Effect of Hydrophobic Core Topology and Composition on the

Article pubs.acs.org/JPCB

Effect of Hydrophobic Core Topology and Composition on the Structure and Kinetics of Star Polymers: A Molecular Dynamics Study Amber C. Carr,† Lisa E. Felberg,‡ Victoria A. Piunova,† Julia E. Rice,† Teresa Head-Gordon,‡,§,∥,⊥ and William C. Swope*,† †

IBM Almaden Research Center, IBM Research, 650 Harry Road, San Jose, California 95120, United States Department of Chemical and Biomolecular Engineering, §Department of Chemistry, and ∥Department of Bioengineering, University of California at Berkeley, Berkeley, California 94720, United States ⊥ Chemical Sciences Division, Lawrence Berkeley National Labs, Berkeley, California 94720, United States ‡

S Supporting Information *

ABSTRACT: We present a molecular dynamics study of the effect of core chemistry on star polymer structural and kinetic properties. This work serves to validate the choice of a model adamantane core used in previous simulations to represent larger star polymeric systems in an aqueous environment, as well as to explore how the choice of size and core chemistry using a dendrimer or nanogel core may affect these polymeric nanoparticle systems, particularly with respect to thermosensitivity and solvation properties that are relevant for applications in drug loading and delivery.

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INTRODUCTION The application of polymeric nanoparticles has become widespread in the field of nanomedicine, where their utility as targeted drug delivery vehicles extends from the cellular to the organ levels.1−7 The desire to develop a vehicle for drug delivery with the solubilizing ability of a liposomal formulation, but with greater stability leading to better control of drug release, has led to the development of star polymer architectures, in which polymeric arms of various compositions are covalently attached to a central core. Two examples of star polymer core architectures include dendrimers, which are repetitively branched molecules, and nanogel cores, which consist of a highly crosslinked material. Star polymers present an immediate benefit to their micellar predecessors, in that the covalent nature of the core ensures nanoparticle stability at any concentration, whereas micelles are only stable above their critical micelle concentration.8,9 In the past, synthetic limitations prevented the exploration and application of star polymers as micellar replacements, but recent advances in synthesis10−12 have led to increased interest in their properties and applications. Of the vast diversity of topologies within the arm components of the star polymer family, including block, mikto, and brush arms, this study focuses on a single type of arm composition, namely, the diblock copolymer arms, wherein each arm of the polymer consists of two regions: the hydrophobic region, bonded covalently to the central core, and an outer hydrophilic region that makes the molecule water-soluble. Star diblock copolymers © 2017 American Chemical Society

are of particular interest to the drug delivery community, as their varied block chemistry allows for the possibility of highly tuned drug release, functionalization, and targeting. The nature of the polymer core, however, is also of interest. Nanogel star polymers, in particular, might represent a unique chemical environment, as the topology and structural properties of the crosslinked core itself provide functionality that is absent from star molecules with smaller cores. For these effects to be fully understood and exploited, a rational methodology for the design and optimization of the nanoparticles, as well as their fundamental characterization, are necessary. Molecular dynamics (MD) simulations provide a methodology to systematically probe the structural, thermodynamic, and kinetic properties of these nanoparticles, and to provide insight into areas where their experimental characterization to date has been lacking. Previously, we undertook a series of MD simulations of star diblock copolymer systems in explicit solvent to better understand the effects of independently varying the composition of the hydrophobic inner block of the arms13 and hydrophilic terminal block.14 Both of these studies quantified structural and kinetic metrics that are relevant to in vivo drug delivery, such as the size and shape of the polymer, the time scales for structural reorganization, the depth and Received: January 26, 2017 Revised: March 8, 2017 Published: March 14, 2017 2902

DOI: 10.1021/acs.jpcb.7b00865 J. Phys. Chem. B 2017, 121, 2902−2918

Article

The Journal of Physical Chemistry B

Figure 1. Schematic of an adamantane-core star polymer with 16 diblock arms. The arms are all identical in length and composition but the hydrophobic blocks of the arms are shown in various colors. The hydrophilic blocks are shown in pink. Systems are built with extended initial structures, and are then partially collapsed in the gas phase before being placed in a simulation cell with solvent. The typical system size is approximately 100 Å.

essentially spherical core around the adamantane center. The star polymers previously simulated were also highly symmetric as constructed. It is possible that this tight collapse and structural symmetry may be an artifact of the use of the small, symmetric adamantane moiety as a model for the core. Indeed, experimentally synthesized small-core stars and dendrimers are believed to be highly symmetric by construction. However, nanogel cores are formed by crosslinking reactive groups through a variety of methods (atom transfer radical polymerization, click chemistry, ring-opening polymerization), and result in disordered, possibly amorphous gel centers. It has been shown that morphological properties as simple as symmetry may have an effect on bulk star polymer properties.18 For the application of star polymers within the field of biomedicine, a thorough understanding and control over these physical properties are required. In addition to an understanding of core shape and its effects, the size of the core may also be important. It has been found that pure dendritic polymers adopt three different conformations as a function of their size.18−21 Typically, dendrimer size is characterized by the number of layers, or generations, that the polymer grows. Generations 0−3 form a structure called flexible scaffolding, which does not effectively encapsulate drug molecules, but may form scaffolding for other components of the polymer and weak drug−dendrimer interactions, adopting a generally ellipsoidal shape. Generations 4−6 exhibit container properties, which are capable of incorporating guest molecules. Higher generations form a rigid molecule, which is impenetrable to small molecules. Depending on the drug chemistry and targeted drug−polymer interactions, the core design and its relative penetrability will be crucial for optimizing drug loading and release. This study builds on our previous work that explored the effect of varying the hydrophobic13 and hydrophilic14 regions within the diblock arms, by examination of the structural and kinetic properties of the star polymer with an arm chemistry composed of a PVL−PEG diblock when the core architecture changes between (1) the model adamantane core used in our previous studies, (2) an intermediate-size dendrimer, and (3) a nanogel star polymer modeled using structures obtained from our previous realistic crosslinking synthesis using a coarsegrained simulation.22 It is interesting to note that because it is based on structures obtained from modeling the synthetic process, this study provides the first plausible all-atom representation of the gelcore crosslinking topology and structure that might be obtained from an actual synthesis when dissolved in water. Additionally, this work serves to investigate the validity of the use of an adamantane-based star polymer as a model for the larger, all-atom crosslinked gelcore

frequency of water penetration into the hydrophobic core, and the surface area and volume that are available for drug loading. These earlier studies considered star systems consisting of 16 identical diblock arms bound to a small adamantane (C10H16) junction, which served simply as a model of a central core. Figure 1 is a schematic of such a diblock star polymer model, showing 16 arms tethered to a central adamantane core. The identical hydrophobic regions of the arms are shown in various colors, and the hydrophilic regions are shown in pink. The structures are built in an extended conformation and are subsequently collapsed slightly in vacuum to be placed inside a simulation cell with water, where they readily undergo further hydrophobic collapse. In the first of our studies,13 increasing the ester content of the hydrophobic block from polyethylene to polyvalerolactone (PVL) to polylactic acid was seen to increase the flexibility of the nanoparticle’s hydrophobic region, although these were all relatively rigid and glassy. The hydrophilic block used in this study was poly(ethylene glycol) (PEG), which was seen to be fully solvated and mobile in water. As a follow up to this work, a subsequent study14 examined the effect of varying the length, composition, and structure of the hydrophilic block of each diblock arm using PEG, polymethyloxazoline, and a polycarbonate-based polymer with a pendant hydrophilic group. The PEG-based system was found to be the most hydrophilic and the most thermosensitive of the three compositions tested and was also found to exhibit signs of phase separation out of the solvent with increasing temperature, suggesting the possibility of a lower critical solution temperature (LCST) transition. This characterization of the temperature-dependent behavior and the indication of potential LCST behavior could have important implications for drug delivery and the design of thermally responsive polymer vehicles. Beginning with the original theoretical model of star polymers proposed by Daoud and Cotton,15 many studies have posited that the size and composition of the central core may play an important role in determining the overall star structural and kinetic properties. Monomers along the star polymer arms experience density variations as a function of their distance from the core; close to the center, the polymer chains are constricted spatially, whereas at the far ends of the polymer arms, the density eventually approaches that of their linear equivalent. In comparison to analogous linear systems, star polymers are more dense and exhibit lower solution viscosity in dilute solutions.15 Differences in local density from linear analogs have also been shown to affect responsiveness to physiological factors such as temperature, ion concentration, and pH.16 In our previous studies,13,14,17 the hydrophobic domain was found to form a highly collapsed, glassy, impenetrable, and 2903


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Figure 2. CPK images of star polymer cores, generated by visual molecular dynamics (VMD). Carbon atoms are represented in teal, oxygens in red and hydrogens in white. The images are not to scale. (a) Adamantane core (hydrogen removed), (b) dendrimer core PEN-[DMPA-DMPA2]4, and (c) crosslinked lactone core of a representative gelcore system (gelcore1 in Table S1).

Figure 3. All-atom models of gelcore star polymers are produced by mapping an all-atom subunit structure (top left) onto sites 1, 2, and 3 of the sixsite model (bottom left) used in the coarse-grained simulation of nanogel star polymer synthesis to produce a fully atomistic version of a crosslinked lactone gelcore as is shown schematically (right). Red lines indicate bonds that are formed between linker molecules.

CH2−O−CO−CH2−CH2−), is connected via a methylene subunit linker (−CH2−) to the hydrophilic block of 24 PEG subunits terminated by a methyl group (PEG = −CH2−O− CH2−). This system is denoted as A[PVL16−PEG24]16 and will be referred to as the adamantane-based diblock star polymer. The second system under study is a dendrimer system, denoted as Dendrimer[PVL16−PEG24]16. This model comprises a central pentaerythritol (PENT) molecule (C5O4H12), which is composed of a central carbon bonded to four methylene oxide groups (Figure 2b). The dendrimer is grown from the PENT core with dimethylolpropionic acid (DMPA: C5H10O4). This molecule has a carboxylic acid component and two alcohol functional groups. To perform generation growth, the OH group is removed from the DMPA carboxylic acid, and that carboxcylic carbon is attached to the oxygen of the previous generation (or to an oxygen site of the PENT core). With each addition of each DMPA molecule, two bonding sites (the DMPA alcohol oxygens) are also added. Four DMPA molecules are attached to the PENT, creating eight attachment sites for the first generation. A second generation is then attached to create 16 attachment sites for the diblock polymer arms. The third and fourth systems under study are models of nanogel star polymers with realistic, crosslinked cores (Figure

system that is obtained through the coarse-grained simulation of its synthesis.

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METHODS Models. Four model systems were built for use in this study. The first was an adamantane-based star polymer similar to those previously studied.13,14 This model was never intended to represent an actual adamantane-based star polymer, as such a polymer would be hard to synthesize with the high arm density used here due to steric effects. However, it was hoped that this small core could serve as a scaffold to generate a structure with centrally tethered diblock arms that takes on the features of a larger and more realistic nanogel star polymer at some characteristic distance from the core. As has been previously described,13,14 this model comprises 16 diblock arms that are tethered to the adamantane (C10H16) core, which is composed of 10 carbon atoms in a diamond lattice structure (Figure 2a). Hydrogen atoms were removed from the adamantane molecule, and each of the 16 hydrogen-attachment sites were used as a connection site for the hydrophobic terminal of a diblock arm. These diblock arms consist of two different covalently bound block subunits. In this case, the hydrophobic block, which contains 16 monomeric units of δ-valerolactone (VL = −CH2− 2904


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The Journal of Physical Chemistry B 2c) formed from modeling22 the ring-opening polymerization reaction between an alcohol-functionalized polymeric arm and a bicyclic VL linker. Models for gelcore star polymer molecules are difficult to generate for a number of reasons. First, experimental structural characterization at atomic resolution is not possible due to the inability of these molecules to form crystal structures that can be probed by X-ray crystallography or NMR. Second, there is inherent variability in their molecular structure due to the stochastic nature of the synthetic process even in very carefully controlled syntheses, which affects the size and topology of the core, as well as the number and length of the arms. To address these issues and to probe the dependence of these structural characteristics on synthetic conditions, a study was performed in which gelcore star polymer synthesis was modeled with the use of coarse-grained representations of reactants.22 In this study of an arm-first synthetic strategy, arm molecules acted as initiators of a ringopening polymerization process with double-ring linker molecules modeled simply as six-site molecules. This reaction results in a highly crosslinked gelcore that grows outward from the arm. Different experimental conditions, such as reactant concentration, were varied in the study and each simulation produced an ensemble of hundreds of star polymer product molecules with a broad distribution of sizes (arm number and core size), compositions, and crosslinking topologies. The cores produced in this study generally had the appearance of blobs of highly crosslinked material connected by filaments of linker. In this work, structural models of the resulting gelcore star polymers with atomic-level detail were generated from the coarse-grained ones. This was done by mapping sites from three-dimensional (3D) all-atom models of fragments of the reactants onto the frameworks described by the coarse-grained components of the molecules. In fact, the coarse-grained models were originally designed to enable this mapping, and we present in this work the first fully atomistic view of nanogel star polymer cores that were obtained through simulations of their synthesis. Figure 3 shows a schematic representation of a region of crosslinked core (right), as well as part of its representation using two coarse-grained six-site linker molecules (lower left) with numbered corresponding sites. The earlier study of the synthetic process produced large numbers of these coarsegrained gelcore star polymers with a range of sizes, shapes, and crosslinked topologies. The figure also shows (upper left) a molecular fragment of 14 sites that is an all-atom representation of half of a linker. This structure of the all-atom form of the linker fragment is representative of that in the product (core), rather than in the reactant, where it is actually a ring. All-atom structural models were obtained by translating and rotating the all-atom molecular fragment to optimally align its three numbered sites to the corresponding ones of the coarsegrained version of the linkers. This was repeated for the other half of the coarse-grained sites, labeled 4, 5, and 6, and for all linkers in each coarse-grained gelcore star polymer. By replacing the coarse-grained versions of the arms that were used to initiate the synthetic process, all-atom diblock arms were attached to each of these crosslinked cores, and these arms were identical to those that were used with the adamantane-core and dendritic star polymers. The all-atom diblock arms of this study were overlaid on the coarse-grained arms by adjusting torsion angles. The resulting all-atom molecules were structurally strained and some structural optimization was required. From the broad distribution of

star polymer products produced by the earlier coarse-grained study, a small but diverse set of 20 molecules, each with 16 arms, was extracted for this study, and the resulting set of allatom versions of these gelcore star polymers is denoted as Gelcore[PVL16−PEG24]16. This small ensemble contains lactone cores ranging in size from 65 to 93 VL subunits (Table S1) and consisting of small, compact structures formed via crosslinking that are tethered to one another by polymeric filaments, as shown in Figure 2c. To investigate the effect of varying arm composition on the structure and dynamic behavior of the nanoparticle, a single nanogel star polymer was built as described above using one of the all-atom core structures of the Gelcore[PVL16−PEG24]16 ensemble described above, but with arms that comprised only a hydrophilic PEG block. The PEG arms were attached to a core that contained 81 VL linker subunits. This polymer is denoted gelcore[PEG24]16, or, sometimes simply as gelcorePEG. The number of monomeric units used for the PEG region was chosen such that the single-block polymeric arm would be identical in length to the hydrophilic component of the diblock PVL−PEG arms that were used in the other three systems. For each system under study, Table 1 gives their sizes in terms of the number of subunits in the core, the total number Table 1. Sizes of Components of the Adamantane, Sendrimer, GelcorePEG, and the Smallest (Gelcore7) and the Largest (Gelcore13) of the Gelcore Ensemble of Systems

system

number of subunits in core

number of atoms in core

number of atoms in nanoparticle

number of water molecules

total number of atoms

adamantane dendrimer gelcorePEG gelcore7 gelcore13

1 1 81 63 93

10 197 2284 1764 2604

6554 6933 5164 8276 9116

44 285 44 131 44 756 43 609 43 278

139 409 139 326 139 432 139 103 138 950

of atoms in the core, the total number of atoms in the nanoparticle, the total number of water molecules in which the nanoparticle was solvated, and the total number of atoms in the system. This table includes data for the members of the gelcore ensemble with the smallest and largest number of lactone core subunits in the gelcore. Table S1 contains the same data for the subset of 18 nanoparticles comprising the gelcore ensemble that was used for this work. Force Fields. The OPLS-AA force field23 was used in this work, with modifications as previously described.13,14 Briefly, parameters similar to those for cyclohexane, but with improvements to the alkane torsion angle energy, were used for the adamantane molecule and for the connection of the adamantane core to the hydrophobic chains. OPLS-AA parameters from the same reference were used to model the PVL core.24 For PEG, we used the modified OPLS-AA parameters that were described in detail in our previous work,13 which reparameterized the charges and backbone torsions for use in an aqueous environment. As in our previous studies, the TIP4P-Ew water model25 was used to represent the explicit solvent. Simulation Details. Initial configurations of the adamantane system were generated as previously described.13 The dendrimer and gelcore systems were built from the core outward with polymer arms completely extended. The crosslinked cores of the gelcore systems were also somewhat 2905


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capture thermal trends in behavior. In our experience, even well-optimized force fields may have difficulty capturing behavior at a single temperature, yet may still describe thermal trends accurately. Even at the highest temperatures simulated, the material remains well behaved and in the liquid state. Analysis. Structural analysis was performed with in-house code. As previously reported,14 the structures with adamantane and dendrimer cores were analyzed with a molecule-centered frame of reference, defined with respect to the central core, allowing the system to be characterized without artifacts due to molecular rotation. For the gelcore molecules, which do not possess a well-defined molecular center, a new method for identifying the center was developed. To define the orientation of the molecular-centered reference frame of the gelcore molecules, three approximately equidistant lactone repeat units defining a triangle in a relatively rigid crosslinked region of the core were identified for each system. The origin of the molecule-based reference frame was the geometric center of the crosslinker and hydrophobic component of the arms. To verify that the structural fluctuations of the reference frame were minimal, at each time at which coordinates were sampled for analysis (every 20 ps), a diagnostic was run which calculated the angle of rotation of the reference frame, as the previous coordinates were sampled. Generally, the angle of rotation between these sampling times was less than 5°, confirming the stability of the reference frame and its suitability for use in defining the molecular center. Using this molecular reference frame, various shape metrics could be studied. Radius of Gyration, Anisotropy. These metrics were calculated as previously described in detail in our previous studies.13,14 Briefly, using eigenvalues of the gyration tensor, the radius of gyration (RG), a metric of molecule size, and the anisotropy (A), a metric of object sphericity, were computed as follows, considering eigenvalues ordered from largest (λ1) to smallest (λ3)

extended, as the coarse-grained simulation used to generate these molecules was performed in an environment approximating that of a good solvent for the core material. The resulting extended-arm structures were then solvated by inserting them into a simulation cell of 46 656 water molecules (TIP4P-Ew) equilibrated at ambient conditions (300 K, 1 atm) with NpT simulations. The edge length of the cubic simulation cell was 111.945 Å. A number of water molecules closest to the polymers were removed from the simulation cell such that the mass of water removed was approximately equal to that of the gelcore star polymer. The resulting model was then equilibrated for a short time (0.5 ns) with NVT simulations, during which the extended arms and core were seen to collapse. For each system, it was verified that after this collapse, there was at least 15 Å between neighboring periodic images, to ensure that the simulation cells were sufficiently large such that there was no interaction between different images. Two systems from the 20molecule gelcore polymer ensemble were discarded because they did not meet this criterion, leaving 18. Production runs were then initiated with NVT simulations (350 K and 0.995 g/ cm**3). The resulting systems were also used as starting configurations for higher temperature (400 and 450 K) simulations. Molecular simulations were performed using the LAMMPS package26 dated May 2015. MD was performed on IBM BlueGene/Q machines and the NERSC supercomputers Hopper and Edison. Each system was simulated at temperatures of 350, 400, and 450 K. At 350 K, the NVT ensemble was used. At 400 and 450 K, the NpT ensemble was used with a pressure of 10 atm, and systems remained in the condensed phase at these temperatures. Thermal control was implemented with a Nosé−Hoover extended Lagrangian procedure with a fictitious thermostat variable. The dynamical integration scheme was velocityVerlet27 with a time step of 1 fs. All bond lengths involving hydrogen, as well as the HOH angle for the TIP4P-Ew model, were constrained using a SHAKE28 procedure to guarantee that the bond length constraints were satisfied to a tolerance of 10−5 Å. Lennard-Jones interactions and direct space electrostatic interactions were truncated at 12.0 Å, and a tail correction for the Lennard-Jones potential beyond this cutoff was included in energy/force and virial pressure calculations. Electrostatic interactions were evaluated with a particle−particle−particle mesh procedure29 with an accuracy parameter (10−5) that resulted in a 3D 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 for analysis every 20 ps of the simulation. Earlier simulation studies13,14 of similar molecules, and using similar force fields, have shown that at temperatures near 300 K equilibration and sampling of these systems is extremely difficult, so the lowest temperature selected here is 350 K. Use of a temperature range allows for the determination of thermal trends in star polymer properties. Although the solvent model that we used has been validated across a wide range of temperatures in the liquid regime of the phase diagram,25 the polymer−solvent and polymer−polymer interactions might not be comparably accurate. Therefore, the polymer behavior we see in simulations at some temperature might not be seen at the same temperature experimentally, but we believe that we can

RG =

λ12 + λ 22 + λ32

A sp = λ1 −

λ 2 + λ3 2

(1a)

(1b)

Correlation Functions. A normalized local orientation vector, u, was created for each repeat unit on each arm of the star polymer. For the PVL repeat unit, the vector was drawn between the alkoxy oxygen site and the first carbon site immediately opposite the nearest carbonyl group. For PEG, the vector was drawn between carbon sites, the first and third heavy atoms on the PEG monomer. The orientational time correlation function (OTCF) is a measure of how the orientation of a monomer is correlated with itself as a function of time. Given a normalized orientation vector for monomer i, at time t, ui(t), the time correlation is simply the time average of the dot product between ui(t) and the vector of monomer i at some time τ later, ui(t + τ). The OTCF for monomer i was averaged across all 16 polymer arms and over all starting times, t, to produce: ⟨ui(0)·ui(τ)⟩. The intermonomer correlation function (ICF) is a measure of how orientation decays along a polymer arm. Given a normalized orientation vector ui for monomer i, and the orientation vector uj for another monomer, denoted j, along the same polymer arm, their correlation is the dot product of the two vectors, averaged across all 16 polymer arms and over time. For this study, the ICFs were computed along the arm 2906


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The Journal of Physical Chemistry B referenced with respect to two origin points: the first monomer attached to the polymer core and the last monomer furthest from the polymer core: ⟨uj·ui⟩. Voronoi Analysis. A Voronoi construction is a method of dividing and quantifying space based only on atomic positions.30,31 The method of using Voronoi constructions to analyze star polymeric structures has been described in detail in the literature.13,14 Voronoi polyhedra are constructed by drawing line segments between each pair of points in space, creating planes normal to these line segments and at their midpoints, and extending the planes until they intersect. The cells constructed by this method completely encapsulate each point in its own polyhedron, delineating the region of space closer to that point than any other. This method produces quantitative information characterizing the volume of space each point occupies, and the surface area shared between neighboring points. In this manner, we have grouped together similar atoms into separate categories for this study: core atoms, PVL atoms, PEG atoms, and water atoms. By summing over all atoms in a category, we are able to quantify the volume that is occupied by that material. By summing over the surfaces shared between two different types of atoms, we are able to quantify the interfacial surface area shared between any two components of the system. To facilitate comparison between polymers that may have regions of vastly different total accessible surface area due to differing chemical composition (for example the adamantane core, which has 10 heavy atoms, and the gelcores, which have on the order of 2500), the surface area calculations are normalized by the amount of material in each component. This method has been previously reported.14 Briefly, extended structures of individual PVL and PEG arm blocks, the core (PENT and DMPA) region of the dendrimer, and the crosslinked lactone core of the gelcore and gelcorePEG systems were each separately solvated in water. Configurations were obtained from brief (100 ps) MD runs, during which the systems maintained their extended structures. Using these configurations, Voronoi calculations were used to compute the total surface area of each structure that is accessible to solvent. The surface area of the adamantane is so small relative to that of the other polymeric components that it may be considered to be negligible. This normalization allows us to represent the Voronoi interfacial area on a scale of 0−1, with a value of 0 indicating that the two regions share no interface and a value of 1 indicating that the entirety of the component’s surface area is in contact with the other. Total accessible surface areas for different star polymer components are given in Table S2. In addition to interfacial surface areas, the Voronoi analysis can be used to identify and characterize interior water molecules, those that are completely surrounded by polymer. For each step at which coordinates were saved and analyzed, the number of interior water molecules was quantified. The interior water might exist as isolated molecules, or it might exist in water clusters of multiple molecules that are completely separated from the bulk water and from any other interior water molecules. For a given interior water molecule or cluster, the type of material that surrounds it, as well as the surface area shared by these surrounding interfaces, is quantified. The Voronoi analysis and the subsequent analysis of internal water and interfacial areas, were performed using in-house code. In our prior work on adamantane systems,13,14 the depth of penetrating waters was calculated relative to the center of mass of the adamantane under the assumption that the hydrophobic

core of the polymer is nearly spherical. This assumption was supported by the reported anisotropy values. This approach also works for dendritic molecules, which have a well-defined center of mass. However, gelcore systems require different treatment, as unlike the adamantane and dendrimer systems, the gelcore systems do not have an easily definable or temporally stable center of geometry from which to reference water location. Moreover, even the adamantane and dendrimer systems, but especially the gelcores, have a rough surface with an extensive amount of channels and grooves. For these topologies, depth from bulk water into the polymer might be a more relevant reference for interior water location than distance from a molecular center. Therefore, in addition to calculating the distance of penetrating waters from the center of geometry of the hydrophobic material, we also used the Voronoi analysis to calculate their distance from the nearest bulk water, thereby giving an effective burial depth of the penetrating waters from the solvent-exposed surface of the polymer. The burial distance was measured from the oxygen atomic site on the interior water cluster to that of the nearest water molecule defined as being part of the bulk solvent. Having used both methods of analysis on the gelcore ensemble, we may examine whether these two methods gave a consistent picture of water penetration depth. To account for the convoluted, aspherical topology of the gelcore systems, as well as the differences in composition and packing of material among particles in the ensemble, we calculated a local density of water molecules inside each polymer. After determining the location of all water molecules within the polymer, we delineated concentric shells of the enclosing polymeric material that were 1 Å in thickness (Figure 4). We divided the number of water molecules in each shell by

Figure 4. Schematic showing partitioning schemes for locations of interior water (a) by creating concentric shells of 1 Å in thickness around the center of geometry of the material and (b) by dividing the material into regions of iso-depth.

the volume of water and polymeric material contained within that shell to report an effective local density of water that accounts for the volume of polymer in each shell. These local densities were averaged over the 18 gelcore polymer systems. Having identified the water molecules that penetrate the interior of the polymer, we may calculate a residence time correlation function, which is the conditional probability that a molecule that is interior at time t will also be interior at time kΔt later, as follows C(k) =

⟨x(i , j) x(i , j + k)⟩ ⟨x(i , j)2 ⟩

(2)

where x(i, j) is an indicator function that is equal to one if molecule i is interior to the polymer at time tj. Through fitting 2907


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Figure 5. (a) Starting structures for the simulation of each system at 400 K and (b) final structures at 400 K: adamantane, dendrimer, gelcorePEG, and a representative from the gelcore ensemble. The top panel shows only the core subunit of each system, in cyan. The second row shows the core subunit in cyan and the PVL block from the diblock arm in purple for each system, with the exception of gelcorePEG, which has only single-block PEG arms. The third row shows both the core subunit and the PVL in pink. The fourth row shows the hydrophobic material (core and PVL) in pink, as in the third panel, with the hydrophilic PEG rendered in gray. Solvent is not shown. Figure created using VMD.

Figure 6. Frames from the simulation of a representative gelcore system at 400 K. See the caption of Figure 5 for an explanation of the coloring scheme.

the correlation functions to an exponential, we obtain the average correlation time for water penetration events in each system. Dihedral Angle Conformers. As discussed in the Introduction, PEG conformations are known to be temperature sensitive, adopting specific backbone conformers to optimize hydrogen bonding with water. The dihedral conformers of heavy atoms along the PEG backbone were quantified to examine temperature sensitivity using code developed in-house. Hydrogen Bonds. Hydrogen bonds between water and PEG were computed using the Hydrogen Bonds Plugin in VMD,32

with default parameters as follows: donor−acceptor distance of 3.0 Å, and an angle cutoff of 20°, using the water molecules as hydrogen-bond donors and the PEG oxygens as hydrogenbond acceptors.

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RESULTS For the adamantane, dendrimer, and gelcore system with single-block PEG arms (referred to as gelcorePEG), the values reported for the analysis below are time averages over the last approximately 20 ns of the single 60 ns simulation that was run for each system. Table S3 gives the total simulation time for 2908


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Figure 7. Structural properties of star polymers. (a) Anisotropy and associated uncertainty estimates (±2 SD) for each star polymer system at each of the three temperatures. (b) Ratio of measured surface area to idealized sphere surface area and associated uncertainty estimates (±2 SD) as a function of temperature for the star polymer hydrophobic region. (c) Radius of gyration and associated uncertainty estimate (±2 SD) for each star polymer system at each of the three temperatures calculated for the hydrophobic core and total polymer.

produces the elongated and filamentous crosslinked core, as seen in the top panel of Figure 5 and in the first snapshot in Figure 6. At low temperature, hydrophobic collapse of the core occurs slowly as this glassy crosslinked network is less able to undergo structural rearrangement. As temperature increases, the crosslinked core undergoes rearrangement into a roughly spherical structure, and the anisotropy values for the gelcore systems are within statistical uncertainty of those for the simple adamantane and dendrimer cores. To quantify the roughness of the surface of each nanoparticle, the degree of surface convolution of the hydrophobic core of each type of particle was calculated using Voronoi analysis. Using the computed Voronoi volume of all of the sites of the hydrophobic material, consisting of the core and the PVL portion of the arms, the surface area of a sphere with that volume was computed. This theoretical surface area was then compared to the measured Voronoi hydrophobic interfacial surface area. For all of the nanoparticles, this ratio ranged from approximately 1.8 to 2.4, indicating a rough topological surface (Figure 7b). For the gelcorePEG system, the roughness at low temperature was much larger than that of the other systems. This calculation supports our observation that all of the gelcore systems had very rough and irregular crosslinked core topologies, but in the system with diblock arms, the PVL collapsed into the crevices of the core, creating a more spherical hydrophobic region and reducing surface defects, as shown in the second row of snapshots in Figure 6. These results indicate that the use of a diblock arm with a nanogel core will lead to shape and surface roughness metrics that, at least in water, are roughly indistinguishable from those of the adamantane and dendrimer systems. If a hydrophilic-only block is used with the nanogel core, the nanoparticle will have a slightly more elliptical shape (Figure 7a) with a slightly greater degree of surface convolution (Figure 7b). This effect can be seen when comparing the first and second rows of structures in Figures 5 and 6. Additionally, we note that the adamantane, dendrimer, and gelcore systems all have strikingly similar values for this convolution metric in spite of the fact that their cores have different topologies and sizes. Even within the ensemble of gelcore molecules, which comprises 18 systems with varying numbers of crosslinkers and varying core topologies, the variation in the convolution metric is extremely small, exhibiting low uncertainty. For all of these systems, the convolution metric approaches a value of approximately 2 at 450 K. The gelcorePEG system, however, exhibits a much

each system, as well as the amount of data that was used for analysis. For the gelcore system with diblock PVL−PEG arms (referred to as gelcore), 18 systems were run at each temperature, and the values reported below in each analysis of the gelcore polymer are averages over the 18 systems that were run at each temperature. Figure 5a shows the initial conformation of each system at 350 K, revealing the structural differences that were present in these systems before the simulations were initiated. Figure 5b depicts the last simulation snapshot of each system at 400 K and indicates that despite the differences in starting structures, the systems all collapse into similar, roughly spherical shapes after the simulations have equilibrated. Figure 6 shows the structural time evolution from the simulation of a representative gelcore system at 400 K as an example of the collapse in water of an initially extended system, produced from a coarse-grained simulation characteristic of a good solvent in which the synthesis was performed, into a roughly spherical shape by the end of the run. Structural Properties. The anisotropy for each system was calculated from the principal moments of the gyration tensor. Figure 7a shows the average anisotropy obtained using only the hydrophobic core (open symbols), as well as the entire star polymer (filled symbols). The adamantane, dendrimer, and diblock gelcore systems are all roughly spherical, having anisotropies that are ≤0.05. Although simulations were initiated with all of these systems in a partially extended state, mimicking their synthesis in a good solvent, subsequent exposure to water caused the hydrophobic core material to self-associate and exclude water, whereas the hydrophilic material remained solvated, as shown in Figure 5b. Anisotropy values for the adamantane and dendrimer systems are invariant of temperature, and the two systems have anisotropy values for both core and total that are nearly equal. The average anisotropy of the gelcore ensemble with diblock arms is seen to decrease slightly as the system becomes more spherical with increasing temperature. At high temperature, the average anisotropies of the core and total for the diblock gelcore nanoparticle are nearly identical to those of the adamantane and dendrimer systems. The gelcore system with PEG-only arms is seen to undergo a marked transition from oblong to spherical as temperature increases from 350 to 450 K. The higher anisotropies of the gelcore and gelcorePEG systems at low temperature are due to the irregular topologies that result from the simulation of their synthesis in good solvent, which 2909


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Figure 8. Time orientation autocorrelation functions for the (a) adamantane, (b) dendrimer, (c) gelcore with diblock arms, and (d) gelcore with PEG arms. Simulation temperature is 400 K. Curves from top to bottom in each panel represent the orientation correlation of repeat units from the closest to the furthest from the core.

Figure 9. Normalized Voronoi interfacial areas quantifying core material interactions with other system components as a function of temperature. (a) Core/PVL interfacial area, (b) core self-interactions, (c) core/PEG interfacial area, and (d) core/water interfacial area.

larger range in the convolution at each temperature, and the uncertainty is larger for this system than for that of any of the others. We hypothesize that the similarity in the convolution metric among the adamantane, dendrimer, and gelcore systems is because these systems have arms that are the same length and composition. The gelcorePEG system, with its PEG-only arms, exhibits significantly different values for the convolution, particularly at low temperature. The length and composition of the arms of the system, therefore, seem to be more important in determining the convolution of the hydrophobic surface than the size or topology of the core. To quantify the spatial extent of different components of the nanoparticle, the radius of gyration (RG), shown in Figure 7c, was calculated using only the hydrophobic core (open symbols) as well as the entire star polymer (filled symbols). The cores of the adamantane and dendrimer systems are seen to have very similar values of RG, which increase slightly with temperature. The crosslinked core of the gelcorePEG system is seen to collapse with temperature until it reaches a value of RG that is quite similar to that of the adamantane and dendrimer systems. The crosslinked core of the gelcore systems with diblock arms is significantly larger than that of any of the other systems, as it

consists of the larger crosslinked gelcore covered with PVL. The value of RG for this system decreases slightly with temperature as its components rearrange into a more favorable conformation. When PEG is included in the calculation of RG, the spatial extent of all of the systems is nearly identical, with that of the gelcore systems being slightly larger than that of the others due to the larger size of its core. Polymer Arm Kinetics. Time orientation autocorrelation functions were calculated for each system to quantify differences in their abilities to undergo structural reorganization (Figure 8). This metric shows the rate of loss in orientation memory of repeat units at different positions along the arms, as outlined in our previous work.13 The PVL monomer that is attached to the adamantane core, as well as the analogous monomer of the diblock gelcore, exhibits minimal decay within the 2 ns time frame; however, the dendrimer appears to be slightly more flexible than the other systems at distances close to the core. Moving down the PVL chain to monomers 8 and 16 of the PVL, the gelcore system exhibits less mobility than that of the adamantane or dendrimer systems, which is likely due to the larger size and rigidity of the crosslinked nanogel core and the propensity of the PVL block to intercalate into 2910


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Figure 10. Normalized Voronoi interfacial areas quantifying PVL material interactions with other system components as a function of temperature. (a) PVL/PEG interfacial area, (b) PVL/water interfacial area, (c) PVL/PVL interfacial area, and (d) PVL/core interfacial area.

Figure 11. Dihedral angle conformers as a function of temperature. (a) Adamantane, (b) dendrimer, (c) gelcore with diblock arms, and (d) gelcore with PEG arms.

grooves and irregularities within the core. Whereas the hydrophobic core of each of these systems appears to be glassy, the PEG subunits exhibit more rapid, decoupled decay. The rate of decay of PEG is similar for all of the systems under study. The ICFs were also examined to quantify the degree of structural alignment of the polymer arms (see Figure S1), and all showed similar behavior. Interfacial Interactions. Voronoi analysis was used to quantify the interfacial surface area between different components of the polymer. In Figure 9, we examine the Voronoi interfacial contact between the core component of each system and its hydrophobic (PVL block), hydrophilic (PEG block), and water components. The core region of the dendrimer system is defined as the third-generation structure comprising the central PENT molecule (C5O4H12) and its attached DMPA molecules, and the core region of the gelcore ensemble is defined as the crosslinked core, which has a different number of residues for each member of the ensemble. The adamantane region has not been included in this calculation because all of its interactions are with itself and the hydrophobic region, whereas the gelcore systems and the dendrimer have interactions between the core and the diblock components.

Here, we see that the dendrimer core region has a low degree of self-interaction and a high degree of interaction with hydrophobic PVL arms, whereas in contrast, the crosslinked cores of the gelcore systems with both diblock and PEG arms have high self-interactions. This observation agrees well with prior studies of the polyamidoamine dendrimer, in which it was found that low-generation dendrimers do not effectively encapsulate drug molecules but instead form scaffolding for other components of the polymer. In our study, we have found that our systems conform to this model as well. The small, three-generation dendrimer core has formed a scaffold, which has been approximately 60% coated by the hydrophobic PVL region, as indicated by the core/hydrophobic Voronoi interactions, and the lesser core self-interactions (Figure 9a,b). The gelcores are large, and their cores are so highly crosslinked that they form rigid, largely self-interacting surfaces, which is verified by relatively high values for core selfinteractions and low values for interactions with the remaining system components of PVL, PEG, and water. Finally, we address differences in core interactions between the gelcore system with PEG arms and those with the diblock arms, which arise from the absence of PVL in the former. Without the presence of a PVL region to coat it, the crosslinked core is more 2911


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Table 2. Average Number of Interior Water Molecules in Each System, Reported as Counts, Before and After Normalization by the Volume of Hydrophobic Materiala average number of water molecules star polymer adamantane dendrimer gelcorePEG gelcore a

350 K 0.9 1.1 1.3 3.6

± ± ± ±

0.06 0.04 0.03 0.9

average number density relative to bulk

400 K 2.7 2.6 1.8 4.1

± ± ± ±

0.06 0.07 0.06 0.2

450 K

350 K

400 K

450 K

± ± ± ±

0.0006 0.00078 0.0017 0.0018

0.0020 0.0018 0.0019 0.0024

0.0036 0.0037 0.0033 0.0041

5.0 5.6 3.1 7.4

0.09 0.09 0.06 0.1

The number density of water molecules in bulk water is 0.033 molecules/Å3.

0.1−0.4% that of pure water. Taken together, these results confirm previous observations, both computational and experimental,13,14 that the core and PVL regions are collapsed and dense, remaining quite impermeable to water and also, most likely, to drug material and other small molecules. Figure 12 shows the average number of interior water clusters in each nanoparticle system, and the number of water

exposed to water and PEG and thus has relatively higher hydrophilic interactions (Figure 9c,d). The interactions of the PVL block are generally independent of core composition (Figure 10). All PVL/PEG interactions remain low (∼10%) and suggest that, as previously found, the PVL region remains quite collapsed. Additionally, the PVL/ water interactions remain unaltered by the varying core. Examining the PVL/PVL interactions (Figure 10c), we see that as a function of increasing core content, hydrophobic selfinteractions decrease, and those interactions are replaced by interactions with the core (Figure 10d). From the hydrophilic− water interactions (Figure S2), we see that although the nanogel systems show a slight reduction in PEG−water interactions generally all of the PEG blocks of all of the polymers are highly solvated with at least 70% of the total PEG surface area in contact with water. PEG Dihedral Angles. To further examine the solubility of the PEG blocks, we quantified the distribution of each possible type of PEG dihedral conformer for each system, as shown in Figure 11. In our prior work on diblock star polymeric systems,13 we improved the agreement of the conformer populations of PEG with those obtained experimentally through the fitting of torsional parameters to quantum chemical results. Linear PEG is known to mix well with water at low temperatures due to an enthalpically favored backbone trans− gauche−trans (tgt) conformation, which is stabilized through the formation of strong water−ether hydrogen bonds.33 At a well-known LCST, entropy drives the release of the bound water, and increases in configurational entropy arise from a shift in populations toward other dihedral angle configurations to create a more disordered form of the PEG backbone. We have previously reported observing an entropy-driven dehydration for the PEG segment of the adamantane system simulated here,13,14 and we see that varying the core size and topology of the star polymers does not result in any differences in the temperature sensitivity of the PEG outer block, as the dihedral conformers of the polymer’s PEG region remain quite similar across all systems studied and the thermosensitivity of the PEG region is maintained across all systems. This result is further confirmed in Figure S3 by an approximately equal extent of decrease in the number of PEG−water hydrogen bonds in each system with increasing temperature. Interior Water Penetration. Table 2 reports the average number of water molecules in each system at each temperature under study and also reports those values normalized by the volume of hydrophobic material in each system. Once the water molecule counts are normalized, it is evident that at each temperature, the average number density of water is quite similar for all of the systems studied. The number density increases slightly with temperature for each system studied. As the number density of water molecules in liquid water is 0.033 molecules/Å3, these concentrations represent approximately

Figure 12. Histogram of the interior water statistics for all systems at 400 K. Water is considered to be internal to the polymer if it has no shared Voronoi interfacial planes with the bulk water. The large figure is a histogram of the presence of interior water clusters. The inset is a histogram of the number of water molecules that comprise an interior water cluster in each system at 400 K.

molecules comprising each of these clusters. Generally, the number of interior water clusters increases slightly as a function of increasing core size due to the increased spatial extent of the hydrophobic material, but this increase is not as significant as that seen previously,14 when the composition of the hydrophilic region was altered. The majority of internal water clusters in all systems consist of single molecules, with only approximately 10% of the internal water being part of a dimer or higher-order cluster. Figure 13 shows the local density of penetrating water measured from the center of geometry of the core and hydrophobic material of the polymer. Note that increasing distance on the x axis of the graphs indicates movement away from this center of geometry, toward the interface of the star polymer with the bulk solvent. The density of water at each distance is normalized against the number density of bulk water (0.033 molecules/Å3). 2912


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Figure 13. Average local density of interior water molecules measured from the center of geometry of the hydrophobic material of the (a) adamantane, (b) dendrimer, (c) gelcore ensemble nanoparticles, and (d) single-block gelcorePEG system.

Figure 14 shows the local density of penetrating water measured from the interface of the star polymer with the bulk solvent. In this figure, increasing distance on the x axis indicates movement away from the bulk solvent and inward toward the hydrophobic interior of the star polymer. These depth and height penetration profiles exhibit similar behavior, as we observe increasing water penetration with temperature, and a roughly equal distribution of internal water molecules over the interior of the hydrophobic core of the polymer. The gelcorePEG system appears to have the deepest penetration of water, which is likely due to a combination of the absence of the intercalating PVL and the small size of the hydrophobic core. At all temperatures, the water content increases slightly at a depth of 6 Å as one moves inward from the polymer−bulk solvent interface, and the three systems show approximately comparable water density at most depths within the polymer. The uncertainties are large at distances close to the center of the gelcore (within approximately 5 Å) because shells at these depths contain very little polymer volume (see Figure 4a) and few water molecules, and water penetration events are rare at those depths. Mass Density Profiles. Mass density curves (Figure 15) support these observations on water location, showing a fairly uniform penetration of water into the hydrophobic core of each

system. Using these curves, we are able to define a distance from the core of each system beyond which all of the systems lose structural artifacts due to core organization, and exhibit similar structural profiles. For distances greater than approximately 15 Å from the core, the profiles of all systems are quite similar in their location of penetrating water and the separation of PEG from the hydrophobic material. The dendrimer and gelcore systems exhibit a greater spatial extent of hydrophobic material because this component of the system is proportionally much larger than those of the adamantane and gelcorePEG systems. As noted above, water appears to penetrate more deeply into the core of gelcorePEG than that of the diblock gelcore system due to the absence of the PVL block in the gelcorePEG. Water Penetration Kinetics. To determine the time frame for water penetration events in each system, we calculated the correlation function for the presence of water internal to the polymer over the last 20 ns of the simulation. The correlation function gives the probability that a water molecule that is interior at some point in time is also interior at some time τ later. The correlation functions were averaged over the 18 gelcore systems at each temperature. Figure 16 shows the resulting curves, which exhibit distinct rates of decay at each temperature. Correlation times for internal water in the 350 K 2913


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Figure 14. Average local density of interior water molecules measured from the polymer−bulk solvent interface of the (a) adamantane, (b) dendrimer, (c) gelcore ensemble nanoparticles, and (d) single-block gelcorePEG system.

Figure 15. Mass density curves calculated at 400 K as a function of distance from the core in the (a) adamantane, (b) dendrimer, (c) gelcore, and (d) gelcorePEG systems, averaged with error bars.

decorrelation by 3 ns. The correlation functions were fit to a single exponential to calculate average correlation times, as given in Table 3. Omitting the gelcorePEG system, which does not have PVL interacting with its core, the water penetration

systems are longest, most likely due to the slow rearrangement of polymeric material and slow dynamics at that temperature. As temperature increases, the correlation functions decay more quickly, with all systems at 450 K showing an almost complete 2914


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Figure 16. Residence time correlation functions for water penetration events in the (a) adamantane, (b) dendrimer, (c) gelcore ensemble, and (d) gelcorePEG systems.

short correlation time, even at 350 K, likely reflects the ease of reorganization of the core, which in this system is unhindered by the intercalation of a PVL block into the core.

Table 3. Residence Correlation Times for Water Penetration Events in the Adamantane, Dendrimer, GelcorePEG, and Gelcore Ensemble Systems adamantane dendrimer gelcorePEG gelcore

350 K

400 K

450 K

200 400 150 730

100 100 130 330

60 ps 50 ps 80 ps 100 ps

ps ps ps ps

ps ps ps ps

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DISCUSSION

In this work, we varied the core topology and size of star polymeric nanoparticles to understand the effect of the core on factors influencing drug loading, such as the nanoparticle size and shape; the kinetics of structural reorganization; and the number, location, and kinetic properties of water penetration into the hydrophobic region of the nanoparticle. Through comparison of the features of nanoparticles with these different core topologies, we can assess the suitability of the simplistic adamantane star polymer for modeling the more complex gelcore and dendrimer systems. Additionally, we simulated two gelcore systems with identical core topologies and compositions, but with different arm compositions: in one case, the arms comprised a single block of PEG, and in the other, a diblock arm composed of PVL−PEG was used. For these gelcore systems with identical cores, our goal was to discover the potential effects on drug loading that could be brought about by the use of arms with different compositions. The starting structures for our simulations were slightly extended, mimicking their synthesis in a good solvent. As in our previous studies,13,14 we found that when placed in a poor

correlation time at each temperature roughly increases with the size and complexity of the nanoparticle core. This trend is related to that reported above for the orientation correlation functions, as the flexibility of the core likely determines the ability of water to enter it and subsequently escape from it. Increasing the temperature from 350 to 450 K, the correlation time for each system decreases. This decrease is by a factor of 3 for the adamantane system, a factor of 8 for the dendrimer, and a factor of 7 for the gelcore. This decrease likely reflects the increasing flexibility of these systems with temperature, and the greater degree of structural reorganization that is undergone by the systems with more complex and elongated cores. The decrease of the water penetration correlation time of the gelcorePEG system with temperature is less than that of adamantane, decreasing by a factor of approximately 2. The 2915


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for structural reorganization may have important implications for drug release, as the current experimental picture indicates that large-scale conformational rearrangements might trigger the release of a drug from the nanoparticle. By considering the reorientation time scales of different arm blocks attached to different types of cores, the release rate of the drug might be tuned and optimized. The optimization of materials is particularly important in light of the differences that we have observed in the interaction of the core with the hydrophobic block. Given that the dendrimer core interacts with the hydrophobic block significantly more than the cores of the other systems do, the choice of hydrophobic block should be particularly important if the dendrimer architecture is chosen for drug loading applications. Because it interacts with both the core and the drug, the hydrophobic block chosen should be optimized for compatibility with both of these components. Similarly, consideration should be made of the extent to which core− hydrophobic and hydrophobic−hydrophobic interactions can be tuned by the choice of material, as the strength of these interactions may affect the location and extent of drug loading. The thermosensitivity of structural and kinetic metrics that is indicated by our work is an important avenue for experimental exploration. The time scales for structural rearrangement are highly dependent upon temperature, and examining the ICFs along with other structural data reinforces our assertion that the structures obtained at 350 K may not be fully equilibrated. If the temperature of the particle is too low, individual structures will be glassy, and an ensemble of particles may exhibit a large deal of variation in size and shape, potentially leading to difficulties in determining drug dosage, as well as control of kinetics of drug release. At higher temperatures, the structures become roughly uniform in shape and size, and exhibit structural rearrangements on a faster time scale. If the temperature is too high, however, the LCST effects cause the PEG to dehydrate and adhere to the hydrophobic surface of the particle, which could potentially lead to the aggregation of nanoparticles, delayed degradation of the particle due to the inability of water to penetrate it, and a decrease in solubility of the particle. Taken together, the results outlined above indicate that the simplistic adamantane system serves as an appropriate model for a gelcore or dendrimer being simulated in an aqueous environment. In all systems, the hydrophobic effect causes a collapse of the hydrophobic core into a nearly spherical conformation that is surrounded by solvated PEG. The similarity in size of the collapsed nanoparticles indicates that the size of the model may be predicted and subsequently controlled by the choice of arm length and composition, as well as by the number of residues comprising the core. The penetration of these systems by water is also quite similar, as they all exhibit very little water content, but somewhat uniform penetration throughout the hydrophobic region. Penetrating waters are primarily monomers, and their residence times are short. Although the adamantane system presents an effective model for more complex star polymeric systems in an aqueous environment, we offer the following caveat. Drug loading is often performed in organic solvents that are good solvents for the hydrophobic core. For example, in a typical loading process, drug molecules are introduced into an organic solvent containing the polymeric nanoparticles, and water is then introduced into the system, causing the hydrophobic drug

solvent for hydrophobic material, such as water, the nanoparticles reorganized via hydrophobic collapse from an extended to a spherical shape, with a dense hydrophobic core surrounded by hydrophilic material and solvent. Considering structural metrics at temperatures of 400 K or greater, at which we may consider the systems to be equilibrated, we found that all of the diblock systems (adamantane, dendrimer, and gelcore) were roughly spherical to similar degrees. The single-block gelcorePEG system exhibited a degree of anisotropy that was slightly higher than that of the other systems, which is likely due to the lack of affinity of the PEG arm for the core material, in contrast to the diblock gelcore system, in which the PVL of the diblock packs into the convolutions of the hydrophobic surface. In considering the need for uniformity in size and shape of the hydrophobic core of a star polymer in potential biomedical applications, it appears that the packing of the hydrophobic block of a diblock arm affords an ensemble of particles that is more uniform and more spherical than that obtained using a single-block, hydrophilic arm. The degree of convolution of the gelcore system with single-block hydrophilic arms is slightly larger than that of the gelcore system with diblock arms, which may be important when considering the use of such a nanoparticle for drug loading. We quantified the degree of convolution in the hydrophobic core of these nanoparticles, expressed as the ratio of the surface area of the hydrophobic core relative to that of a sphere with the same volume, and found that the degree of convolution is similar for the three diblock systems, increasing for all systems as the temperature increases from 400 to 450 K. The singleblock system has a slightly higher degree of convolution than that of the other systems at these temperatures, thus indicating that changing the composition of the arms, and thereby their propensity to pack in the hydrophobic region, may cause a change in the degree of convolution of the core. The degree of convolution has important implications for design, particularly if we consider that drugs might sit at the interface between the hydrophobic material and the bulk water, as we have previously hypothesized.34 If the drug being used with the nanoparticle loads in the interior of the hydrophobic core, then the volume of the core should be maximized. If the drug is found to load at the interface between the hydrophobic core and the solvent, then the degree of convolution, that is, the surface area, of the core should be maximized. Further work is needed to determine conclusively where drugs load in gelcore systems with single-block and diblock arms to predict the effect of composition on loading, and we have initiated simulations that will examine this question in atomistic detail. Although the structural metrics of these nanoparticles are largely invariant to differences in core topology, we saw differences in their kinetic behavior, as steric hindrance determined by the topology of the core region affected the rate at which these systems approached their equilibrated conformations and sampled alternative conformations. The adamantane system is most constrained at the hydrophobic monomers that are close to the core, but regions along the polymer chain moving outward from the core quickly gain flexibility. The dendrimer exhibited somewhat slower dynamics, which is likely due to its larger and more topologically complex core. The hydrophobic region of the diblock gelcore exhibited slower dynamics than that of the other systems, due to the large size and crosslinking of the core and the tendency of the PVL to intercalate between the core convolutions. These time scales 2916


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hydrophobic region in all systems, as confirmed by local density profiles that examined water density from the center of geometry of the polymer outward and from the polymer−bulk water interface, as well as mass density profiles measured from the polymer center of geometry. The majority of the penetrating water molecules were monomers, and their residence times indicate that their penetration into the molecular core is short-lived. The similarity of these systems affirms the choice of an adamantane core for previous studies of star polymeric nanoparticles in explicit water and for future efforts considering the effect of variation in other regions of the star polymer in an aqueous environment. Additionally, the lactone nanogel core was found to be highly collapsed and impenetrable to water, which is important for the loading of hydrophobic drugs commonly thought to occur primarily in the hydrophobic domain of the nanoparticle. Due to this tight collapse of the core, we postulate that drug loading might be most efficient at the interface of the water and the hydrophobic material and are currently pursuing this line of inquiry for future studies. Finally, we encourage experimental investigations of real star polymeric nanoparticles to support, or challenge, some of these observations from these simulations. In particular, we feel calorimetry experiments might determine if a glass transition (for the core and/or for the hydrophobic component of the diblock arms) is observed at some temperature in molecules of the compositions we have studied. This could help confirm the relative solidity and dynamical behavior of the core we observe. Small-angle neutron-scattering experiments could help to determine the location within the star polymer of water and drug cargo and support our observations of the relative dryness of the core as well as the prediction that the site of drug loading is probably at or near the interface of water and the hydrophobic core. Gel permeation chromatography may help to determine if the size of the various regions of these nanoparticles changes in different solvents as one goes from a poor solvent (water) to a good solvent (toluene) for the hydrophobic component of the arms and/or the crosslinked core region.

molecules to associate with the hydrophobic region of the nanoparticle, which is then believed to collapse around the drug due to hydrophobic interactions. To make predictions about drug loading, modeling the loading process might therefore require use of the more structurally complex gelcore model for reliable results, as the core of the nanoparticle opens and is exposed to solvent during the loading process. Due to the unique filamentous nature of the crosslinked core,22 the hydrophobic core of the gelcore system can unravel and present a much greater effective surface area to solvent and drug molecules compared to that of the adamantane and dendrimer systems, which are tethered to a single point and are therefore more sterically hindered. We believe that although adamantane is a good model for the gelcore systems in water, the differences in star topology indicate that for simulations of the drug loading and delivery process, the use of the gelcore system will likely be required.

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CONCLUSIONS We have performed MD simulations to explore the effect of core structure and chemistry on star diblock copolymer structural and kinetic properties. We examined three different core chemistries: simple adamantane, open-scaffold dendrimer, and crosslinked nanogel core. We considered four systems: for the first three, the arm block chemistry was a polymer diblock of PVL and PEG, and the fourth system had arms that comprised only PEG. We found that the overall system properties are generally unaffected by the choice of core chemistry. Independently, the cores are quite different from one another in chemistry and structure, as the adamantane is a small 10-carbon moiety; the dendrimer is a large, symmetrically branched structure; and the crosslinked nanogel core is dense, globular, and asymmetric. But when bonded to the PVL hydrophobic domain and solvated in water, these initial structural differences were reconciled by the tight collapse of the PVL domain onto the core surface, resulting in spherical particles. The gelcorePEG system was slightly less spherical than the other systems, most notably at low temperatures, due to the lack of PVL material on its polymer arms. The roughness of the hydrophobic surface was also compared between the systems containing PVL and the gelcorePEG, and it was found that the addition of PVL slightly reduced the material’s surface roughness. The interaction between the core and PVL material is important for drug design applications, for improving the size uniformity of drug delivery nanoparticles, as well as for improving the loading of hydrophobic drugs. Solvation and thermosensitivity in the hydrophilic PEG domain were conserved across all systems, as confirmed by Voronoi surface area calculations in which PEG interfacial interactions were primarily with water; dihedral angle calculations, where the desolvation of the PEG arm was confirmed by a characteristic decrease of the hydrogen-bondpreferential tgt conformer; and hydrogen-bond calculations which showed a reduction in the number of PEG−water hydrogen bonds as a function of increasing temperature. These results indicate that the LCST behavior of the PEG arms is conserved across all systems, independent of the core chemistry. Due to the tight collapse of the core and PVL domains, each of the systems exhibited very low average water loading, at concentrations that were only 0.1−0.4% of the concentration of bulk water. Considering the location of the penetrating waters, they were found to be evenly distributed throughout the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b00865. Detailed descriptions of gelcore systems; interfacial surface areas used for normalization; simulation equilibration and run time details; intermonomer orientational correlation functions; hydrophilic interfacial surface area statistics; hydrogen bonding statistics for PEG blocks (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Teresa Head-Gordon: 0000-0003-0025-8987 William C. Swope: 0000-0002-5299-4145 Notes

The authors declare no competing financial interest. 2917


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ACKNOWLEDGMENTS This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. L.F. was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400. We would also like to acknowledge Jed Pitera for many helpful discussions in particular about the coarse-grained modeling and the production of all-atom structures from it.

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