3169, Australia Australian Synchrotron, Clayton 3168, Australia § Monash Institute of Pharmaceutical Sciences, Parkville 3052, Australia ∥ Latrobe Institute for Molecular Science, Bundoora 3083, Australia ⊥ School of Chemical and Physical Sciences, Flinders University, Bedford Park 5042, Australia ‡

S Supporting Information *

ABSTRACT: Dispersed amphiphile-fatty acid systems are of great interest in drug delivery and gene therapies because of their potential for triggered release of their payload. The mesophase behavior of these systems is extremely complex and is affected by environmental factors such as drug loading, percentage and nature of incorporated fatty acids, temperature, pH, and so forth. It is important to study phase behavior of amphiphilic materials as the mesophases directly influence the release rate of the incorporated drugs. We describe a robust machine learning method for predicting the phase behavior of these systems. We have developed models for each mesophase that simultaneous and reliably model the effects of amphiphile and fatty acid structure, concentration, and temperature and that make accurate predictions of these mesophases for conditions not used to train the models. KEYWORDS: amphiphilic drug delivery system, triggered release, mesophases, quantitative structure−property relationships modeling, machine learning

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INTRODUCTION Amphiphilic materials are finding increasing application as soft nanomaterials for drug delivery.1−7 Nanoscale drug delivery systems using liposomes and other soft nanoparticles provide a rational platform for delivery of drugs that provides improved pharmacokinetic properties, controlled and sustained release, and lower toxicity. Although they are able to adopt a relatively wide variety of mesophases, these phases are extremely hard to predict a priori by commonly used physics-based methods like molecular dynamics, particularly as they are very sensitive to the incorporated drug, temperature, and particle composition.8 In simple mesophase systems, it is possible to make prediction of the phase behavior using simple geometric arguments such as packing parameters. More sophisticated coarse grained self consistent field theory calculations can generate phase diagrams for simple liquid crystal systems that are qualitatively similar to experimental phase diagrams.9 However, for more complex multicomponent, dynamic amphiphilic systems with drug payloads such methods are lacking. In spite of the complexity of these systems, we have previously shown that their behavior can be predicted with good accuracy if the appropriate modeling methods are used that can account for the complex interplay between the components, solvents, cargo, and temperature. We have successfully employed sparse and robust machine learning Published XXXX by the American Chemical Society

techniques, a Bayesian regularized neural network (BRANN) and sparse multiple linear regression (MLR), to generate models that can make quantitative predictions about the phase behavior of different lyotropic liquid crystals loaded with different types and concentrations of drugs under various conditions.8,10,11 These models take into account the molecular properties and concentration of the incorporated drugs, temperature, time, as well as the structures of the lipids making up the delivery systems. The validity of these models was tested by subsequent synthesis of amphiphilic nanoparticles with new drug payloads and measurement of the mesophases they form. The quest for smarter soft materials has driven recent research toward the engineering of even more complex lyotropic liquid crystalline lipid systems with controllable functionalities. One way this has been achieved is by introducing into the lipid systems various biomolecules including, but not limited to, saturated and unsaturated fatty acids.7,12−19 For example, Negrini et al. reported that adding linoleic acid to monolinolein in bulk created a pH sensitive liquid crystal system that underwent a mesophase transitions Received: November 9, 2015 Revised: January 14, 2016 Accepted: January 29, 2016

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DOI: 10.1021/acs.molpharmaceut.5b00848 Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Molecular Pharmaceutics

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from the Im3m reverse bicontinuous cubic phase to an HII reverse columnar hexagonal phase between pH 7 and pH 2, simulating conditions in the intestine and stomach.14 Similarly, Fong et al. utilized a system of phytantriol and vitamin E acetate to achieve thermoresponsive glucose “on-demand” release.20 Their delivery system reversibly switched between the bicontinuous cubic (Q2) and inverse hexagonal (H2) nanostructures in response to an external change in temperature near the physiological range. As drug release is diffusion controlled and dependent on the pore sizes, as they change with the mesophase, the drug release profiles will change. Although the introduction of biomolecules to lipid systems expanded the diversity of mesophase nanostructures and consequently the applicability of the systems, it also added another level of complexity in term of predicting the mesophase behavior. Several phases can and often do coexist; phase changes may occur relatively abruptly, and only some types of mesophases are useful for drug delivery.8,19,21,22 In this study, we were interested in how mixtures of nonlamellar forming lipids, such as monoolein, monopalmitolein, and phytantriol, and saturated fatty acids would interact and whether we could predict the phases of the nanoparticles that would result from this more complex self-assembly system in a similar way to our previous work. In these dispersed nanoparticle systems, typically one or more of the following mesophases were observed to form: the emulsified microemulsion (EME), inverse hexagonal (HII), inverse bicontinuous diamond cubic (Pn3m), inverse bicontinuous primitive cubic (Im3m), and lamellar crystal (Lc) phases depending on the concentration of fatty acid (Figure 1)

MATERIALS AND METHODS Amphiphilic Nanoparticle Synthesis and Characterization. The experiments mixed fatty acids with amphiphiles to form self-assembled nanoparticles in excess water as described by Tran et al.24 Three data sets, each consisting of one lipid system and ten saturated fatty acids from C7 to C16 with 12 different fatty acid:lipid weight ratios (r) at five different temperatures (25, 37, 40, 45, 50 °C) were used to generate quantitative structure−property relationships (QSPR) models using sparse modeling methods. The lipids, whose structures are represented in Figure 2, were monolein, phytantriol, and

Figure 1. Characteristics of the mesophases. Note: the inverse bicontinuous cubic phases consist of two continuous but nonintersecting water channels divided by a lipid bilayer which is contorted into a periodic minimal surface with zero average curvature.23 The rods in the cubic phases represent the water channels. Used with permission from Tran et al.17

Figure 2. Structures of three lipids used to form nanoparticles with different mesophases.

monopalmitolein. They differ in length of hydrocarbon chain and the existence of the double bond in the nonpolar tail and the nature of the functional groups in the polar headgroup. These differences were captured in the molecular descriptors used as the inputs of the models. The mesophases formed when these lipids were mixed with the fatty acids were identified using synchrotron small-angle Xray scattering (SAXS) and the experimental data was reported very recently by Tran et al.24 More descriptions of mesophases and phase behavior of lyotropic liquid crystalline materials are provided in several reviews.1,25,26 Individual QSPR models were generated to predict each of the five separate mesophases observed in the experiments. These used five data sets, each of which comprised 1800 data points (3 lipids × 10 fatty acids × 12 ratios × 5 temperatures).

The ultimate aim of our work was the rational design of amphiphilic delivery systems for therapeutics that could be triggered, for example, by a change in temperature or pH, to release their cargo. We now report the application of these very effective computational methods to the simultaneous modeling and prediction of the phase behavior of dispersions composed of three lipids, monoolein, monopalmitolein, and phytantriol, incorporating a diverse range of ten saturated fatty acids at five temperatures. B



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Molecular Descriptors. Molecular descriptors (mathematical objects capturing the structures and physicochemical properties of lipid and acid molecules) and experimental parameters (fatty acid:lipid weight ratio (r) and temperature) were both used as input descriptors for the QSPR models. For fatty acid molecules, the number of carbon atoms in the aliphatic chain (from 7 to 16) was the most relevant descriptor. For lipid molecules, a pool of 282 molecular descriptors were initially calculated using the DRAGON software.27 Highly correlated descriptors (r2 greater than 0.9) were then removed. This resulted in 12 molecular descriptors all of which were used as inputs for the QSPR models. A list of these and their descriptions are given in Table 1.

provided to stop training, and the network effectively pruned network weights that were of low relevance to the model. This avoids the need for a validation set to determine when training should be stopped in order to prevent overtraining of the network. We have previously shown that this type of neural network does not require a test set (see ref 30 and references therein), as it automatically and objectively generates models with optimal prediction ability. Nonetheless, as an additional check that this assumption is valid, we have also randomly divided the data set into training and test sets of 80% and 20%, respectively, to ensure that the predictivity of the test sets was similar to that of the training set. Models were trained on training set data and their predictivities assessed by comparing the measured and predicted properties of the test set experiments that the models had not seen. The performance of models obtained using these training and test sets is given in the Supporting Information. The predictions were for bulk liquid crystalline assemblies.

Table 1. List of Molecular and Physicochemical Descriptors Used in the Models descriptor

description

MW Sv SCBO nDB ZM1 rGyr nCp nCt nOHt nHDon nHBonds MlogP

molecular weight sum of atomic van der Waals volumes (scaled on carbon atom) sum of conventional bond orders (H-depleted) number of double bonds first Zagreb index M1 radius of gyration (mass weighted) number of terminal primary C(sp3) number of total tertiary C(sp3) number of tertiary alcohols number of donor atoms for H-bonds (N and O) number of intramolecular H-bonds (with N, O, F) Moriguchi octanol−water partition coefficient (log P) − measure of lipophilicity

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RESULTS AND DISCUSSION Separate BRANN models were constructed to predict each individual phase that the lipidic materials adopted. The models for each of the five mesophases incorporated data for all three amphiphiles and all 10 of the fatty acids so comprehensively captured a relative broad range of amphiphile and fatty acid structures. Details of the optimum BRANN models are summarized in Table 2. These models were generated using multiple linear regression (MLR) and the sparse nonlinear modeling method BRANNLP (a BRANN employing a sparsityinducing Laplacian prior) using three nodes in the hidden layer, with the exception of the Pn3m phase model for which two nodes in the hidden layer were sufficient. The maximum number of effective weights (parameters that were adjusted during model training) for these models was much smaller than the number of data points, so the models were clearly not overfitted. The BRANNLP models predicted the correct mesophases at least 90% of the time, significantly better than the prediction accuracies of the of the MLR models. Overall, for the optimal BRANNLP model out of 9000 individual phase predictions, there were a total of 491 prediction errors. This means that the overall accuracy of our prediction was 95%. The truth tables of the prediction results for the BRANNLP models are shown in Figure 3. These truth tables show the number of false positive, true positive, false negative, or true negative predictions for each of the five phases. False positive means that the experiment indicated the specific phase did not form but the model did predicted its existence. In contrast, false negative means the experiment showed a specific phase was formed but the model did not predict the existence of this phase. As the predictions for all the five phase formations were highly accurate, the total numbers of false positive and false

Quantitative Structure−Property Relationships Modeling for Mesophases. We employed both linear and nonlinear QSPR methods to build separate models predicting the formation of each individual mesophase. Each of the nonlinear Bayesian regularized artificial neural networks (BRANN)28−30 used consisted of one input, one hidden, and one output layer. The number of nodes in the input layer was equal to the number of descriptors described in the Molecular Descriptors section, whereas the output layer had only one node corresponding to the presence or absence of a given phase (1 when the phase occurs and 0 when the phase does not occur). Clearly, as we have seen previously, multiple phases can coexist for some combinations of experimental conditions. Two or three nodes in the hidden layer were found to be sufficient to build good models, and increasing the number is unnecessary because the Bayesian regularization automatically controls the complexity of the models to optimize predictivity.31,32 The entire data sets were used to train the models as an objective Bayesian stopping criterion (maximum in the evidence) was

Table 2. Summary of the Best MLR and BRANN Models Predicting Each Individual of the Five Phases: Emulsified Microemulsion EME, Hexagonal HII, Diamond Cubic Pn3m, Primitive Cubic Im3m, and Lamellar Crystal Lc MLR

BRANN

phase

number of effective weights

total prediction errors

accuracy of model %

number of effective weights

total prediction errors

accuracy of model %

EME HII Pn3m Im3m Lc

16 16 16 16 16

94 523 678 210 113

95 71 62 88 94

55 21 52 22 52

33 161 185 63 49

98 91 90 97 97

C



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Figure 3. Truth tables showing best BRANNs models prediction results for each of the five phases: emulsified microemulsion (EME), hexagonal (HII), diamond cubic (Pn3m), primitive cubic (Im3m), and lamellar crystal (Lc). The tables show the number of true negative, false negative, true positive, and false positive predictions (in clockwise order, starting from the top left value).

Figure 4. Predicted phase diagrams for monoolein at 25 °C under the effect of different fatty acids. The ordinates are the hydrocarbon chain length and the abscissae are the ratio, r, of fatty acid to lipid for each phase. These diagrams show the phase prediction results from the best neural network models for each of the five individual phases: emulsified microemulsion (EME), hexagonal (HII), diamond cubic (Pn3m), primitive cubic (Im3m), and lamellar crystal (Lc). Samples that are marked with × indicate that the phases for these samples were predicted incorrectly.

negative were very low relative to those with correct phase predictions. The ability of the models to predict test set data

that they have not seen before was equally good, as the table in the Supporting Information illustrates. D



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Figure 5. Predicted phase diagrams for monopalmitolein at 25 °C under the effect of different fatty acids. The ordinates are the hydrocarbon chain length and the abscissae are the ratio, r, of fatty acid to lipid for each phase. These diagrams show the phase prediction results from the best neural network models for each of the five individual phases: emulsified microemulsion (EME), hexagonal (HII), diamond cubic (Pn3m), primitive cubic (Im3m), and lamellar crystal (Lc). Samples that are marked with × indicate that the phases for these samples were predicted incorrectly.

The prediction results for each of the five phases at 25 °C for monoolein, monopalmitolein, and phytantriol are illustrated in Figures 4, 5, and 6, respectively. The actual phase behavior of the system corresponds to the five phase diagrams in each figure being “stacked” onto each other. As Figures 4−6 show, the combined phase behavior of the systems includes conditions under which two or more mesophases coexist (colors occupying the same cell in a stacked phase diagram). If the phase existence prediction was incorrect for a specific sample, the corresponding square in the figures was marked with ×. As can be seen, BRANNs models could predict correctly the majority of meso phase formations. Errors usually occurred at the phase transition edges where mislabeling of the phases was more likely, where different phases could coexist, or where there was inconsistency among the phase behaviors at various temperatures. A full list of the prediction results is provided in the Supporting Information. Although the linear models had lower prediction accuracies than those generated by the nonlinear BRANN method, they were of sufficient quality for them to be used to analyze the importance of the various molecular and experimental descriptors to mesophase formation. The level of influence of all descriptors used in the models on the formation of different mesophases is shown in Figure 7. A positive value of the MLR coefficient for a descriptor indicates that a larger value for the descriptor promotes the formation of a given phase whereas a

negative value of the MLR coefficient suggests that a larger value for the descriptor inhibits its formation. The models found that the fatty acid:lipid weight ratio was the most significant factor affecting the formation of most of the mesophases (except for the hexagonal phase). This parameter has positive MLR coefficient values for the EME, hexagonal, and lamellar crystal phases. This means that the higher the fatty acid:lipid weight ratio, the higher the probability that these will form laminar or “rolled laminar” phases. In contrast, the ratio has negative MLR coefficient values for the diamond and primitive cubic phases. Lower fatty acid:lipid weight ratios promotes the formation of these bicontinuous cubic liquid crystalline phases. As the curvature at the amphiphile−water interface plays an important role in mesophase formation it can be modulated by environmental parameters (e.g., temperature, pressure, solvation).1 Environmental conditions, such as those imposed by the temperature, pH, and degree of fatty acid incorporation, will change the balance of lateral stresses in the surfactant monolayer and, thus, the phase. The number of carbon atoms in the fatty acid chains has a relatively large effect on the formation of the hexagonal and lamellar crystals. Indeed, acids with longer chains are more likely to form these phases. However, this factor is not an important influence on the formation of the other three phases (EME, diamond, and primitive cubic). Temperature and molecular features of lipids studied do not contribute substantially to the overall phase E



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Figure 6. Predicted phase diagrams for phytantriol at 25 °C under the effect of different fatty acids. The ordinates are the hydrocarbon chain length and the abscissae are the ratio, r, of fatty acid to lipid for each phase. These diagrams show the phase prediction results from the best neural network models for each of the five individual phases: emulsified microemulsion (EME), hexagonal (HII), diamond cubic (Pn3m), primitive cubic (Im3m), and lamellar crystal (Lc). Samples that are marked with × indicate that the phases for these samples were predicted incorrectly.

has shown that we can similarly predict with high accuracy the mesophases formed when those types of amphiphiles are loaded with a broad range of drugs. We now have confidence that it will be possible to develop accurate and predictive machine learning models of mesophase formation when the drug loading, concentration, temperature, and release agent are combined in one drug delivery system.

behavior. Their influence could be seen most clearly in the hexagonal, primitive cubic, and lamellar crystal phases. This may be an artifact of the relatively small number of lipids studied (three) and the lipid descriptors may not be the most relevant for predicting the inhibition or formation of a particular phase. The geometric isomerism of chain unsaturation in lipids is known to be an important factor in their phase behavior as a kink in the hydrocarbon chain influences its radius of gyration and packing during self-assembly.33 As we only studied three amphiphiles, one with a saturated chain and two with one degree of unsaturation, and both of these were the Z (cis) isomer, it is hard to draw any conclusions about the role of the double bond isomerism. Consequently, the number of double bonds descriptor, nDB, has only a small range. The presence of a double bond does not seem to affect the formation of the EME, Lc, and Pn3m mesophases, as their contributions in Figure 7 illustrates. For the HII mesophase, the presence of a double bond appears to inhibit its formation, and for the Im3m mesophase the double bond promotes its formation but, compared with other amphiphile descriptors, the effects are not very significant. By increasing the number of lipids studied, the role of these properties will become clearer. We have now shown that its is possible to make predictions of the likely mix of mesophases occurring for a range of amphiphiles and fatty acid release agents. Our previous work

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CONCLUSIONS

The complex phase behavior of lipid materials combined with different fatty acids can be modeled very effectively using Bayesian regularized neural networks. We have developed robust single models for each mesophase that incorporate considerable complexity, accounting for the effects of the three types of amphiphiles, ten fatty acids, a range of fatty acid/lipid ratios, and temperature. This approach resulted in high predictivity QSPR models for all five phases of the materials observed experimentally including the EME, hexagonal (HII), diamond cubic (Pn3m), primitive cubic (Im3m) and lamellar crystal (Lc). The accuracy of predictions for each individual phase was higher than 90%, except for the hexagonal phase (89%) and for the combination of all phases was 95%. The ability of the models to accurately predict the mesophase behavior for complex materials in the independent test set F



Article

Figure 7. Descriptors used in the models and their influence on the formation of different mesophases.

developed the modeling methods and conceived the modeling approach.

suggests that this computational approach will be useful for the rational design of bespoke amphiphilic drug delivery systems.

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Notes

The authors declare no competing financial interest.

ASSOCIATED CONTENT

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S Supporting Information *

ACKNOWLEDGMENTS The authors acknowledge financial support from the CSIRO Advanced Materials Transformational Capability Platform. The authors are grateful for the assistance provided by Dr. Adrian Hawley, Dr. Stephen Mudie and Dr. Nigel Kirby at the SAXS/ WAXS beamline, Australian Synchrotron. The authors thank Dr. Benjamin Muir and Dr. Shaun Howard at the Rapid Automated Materials Processing (RAMP) Centre of CSIRO for their help preparing the samples for the experimental work. N.T. is supported by a John Stocker Postdoctoral Fellowship provided by Science and Industry Endowment Fund (SIEF) Australia. This research includes work undertaken on the SAXS/WAXS beamline at the Australian Synchrotron, Victoria, Australia.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.molpharmaceut.5b00848. Spreadsheets listing the mesophase predictions for all 1800 samples in the study, truth tables for prediction of mesophases in training and independent test sets. (XLSX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

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RMIT University, School of Science, Melbourne VIC 3000, Australia

ABBREVIATIONS QSPR, quantitative structure−property relationships; EME, emulsified microemulsion; Lc, lamellar crystal; BRANN, Bayesian regularized artificial neural network; BRANNLP, Bayesian regularized artificial neural network with a (sparse) Laplacian prior; MLR, multiple linear regression

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. T.C.L. and D.A.W. carried out the modeling, N.T. and X.M. carried out the experimental work, D.A.W. G



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NOTE ADDED AFTER ASAP PUBLICATION After this paper was published ASAP February 10, 2016, text was added to the Acknowledgments section. The revised version was reposted February 11, 2016.

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Modeling the Influence of Fatty Acid Incorporation on Mesophase

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