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Original article
12 (
8
); 2372-2383
doi:
10.1016/j.arabjc.2015.03.003

Computational simulation of palm kernel oil-based esters nano-emulsions aggregation as a potential parenteral drug delivery system

, , , ,
a Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
b Enzyme and Microbial Technology Research Centre, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
c Department of Medicine, Faculty of Medicine and Health Sciences, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

⁎Corresponding author at: Department of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. rosa.abedi@gmail.com (Roghayeh Abedi Karjiban) roghayeh@upm.edu.my (Roghayeh Abedi Karjiban)

Received: , Accepted: ,
© The Author(s) 2015
Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The self-assembled structure of palm kernel oil-based esters (PKOEs) nano-emulsions has shown a great potential used for parenteral drug delivery applications. Here, all-atom level molecular dynamics (MD) was applied to investigate the aggregation process of PKOEs nano-emulsion system. The system consisted of palm kernel oil-based esters (PKOEs) and dipalmitoylphosphatidylcholine (DPPC) in water. The ratio of all constituents was taken from the homogenous region of a ternary phase diagram determined experimentally. The molecules started to aggregate very rapidly from random configurations. A doughnut-like toroidal assembled structure formed at 50 ns with PKOEs surrounded by DPPC molecules. The structural and dynamical properties of the self-assembled doughnut-like toroidal aggregate were analyzed using the principle moment of inertia, eccentricity and radius of gyration. The aggregation structures were compact with the average radius of gyration of 4.10 (±0.02) nm over the last 5 ns. Additionally, both hydrophobic and hydrophilic interactions were involved in aggregation process with a total solvent accessible surface area of 551.72 (±5.88) nm2.

Keywords

Palm kernel oil-based esters
Dipalmitoylphosphatidylcholine
Self-assembly
Doughnut-like toroidal
Molecular dynamics simulation
1

1 Introduction

Drug delivery is the process of transporting drugs across the biological membrane to the targeting cell to achieve the therapeutic effect. Generally, drug delivery is classified through the anatomical routes such as parenteral, oral, topical, transdermal, ocular and pulmonary (Devarajan and Ravichandran, 2011; Prakash and Thiagarajan, 2011). Parenteral drug delivery is defined by the administration of drug via injection and intra-arterial routes. As compared to other routes, parenteral delivery permits therapeutic agents to gain direct admission into the systemic circulation (Repka et al., 2011). Therefore, drugs reach to the specific sites more rapidly which results in a better control of drug release (Constantinides et al., 2008). Recently, delivering nano-emulsions loaded with drugs via parenteral administration has shown very promising results.

Nano-emulsions are produced by mixing of oil with an aqueous phase under high shear stress or mechanical shear-induced rupturing to form a stable emulsion with uniform droplet size in the range of 20–200 nm (Shah et al., 2010; Solans et al., 2005). Nano-emulsions are classified as a kinetically stable liquid dispersion of an oil phase and a water phase or reverse with the combination of surfactant (Devarajan and Ravichandran, 2011). Generally, surfactant has been used to reduce the size of nano-emulsions droplet. However, higher concentration of surfactant in the formulation may lead to toxicity and irritancy problems. Thus, an appropriate amount of oil, water, and surfactant should be used to solvate drugs for an optimal drug loading (Sinha and Ghai, 2010).

Nano-emulsions can also be applied as a carrier to deliver insoluble drug. The capacity of nano-emulsions to dissolve large quantities of hydrophobic drugs, along with their ability to protect the drugs from hydrolysis and enzymatic degradation makes them ideal for parenteral delivery (Lovelyn and Attama, 2011). The parenteral delivery of nano-emulsions has interesting application to control vaccine delivery, drug delivery and drug release for bioactive compounds to the targeting sites (Solans et al., 2005). Nano-emulsions formulation has been reported as a good carrier due to their nano size. They can easily be targeted to the specific area such as tumor site (Primo et al., 2007). Here, the main objective is to apply molecular dynamics simulation to investigate self-assembly and aggregation of the potential palm kernel oil-based esters (PKOEs) with lecithin in water as a nano-emulsion model system to be used for parenteral drug delivery.

Lecithin (1,2-diacyl-sn-glycero-3-phosphatidylcholine) is a complex mixture of acetone-insoluble phosphatides, which predominantly consists of phosphatidyl choline, phosphatidyl ethanolamine, phosphatidyl serine and phosphatidyl inositol combined with other triglycerides and fatty acids. It is a major component of cell membrane in plants and animals which mainly isolated from soybeans or eggs yolk. Lecithin is an amphiphilic molecule in nature with polar head groups which can attract polar drugs and non-polar tails which can solubilize non-polar drugs. Therefore, lecithin has a unique chemical structure (Fig. 1) to be used as an emulsifier, viscosity modifier, stabilizer and solubilizer (Raut et al., 2012). The polar structure of lecithin brings the molecule as a potential emulsifying agent. Furthermore, lecithin is among the safest emulsifying agents which can be safely used even for sensitive route of drug delivery (Baker and Naguib, 2005).

Molecular structure of oleyl caproate, oleyl caprylate, oleyl caprate, oleyl laurate, oleyl myristate, oleyl palmitate, oleyl stearate, oleyl oleate, oleyl linoleate, and DPPC.
Figure 1 Molecular structure of oleyl caproate, oleyl caprylate, oleyl caprate, oleyl laurate, oleyl myristate, oleyl palmitate, oleyl stearate, oleyl oleate, oleyl linoleate, and DPPC.

Apart from its emulsifying property, lecithin has been reported to improve the solubilization of drugs, to reduce toxicity and to increase absorption (van Nieuwenhuyzen and Thomas, 2008; Sznitowska et al., 2002). In this study, lecithin has been used as a surfactant in the formulation. This phospholipid mixture has been used to increase the stability of emulsion (Klang and Valenta, 2011). Moreover, the use of lecithin in nano-emulsions formulation helped to form a highly translucent or almost transparent fluid (Mason et al., 2006). Therefore, PKOEs nano-emulsions can be classified as lipid nano-emulsions. Many studies have been reported the lipid nano-emulsions as a parenteral drug delivery device. These nano-emulsions can circulate in the blood for long period of time (Anuchapreeda et al., 2012) and minimize the pain by exposing the tissue to lower concentrations of drugs (Zainol et al., 2012). Furthermore, PKOEs with relatively shorter chain ester are potentially good for delivery of drug into the body (Keng et al., 2009).

Molecular dynamics (MD) has been used to study macromolecular structures and self-assembly process for several years. MD is the representation of molecules and atoms using a number of classical degrees of freedom and interaction energies via potential energies called force fields. MD acts based on the integration of Newton second law of motion (Van Gunsteren et al., 2008). All-atom level MD simulations are based on a realistic potential approach to explore the self-assembly of ionic surfactants such as sodium octanoate (De Moura and Freitas, 2005) and sodium dodecyl sulfate (SDS) (Bruce et al., 2002), cationic surfactants (Maillet et al., 1999), nonionic surfactants such as Octyl Glucoside (Bogusz et al., 2000), C12E4 in β-Cyclodextrin (Cunha-Silva and Teixeira-Dias, 2002) and palmitate ester with non-ionic surfactant of Tween80 (Abedi Karjiban et al., 2012). Thus, the structural and dynamical properties of nano-emulsions can be determined at nano level using simulation studies which can complement the experimental data.

2

2 Methodology

The system consisted of palm kernel oil-based esters (PKOEs) along with Lecithin as a surfactant in water with the ratio of PKOEs/DPPC/Water (10:20:70). The composition for our simulation was chosen from the homogenous region of a ternary phase diagram determined experimentally. PKOEs were synthesized by enzymatic trans-esterification of palm kernel oil with oleyl alcohol which produced the highest value of oleyl laurate with the composition of 54.1%. Palm kernel oil is extracted from the nut in the Malaysian palm oil fruit (Keng et al., 2009). Lecithin is generally harmless toward animal and human skin with less adverse effects (Paolino et al., 2002). For simplicity of the model prepared, we used dipalmitoylphosphatidylcholine (DPPC) instead of Lecithin. DPPC is a spherical bilayer component of Lecithin that is able to surround the oil components (Shaari et al., 2014).

Total number of molecules in the PKOEs nano-emulsion model was determined by calculating the ratio of PKOEs/DPPC to the molecular weight of each component multiplied by the Avogadro’s number. Based on the PKOEs fraction, the number of each components used in the formulation was calculated from the total number of PKOEs. Finally, a model system was built using oleyl caproate, oleyl caprate, oleyl caprylate, oleyl laurate, oleyl myristate, oleyl palmitate, oleyl stearate, oleyl oleate, oleyl linoleate, and DPPC with the total molecule of 1, 7, 8, 61, 15, 6, 1, 6, 2, and 246, respectively. The molecular structures of all components are represented in Fig. 1.

2.1

2.1 Molecular dynamics simulation

The initial structures were prepared using MacMolPlt version 7.4.1 (Bode and Gordon, 1998) and then optimized using GAMESS software (Schmidt et al., 1993). The quantum mechanics (QM) calculation was performed to prepare reliable topology and coordinate files according to OPLS-AA force field. Due to the large size of esters and DPPC, the structures were first optimized at STO-3G level of theory followed by optimization at 6-31G level. GAMESS program is available for structure optimization using quantum chemical calculations. A geometry optimization at the restricted Hartree–Fock (HF) level of theory in vacuum was also performed to determine the most stable conformation. The atomic charges were calculated using RESP model (Bayly et al., 1993). The topology and coordinate files were created using ANTECHAMBER tool of AMBER 8.0 (Case et al., 2004) according to the general AMBER force field (GAFF) (Wang et al., 2004) and later on converted to GROMACS topology and coordinate files using a perl script. PKOEs and DPPC molecules were then packed together in random positions using Packmol (Martinez and Martinez, 2003).

MD simulations were performed using GROMACS version 4.5.5 (Lindahl et al., 2001; Van der Spoel et al., 2005) based on OPLS-AA force field (Jorgensen et al., 1996) and SPC water model (Ferguson, 1995) for solvent molecules. The box sizes of the model were chosen as 10.00 × 10.00 × 10.00 nm3. Energy minimization was carried out using steepest descent and conjugate gradient methods until the system was converged to the energy with the maximum force of less than 50 kJ/mol followed by heating the system in which the temperature coupling was turned on and the system was allowed to relax with the new condition. The thermodynamics of the canonical NVT ensemble were applied at a constant number of particles (N), volume (V) and temperature (T) for 200 ps with 2 fs time steps at 300 K. LINCS algorithm (Hess et al., 1998) was applied to all bonds and 1.0 nm cutoff was chosen for treating the electrostatic interactions by using Particle–Mesh–Ewald (PME) method (Essman et al., 1995). The cutoff value for van der Waals interaction was set at 1.4 nm. Berendsen thermostat was used to maintain temperature at 300 K with τT = 0.5, while pressure coupling was turned off (Berendsen et al., 1984).

A short equilibration was carried out for 1 ns in a constant number of particles (N), pressure (P) and temperature (T) of the NPT ensemble to ensure that esters, DPPC, and water molecules were mixed adequately. The temperature and pressures were kept constant at 300 K and 1.0 bar using the Berendsen thermostat and Parrinello–Rahman coupling (Parrinello and Rahman, 1981). All bonds were constrained using LINCS algorithm. PME algorithm was used to calculate the long-range Columbic interactions with the cutoff value of 1.0 nm, and the van der Waals forces were cutoff at 1.2 nm. MD production simulation was performed for 50 ns in an NPT ensemble (Table 1). Periodic boundary condition was applied to all directions of the system with constraint applied to all bonds with hydrogen atoms (Hess et al., 1998).

Table 1 An overview of MD production of PKOEs nano-emulsion simulation during 50 ns.
Model Composition # SPC water Box edge (nm) Average density (g/cm3) Average total energy (kJ/mol)
PKOEs:DPPC:Water 10:20:70 23399 10.00 989.41 ± 0.10 −7.46x105 ± 80.00

3

3 Results and discussion

Molecular self-assembly is a spontaneous process involving the aggregation of molecules. The structures generated in molecular self-assembly usually existed in equilibrium states. The self-assembly process seems to offer one of the most general strategies for generating nano-emulsion structures. The self-assembly behavior based on various self-assembling building block amphiphiles has been investigated with a variety of supramolecular models (Wang et al., 2012; Lim et al., 2009; Palmer and Stupp, 2008; Ajayaghosh and Praveen, 2007; Shimizu et al., 2005). A well-defined size and shape consist fibers, ribbons, tubes, helices, cylindrical micelles, vesicles, spherical micelles, bilayer, and toroids have been observed on the supramolecular architectures (Kim et al., 2009; Lee et al., 2009a,b). Self-assembly into the toroidal nano-structure has not been widely studied compared to the other fibers, micelles, sheets and vesicles structures. However, there is a new interest in investigating unconventional micellar shapes such as toroids, tubes, disks, helices, and other complex structures.

Generally, the shape of the aggregated structure is depending on the concentration of surfactant, temperature, and other physicochemical parameters. Small spherical micelles are formed at low concentration of surfactant close to the critical micelle concentration. Doughnut-like toroidal structure which is topologically different from typical micelles of spheres-like and cylinders-like shapes is given an interesting kind of aggregates. Spheres, cylinders, vesicles, toroidal and disk-like micelles are formed by equilibrating different interactions between two amphiphilic blocks and the solvent. Toroidal structure can be formed in aqueous solutions with a hydrophilic exterior. In the toroidal model, the hydrophilic part of peptide channels associates with the hydrophilic head groups of lipids to form a monolayer lipid on both sides of the membrane to be connected continuously through the pore. The pore inducing peptides are amphipathic because the peptides are located at the water–lipid interface in the polar head-groups throughout the channel. The toroid with hydrophilic exterior functions as proton channels across a lipid bilayer (Kim et al., 2013).

Toroids have a unique annular shape with an internal pore in the central region (Lim et al., 2011; Lim and Lee, 2011) and unique symmetrical shape which is similar to β-barrel and α-helical bundle transmembrane protein shapes (Jang et al., 2008; Brogden, 2005). They show a short nanotube-like shape with a length of a few nano-meters. Interestingly, a structure of toroidal nanostructures was commonly found in many transmembrane proteins. Several research groups have designed and constructed self-assembled structure of toroid through amphiphilic block copolymers, DNAs, rod-coil amphiphiles, peptides and proteins (Butterfield and Lashuel, 2010; Huang et al., 2009; Yagai et al., 2008; Carlson et al., 2006; Djalali et al., 2004; Pochan et al., 2004; Jain and Bates, 2003). Therefore, self-assembly of rigid-flexible amphiphiles and synthetic peptide-based amphiphiles can be attractive to generate toroidal nano-structures. The formation of curvature at the interface of building blocks or the stacking of the macrocycles has become the principle of toroids formation. Many anti-microbial peptides, which contain many tissues and cell types, induce the formation of an aqueous pore across the membrane bilayer by the toroidal pore model. Toroidal nano-structures have been reported to be used as artificial transmembrane channels based on antimicrobial peptides (Jang et al., 2008; Brogden, 2005).

The doughnut-like or ring-shaped toroid structure was first found in an amphiphilic poly(acrylic acid)-block-poly(methyl acrylate)-block-polystyrene ABC triblock copolymer mixture with divalent organic counterion (Pochan et al., 2004). The rigid-flexible amphiphilic small molecules that consist of rigid aromatic segments and flexible coil segments can form a nano-meter size of toroids structures (Lee et al., 2001). A rigid hydrophobic core surrounded by flexible hydrophilic chains in an aqueous solution was obtained from this amphiphilic formulation (Kim et al., 2011). Furthermore, all doughnut-like shape micelles have been reported as the ring-closure to rod-shaped which coexist with the precursor micelles. A pure toroidal micelle with a uniform shape and size has not been identified. Hence, the formation of toroidal micelle information has been restricted for a few specific systems (Huang et al., 2009).

Toroidal micelles have been observed to form from ABC, ABA and AB amphiphilic block copolymer (Fu et al., 2009; Hoogenboom et al., 2008; Liu et al., 2008; Tsitsilianis et al., 2008; Reynhout et al., 2007; LaRue et al., 2006; Zhu et al., 2004). Toroids shape formed through the elimination of high free energy end caps of cylindrical micelles and also by the perforation of disc-like micelles which were energetically unfavorable spherical micelle (Cui et al., 2009). In contrast, the stirring rate was the principle factor in the formation of toroids from a poly (4-viny-pyridine)-block-polystyrene-block-poly (4-vinylpyridine) in a dioxane/water mixture. Faster rates led to an increasing number of toroids formed through a cylinder-sphere-vesicle-ring transformation (Yu and Jiang, 2009). A previous study found a ring-shaped toroidal structural miracle of a poly (4-vinyl pyridine) ABA triblock copolymer in an aqueous solution. They found that the transition structure of ring-shaped formed very slowly from a rod-shape micelle (Zhu et al., 2004).

The spontaneous aggregation of the PKOEs/DPPC nano-emulsion is illustrated in Fig. 2. The first aggregate was observed at 3 ns then internally reorganized to form doughnut-like toroidal structure within 50 ns. The first aggregate of a toroidal structure with multiple end caps (3 ns), subsequently evolves into toroidal structure with one end cap (18 ns). The ring of doughnut-like structure was geometrically circular with minimal ellipticity within 25 ns (Fig. 2). Finally, a closed toroidal structure was formed by merging the end caps into the doughnut-like toroid during 50 ns of simulation. At the end of simulation, the overall structure of oil-in-water (o/w) nano-emulsion represented the fusion of PKOEs inside the DPPC molecules in the aggregate. DPPC molecules are part of cell membrane with a tendency to form toroidal aggregate structure.

Snapshot pictures during molecular dynamics (MD) simulations of PKOEs/DPPC system at t = 0 ns, 3 ns, 18 ns, 25 ns, 35 ns, and 50 ns. Snapshots taken from a simulation show the spontaneous self-assembly of PKOEs together with the DPPC into the doughnut-like toroidal micelle after 25 ns. The PKOEs are shown in green and DPPC in blue. Water molecules have been removed for clarity.
Figure 2 Snapshot pictures during molecular dynamics (MD) simulations of PKOEs/DPPC system at t = 0 ns, 3 ns, 18 ns, 25 ns, 35 ns, and 50 ns. Snapshots taken from a simulation show the spontaneous self-assembly of PKOEs together with the DPPC into the doughnut-like toroidal micelle after 25 ns. The PKOEs are shown in green and DPPC in blue. Water molecules have been removed for clarity.

The aggregate formation process can also be illustrated by evolutions of cluster number within simulation time in Fig. 3. The size of the cluster–cluster aggregates was gained when the toroidal aggregate was formed by the association of primary particles with similar structures. The number of the clusters formed was calculated by distances less than 0.35 mm in the same cluster. Therefore, all clusters with the same number (N) showed a similar shape of the aggregate. The formation of clusters represented in the PKOEs/DPPC system was used to predict the mechanism of aggregation of the PKOEs and DPPC particle in the nano-emulsion system. The aggregation of the particles in an aqueous solution provides a theoretical description of nano-emulsion suspensions based on the cluster particle size distribution as a function of nano-scale interaction forces between the particles. Hence, the rate of the formation of aggregates is depending on the van der Waals attraction between the aggregate structures during the simulation times.

The number of cluster throughout the simulation during the self-assembly process shows the system contained 4 clusters at 0 ns. The number of clusters was reduced to 1 cluster at the end of simulation.
Figure 3 The number of cluster throughout the simulation during the self-assembly process shows the system contained 4 clusters at 0 ns. The number of clusters was reduced to 1 cluster at the end of simulation.

The number of cluster versus the simulation time showed the model system contained 4 clusters at 0 ns. The structure then underwent restructuring to form final equilibrium arrangement. The fluctuated number of clusters along the period of simulation may suggest that the aggregation and disaggregation happened due to the collision between molecules during the self-assembly process. Furthermore, the molecules that were located at the surface of the smaller clusters tended to disengage themselves to attach to each other to form bigger clusters during the repetition of Ostwald ripening process until a stable aggregate obtained (Ratke and Voorhees, 2002). The numbers of clusters were reduced to 1 cluster at the end of simulation which showed the most stable self-assembled structure in the aggregate (Fig. 3). The randomly positioned molecules of PKOEs and DPPC first aggregated into small clusters, then they came together to form a completely aggregated structure as a single toroidal structure within 15 ns. The PKOEs and DPPC molecules remained as a one doughnut-like toroidal aggregate until the end of simulation. The formation of doughnut-like micelle involves intra- or inter-micellar coalescence to keep the integrity of the aggregate shape (Jiang et al., 2005).

The shape of aggregate was analyzed with an estimation of the ratio of the average principal moments of inertia (Fig. 4). The principal moments of inertia values over the course of simulation showed the values of z-axis were higher than x and y axes. This indicates that the aggregate tends to be in the z-axis where the axis is symmetrical at the center of the doughnut-like toroidal shape. In fact, the values of all moments of inertias are equal or close to each other for a spherical aggregate (Tieleman et al., 2000). From our results, the principal moments of inertia of PKOEs/DPPC nano-emulsion model for 50 ns indicated a non-spherical shape with a ratio of 1.0:1.2:1.8 (Table 2).

The principal moments of inertia of PKOEs nano-emulsion model during 50 ns of the simulation indicated a non-spherical shape. I1, I2, I3, and Itot represented x, y, z axis, and total principle moments of inertia.
Figure 4 The principal moments of inertia of PKOEs nano-emulsion model during 50 ns of the simulation indicated a non-spherical shape. I1, I2, I3, and Itot represented x, y, z axis, and total principle moments of inertia.
Table 2 Total moment of inertia (Itot) and the eccentricity (e) value of the PKOEs/DPPC/H2O model at 50 ns.
Itot (106 amu nm2) 〈I1〉 (106 amu nm2) 〈I2〉 (106 amu nm2) 〈I3〉 (106 amu nm2) I1:I2:I3 e
3.41 1.43 1.73 2.55 1.0:1.2:1.8 0.25

Additionally, the shape of the aggregate can be further characterized by examining the eccentricity (e). The eccentricity (e) of the aggregate can be evaluated from Eq. (1) where Imin is the moment of inertia along either the x, y or z axis with the smallest value and Iave is the averaged value over all three moments of inertia. Table 2 reports the moment of inertia and eccentricity values at 50 ns of production run. For a perfect sphere, the value of e should be zero (Tieleman et al., 2000). Therefore, the eccentricity value of 0.25 shows a deviation from a perfect spherical object. Our calculated eccentricity value was consistent with the average moment of inertia analysis and the snapshot pictures of the simulated model system which showed the toroidal doughnut-like aggregate (Fig. 5).

(1)
e = 1 - I min I ave
Eccentricity of the aggregate during 50 ns of the simulation time shows a deviation from zero value which obtained of non-spherical aggregate.
Figure 5 Eccentricity of the aggregate during 50 ns of the simulation time shows a deviation from zero value which obtained of non-spherical aggregate.

The compactness of the structure which is related to aggregation size distributions during the simulation was determined by the radius of gyration (Rg). Radius of gyration was calculated based on the average distance between an atom and its center of mass. As shown, the Rg gradually declined due to the effect of hydrophobic interaction until the structure moved toward a stable state (Fig. 6). This decrease is associated with the loss of monomer to form an aggregate which may correspond to the behavior of an aggregate near equilibrium. The average radius of gyration (Rg) of PKOEs/DPPC aggregate fluctuated around the average value of 4.10 (±0.02) nm for the last 5 ns of simulation time. The structure became more compact from 15 ns to 50 ns in the range of 3.9–4.1 nm. The formation of toroidal micelles occurred as a result of forming a stable structure following the conventional toroidal micelle coalescence pathway observed in the self-assembly process.

Radius of gyration (Rg) fluctuation versus time for PKOEs nano-emulsion molecules in the self-association simulations at constant temperature and pressure for 50 ns.
Figure 6 Radius of gyration (Rg) fluctuation versus time for PKOEs nano-emulsion molecules in the self-association simulations at constant temperature and pressure for 50 ns.

The root mean square deviation (RMSD) was analyzed to investigate the stability of the aggregate during the structural transition. RMSD was calculated as a measure of the average distance between the atoms in the PKOEs/DPPC aggregate. RMSD fluctuation over the 50 ns of the self-assembly process was used to measure the structural differences from the initial coordinates (Fig. 7). The RMSD of the aggregated structure was gradually increased over the entire simulation time. The RMSD values were fluctuated around 4.96 (±0.03) nm during last 5 ns. The plot showed an increase of the root mean square deviation from 14 ns to 15 ns of simulation time with an average RMSD of 4.51 (±0.13) nm due to the molecular rearrangement to form a doughnut-like toroidal structure in agreement with the number of aggregate in the cluster reported above (Fig. 3).

Root mean square deviations (RMSD) of the doughnut-like toroidal aggregate of PKOEs/DPPC model system as a function of simulation time.
Figure 7 Root mean square deviations (RMSD) of the doughnut-like toroidal aggregate of PKOEs/DPPC model system as a function of simulation time.

The average hydrophobic and hydrophilic solvent accessible surface area (SASA) values and the total SASA value were calculated to show the surface area of the aggregate which was available to interact with water. Fig. 8 shows the area related to the hydrophobic parts decreased significantly for the first 5 ns of simulation indicating that the hydrophobic interaction was reduced. The hydrophobic SASA value, then remained more or less constant until the end of simulation. This trend was also repeated for the total SASA fluctuation while for the hydrophilic SASA, the fluctuation remained almost constant for the whole simulation. The average total SASA, the hydrophobic SASA, and the hydrophilic SASA averaged over the last 5 ns of the simulation time were 551.72 (±5.88), 292.33 (±2.33) and 259.41 (±2.87) nm2. The hydrophobic part of surfactant molecules can aggregate together in the PKOEs interior, whereas the hydrophilic part tends to maximize the contacts with the outer water molecules. Both hydrophobic and hydrophilic effects are involved in the aggregation process (Abedi Karjiban et al., 2012). As a result, hydrophobic forces are required to stabilize the packing of the nano-emulsion.

Solvent-accessible surface area (SASA) fluctuations per molecule for 50 ns show the hydrophobic interaction was reduced during the simulation.
Figure 8 Solvent-accessible surface area (SASA) fluctuations per molecule for 50 ns show the hydrophobic interaction was reduced during the simulation.

Radial distribution function, g(r) was analyzed to investigate the interatomic interactions in order to determine the structural properties of the self-assembled structure formed. The g(r) values were calculated around the PKOEs and DPPC particle in the system to describe the probability of finding the interaction of the particle between the nearest neighbors. Therefore, we used g(r) to describe the average structure of the aggregate from the MD simulation as shown in Fig. 9. The repulsive interaction forces between the aggregate were detected at very short distances of r ⩽ 0.17 nm with the g(r) value equal to 0 during the self-assembly process. The self-assembly of DPPC and PKOEs molecules is due to the amphiphilic properties of these molecules. Therefore, a strong interaction between hydrophilic and hydrophobic part of the molecules will be involved (Israelachvili and Ladyzhinski, 2005). When r exceeded 0.20 nm, the values of radial distribution increased. The first peak occurred at r = 0.53 nm, with g(r) having a value of about 2.13 which was almost similar to r = 1.41 nm. The radial distribution function, g(r) value equals to 2.25 displayed a weak maximum at r ≈ 0.95 nm. Later on, the g(r) value fell off and passed through a minimum value around r = 0.89 nm. The radial distribution function exhibited a global minimum at 0.95 nm from the distance of closest approach with a local maximum at aggregate contact radius. The average value of radial distribution was 1.52 (±0.57) with the maximum distances of 5.00 nm through 50 ns of the simulation time.

Radial distribution function, g(r) can determine the interaction between the closet particle of PKOEs and DPPC during 50 ns of molecular dynamics simulation for PKOEs nano-emulsion.
Figure 9 Radial distribution function, g(r) can determine the interaction between the closet particle of PKOEs and DPPC during 50 ns of molecular dynamics simulation for PKOEs nano-emulsion.

The self-diffusion coefficient was measured by determining the mean square displacement (MSD). The mean square displacement was analyzed to characterize the dynamical properties of the particles in PKOEs nano-emulsion system. Furthermore, MSD is useful for exploring the lateral diffusion along the aggregate at interfaces by calculating the value of the diffusion coefficient based on the average mass of the aggregate. The particles of mass (m) move in a dense medium which generates friction and random collisions based on Brownian motion theory. Therefore, MSD of the PKOEs nano-emulsion analysis is able to measure the Brownian motion during the aggregation of the droplet. Brownian aggregation is the result of random Brownian movement of the droplet. Brownian motion caused by entropic driving forces, keeps the droplets suspended over long periods of time.

Fig. 10 shows time-dependent MSD calculation for the PKOEs nano-emulsion self-assembled structures to identify the evolution of viscosity, elasticity and structural properties of the aggregate. From Fig. 10, the rate of the diffusion process increased slowly which is happening naturally in the fluid with the average diffusion coefficients (D) value of 0.05 × 10−5 cm2 s−1. The diffusion constant turns out to be proportional to the temporal correlation of the random fluctuations of the particle movement. The overall effect of the interaction between a suspended particle and the surrounding molecules is a random drift in the trajectory of the particle. Moreover, molecules in the collisions process will be collided in an approximate straight line. Generally, the rate of diffusion depends on the solubility of the dispersed phase in the continuous phase. The diffusion rate is also impacted directly by the viscosity of the continuous phase. Therefore, the diffusion coefficient of DPPC at the O/W interface can be controlled by the viscosity of non-aqueous phase depending on the concentration of DPPC at the interface.

Mean square displacement (MSD) of PKOEs nano-emulsion self-assembled structure as a function of time.
Figure 10 Mean square displacement (MSD) of PKOEs nano-emulsion self-assembled structure as a function of time.

4

4 Conclusion

The presented molecular dynamics simulation study gave a more detailed insight into understanding the complexity of the self-assembly process in palm kernel oil-based esters nano-emulsions. Our results provided more information on the aggregation pattern, formation pathway of the aggregate and the aggregate structure. All-atom level MD simulation was carried to study the aggregation of palm kernel oil esters (PKOEs) and dipalmitoylphosphatidylcholine (DPPC) for 50 ns. The self-assembly process was observed rapidly after 3 ns and continued with the formation of a doughnut-like toroidal shape at the end of simulation based on the principle moment of inertia, eccentricity and radius of gyration analysis. The PKOEs/DPPC aggregate had the average radius of gyration (Rg) of 4.10 (±0.02) nm and 551.72 (±5.88) nm2 contact area with water molecules. The repulsive interaction forces between the aggregates were detected at r ⩽ 0.17 during the self-assembly process. Moreover, the rate of the diffusion process increased slowly with the average diffusion coefficients (D) value of 0.05 × 10−5 cm2 s−1. Our simulation results may suggest that PKOEs/DPPC nano-emulsion model has a potential to be used in parenteral drug delivery by carrying the drug inside the ring due to the low energy of the formation pathway of aggregate. Therefore, the toroidal nano-structure obtained can provide a fundamental understanding for the development of nano-emulsions.

Acknowledgment

The authors gratefully acknowledge financial support from University Putra Malaysia Research Grant RUGS 9342300.

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