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Jan 31, 2018 - *E-mail: [email protected] This article is part of the Ken A. Dill Festschrift special issue. Cite this:J. Phys. Chem. B 122, 21, 5356-...
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Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

Influence of Solvent on the Drug-Loading Process of Amphiphilic Nanogel Star Polymers Amber C. Carr,† Victoria A. Piunova,† Hasmerya Maarof,‡ Julia E. Rice,† and William C. Swope*,† †

IBM Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States Department of Chemistry, Universiti Teknologi Malaysia, Johor Bahru, 81310 Johor, Malaysia



S Supporting Information *

ABSTRACT: We present an all-atom molecular dynamics study of the effect of a range of organic solvents (dichloromethane, diethyl ether, toluene, methanol, dimethyl sulfoxide, and tetrahydrofuran) on the conformations of a nanogel star polymeric nanoparticle with solvophobic and solvophilic structural elements. These nanoparticles are of particular interest for drug delivery applications. As drug loading generally takes place in an organic solvent, this work serves to provide insight into the factors controlling the early steps of that process. Our work suggests that nanoparticle conformational structure is highly sensitive to the choice of solvent, providing avenues for further study as well as predictions for both computational and experimental explorations of the drug-loading process. Our findings suggest that when used in the drug-loading process, dichloromethane, tetrahydrofuran, and toluene allow for a more extensive and increased drug-loading into the interior of nanogel star polymers of the composition studied here. In contrast, methanol is more likely to support shallow or surface loading and, consequently, faster drug release rates. Finally, diethyl ether should not work in a formulation process since none of the regions of the nanogel star polymer appear to be sufficiently solvated by it.



INTRODUCTION Polymeric materials show potential for use in targeted drug delivery in the form of biodegradable nanoparticles, which have been developed with a range of structural properties and possible therapeutic functionalities.1−12 Generally, these materials consist of a hydrophobic core with an affinity for hydrophobic drug molecules, and a hydrophilic exterior that serves to solubilize the polymeric nanoparticle−drug complex, and that could also be engineered to allow its transport to targeted regions within the body, and to shield it from recognition by the immune system. Among the many classes of such polymeric nanoparticles are the nanogel star polymers, which have a relatively large covalently bound cross-linked core with attached linear polymeric diblock arms.1,2 In comparison with other star polymeric architectures, the nanogel core star polymers can potentially increase the drug loading capacity. Currently, very little is known experimentally at the atomic level about drug-loading into nanogel star polymers, and there is no standardized procedure available that can be used to predict and optimize the drug-loading characteristics of a specific type of polymeric material or nanoparticle architecture. For example, a currently unresolved issue is whether loaded drugs reside within the interior volume of the hydrophobic core of the nanoparticle, or if they are more stably situated at the interface between the hydrophobic material and the surrounding water. Experiments and simulations13,14 have produced preliminary findings that the latter might be the case, but detailed knowledge in this area remains forthcoming. In addition to drug-loading efficiency, it is also important to be able to control the rate of drug release, which has important © XXXX American Chemical Society

therapeutic implications, since the rapid release of drug molecules has the potential to lead to harmful side effects. Understanding the factors that control drug uptake by the nanoparticle will drive the rational design of nanoparticles with both high loading capacity and desired release rates. Factors other than the polymer composition and architecture can have profound effects on drug-loading characteristics. These include the details of the formulation process, by which a hydrophobic drug is loaded into a polymeric nanoparticle. Earlier work15−22 has shown that when the nanoparticles are placed in water, the hydrophobic effect serves as a driving force to cause the hydrophobic core and any hydrophobic arm-blocks to reorganize into an approximately spherical and compact region while the hydrophilic arm-blocks remain solvated. Consequently, in water, not only is it difficult to dissolve hydrophobic drug molecules, but the polymeric nanoparticle may not be able to adopt conformations conducive to drugloading. Therefore, in the drug-loading process, the nanoparticle usually is first placed in a water-miscible organic solvent that is a good solvent for both the drug and the hydrophobic material of the core, such as tetrahydrofuran. Next, drug molecules are introduced into this mixture, and, finally, water is titrated in, providing the driving force for the hydrophobic drug to associate with the hydrophobic core of the nanoparticle, Special Issue: Ken A. Dill Festschrift Received: October 24, 2017 Revised: January 16, 2018 Published: January 31, 2018 A

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polymerization reaction went to completion and produced a very broad distribution of resulting star polymer sizes and structures. At the end of the simulations, all star polymers, which had 16 arms, were extracted, producing a set of 20 diverse structures and representing an intermediate size (arm count) within the overall distribution of product molecules. These 16 arm star polymers had a range of core sizes from 63 to 93 linker components, with an average of 81, as was determined by the 1:5 reactant ratio. An ensemble of 20 allatom structures was subsequently generated through a mapping procedure21 on the coarse-grained ones. The 16 diblock arms, tethered to the cores each, contained 16 monomeric units of delta-valerolactone (VL = −CH2−CH2−O-CO−CH2−CH2−), that were connected via a methylene subunit linker (−CH2−) to the hydrophilic block of 24 polyethylene glycol (PEG) subunits (PEG = −CH2−O−CH2−) and were terminated by a methyl group. We denote the structure of these nanoparticle systems as Gelcore[PVL16-PEG24]16.. Simulations on the members of this ensemble were performed to determine their structural and kinetic features in water. In spite of the apparently large size range, after solvation and equilibration in water at 350 K, these all collapsed into structures with a relatively dense hydrophobic core (the cross-linked lactone linker and the PVL part of the arms), having an average radius of gyration (Rg) of 20.5 Å (SD = 0.8) and 23.5 Å for the overall polymer (SD = 0.5). From this ensemble of 20, one representative star polymer system was chosen, and, to make the comparisons among the various solvents more straightforward, this same star polymer was simulated in each of the nonaqueous solvents for this work. This star polymer consists of a cross-linked lactone core with 92 lactone linker subunits. Figure 1a depicts only the cross-linked lactone core of the

which is believed to simultaneously collapse into a spherical conformation which houses the drug.13 Since the structure of the nanoparticle is likely to be strongly affected by the nature of the solvent, we believe that the details of the loading process, in particular the choice of solvent and drug, may lead to differences in loading efficiency as well as the location of the drug once loaded. Due to the dearth of atomic-level information that is currently available from experiments involving nanogel star polymers and the pressing need to move toward the rational exploration of the space of polymeric materials, molecular dynamics simulations have been used in a predictive capacity to provide much-needed information about these systems.15−22 All-atom simulations of star polymers have proven their utility in providing an atomic-level picture of the structural and kinetic behavior of these systems, elucidating the dependence of these behaviors on factors such as temperature and the chemical composition of the core and arms. Additionally, coarse-grained simulations23 have provided insight into factors controlling the synthesis of these nanoparticles, outlining the influence of parameters, such as composition, concentration, and reactant ratios, on the size distributions and atomic-level architecture of the resulting product nanoparticles. Significantly, the coarsegrained structures produced from these simulations were designed to be converted to all-atom structures, providing a realistic ensemble of structures that we have used in order to provide the most detailed and structurally realistic simulations of these particles to date.21 Each of our prior simulation studies was conducted with water solvating the star polymer in order to mimic the in vivo environment in which the nanoparticle will ultimately function. In this work, we take initial steps toward understanding the drug-loading process by simulating a realistic, all-atom nanogel star polymer in various nonaqueous solvents. The goal of this work is, therefore, to understand how organic solvents influence the conformations of nanogel star polymers, and to provide starting structures for a subsequent study to simulate the entire drug-loading process. Previous simulation work in this area22 has been performed by Sharma et al., on model tethered amphiphilic polymeric systems where the conformations of three different systems were studied in both water and toluene. Our work expands upon this prior study, using a more complex all-atom nanogel star polymer in a range of solvents of varying polarities and dielectric constants. Some of these solvents, such as toluene and tetrahydrofuran, are commonly used in the synthesis and formulation processes of star polymers, while others are not directly relevant to experimental processes, but allow for a systematic exploration that may lend insight into the effects of polarity and dielectric properties on the conformation of nanogel star polymeric systems.

Figure 1. (a) Schematic of the cross-linked lactone core of nanogel star polymer system. Carbon atoms are represented in teal and oxygens in red. (b) Image showing van der Waals surface of complete nanogel star polymer system following hydrophobic collapse in water, with cross-linked lactone core and PVL arm block shown in pink, and PEG shown in gray. Images, not to scale, were rendered using VMD.24



METHODS Nanogel Star Polymeric Nanoparticle and Organic Solvents. The model for the star polymer system used in these simulations is a realistic all-atom representation of a nanogel star polymer with a cross-linked core and diblock arms. This nanoparticle was produced by undertaking a coarse-grained simulation23 of nanogel star polymer synthesis via the ringopening polymerization reaction between a bicyclic valerolactone linker and an alcohol-functionalized polymeric arm. The simulation of the synthetic process used reactants in the same proportion (five linker molecules per arm molecule) as in actual star polymer synthesis experiments. In these simulations, the

nanoparticle; Figure 1b depicts the cross-linked core with its 16 arms attached, after undergoing hydrophobic collapse in water. After equilibration in water, this polymer had a (time averaged) Rg for the hydrophobic core of 20.6 Å and an overall Rg of 23.6 Å, falling very close to the mean of the 20-member ensemble. We note that this model of a star polymer is somewhat smaller than what is usually described in experimental papers, where the arms are often formed from PEG chains of 100 repeat units (instead of 24), and the hydrophobic core is also larger. B

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fs. Lennard-Jones and direct-space electrostatic interactions were truncated at 12.0 Å (for DCM, DEE, and DMSO) or 14.0 Å (for MeOH, THF, and toluene), and a tail correction for the Lennard-Jones potential beyond this cutoff was included in energy and virial pressure calculations. Electrostatic interactions were evaluated with a particle−particle−particle−mesh procedure, with an accuracy parameter of 10−5 that resulted in a three-dimensional k-space grid of 120 × 120 × 120. In accordance with the OPLS-AA potential, neither Coulomb nor Lennard-Jones interactions were evaluated for 1−2 or 1−3 particle pair interactions, and both of these interactions were scaled by a factor of 0.5 for 1−4 interactions. Geometric combining rules were used to establish the Lennard-Jones parameters. Coordinates were saved every 20 ps of the simulation for later analysis. All simulations were performed using the LAMMPS package dated April 2013 on IBM BlueGene/Q supercomputers.33 Following the neat solvent simulations, the 1000 molecule solvent boxes were replicated in order to assemble solvent boxes large enough to host the simulation of the nanoparticle. Previous work,21 simulating an ensemble of similar star polymers in water, showed that rapid collapse, equilibration, and adequate sampling was observed in water at 350 K on the time scales studied here, and so one representative simulation in water was prepared. However, since the kinetics of conformational change in other solvents is expected to be different and unknown, for each nonaqueous solvent box, two separate simulations incorporating the nanoparticle were run: one in which the initial conformation of the nanoparticle was partially extended, and one in which it was partially collapsed. These initial nanoparticle structures were obtained from the gas-phase simulation21 used to initially collapse the nanoparticle system, which was built with all arms in an extended, linear conformation. The nanoparticle was then inserted in the solvent box, removing a number of solvent molecules closest to the nanoparticle, such that the mass of solvent removed was approximately equal to the mass of the nanoparticle added.19,20 Different numbers of solvent molecules were required in each system to fully solvate the nanoparticle (see Table 1). For each solvent, the same number of solvent molecules was used with both the collapsed and extended nanoparticle systems. Similar to the procedure described above for the neat solvent boxes, the simulation boxes incorporating both solvent and nanoparticle underwent structure optimization, followed by 5 ns of equilibration in the NVT ensemble at 350 K, with a direct-space electrostatic cutoff at 14.0 Å. Following this equilibration, production runs were initiated at 350 K in the NpT ensemble at a pressure of 1.0 atm and a direct-space electrostatic cutoff at 14.0 Å, with all other parameters identical to those outlined above for the production runs of the neat solvent boxes. Based on experience from our previous work,19−21 these systems were simulated at 350 K rather than 300 K to allow for improved sampling. Each system was simulated for a total of 100 ns. Force Fields. The OPLS-AA (all-atom) force field34 was used for the nanoparticle system, with modifications19 for PEG, which have been shown to improve the model’s accuracy in the aqueous environment represented by the TIP4P-Ew water model.35 The OPLS-AA force field was used with toluene, THF, DCM, DEE, and MeOH. The water model used was TIP4P-Ew. (For DCM, consistent with earlier practice36 established for obtaining nonbonded parameters for RCH2X alkyl halides, charges were assigned as follows: −0.200 on

We were interested in the behavior of this small nanogel star polymeric nanoparticle in representative organic solvents that are common choices as media for organic synthesis and for the preparation of drug formulations. We selected six different solvents (Table 1) spanning a range of polarities: toluene, Table 1. For Each Simulated Solvent−Nanoparticle System, the Experimental25 Dielectric Constant and Dipole Moment of the Solvent, the Number of Solvent Molecules Solvating the Nanoparticle, the Total Number of Atoms of the System, and the Length of the Edge of One Side of the Cubic Simulation Cell Are Givena system

dielectric constant

dipole moment (D)

number of solvent molecules

total number of atoms

box edge length (Å)

toluene DEE THF DCM MeOH DMSO water

2.4 (25 °C) 4.3 7.5 8.9 32.6 (25 °C) 47 80

0.36 1.15 1.66 1.6 1.69 4.3 1.85

26341 26181 63158 63287 62106 63223 43289

404203 401803 830142 325523 381724 641318 138955

172.9 56.0 212.4 190.8 162.1 196.2 112.0

a

The total number of atoms in the nanoparticle in each case is 9088, which is included in the total number of atoms in the system. Dielectric constant data25 are for 20 °C, unless otherwise noted.

diethyl ether (DEE), tetrahydrofuran (THF), dichloromethane (DCM), methanol (MeOH), and dimethyl sulfoxide (DMSO). Water was also included in the comparison. These solvents offer a wide range of polarities, with experimentally determined25 dipole moments ranging from 0.36 (nonpolar) to over 4 D, and dielectric constants25 ranging from about 2 to 80. In this study, we simulated the nanogel star polymer in these solvents to systematically explore their effect on the conformational preferences of the nanoparticle. The PVL that comprises the hydrophobic core (including both the crosslinked core and the PVL part of the diblock arms) of the nanoparticle is insoluble in water, but is soluble in most organic solvents.26 The PEG that comprises the outer shell of the nanoparticle is highly soluble in water, due to hydrogen bonding and bridging water molecules, which stabilize an extended and somewhat helical structure.27 PEG is also known to be soluble in many common organic solvents, with the exception of DEE.28,29 Simulation Details. For each solvent, three types of systems were simulated. In order to characterize the quality of the force field parameters, a box of neat solvent molecules in the liquid state, as well as a single molecule in vacuum, were simulated for each system in order to calculate the enthalpy of vaporization and neat liquid density. A larger box of each solvent was then used to solvate the nanoparticle system. For the neat solvent simulations, the protocol was as follows. A box of 1000 molecules underwent structure optimization followed by 4 ns of MD equilibration in the NVT ensemble at a temperature of 300 K and at experimental density. Molecular dynamics simulations were then performed on each system in the NpT ensemble at a temperature of 300 K and a pressure of 1.0 atm, for a total of 10 ns. Bond lengths involving hydrogen were constrained using RATTLE,30 with bond-length constraints satisfied to a tolerance of 10−5 Å. Thermal control was implemented via a Nosé−Hoover extended Lagrangian procedure with a fictitious thermostat variable.31 The dynamical integration scheme was velocity−Verlet,32 with a time step of 1 C

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the geometric center of the cross-linked core and hydrophobic arm block as the center of the molecular reference frame of the nanoparticle. Radius of Gyration. The radius of gyration (RG), which quantifies the spatial extent of an object, was computed as follows, considering eigenvalues of the gyration tensor ordered from largest (λ1) to smallest (λ3):

chlorine, 0.103 on hydrogen, and 0.194 on carbon, in electronic charge units.) OPLS-AA torsion parameters were not available for dimethyl sulfoxide (DMSO), but were borrowed from those for acetone. (Torsion energies based on the H−C−S−O and H−C−S-C torsion angles have 1−4 nonbonded interactions similar to acetone.) The OPLS-AA model for acetone employs an improper torsion term to enforce a planar arrangement of the heavy atoms of this molecule. However, the heavy atoms of DMSO should be pyramidal rather than planar. We neglected to remove the improper torsion term from our DMSO force field, so the heavy atoms of our DMSO model are planar rather than pyramidal. We found that this oversight had only a minor effect on the DMSO neat liquid properties, changing the density to 1.091 from 1.099 g/cm3, and changing the heat of vaporization to 13.54 from 13.23 kcal/mol (Table 2),

RG =

Voronoi Analysis. Voronoi analysis was used to quantify the interfacial surface area shared between any two components of the system, including the solvent, and to identify solvent molecules that reside in the interior of the polymer.19−21 Dihedral Angle Conformers. The dihedral angles of PEG adopt specific backbone conformers in order to optimize hydrogen bonding with water, stabilizing a helical structure. In order to explore the sensitivity of PEG conformations to the solvent and its propensity to hydrogen bond, we quantified the dihedral conformers of heavy atoms along the PEG backbone. The conformation of each overlapping −C−O−C−C−O−C segment as one moves along the PEG backbone was characterized20,21,27 by three torsion angles, each of which can be classified as either trans (T) or gauche (G).

density (g/cm3)

system

experiment

simulation

experiment

simulation

DCM DEE DMSO MeOH THF toluene

6.984(1) 6.56(3) 12.782(1) 8.95(3) 7.61(3) 9.539(1)

7.137 6.86 13.54 8.60 7.43 9.335

1.318(2) 0.708(3) 1.095(2) 0.786(3) 0.884(3) 0.865(2)

1.305 0.708 1.091 0.771 0.852 0.863

(1) 39,40

Table 2. For Each Simulated Solvent, the Values of the Enthalpy of Vaporization and the Density As Determined by Experiment and Calculated through Simulationsa,b ΔHvap (kcal/mol)

λ12 + λ 22 + λ32



RESULTS Figure 2 shows representative structures of the nanoparticle in each solvent at the end of the 100 ns runs, with simulations begun from both the semicollapsed and semiextended states. In this figure, the different components of the nanoparticle are depicted using different color schemes. It is clear that the choice of solvent affects the conformational preferences of different components of the nanoparticle in different ways. In certain solvents, such as DEE and MeOH, the cross-linked PVL core has undergone extensive solvophobic collapse, exhibiting behavior similar to that seen in water. In other solvents, such as DCM, DMSO, THF, and toluene, the cross-linked component opens partially or completely to solvent, exhibiting its filamentous structure when extended. Similarly, the linear PVL that comprises the hydrophobic block of the arm is seen in certain solvents to collapse back onto the core or to aggregate with itself, while in others it extends freely to interact with the solvent. Generally, the PEG block of the arm is well solvated in all solvents with the exception of DEE, in which it appears to simultaneously self-aggregate and to aggregate with the hydrophobic PVL of the core and arm. In some solvents, such as water and methanol, the PEG appears to adopt a distinctive helical shape, while in others, such as DCM, it extends more linearly into the solvent. Radius of Gyration Analysis. In order to quantitatively characterize these differing types of conformations, we calculated the radius of gyration (Rg) of each component of the nanoparticle in each solvent, averaged over the last 20 ns of the simulation. These values, along with their associated statistical uncertainty, are depicted in Figure 3. Note that the values given here for Rg are totals calculated moving outward from the center of geometry of the nanoparticle, so the smallest value reported is for the cross-linked PVL core, the middle value is for the cross-linked PVL core plus the PVL component of the diblock arms, and the largest value is for both of the PVL components plus the PEG block of the diblock arms. Table S1 in the Supporting Information contains the numerical values corresponding to this figure.

a

Simulation results are for 300 K and 1 atm, experimental data is from 298 K. Statistical uncertainties (one standard deviation) for computed enthalpies of vaporization are approximately 0.04 kcal/mol; and for density, approximately 0.0004 g/cm3. bExperimental data are from (1) ref 37, (2) ref 38, and (3) ref 34.

differences that are actually rather small compared to statistical uncertainty and differences between the models and experimental results. Although we would not recommend use of this model in future work, we felt it was adequate for elucidating the qualitative trends we wanted to explore in this work. In order to characterize the force field used for each solvent (Table 2), a single molecule in vacuum, as well as cubic boxes of neat solvent, were run with 1000 molecules in each box for a total of 10 ns of simulation time, following the protocol described above. The enthalpy of vaporization was calculated for each system by taking the difference of the average potential energy of the gas phase molecule and the average potential energy per molecule in the liquid and adding RT to this difference. When compared to the experimentally determined27,34 heats of vaporization, the simulated results ranged from 4% too low to about 6% too high, but the rank ordering was preserved. Simulations for all systems also slightly underestimated the density, but the difference between experiment34,38 and simulation was less than 1%, except for MeOH (2% low) and THF (4% low). The rank order in the densities was also preserved, except for the reversal of THF and toluene, whose densities were very close in value. Analysis. Each nanoparticle system was simulated for 100 ns, and the last 20 ns of simulation data were used in the analysis of each system. We very briefly describe the analysis here, as the protocol follows that previously published19−21 for the molecular dynamics simulation of the same nanoparticle in water. As in that study, structural metrics were calculated using D

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Figure 2. Representative structures at the end of the 100 ns simulation time, with simulations initiated from both collapsed and extended structures of the same nanoparticle in each solvent: DCM, DEE, DMSO, MeOH, THF, toluene, and water. For each system, there are five images and the different components of the same nanoparticle conformation are shown using two different coloring schemes. The top image in each case shows just the cross-linked core, the middle pair of images shows the cross-linked core and the PVL block of the arms, and the bottom pair of images shows the entire star polymer. In the coloring scheme on the left-hand column of each set of three images, the cross-linked PVL core is shown in cyan, the PVL arm block in purple, and the PEG arm block in gray. In the coloring scheme on the right-hand column set of two images, the hydrophobic core (cross-linked PVL plus linear PVL arm block) is shown in pink, and the PEG arm block in gray. Solvent is not included in these images. Images, not rendered to scale, were created using VMD.24 E

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Figure 3. Average radius of gyration with its associated statistical uncertainty for each component of the nanoparticle system, with the cross-linked PVL shown in black, the cross-linked PVL plus the linear PVL block of the arm in red, and both PVL blocks plus the PEG block of the arm in purple. Results from partially collapsed starting states are on the left of each pair; from partially extended, on the right. Values are averages over the last 20 ns of each simulation.

Figure 4. Radius of gyration of the PEG component of the nanoparticle in each solvent, calculated independently from the PVL core and averaged all 16 arms of each polymer over the last 20 ns of the simulation. Results from partially collapsed starting states are on the left of each pair; from partially extended, on the right.

PVL is known to be insoluble26 in DEE, MeOH, and water, and the relatively low values of Rg for the cross-linked core and PVL block of the diblock arm reflect their insolubility in these solvents and reproduce this experimental observation. Similarly, experimental studies of PVL have indicated that it is soluble26 in DCM, THF, DMSO, and toluene. Our simulations show high solubility of both cross-linked and arm PVL in DCM and DMSO. In THF and toluene, the simulations starting from collapsed initial structures exhibit insoluble cross-linked PVL regions, while the arm PVL regions appear to be much more soluble than the cross-linked core. Simulations in these solvents starting from extended structures exhibited solubility of both the cross-linked and arm regions. These differences in results from different types of starting conformations, even after 100 ns of simulation, suggest the presence of a kinetic barrier to solvation of the collapsed cross-linked PVL in these solvents, and underscore the importance of initiating simulations from both semicollapsed and semiextended states. In order to gain a better understanding of the solubility of the PEG component of the arm, we calculated its Rg independently from the rest of the nanoparticle, as shown in Figure 4. Because the PEG chains comprise the outer layer of the nanoparticle and have one untethered end, their Rg should be only weakly dependent on the size and shape of the PVL components of the core. Experimentally, PEG is known to be soluble in all of the solvents tested with the exception of DEE, and our results reproduce this finding with the PEG component of the nanoparticle exhibiting the smallest Rg in this solvent. Interestingly, the values of Rg in DEE are significantly different depending upon whether the simulation is initiated from the partially collapsed or partially extended state. In this case, the smaller Rg in the system that was initiated from the partially extended state might be due to that extended state affording the nanoparticle the opportunity to undergo optimal rearrangement of its components during solvophobic collapse, minimizing its exposure to solvent. PEG chains in THF, toluene, and water also exhibit relatively low values of Rg. PEG chains in MeOH, DMSO, and DCM have relatively larger Rg values than those of the other systems. PEG Dihedral Angle Analysis. We may relate the radius of gyration of the PEG component of the nanoparticle to the

dihedral conformation of the PEG in each solvent. In water, PEG forms relatively strong hydrogen bonds with water through the adoption of the trans−gauche−trans (TGT) backbone conformations, which are enthalpically favored. Figure 5 depicts the average populations of different PEG dihedral conformations, averaged over the last 20 ns of each simulation. Only the results for the initially collapsed systems are shown, as there was no significant difference between the simulations initiated from collapsed and extended starting conformations. The results for water indicate the predominant adoption of the TGT backbone conformation, followed by trans−gauche−gauche (TGG) and trans−gauche−gauche′ (TGG′). This conformational signature is unique to PEG in water and is seen in none of the other systems. Although the TGT conformation is also favored by DCM, DMSO, and MeOH, these systems have larger populations of TGG′ than TGG. In toluene, THF, and DEE, the predominant backbone conformation of the PEG is TGG′. Interestingly, these conformational preferences are correlated with the Rg of the PEG as reported in Figure 4, as the largest Rg are reported in solvents in which the TGT conformation is the most populated. Solvents in which the PEG component has a relatively smaller value of Rg, such as toluene, THF, and DEE, exhibit a preference for the TGG′ conformation. Intercomponent Contact Analysis. The adoption of different torsion angles in different solvents may affect the solubility of PEG through its ability to interact with solvent and to interact with itself. In order to quantify the amount of contact between PEG and each of the other components of the nanoparticle−solvent system, Voronoi analysis was used to calculate interfacial surface areas between each of the system components, and the results were averaged over the last 20 ns of the simulation. Figure 6 shows the percentage of PEG surface area shared with other components of the system. In all systems, PEG is predominantly exposed to either solvent or to other PEG chains, with very little exposure to the hydrophobic components of the core. In nonaqueous solvents in which the TGT conformation of PEG is dominant (DCM, DMSO, and MeOH), the PEG contacts are predominantly with solvent. In nonaqueous solvents in which the TGG′ conformation is dominant (THF, toluene, and DEE), the PEG exhibits relatively less interaction with solvent, favoring self-interactions F

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Figure 5. Relative populations of different backbone conformations of the PEG chain of the nanoparticle in each solvent. Values were averaged over the last 20 ns of each simulation.

in the case of DEE, and exhibiting approximately equal percentages of self-interactions and interactions with solvent in the cases of THF and toluene. In this latter group of solvents, the PEG shows a relatively higher percentage of PEG−PEG contact, possibly indicating that the TGG′ conformation allows for the self-aggregation of PEG. Similar to this analysis of interfacial contacts made by the PEG component of the nanoparticle, Figure 7 shows the

average percentage of interfacial area that the cross-linked lactone core makes with each of the other nanoparticle components. With the exception of the nanoparticle systems in DEE and water, which still exhibit only a very a small proportion of lactone−PEG and PVL−PEG interactions, the components of the cross-linked cores generally do not interact with the PEG. Although the PVL components of the nanoparticle undergo solvophobic collapse in DEE and water, G

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Figure 8. Interfacial areas between the PVL arm block and the other components of the nanoparticle−solvent systems as a percentage of the total interfacial area available to the PVL, calculated using Voronoi analysis and averaged over the last 20 ns of each simulation.

Figure 6. Interfacial areas between PEG and the other components of the nanoparticle−solvent systems as a percentage of the total interfacial area available to the PEG chain, calculated using Voronoi analysis and averaged over the last 20 ns of each simulation.

cross-linked core, with a slight preference for itself in all systems but the DCM one. The linear PVL of the nanoparticle solvated in DEE interacts approximately equally with itself, with the cross-linked lactone, and with solvent. The system solvated in MEOH exhibits a similar profile to that of DEE, with a slightly greater preference for self-interactions versus interactions with other components of the nanoparticle. As one might expect, these interactions follow a similar trend to those of the lactone core, with the linear PVL exhibiting the lowest exposure to solvent in solvents that cause the solvophobic collapse of the core of the nanoparticle (DEE, MeOH, and water), and the largest exposure to solvents in which the PVL is soluble (DCM, DMSO, THF, and toluene). Analysis of Solvent-Loading in the Polymer Interior. In our prior studies of nanogel star polymers in water, Voronoi analysis was used to determine whether solvent penetrated the nanoparticle. We found that in water these nanoparticles were dry, with rare and short-lived water penetration events that yielded an internal concentration of water that represented approximately 0.1−0.4% the concentration of bulk water.19−21 We performed the same analysis here in order to compare the nonaqueous solvent content of the nanoparticle to that previously determined in water, and report the average number of interior solvent molecules in Table 3. We present these results noting that in the Voronoi analysis scheme, a solvent molecule must be completely surrounded by a layer of nanoparticle material in order to be classified as an interior molecule. This definition is appropriate for identifying solvent molecules that penetrate a dense and mostly dry core. However, because the PVL components of the nanoparticles in toluene, DCM, DMSO, and THF do not collapse completely, very few solvent molecules in these systems were ever completely enclosed by polymer. Therefore, although very little solvent is actually identified as encapsulated, these solvents surround and permeate the PVL cores of the nanoparticles, and a high fraction of their surface area is exposed, as indicated in Figures 7 and 8. The data in Table 3 for toluene, DCM, DMSO, and THF should not be interpreted as indicating a dry interior. The interior solvent classification scheme is more appropriate for compact structures, such as the DEE and MeOH systems, that undergo solvophobic collapse of their PVL cores. These exhibit penetration or capture of solvent, with a load ranging

Figure 7. Interfacial areas between the cross-linked lactone core and the other components of the nanoparticle−solvent systems as a percentage of the total interfacial area available to the lactone, calculated using Voronoi analysis and averaged over the last 20 ns of each simulation. The symbols for LAC−LAC and LAC−PVL coincide for DMSO.

the linear PVL component of the polymer does not completely coat the collapsed cross-linked lactone core, as exhibited in Figure 2, leaving some exposed areas where surface interactions between the cross-linked core and PEG, as well as cross-linked core and solvent, are able to occur. In the DCM, DMSO, THF, and toluene systems, the contacts made by the cross-linked lactone are predominantly with solvent. The cross-linked cores of the nanoparticle systems in THF and toluene have slightly larger self-interactions and interactions with PVL, as the solvophobic components of the system undergo slight collapse, as exhibited in Figures 2 and 3. In the DEE and MEOH systems, which both undergo fairly extensive collapse of the solvophobic core, the cross-linked cores interact predominantly with the linear PVL arms, but also exhibit almost equal percentages of interaction within the cross-linked core and with solvent. In Figure 8, we quantify the interfacial contacts of the linear PVL of the diblock arms. In the DCM, DMSO, THF, and toluene systems, PVL is predominantly exposed to solvent and has approximately equally small exposure to itself and to the H

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outlined in this work allow us to make contact with the experimental formulation protocol for loading drugs into these nanoparticles. A typical loading process for a hydrophobic drug involves first dissolving the polymeric nanoparticle in an organic solvent that is a good solvent for both the PVL core and arms, resulting in the exposure of hydrophobic components to solvent. Drug molecules are then introduced into the mixture, followed by the addition of water, which causes the association of the hydrophobic drug molecules with the hydrophobic region of the nanoparticle. This hydrophobic region is then believed to collapse around the drug due to solvophobic interactions, forming a nanoparticle with a spherical core.13 The simulations described in this work have replicated the first step of this process, and have thus provided us with starting structures, with which we may subsequently simulate the next steps of the drug-loading process. They also provide insight into potentially gaining control over the loading process through the choice of solvent. Table 4 compares the solubility of each component of the nanoparticle in each solvent determined through simulation

Table 3. For Each System, the Average Number of Solvent Molecules that Were Observed To Penetrate the PVL Interior of the Nanoparticle over the Last 20 ns of the Simulationa average number of solvent molecules system

collapsed

extended

DCM DEE DMSO MeOH THF toluene water

0.016 2.2 0.084 5.5 0.13 0.013

0.015 3.9 0.001 7.3 0.073 0.013 3.6

a

The small values for DCM, DMSO, THF, and toluene indicate that essentially no solvent is enclosed by the core because the core is well solvated. The larger values for DEE, MeOH, and water suggest fully enclosed solvent inside a relatively compact core.

from 2 to 7 internal solvent molecules. These results are similar to those that were calculated for water, which had an average of 3.6 interior water molecules over the simulation. As these low numbers of interior solvent represent only a fraction of a percent of the concentration of bulk solvent, we may conclude that the collapsed nanoparticle cores are dense and largely impermeable to solvent molecules. Mass Density Histograms. Figure S1 gives the orientationally averaged mass density of each component of the nanoparticle−solvent system as a function of the distance from its center of geometry, which was located within the crosslinked PVL core of each nanoparticle. For the systems that exhibit solvophobic collapse in DEE and MeOH, the mass density histograms exhibit cross-linked PVL cores with a fairly localized structure that peaks at short distances from the center of geometry and does not exhibit significant penetration by solvent. The profiles of the PVL arm-block are similar to those of the cross-linked cores, as the PVL in these systems generally collapses onto the cross-linked core. With the exception of DEE, the PEG block of the arm exhibits a flat distribution in all systems, indicating that it extends out into the solvent and can freely reorient. In the case of DEE, the PEG curve exhibits a maximum near the interface between the PVL of the arm block and the solvent. The PEG curve for the star polymer in DEE reflects the tendency of the PEG to both self-aggregate and interact with the surface of the PVL. For the systems that do not undergo solvophobic collapse, the solvent curves are generally seen to interpenetrate both PVL curves, or to have a higher density than either of these polymers at distances close to the center of geometry of the nanoparticle. This signature indicates that the cross-linked core and the PVL component of the arms are exposed to solvent.

Table 4. Comparison of the Solubility of Each Component (Lactone Core, PVL Arms, and PEG Arms) of the Nanoparticle in Each Solvent Determined through Simulation against That Known from Experiment for the Solubility of Linear Polymers in the Same Solventsa LAC

a

PVL

PEG

solvent

sim

expt

sim

expt

sim

expt

DCM DEE DMSO MeOH THF toluene water

S I S I S S I

S I I I S S I

S I S I S S I

S I I I S S I

S I S S S S S

S I S S S S S

I = insoluble, S = soluble.

against that known from experiment for the solubility of linear polymers.26 Generally, we found that some organic solvents behave similarly to water (DEE and methanol) and cause the cross-linked PVL core and linear PVL arms of the nanoparticle to undergo solvophobic collapse. By contrast, in THF, toluene, DMSO, and DCM, the PVL components are soluble, and the cross-linked polymeric core and linear polymeric arms interact with the solvent to differing extents in each system. Although in simulations PVL appears to be soluble in DMSO, experimental results indicate that PVL is insoluble in DMSO.26 Other than for this, the results for PVL solubility that we obtained are in good agreement with experimental findings for linear polymer chains,26 which indicate that PVL is insoluble in MeOH, DEE, and water and soluble in DCM, THF, and toluene. Interestingly, we note that the cross-linked and tethered topologies of the PVL core and arm components do not appear to affect the solubility of the polymer versus experiments with linear polymer chains. Additionally, we note that although the parameters that describe the nanoparticle were optimized for its solvation in water, these parameters appear to be transferable to other organic solvents and to reproduce qualitative experimental findings. With the exception of DEE, we found the PEG component of the nanoparticle to be soluble in all of the solvents tested, which agrees with experimental findings. Interestingly, we



DISCUSSION AND CONCLUSIONS In this work, we modeled by molecular dynamics the solvation of a nanogel-core diblock star polymeric nanoparticle in a series of solvents with a range of properties, with the goal of gaining a better understanding of the influence of solvent properties on the conformational preferences of the nanoparticle. The study also allowed us to validate our force field parameters based on comparison with experimental findings regarding the solubility of PVL and PEG polymers in different solvents. We are particularly interested in the development of these polymeric systems for drug delivery applications, and the simulations I

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In addition to controlling the location of drug-loading, we suggest that the choice of solvent used during drug-loading may also affect the release rate of the drug. We noted above that different solvents may preferentially expose different components of the nanoparticle to solvent and drug during the drugloading process. If the cross-linked core and PVL arms are both exposed to solvent and drug, the drug may load into the crosslinked core as well as throughout the volume defined by the PVL block of the arm. This loaded nanoparticle would likely exhibit the slowest release rate for the drug after loading, as the drug molecules would have the largest distance to travel in order to be released from the nanoparticle. If a solvent is used that does not result in the exposure of the cross-linked core to drug and solvent, but does result in the exposure of the layer of material defined by the PVL of the arm block, the drugs will likely load into this intermediate layer of material, and might be released more quickly than drug that is loaded into the crosslinked core. If a solvent is used that does not expose either of the PVL components to solvent, the drug might sit at the interface between the exterior PVL layer and the solvent, resulting in its quick release from the nanoparticle. This suggests that the solvent used in loading should be compatible with the polymer component that comprises the cross-linked core, as well as the component that is used on the diblock arm, to maximize the extent of loading and reduce the drug release rate. In this work, both of the hydrophobic polymeric components were made of the same material, but in practice, the materials may be varied in order to optimize different types of interactions and compatibility with the drug and solvent, and to control the location of loading and rate of release. In conclusion, our work suggests interesting avenues for further computational and experimental exploration. Given that we now have starting structures for simulation of the loading process, we plan to continue with simulations that will lend insight on the steps of the process in which drugs are encapsulated. We have successfully simulated ibuprofen uptake in simple adamantane-core model star polymers, and we can imagine using the atomistic nanogel polymeric system while varying the drug and solvent combinations. Recent SANS experiments,14 in which ibuprofen was loaded into a PVL−PEG nanogel star polymeric nanoparticle using THF, indicate that the drug molecules do not penetrate the cross-linked core, but rather reside in the intermediate layer of PVL that is part of the diblock arm. Our simulations of these nanoparticles, initiated from semicollapsed structures in THF, indicate that the core would not be accessible to solvent, but the PVL arm block would be. These results underscore the importance of further exploring the effect of the barriers to PVL solubility that are exhibited by the majority of the solvents that we tested. Gaining a better understanding of the factors controlling conformational changes in the nanoparticle will allow for optimization of nanoparticle characteristics through the judicious choice of materials and solvent.

found that different solvents cause the PEG to favor different dihedral angle conformations. Water is unique in that PEG overwhelmingly adopts TGT conformers when solvated in it, with much smaller populations of TGG and TGG′ dihedral angle conformations. In DMSO, DCM, and MeOH, the TGT conformation is favored, as it is in water, although to a lesser extent. However, in THF, toluene, and DEE, the TGG′ conformation is favored. These dihedral preferences were seen to correlate with different degrees of PEG−solvent interfacial contact (based on Voronoi analysis), as PEG chains in DCM, DMSO, and MeOH had greater contact with the solvent, while THF, toluene, and DEE appeared to induce some degree of self-association of PEG. We note that these simulations were of only a single nanoparticle, whereas the experimental protocol for loading involves rather concentrated nanoparticles in solvent, wherein the aggregation of nanoparticles becomes a potential issue. In order to reduce the potential for nanoparticle aggregation, a solvent must be chosen in which the PEG chains favor interaction with solvent over self-association, as the propensity to self-interact may lead to the aggregation of nanoparticles. These results remind one, that the solubility of polymeric nanoparticle components in various organic solvents (Table 4) may not correlate in a straightforward manner with the polarity (dipole moment and dielectric constant) and heat of vaporization properties of the solvent (Tables 1 and 2). Moreover, the chain lengths of arm components and size, topology, and cross-linking density of the core are likely to have entropic contributions to the solubility properties that may make predictions challenging. In simulating the first steps of the drug-loading process in different organic solvents, this work provides some validation for the parameters used for the nanoparticle, the solvents, and their interaction. Using the behavior of the cross-linked PVL core and linear PVL arms that was exhibited in these simulations, we may make predictions concerning how the choice of solvent might affect the loading process. In cases in which the hydrophobic core of the nanoparticle is insoluble in the chosen solvent, such as in water or MeOH, our Voronoi calculations above indicate the impermeability of the nanoparticle. This is in agreement with prior experimental work,13 which suggests that hydrophobic drugs might not be loaded deeply into the cross-linked core of the molecule, but rather stably reside at the interface between the hydrophobic core and the bulk solvent. In this case, the loading efficiency would depend upon the surface area and degree of surface convolution of the nanoparticle rather than on the volume of its interior, and the polymeric material could be engineered in order to maximize this metric. In order to maximize the loading of a hydrophobic drug into the interior of the nanoparticle rather than on its surface, a solvent should be chosen for loading, which maximizes the exposure of the cross-linked PVL core and linear PVL arm-blocks to solvent. In this work, the use of DCM, THF, and toluene was seen to maximize the interfacial areas between each of these hydrophobic regions and the solvent, indicating that drug-loading deep into the interior of the nanoparticle may be most efficient when performed in these solvents. We note, however, that our simulations indicated the presence of a barrier to solvation for the hydrophobic region, particularly the cross-linked core, in THF and toluene. Further computational and experimental investigation may be necessary in order to examine the effects of that barrier on the efficiency of drug loading.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b10539. Radius of gyration data for different components of the star polymer in different solvents; torsion angle distributions for the PEO component of the star polymer in different solvents; and orientation-averaged mass J

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(14) Wei, G.; Prabhu, V. M.; Piunova, V. A.; Carr, A. C.; Swope, W. C.; Miller, R. D. Spatial distribution of hydrophobic drugs in model nanogel-core star polymers. Macromolecules 2017, 50, 9702−9712. (15) Huynh, L.; Neale, C.; Pomes, R.; Allen, C. Systematic design of unimolecular star copolymer micelles using molecular dynamics simulations. Soft Matter 2010, 6, 5491−5501. (16) Huynh, L.; Neale, C.; Pomès, R.; Allen, C. Computational approaches to the rational design of nanoemulsions, polymeric micelles, and dendrimers for drug delivery. Nanomedicine 2012, 8, 20−36. (17) Grest, G. S.; Fetters, L. J.; Huang, J. S.; Richter, D.. Star polymers: Experiment, theory, and simulation. In Advances in Chemical Physics;; Prigogine, E., Rice, S. A., Eds.; John Wiley & Sons: New York, 1996; Vol. 94, pp 67−163. (18) Lee, H.; Larson, R. G. Molecular dynamics study of the structure and interparticle interactions of polyethylene glycol-conjugated PAMAM dendrimers. J. Phys. Chem. B 2009, 113, 13202−13207. (19) Swope, W. C.; Carr, A. C.; Parker, A. J.; Sly, J.; Miller, R. D.; Rice, J. E. Molecular dynamics simulations of star polymeric molecules with diblock arms, a comparative study. J. Chem. Theory Comput. 2012, 8, 3733−3749. (20) Felberg, L. E.; Brookes, D. H.; Head-Gordon, T.; Rice, J. E.; Swope, W. C. Role of hydrophilicity and length of diblock arms for determining star polymer physical properties. J. Phys. Chem. B 2015, 119, 944−957. (21) Carr, A. C.; Felberg, L. E.; Piunova, V. A.; Rice, J. E.; HeadGordon, T.; Swope, W. C. Effect of hydrophobic core topology and composition on the structure and kinetics of star polymers: A molecular dynamics study. J. Phys. Chem. B 2017, 121, 2902−2918. (22) Sharma, A.; Liu, L.; Parameswaran, S.; Grayson, S. M.; Ashbaugh, H. S.; Rick, S. W. Design of amphiphilic polymers via molecular dynamics simulations. J. Phys. Chem. B 2016, 120, 10603− 10610. (23) Swope, W. C.; Rice, J. E.; Piunova, V. A.; Carr, A. C.; Miller, R. D.; Sly, J. Simulation and experiments to identify factors allowing synthetic control of structural features of polymeric nanoparticles. J. Phys. Chem. B 2016, 120, 7546−7568. (24) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33−38. (25) CRC Handbook of Chemistry and Physics, 87th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2006. (26) PolySciTech, a division of Akina, Inc., West Lafayette, IN, Polymer Solubility Chart https://akinainc.com/polyscitech/products/ polyvivo/info.php (accessed September 29, 2017). (27) Goutev, N.; Ohno, K.; Matsuura, H. Raman spectroscopic study on the conformation of 1,2-dimethoxyethane in the liquid phase and in aqueous solutions. J. Phys. Chem. A 2000, 104, 9226−9232. (28) Ö zdemir, C.; Güner, A. Solubility profiles of poly(ethylene glycol)/solvent systems, I: Qualitative comparison of solubility parameter approaches. Eur. Polym. J. 2007, 43, 3068−3093. (29) Dinc, C. Ö .; Kibarer, G.; Güner, A. Solubility profiles of poly(ethylene glycol)/solvent systems. II. Comparison of thermodynamic parameters from viscosity measurements. J. Appl. Polym. Sci. 2010, 117, 1100−1119. (30) Andersen, H. C. Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 1983, 52, 24−34. (31) Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant pressure molecular dynamics algorithms. J. Chem. Phys. 1994, 101, 4177−4189. (32) Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 1982, 76, 637−649. (33) Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1−19. (34) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 1996, 118, 11225−11236.

density as a function of distance from the center of geometry of different components of the star polymer in different solvents (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] ORCID

William C. Swope: 0000-0002-5299-4145 Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS H.M. wishes to acknowledge financial support from NanoMalaysia. The authors also wish to thank Professor Ken Dill for many discussions about solvent effects on polymer conformational preferences related to this work.



REFERENCES

(1) Lee, V. Y.; Havenstrite, K.; Tjio, M.; McNeil, M.; Blau, H. M.; Miller, R. D.; Sly, J. Nanogel star polymer architectures: A nanoparticle platform for modular programmable macromolecular self-sssembly, intercellular transport, and dual-mode cargo delivery. Adv. Mater. 2011, 23, 4509−4515. (2) Appel, E. A.; Lee, V. Y.; Nguyen, T. T.; McNeil, M.; Nederberg, F.; Hedrick, J. L.; Swope, W. C.; Rice, J. E.; Miller, R. D.; Sly, J. Toward biodegradable nanogel star polymers via organocatalytic ROP. Chem. Commun. (Cambridge, U. K.) 2012, 48, 6163−6165. (3) Heise, A.; Hedrick, J. L.; Frank, C. W.; Miller, R. D. Starlike block copolymers with amphiphilic arms as models for unimolecular micelles. J. Am. Chem. Soc. 1999, 121, 8647−8648. (4) Adams, M. L.; Lavasanifar, A.; Kwon, G. S. Amphiphilic block copolymers for drug delivery. J. Pharm. Sci. 2003, 92, 1343−1355. (5) Aliabadi, H. M.; Elhasi, S.; Mahmud, A.; Gulamhusein, R.; Mahdipoor, P.; Lavasanifar, A. Encapsulation of hydrophobic drugs in polymeric micelles through co-solvent evaporation: The effect of solvent composition on micellar properties and drug loading. Int. J. Pharm. 2007, 329, 158−165. (6) Gref, R.; Minamitake, Y.; Peracchia, M.; Trubetskoy, V.; Torchilin, V.; Langer, R. Biodegradable long-circulating polymeric nanospheres. Science 1994, 263, 1600−1603. (7) Hawker, C. J.; Wooley, K. L.; Frechet, J. M. J. Unimolecular micelles and globular amphiphiles: dendritic macromolecules as novel recyclable solubilization agents. J. Chem. Soc., Perkin Trans. 1 1993, 0, 1287−1297. (8) Liu, M.; Kono, K.; Frechet, J. M. Water-soluble dendritic unimolecular micelles: their potential as drug delivery agents. J. Controlled Release 2000, 65, 121−131. (9) Liu, J.; Duong, H.; Whittaker, M. R.; Davis, T. P.; Boyer, C. Synthesis of functional core, star polymers via RAFT polymerization for drug delivery applications. Macromol. Rapid Commun. 2012, 33, 760−766. (10) Oerlemans, C.; Bult, W.; Bos, M.; Storm, G.; Nijsen, J. F.; Hennink, W. E. Polymeric micelles in anticancer therapy: targeting, imaging and triggered release. Pharm. Res. 2010, 27, 2569−2589. (11) Wang, Y.; Grayson, S. M. Approaches for the preparation of non-linear amphiphilic polymers and their applications to drug delivery. Adv. Drug Delivery Rev. 2012, 64, 852−865. (12) Ren, J. M.; McKenzie, T. G.; Fu, Q.; Wong, E. H. H.; Xu, J.; An, Z.; Shanmugam, S.; Davis, T. P.; Boyer, C.; Qiao, G. G. Star polymers. Chem. Rev. 2016, 116, 6743−6836. (13) Miller, R. D.; Yusoff, R. M.; Swope, W. C.; Rice, J. E.; Carr, A. C.; Parker, A. J.; Sly, J.; Appel, E. A.; Nguyen, T.; Piunova, V. Water soluble, biodegradable amphiphilic polymeric nanoparticles and the molecular environment of hydrophobic encapsulates: Consistency between simulation and experiment. Polymer 2015, 79, 255−261. K

DOI: 10.1021/acs.jpcb.7b10539 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B (35) Horn, H. W.; Swope, W. C.; Pitera, J. W.; Madura, J. D.; Dick, T. J.; Hura, G. L.; Head-Gordon, T. Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. J. Chem. Phys. 2004, 120, 9665−9678. (36) Jorgensen, W. L.; Ulmschneider, J. P.; Tirado-Rives, J. Free energies of hydration from a generalized born model and an all-atom force field. J. Phys. Chem. B 2004, 108, 16264−16270. (37) Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Giles, N. F. DIPPR Data Compilation of Pure Chemical Properties; Design Institute for Physical Properties, AIChE: New York, 2012. (38) Yaws, C. L. The Yaws Handbook of Thermodynamic Properties for Hydrocarbons and Chemicals; Gulf Publishing Company, 2007. (39) Brostow, W.; Dussault, J.-P.; Fox, B. L. Construction of Voronoi polyhedra. J. Comput. Phys. 1978, 29, 81−92. (40) Finney, J. L. A procedure for the construction of Voronoi polyhedra. J. Comput. Phys. 1979, 32, 137−143.

L

DOI: 10.1021/acs.jpcb.7b10539 J. Phys. Chem. B XXXX, XXX, XXX−XXX