Computer-Assisted Drug Formulation Design: Novel Approach in Drug

Jun 24, 2015 - The developed approach would be an efficient tool in the drug delivery science that would save researchers and formulators much experim...
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Computer-Assisted Drug Formulation Design: Novel Approach in Drug Delivery Abdelkader A. Metwally† and Rania M. Hathout*,†,‡ †

Department of Pharmaceutics and Industrial Pharmacy, Faculty of Pharmacy, and ‡Bioinformatics Program, Faculty of Computer and Information Sciences, Ain Shams University, Cairo 11566, Egypt ABSTRACT: We hypothesize that, by using several chemo/bio informatics tools and statistical computational methods, we can study and then predict the behavior of several drugs in model nanoparticulate lipid and polymeric systems. Accordingly, two different matrices comprising tripalmitin, a core component of solid lipid nanoparticles (SLN), and PLGA were first modeled using molecular dynamics simulation, and then the interaction of drugs with these systems was studied by means of computing the free energy of binding using the molecular docking technique. These binding energies were hence correlated with the loadings of these drugs in the nanoparticles obtained experimentally from the available literature. The obtained relations were verified experimentally in our laboratory using curcumin as a model drug. Artificial neural networks were then used to establish the effect of the drugs’ molecular descriptors on the binding energies and hence on the drug loading. The results showed that the used soft computing methods can provide an accurate method for in silico prediction of drug loading in tripalmitin-based and PLGA nanoparticulate systems. These results have the prospective of being applied to other nano drug−carrier systems, and this integrated statistical and chemo/bio informatics approach offers a new toolbox to the formulation science by proposing what we present as computer-assisted drug formulation design (CADFD). KEYWORDS: informatics, nanoparticles, molecular dynamics, formulation, docking, neural networks

I. INTRODUCTION Nanoparticulate drug delivery systems such as liposomes, solid lipid nanoparticles (SLN), and polymeric nanoparticles are widely used in medicine to deliver both small drug molecules and macromolecules.1−3 Successful drug formulation and delivery that ensure both the optimal drug loading and the desired drug release characteristics is traditionally investigated through the selection of the appropriate delivery systems, carriers, and drug molecules.4 However, experimenting different carriers and determining the different drug loadings remains a tedious task to perform that can be economically and/or timewise expensive. Since the loading of drugs depends on several mechanisms that depend on the constitutional, electronic, and topographical physicochemical properties of the involved compoundsthe carrier and the drugtherefore, simulating and modeling the interaction between these two elements suggests a highly successful approach for drug loading estimation, especially when adopting nanoparticulate delivery systems that comprise a major carrier core-component. In this context, we propose in this manuscript a novel computational approach, namely, computer-assisted drug formulation design (CADFD), for estimating the loading of different drugs on their potential carriers utilizing several informatics tools such as molecular dynamics, molecular docking, data mining and artificial neural networks. Relating the loading results with the docking binding energies is one © 2015 American Chemical Society

task, while predicting these energy values from the important physicochemical and electronic descriptors using an artificial intelligence technique such as artificial neural networks modeling is another task, and both comprise the basis of this new approach. The all-atom molecular dynamics (MD) simulation run is a collection of iterative steps by which the forces acting on each atom in the simulated system are calculated by numerically solving Newton’s laws of motion. In each molecular dynamics simulation step, the position of each atom and its velocity are updated. The force field is the set of equations and physical constants that are used to calculate such forces. While molecular dynamics is extensively used in biophysical studies, fewer studies investigated its usage in drug formulation.5,6 Similarly, molecular docking is another virtual process in which two molecules fit together in 3D space. This method was usually used to speed up drug discovery, although it has recently proven useful for other tasks.7 In another encounter, black-box modeling algorithms such as the artificial neural networks (ANNs) are capable of modeling nonlinear systems and are gaining the scientific community Received: Revised: Accepted: Published: 2800

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acceptance because of their simplicity, accuracy, and high prediction performance. Artificial neural networks are mathematical models having the ability to learn the correlation between experimental factors (input) and response (output) values by means of iterative test and error trials.8 They are considered a type of artificial intelligence that simulates the human brain through supervised learning. This is usually accomplished by data modeling and pattern recognition even for complex multidimensional problems. In one study, two evolutionary ANNs were constructed to predict the microemulsion type from its composition or from its DSC curves. Both ANNs demonstrated more than 90% accuracy in prediction.9 The ANN mimics the human brain functioning and potentially fulfills the cherished dream of scientists to develop machines that can think like human beings. A significant difference between ANNs models and statistical models is that the ANN can generalize the relationship between independent and dependent variables without a specific mathematical function. Thus, ANNs are powerful in solving nonlinear problems of multivariate and multiresponse systems.10 To this end, it is now understood that all one needs is some input−output data from the process being investigated in order to model any system. These data are usually used first in training the neurons and later to validate and test the resulting model.11 Meanwhile, the number of research studies on drug nanodelivery systems have emerged extensively in the past decade that we now possess an unexploited fortune of literature. This fortune was used in the current study to construct a correlation between several reported drug entrapment efficiencies in tripalmitin-based SLN and PLGA polymeric nanoparticles and their docking binding energies on a simulated tripalmitin and PLGA matrices. A model lipophilic drug such as curcumin was consequently chosen for the experimental validation of the correlation sought. Going further, the selected descriptors were used as inputs to build an ANN correlating the specified descriptors of drugs with their corresponding binding energies. The constructed ANN was used to predict the binding energy of some tested drugs. To this end, knowing selected calculated descriptors of a drug (using computer bioinformatics/cheminformatics algorithms) would be enough to deduce its corresponding binding energy and consequently the loading extent. By this, the cargo (the drug) is just translated into comprehensive numbers that can be utilized by formulators in the drug delivery laboratories. Figure 1 represents a chart summarizing the combination of the soft computing methods used in the different steps of this study. The developed approach would be an efficient tool in the drug

delivery science that would save researchers and formulators much experimentation effort and time when designing new drug carrier systems by boasting the understanding of the influential factors affecting the drug loading in a particular carrier(s) and by preemptively selecting efficient formulations for further laboratory experimentation.

2. METHODOLOGY 2.1. Materials. Tripalmitin, Tween 80, and curcumin were purchased from Sigma-Aldrich, Taufkirchen, Germany. Poly(D,L-lactic-co-glycolic acid) (50/50) (PLGA) was supplied by Purac Groningen, The Netherlands. 2.2. Methods. 2.2.1. Data Mining Using Scientific Literature Databases. The entrapment efficiencies and mass of drug loaded per 100 mg lipid of 11 different drugs: aceclofenac,12 artmether,13 clozapine,14 etopside,15 mepivacaine,16 piroxicam,17 praziquental,18 raloxifene,19 silibenin,20 tamoxifen citrate,21 vinpocetine,22 entrapped in tripalmitinbased SLN were gathered from the scientific literature databases using PubMed, Scopus, and Web of Science. Similarly, the entrapment efficiencies and mass of drug loaded were also obtained for 10 PLGA laoded drugs, namely: Docetaxel,23 paclitaxel,24 triamcinolone acetonide,25 indomethacin,26 cyclosporin A,26 ketoprofen,26 cytarabine,27 vancomycin,26 phenobarbital,26 and valproic acid.26 2.2.2. Construction of the Virtual Carrier Using Molecular Dynamics Simulations. All-atom molecular dynamics simulations were carried-out using GROMACS28 v4.6.5 software package. The parameters of tripalmitin and PLGA systems together with designed hypothetical probes were obtained using CgenFF29 available online (https://cgenff.paramchem. org/). Two systems were prepared, the tripalmitin system and the PLGA system. The tripalmitin system contains 64 molecules of tripalmitin associated with five molecules of a hypothetical probe. The second systemPLGA system contains 32 molecules of polylactic acid and 32 molecules of polyglycolic acid, both of which are composed of 35 monomers and are end-capped with a methyl group. All systems were subjected to energy minimization using the steepest descent method. The tripalmitin and PLGA systems were then subjected to a molecular dynamics run, with a time step of 2 fs, full periodic boundary conditions, and a cutoff distance for van der Waals and electrostatic interactions of 10 Å. PME was chosen to calculate electrostatic interactions. LINCS algorithm was used to constrain all bonds. The tripalmitin and PLGA systems were equilibrated at 65 and 25 °C, respectively, using a v-rescale thermostat, and at a pressure of 1 bar using a Berendsen barostat for 7 ns. 2.2.3. Preparing the Drug Chemical Structures for Docking. The chemical structures of the studied drugs in addition to a model drug; curcumin, were generated using ChemDraw Ultra version 10 (Cambridgesoft, Waltham, MA). The corresponding Mol2 or pdb files needed for docking using the software adopted in this study was obtained using Chem3D Ultra version 10 (Cambridgesoft, Waltham, MA) after energy minimization using the MM2 force field of the same program. 2.2.4. Docking of the Literature-Gathered Drugs on the Investigated Carrier. The docking analysis was generated by ArgusLab version 4.0.1. for tripalmitin SLN experiments (Mark Thompson and Planaria Software LLC, Seatle, WA) and Autodock Vina for the PLGA systems (Molecular Graphics Laboratory, The Scripps Research Group, La Jolla, CA). For tripalmitin systems, the five hypothetical probe molecules were

Figure 1. A chart summarizing the combination of the soft computing methods used in the different steps of the current study. 2801

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unentrapped drug in the filtrate was left to settle down for 48 h and then dissolved in methanol to be determined colorimetrically at 427 nm using a UV−visible spectrophotometer (model UV-1601 PC, Shimadzu, Kyoto, Japan). The EE% was calculated as follows:

utilized to construct the corresponding five binding sites on the carriers for ArgusLab docking of the drugs. The AScore was utilized for calculating the scoring function in case of docking experiments performed used ArgusLab, while a similar but a unique Vina scoring function was utilized for the experiments adopted using Autodock Vina. The size of the display docking grid box in the x, y, and z dimensions were 15 × 15 × 15 Å, as these dimensions were suitable to the size of the docked molecules and ensured a central position for them inside the lipid matrix. Furthermore, ArgusDock was used as the docking engine for ArgusLab experiments and the type of calculation and ligand (as chosen from the software options) were Dock and Flexible, respectively. Binding energies (ΔG, kCal/mol) reflecting the docking successfulness, were obtained for all the literaturegathered drugs plus the chosen model drug using this method. On the other hand, Vina uses a sophisticated gradient optimization engine in its local optimization procedure.30 2.2.5. Experimental Validation of the Developed Correlation between Entrapment Efficiencies and Binding Energies. 2.2.5.1. Preparation of Curcumin Loaded Tripalmitin-Based Solid Lipid Nanoparticles. In order to experimentally validate the theoretical results obtained, curcumin-loaded SLN were prepared in our laboratory, where eventually the experimental curcumin entrapment efficiency will be compared with that predicted using the docking results. The curcumin loaded SLN were prepared using the modified high shear homogenization method,31,32 where the total amount of the lipid (1 g), tripalmitin, was kept at 5% (%, w/w), while the surfactant concentration was 1% (%, w/w). This lipid was heated to 80 °C before the curcumin (10 mg) was homogeneously dispersed throughout the molten phase. Meanwhile, the surfactant (Tween 80) was heated to the same temperature. Both the lipid and the aqueous phases were magnetically stirred at this temperature at 600 rpm for 5 min; then the aqueous phase was poured on the hot lipid phase. After, high-speed homogenization was carried out at 15 200 rpm for 5 min using a homogenizer (Ultra Turrax T25, IKA, Staufen, Germany). Consequently, SLN were obtained by allowing the produced hot nanoemulsion to cool at room temperature before being refrigerated at 4 °C. 2.2.5.2. Preparation of Curcumin Loaded PLGA Nanoparticles. Curcumin-loaded nanoparticles were prepared using the emulsification-solvent evaporation technique. Briefly, 10 mg of the drug and 200 mg of PLGA were dissolved in 5 mL of chloroform and injected at a rate of 1 mL/min into 20 mL of 2.5% PVA aqueous solution. Afterward, homogenization was performed at 20 000 rpm agitation speed using the IKA highspeed homogenizer (Ultra-Turrax, IKA T-18, Germany) for 5 min. Then, the emulsion was left overnight for solvent evaporation. Hence, the obtained suspension was centrifuged at 17 100 g and for 15 min at 4 °C, and the supernatant was discarded. The pellets were redispersed in water after vortexing. Washing and centrifugation was performed three times. 2.2.5.3. Determination of Curcumin Entrapment Efficiency. The nonentrapped drug was separated by filtration/ centrifugation using Nanosep centrifuge tubes possessing molecular cutoff of 100 kDa (Pall Life Sciences, Port Washington, NY). Specifically, a definite volume of the prepared SLN dispersion was diluted with distilled water, from which 500 μL were transferred to the upper-chamber of the Nanosep. The Nanosep was centrifuged at 9000 rpm at 20 °C for 2 h (Z216, Hermle, Gosheim, Germany). The

⎛ D − Dun ⎞ EE% = ⎜ t ⎟ × 100 ⎝ Dt ⎠

(1)

The total mass of loaded drug per 100 mg lipid was calculated as follows: loaded mass =

EE% × initial incorporated amount (in mg) 1000 (2)

where Dt is the total amount of drug used in the formulation and Dun is the total amount of unentrapped drug calculated from the remaining amount in the filtrate plus the maximum amount of curcumin soluble in the aqueous phase. In case of the curcumin-loaded PLGA nanoparticles, a direct method was adopted where the pellets were dissolved in 1.5 mL of methanol, an aliquot of 100 μL of this solution was again diluted with 1.5 mL of methanol, and the UV absorbance of the solution was measured at 427 nm. The EE% was calculated as follows: EE% =

amount of drug in 100 μL × 1.5 × 100 initial amount of added drug

(3)

And the total mass of loaded drug per 100 mg PLGA was calculated as follows: loaded mass =

EE% × initial incorporated amount (in mg) 200 (4)

The experimental obtained EE% and the loaded mass of the drug per 100 mg lipid values were compared to those obtained from the developed correlation between these results and ΔG, and the percentages bias (bias %) was calculated as follows:33,34 bias% =

|predicted value − actual value| × 100 actual value

(5)

2.2.6. Using the Drugs’ Molecular Descriptors and Artificial Neural Networks in the Prediction of Binding Energies. 2.2.6.1. Calculating the Important Descriptors of the Investigated Drugs. In order to explain the differences in docking scores observed for the studied drugs and relate them to their reported entrapment efficiencies, crucial constitutional, electronic, and topological descriptors were calculated for the studied drugs. The selected descriptors were the molecular weight, xLogP, topological polar surface area, and finally the fragment complexity. The descriptors were calculated using Bioclipse version 2.6 (Bioclipse project, Uppsala University, Sweden) using the molecules mol files generated using ChemDraw Ultra version 10. 2.2.6.2. Modeling Using Artificial Neural Networks (ANNs). The modeling of the generated binding energies (Response) from the docking process was accomplished using ANNs modeling in JMP 7.0 (SAS, Cary, NC). Two networks were generated for each of the tripalmitin SLN and PLGA nanoparticles, respectively. The x factors (inputs) for the constructed network were the descriptors that were calculated in section 2.2.6.1. K-fold cross-validation with k = 5 in the case of drug descriptor−tripalmitin binding energy network and 2802

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random hold backcross-validation in the case of drug descriptor−PLGA binding energy counterpart were used to validate the results. Both networks contained three hidden nodes with overfit penalty of 0.001. The number of tours generated was 16 with 50 maximum iterations. Figure 2 depicts the design of the currently used ANNs in this study.

Figure 2. Constructed artificial neural network (ANN) between the molecular descriptors of every investigated drug as inputs and the corresponding binding energy as outputs.

2.2.6.3. Validating the Predicting Power of the Developed ANN. The predicting power of the used ANN was evaluated by calculating the molecular descriptors of three different tested drugs in case of tripalmitin-based SLN: resveratrol, lomefloxacin, and testosterone and two drugs in case of PLGA nanoparticles: prednisolone and testosterone using Bioclipse v.2.6 (Bioclipse project, Uppsala University, Sweden). Consequently, the descriptors of each tested drug were fed into the prediction profiler of the developed ANN in section 2.2.6.2, and the corresponding binding energies were calculated and compared with the actual docking results. The percentage bias (% bias) was calculated as previously explained in section 2.2.5.3.

3. RESULTS AND DISCUSSION The objective of applying the molecular dynamics simulation in this study was to prepare the carrier system that will be used to further study the drug−carrier interactions. Molecular dynamics simulations allow a near-realistic representation of the evolution of the system under investigation in terms of atom positions, interatomic forces, and system thermodynamic properties. The accuracy of the molecular dynamics simulations depends on the choice of the force fields and conditions of the molecular dynamics run, as well as on the proper choice of the experimental objective of the molecular dynamics simulation. The CHARMM general force field (CGenFF) was chosen to calculate the forces and potential energies between atoms of the system. CgenFF is suited for a wide range of biomolecules and drug-like molecules.29 The conditions of the molecular dynamics simulation were chosen to be as close as possible to the experimental conditions used to prepare SLN. The basic chemical structure of the chosen carriers in this study (tripalmitin and PLGA) together with the constructed hypothetical chemical compound (probe) required for the docking experiments are shown in Figure 3 (a and b, and c, respectively). The PLGA system was constructed to contain 32 molecules of polylactic acid and 32 molecules of polyglycolic acid (each contains 35 monomers) in order to simulate the higher molecular weight PLGA polymertypically with hundreds of monomerschemical environment, while keeping the size of the system within a reasonable limit that is suitable for molecular dynamics simulation. The polylactic acid and

Figure 3. Chemical structure of (a) tripalmitin, (b) tripalmitin designed probe, and (c) PLGA system.

polyglycolic acid molecules were end-capped with methyl groups to better simulate the PLGA polymer used in wet-lab experiments which has a lower numbers of hydroxyl and carboxylic groups relative to the number of monomers in each high molecular weight PLGA molecule. Snapshots of the equilibrated trajectory of the tripalmitin-probe and PLGA systems at the end of the molecular dynamics simulation runs are shown in Figure 4a and b, respectively. The docking calculations provide the binding energies between the investigated drugs and the carrier systems. The docking results of the literature-gathered drugs on the simulated carrier in addition to their reported entrapment efficiencies as percentages in the investigated carrier were tabulated in Table 1. The obvious correlation between the docking binding energy of the tripalmitin loaded drugs and their corresponding entrapment efficiencies was demonstrated in Figure 5a, where a very high linear correlation (r ≈ 0.90) was obtained. The linear equation describing this correlation was: 2803

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Table 1. Calculated Binding Energies (ΔG) of the Investigated Drugs after Docking on the Simulated Carrier Together with Their Literature-Reported Entrapment Efficiencies carrier tripalmitin

PLGA

drug aceclofenac etoposide artemether mepivacaine praziquental raloxifene clozapine piroxicam silibinin tamoxifen vinpocetine phenobarbital indomethacin ketoprofen valproic acid cytarabine docetaxel paclitaxel triamcinolone acetonide vancomycin cyclosporin A

binding energy (ΔG) kcal/mol

reported EE (%)*

−3.84 ± 0.05 −4.60 ± 0.11 −4.78 ± 0.05 −4.43 ± 0.04 −4.32 ± 00 −4.22 ± 0.02 −4.53 ± 0.04 −4.3 ± 0.07 −4.33 ± 0.007 −4.03 ± 0.04 −4.36 ± 0.04 −7.2 ± 0.04 −7.8 ± 0.01 −8.2 ± 0.01 −5.4 ± 0.02 −6.9 ± 00 −9.5 ± 0.03 −9.0 ± 0.02 −8.6 ± 0.01

64 96 92 99 80 95.5 94.5 87 86.3 69.2 93 9.4 93.9 46.2 5.6 20 97.4 90 31.67

−7.8 ± 0.01 −8.9 ± 0.03

12.1 83.7

*

Average EE% was taken when several formulations were tested in the same study.

mass of loaded drug per 100 mg PLGA = 0.0002 × e(−1.13 ×ΔG)

(9)

In the current study, the ArgusLab docking results were based on the calculations of the AScore, which is obtained from the XScore calculated according to the following equation:35 ΔG bind = ΔGvdw + ΔG hydrophobic + ΔG H‐bond

Figure 4. Molecular dynamics simulation of (a) tripalmitin (gray) and the hypothetical designed probe (green) and (b) PLGA system.

EE% = − 36.30ΔG − 69.70

+ ΔG H‐bond(chg) + ΔGdeformation + ΔG0

(6)

while the Autodock vina docking results were generated using the vina similar scoring function as follows:

from which the entrapment efficiencies in the investigated model carrier (tripalmitin-based SLN) of drugs can be easily predicted. Similarly, the relation between the mass of the loaded drug per 100 mg lipid and ΔG was easily exponentially modeled (Figure 5b) with r2 = 0.87 as follows:

ΔG bind = ΔGGauss + ΔGrepulsion + ΔG H‐bond + ΔG H‐bond(chg) + ΔG hydrophobic + ΔGtors

(7)

In the same context, Figure 6 demonstrates the excellent exponential relationships (r2 = 0.90) obtained between the binding energies of PLGA nanoparticle-loaded drugs with their entrapment efficiencies at one side, where EE% = 0.05 × e(−0.81 ×ΔG)

(11)

where ΔGbind is the total calculated binging energy, ΔGvdw and ΔGrepulsion are similar functions representing the binding energy due to van der Waals force and depends on the distance between the docking molecules, ΔGGauss is a dispersion term, ΔGhydrophobic is the binding energy due to hydrophobic forces, ΔGH‑bond is the binding energy due to H-bonding, ΔGH‑bond (chg) is the binding energy due to H-bonding due to charged molecules, ΔGdeformation and ΔGtors are similar terms reflecting the energy due to rotational bonds and atoms involved in torsions (rotors) that were frozen due to binding, and finally, ΔG0 represents the regression obtained binding energy. Accordingly, the equations terms encompass nearly all the possible interactions that can occur between the drug and its carrier leading to entrapment, and this explains the high correlation value obtained. It is also worth mentioning that the

mass of loaded drug per 100 mg lipid = 2 × 10−8 × e(−4.52 ×ΔG)

(10)

(8)

and with the mass of loaded drug per 100 mg of the carrier at the other side, where 2804

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Figure 5. Developed relationships between (a) the entrapment efficiencies and (b) the incorporated masses per 100 mg lipid of the literaturegathered drugs versus their corresponding calculated ΔG.

Figure 6. Developed relationships between (a) the entrapment efficiencies and (b) the incorporated masses per 100 mg PLGA of the literaturegathered drugs versus their corresponding calculated ΔG.

Table 2. Main Constitutional, Electronic, and Topological Descriptors of the Investigated Drugs (Inputs or x-Factors for the Artificial Neural Network Analysis)a carrier tripalmitin SLN

PLGA nanoparticles

a

drug

MW

xLogP

TPSA

fragment complexity

aceclofenac etoposide artmether mepivacaine praziquental oryzalin raloxifene clozapine piroxicam silibinin tamoxifen vinpocetin resveratrol lomef loxacin testosterone docetaxel indomethacin ketoprofen triamcinolone acetonide valproic acid phenobarbital paclitaxel cytarabine vancomycin cyclosporin A prednisolone resveratrol

353.02 588.18 298.18 246.17 482.12 350.13 473.17 326.13 331.06 482.12 371.2 350.2 228.08 351.14 288.21 807.35 338.14 255.1 436.23 145.12 232.08 853.33 245.1 1449.25 1201.84 360 228.08

1.92 0.12 3.33 1.46 0.86 −1.52 2.72 2.51 0.43 0.86 6.34 3.30 2.05 2.27 3.63 5.67 3.78 4.78 1.09 2.53 2.77 6.15 −1.52 −0.37 8.41 1.06 2.05

75.63 160.83 46.15 32.34 155.14 47.24 98.24 30.87 107.98 155.14 12.47 34.47 60.69 72.88 37.3 221.29 30.71 17.07 96.22 0 75.27 221.29 105.75 530.49 278.8 94.8 60.69

863.07 4678.13 2080.05 1375.03 2531.1 1175.11 3103.06 1519.05 119.08 2531.1 144 311.04 628.03 129.08 309.02 663.15 1249.05 814.03 3426.07 535.02 628.05 1994.15 689.08 6029.35 3127.23 924 628.03

Drugs written in italics were used as experimental validating points for the adopted artificial neural networks analysis.

x-intercept of the obtained linear equation in the lipid EE %−ΔG relationship equals −1.95, meaning that at this value no

entrapment occurs despite the negative binding energy obtained. In this case, the small value obtained reflects very 2805

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Figure 7. (a and c) Predicted versus actual while (b and d) residual plots for the generated drug−descriptor tripalmitin binding energy and drug− descriptor PLGA binding energy ANNs, respectively.

Figure 8. Generated (a and b) drug−descriptor tripalmitin binding energy ANN and (c and d) drug−descriptor PLGA binding energy ANN contour plots displaying the effect of molecular descriptors (in pairs) on the binding energy: (a and c) MW vs xLogP while (b and d) fragment complexity vs TPSA.

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weak interactions between the drug and the carrier (due to van der Waals forces for example) that are not strong enough to permanently hold the drug inside its vehicle and thereby can be overcome by normal diffusion into the dispersion medium during preparation of the SLN. In an attempt to experimentally evaluate the predictability of the obtained equations, a model drug, curcumin, was formulated in tripalmitin SLN and PLGA nanoparticles, and its entrapment efficiency inside the prepared carriers was determined to be 75.16% ± 3.35 and 19.34 ± 2.45, respectively equivalent to an incorporated mass of 0.75 and 0.97 mg per 100 mg of tripalmitin and PLGA, respectively. Docking of this drug on the carrier resulted in a binding energy equivalent to −3.83 ± 0.09 kcal/mol. Substituting in the obtained models, resulted in a predicted entrapment efficiencies of 69.3% and 19.73% equivalent to 0.66 and 0.96 mg loaded drug per 100 mg lipid and PLGA, respectively. Consequently, the corresponding calculated % bias between the actual and the predicted values were 7.6% and 12% for EE% and mass of loaded drug in tripalmitin SLN at one side and 1.23% and 2.03% for the same responses in case of PLGA nanoparticles at the other side. These obtained values are considered highly acceptable.34 Such “cause−effect” relationships are clearly useful to the rational and efficient development and formulation of drug delivery systems. It can also be inferred that the introduced method would not only help in predicting the drug loading in a given carrier, but also it can help in comparing different carriers regarding this aspect and thereby aids in the selection of the most appropriate one. Hence, in the current study, it can be easily predicted through the models that the PLGA matrix can accommodate more masses of curcumin than the tripalmitin counterpart: a conclusion confirmed experimentally. In order to allow for highly efficient and rapid means of comparison between the structures of different molecules, those structures can be reduced to a set of different numerical “molecular descriptors”.36 Thus, we targeted more modeling by treating the drugs as mere numbers through converting them into selected important constitutional, topological, and electronic descriptors as shown in Table 2. These calculated descriptors were connected to the corresponding docking binding energies for tripalmitin SLN and PLGA nanoparticles using constructed artificial neural networks as explained in section 2.2.6.2 with r2 = 0.999 for both generated networks, a value that reflects the extremely efficient modeling of the ANN technique. This is due to the characteristic high adaptability and generalization capability of the neural networks that distinguish them from other analytical methods in dealing with multiple factors and responses.37 To further evaluate the robustness of the ANNs, several plots are usually used such as the predicted versus actual experimental values, and the residual by predicted values plots, as shown in Figure 7a, c and b, d, respectively. The linear relationship between the observed and predicted values and the randomized distribution of the residuals about the zero mean emphasized the higher predictive capacity of the generated ANN model.37,38 Figures 8 and 9 present the effect of the different descriptors on the binding energy by contour and 3D surface plots, respectively. It is obvious from the Figures 8a and 9a that while decreasing the molecular weight (M.W.) of drugs docked into the tripalmitin matrix causes the binding energy to decrease into more negative values (indicating better docking) probably due to more structure simplicity and less steric occupation,

Figure 9. Generated (a and b) drug−descriptor tripalmitin binding energy ANN and (c and d) drug−descriptor PLGA binding energy ANN 3D surface plots displaying the effect of molecular descriptors (in pairs) on the binding energy: (a and c) MW vs xLogP while (b and d) fragment complexity vs TPSA.

there is an optimum xlogP values almost ranging from 1.5 to 4 to obtain such reduction. This is anticipated for a lipophilic carrier such as the SLN which can efficiently incorporate lipophilic drugs.39,40 Fragment complexity is another important descriptor that is usually used in quantitative structure−activity relationship studies.41,41 Logically, the fragment complexity of the molecule, comprising the number of bonds, number of nonhydrogen atoms, and number of heteroatoms, plays a role in docking results, with certain ranges decreasing the ability of the molecule to be docked efficiently on the targeted site. This is demonstrated in Figures 8b and 9b. Nevertheless, increasing the topological polar surface area (TPSA) of the molecules led to a sharp increase in the binding energy (reduction in docking affinity). This may be ascribed to the nonpolar nature of the used lipid: tripalmitin thus lacking the charged surfaces that can interact with polar groups of drugs possessing high TPSA. This relation is clearly demonstrated in Figures 8b and 9b as well. Similar results regarding the descriptors: molecular weight and xlogP were obtained for the docking of the investigated drugs on the PLGA built matrix, where again decreasing the molecular and optimum xlogP value weight caused reduction in the binding energy (Figures 8c and 9c, respectively). However, different conclusions were reached regarding the other two descriptors, where an optimum total polar surface area and an increase in the fragment complexity caused the desired lowering of binding energy (Figures 8d and 9d, respectively). This may be ascribed to the more complex structure of the PLGA associated with the presence of different polar groups on its structure compared to a lipid matrix such as the tripalmitin. Computational validation was done to further evaluate the obtained ANNs using three tested drugs for the drug− descriptor tripalmitin binding energy ANN; resveratrol, lomefloxacin, and testosterone, and two for the drug− descriptor PLGA binding energy ANN; prednisolone and resveratrol, where their descriptors were calculated and thereby, their individual binding energies were estimated using the predictor profiler of the adopted software (Figure 10). 2807

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Figure 10. Calculating the binding energy of three validating drugs for the tripalmitin SLN ANN: (a) resveratrol, (b) lomefloxacin, and (c) testosterone, and two validating drugs for the PLGA nanoparticles ANN: (d) prednisolone and (e) resveratrol utilizing the prediction profiler tool in JMP software.

The ANN predicted ΔG for each of the tested drugs was compared with the results obtained from docking experiments and the bias percentages were calculated as shown in Table 3.

hydrophobicity reflected by the xlogP, such as the molecular weight, the total polar surface area, and the fragment complexity that govern the drug−carrier interaction by different forces (van der Waals, hydrophobic, and hydrogen bonding) with consideration to bond angles and torsions and hence contribute to the loading process.

Table 3. Calculating the % Bias between the Actual Docking Binding Energies and Those Predicted from the Artificial Neural Networks Analysis for the Validating Used Drugs carrier tripalmitin SLN PLGA nanoparticles

drug

actual ΔG (kcal/mol)

predicted ΔG (kcal/mol)

% bias

resveratrol lomefloxacin testosterone prednisolone resveratrol

−4.11 −4.20 −4.72 −8.00 −7.80

−3.95 −4.42 −4.33 −7.30 −6.64

3.66 5.25 7.87 8.75 14.9

4. CONCLUSION AND FUTURE PERSPECTIVES We have proven that, by integrating the use of several chemo/ bio informatics and statistical tools, the efficiency of drug loading in a particular carrier can be predicted computationally. We have successfully deduced relationships between the docking binding energy (ΔG) and both the entrapment efficiency percentage (%EE) and the incorporated mass for different drugs loaded on tripalmitin-based SLN and PLGA nanoparticles using molecular dynamics and molecular docking techniques. Such cause-effect relationships would be extremely beneficial in drug delivery science and would save researchers huge time of experimentation in the selection of optimum drugs/carriers pairs. We have also successfully shown that artificial neural networks (ANNs) can capture strong relationships between certain molecular descriptors of drugs and their docked binding energies on carrier systems with high prediction capabilities. This would allow the presentation of these drugs merely by these descriptors and thus the fast prediction of ΔG with no need for docking studies leading to the subsequent and accurate estimation of entrapment efficiencies and loaded masses without exhaustive laboratory experimentation. The combination of the different informatics tools and modeling techniques presented in this paper can be utilized for any carrier system that can be simulated by molecular dynamics. We believe that the way in which the nanotechnology based medicines are developed, which is based on exhausting trial and error experiments and is only supple-

Hence, the mean bias percentage for the results obtained from the two generated tripalmitin and PLGA ANNs was 8.09% ± 4.32, indicating the high accuracy of the ANNs results. To this end, utilizing the built ANNs and transforming any drug to the aforementioned important descriptors (provided that the same types of descriptors are used and their values lie in the same ranges as those used to model the ANNs) would allow the accurate prediction of its docked ΔG and consequently the determination of its entrapment efficiency percent and the total mass that can be incorporated throughout the lipid or polymeric matrices in silico using the aforementioned validated linear and exponential relationships. It is worth noting that the development of these descriptor binding energies and consequently loading results can provide a solid explanation about some unsufficiently explored formulation issues such as the relatively low entrapment of corticosteroidsalthough quite hydrophobicin polymeric carriers of the same nature like PLGA nanoparticles. This can be attributed to the presence of other influencing constitutional, electronic, and topological factors (descriptors) other than the 2808

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mented by the previous experience and knowledge of the formulator, should be changed. This new approach of computer-assisted drug formulation design (CADFD) should cause a major shift in this science.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +2 (0) 100 5252919; + 2 02 22912685. Fax: +2 02 24011507. E-mail: [email protected]. Author Contributions

The authors have equally contributed in this manuscript. Notes

The authors declare no competing financial interest.

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