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Proteinlike Copolymers as Encapsulating Agents for Small-Molecule Solutes Ravish Malik, Jan Genzer,* and Carol K. Hall* Department of Chemical & Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905, United States S Supporting Information *

ABSTRACT: We describe the utilization of proteinlike copolymers (PLCs) as encapsulating agents for small-molecule solutes. We perform Monte Carlo simulations on systems containing PLCs and model solute molecules in order to understand how PLCs assemble in solution and what system conditions promote solute encapsulation. Specifically, we explore how the chemical composition of the PLCs and the range and strength of molecular interactions between hydrophobic segments on the PLC and solute molecules affect the solute encapsulation efficiency. The composition profiles of the hydrophobic and hydrophilic segments, the solute, and implicit solvent (or voids) within the PLC globule are evaluated to gain a complete understanding of the behavior in the PLC/solute system. We find that a single-chain PLC encapsulates solute successfully by collapsing the macromolecule to a well-defined globular conformation when the hydrophobic/ solute interaction is at least as strong as the interaction strength among hydrophobic segments and the interaction among solute molecules is at most as strong as the hydrophobic/solute interaction strength. Our results can be used by experimentalists as a framework for optimizing unimolecular PLC solute encapsulation and can be extended potentially to applications such as “drug” delivery via PLCs.

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liposomes11 or multimolecular polymeric micelles.12 Dendrimer-based capsules have been proposed as alternatives to intermolecular polymeric micelle nanoparticles. Dendrimers are synthetic, highly branched, spherical, monodisperse macromolecules of nanometer dimensions prepared by an iterative13,14 synthetic methodology. The size of the core−shell architecture of dendrimers with hydrophobic internal cavities15 and modifiable surface functionality16 grows linearly in diameter as a function of the added generations and exponentially with respect to the surface groups. These characteristics, along with water solubility, make dendrimers attractive for biological and drug-delivery applications.17−20 Unlike intermolecular polymeric micelles, dendrimers do not dissociate because they are covalently bound. With the exception of dendrimers, the encapsulation takes place nearly exclusively inside a capsule comprising multiple amphiphilic molecules. We suggest that proteinlike copolymers (PLCs) could, in principle, be used to fabricate single-macromolecule functional nanodevices, and here we provide a theoretical framework that describes the encapsulation of solutes by PLCs as a potential new solute encapsulant, focusing in particular on the solutes’ effect on PLC globule formation and aggregation.

INTRODUCTION Encapsulation refers generally to entrapping objects inside a corona typically made of a soft material coating. The objects entrapped include solids, liquids, or gases. Examples include nanoparticles,1 solvents,2 organic molecules,3 dyes,4 proteins,5 cells,6 or DNA.7,8 The reasons for encapsulation are either to trap the cargo inside the core of the encapsulating vehicle permanently or to release it at a controlled rate from the functional capsule. The latter concept is employed routinely in drug delivery. The properties of the shell/membrane of the encapsulating capsule determine whether the object to be encapsulated is trapped permanently or is being released at a controlled rate. Typical examples of shell materials in encapsulating particles include polymers or lipids of various architectures and chemical compositions. Nanoparticles currently being used or investigated as encapsulating agents include (1) polymeric biodegradable nanoparticles, (2) liposomes, (3) intermolecular polymeric micelles, (4) dendrimers, and (5) unimolecular micelles. These nanoparticle-based devices can be roughly divided into two classes: (1) multimolecule carriers comprising nanoparticles created via the assembly of groups of molecules such as polymeric biodegradable nanoparticles and (2) intermolecular polymeric micelles and liposomes, and single-molecule carriers such as dendrimers and unimolecular micelles. Polymeric biodegradable nanoparticles9,10 can be fabricated in a wide range of sizes and from a variety of materials, including © 2015 American Chemical Society

Received: January 6, 2015 Revised: February 28, 2015 Published: March 3, 2015 3518

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interaction strength is at least as strong as the interaction strength among hydrophobic units and when the interaction strength among solute molecules is at most as strong as the hydrophobic−solute interaction strength. The optimal value of the interaction strength among solute molecules depends on the hydrophobic−solute interaction strength. A very strong interaction strength among solute molecules causes the solute to form solute clusters, around which the PLC chain wraps. The multichain PLC−solute system (unlike the single-chain PLC−solute system) succeeds in encapsulating solutes even when the hydrophobic/solute interaction is as strong as the interaction strength acting among hydrophobic units; however, lower values of the hydrophobic−solute/solute−solute interaction strengths favor uniform solute dispersion. In the next section, we describe the model and MC method. The subsequent section presents the simulation results for PLC nanoparticles as carriers for solubilizing solute molecules. The final section concludes with a short summary of the results and a discussion.

PLCs represent a new class of functional copolymers that exhibit large-scale compositional heterogeneities and long-range correlations along the comonomer sequences.21−23 The concept of PLCs was first introduced by Khokhlov and coworkers, who used computer simulations to demonstrate that random copolymers with tunable monomer sequences could be generated by adjusting the compactness of a parent homopolymer composed of component A and then converting exposed segments on the polymer globule surface into B segments by reacting them with reactive species present in the surrounding solution. Our recent computer simulations suggest that the sequence along the PLC plays a dominant role in its interfacial behavior.24−28 Our interest in using PLCs as solute encapsulants was sparked, in part, by their resemblance to dendrimer-based and unimolecular micelle nanodelivery systems. Like dendrimers and unimolecular micelles, PLCs could function as unimolecular solute containers in which the payload is physically entrapped. However, unlike dendrimers, whose stationary branched configuration serves as a sponge for solute molecules, PLCs could adsorb or release solute molecules as they undergo a coil-to-globule transition in response to an external stimulus. The coil-to-globule transition can be induced by varying the solvent quality or changing the pH and/or ionic strength for polyelectrolytes. The globule thus formed would adopt a structure comprising a dense hydrophobic core surrounded by a loose hydrophilic corona, making it highly soluble in aqueous media. Moreover, the globular state of PLCs would be more stable than random and random-block copolymers with the same chemical composition and “degree of blockiness”.29 Here we suggest exploiting the coil-to-globule transition of PLCs to encapsulate solutes. Although our main focus is on singlemacromolecule PLCs, we also consider the multimolecular PLCs to explore further opportunities for solute encapsulation in concentrated PLC systems. We use lattice Monte Carlo (MC) computer simulation based on the bond fluctuation model (BFM) to investigate the behavior of a model PLC−solvent system in the presence of model solute molecules with the objective of assessing the potential of PLCs as nanoscale solute encapsulants. MC simulations are performed on both single-chain and multichain 100-mer PLC systems to mimic low and high PLC concentrations, respectively. The single-chain PLC system consists of one 100-mer PLC and 400 solute molecules, and the multichain PLC system consists of 20 100-mer PLCs and 8000 solute molecules. The solvent is implicit for both the single-chain and multi-PLC-chain systems. We explore the impact of the interaction range, PLC chemical composition, interaction strength between hydrophobic segments on the PLC and the solute particles, and the solute−solute interaction on the behavior of the PLC−solute system and its solute encapsulation efficiency. We also present computer simulation snapshots and composition profiles in an effort to understand the solute encapsulation behavior of PLCs. Highlights of our results are as follows. For single-chain PLC−solute systems, the interaction range extending to the nearest 26 neighbors is desirable for encapsulation. For multichain PLC−solute systems, the interaction range extending to the nearest 18 or 26 neighbors is required for solute encapsulation. The solute encapsulation efficiency increases with increasing hydrophobic content of the PLC. A single PLC chain successfully encapsulates solute molecules by collapsing to a globular conformation when the hydrophobic−solute

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MODEL AND METHOD The PLCs are generated via a simulation-based instantaneous coloring procedure proposed by Khokhlov et al.21−23 A detailed description of our implementation of Khokhlov’s coloring procedure to generate 100-mer PLCs via discontinuous molecular dynamics (DMD) simulation can be found in our previous work.24 PLCs are modeled as self-avoiding walks on a three-dimensional (3D) cubic lattice. The single-chain PLC system consists of 400 solute (S) molecules and a single 100-mer PLC containing H (hydrophobic) and P (hydrophilic) monomers. In our work, we vary the chemical composition of the PLC by altering the mole fraction of H, xH, along the PLC; we design PLCs with xH = 0.3, 0.5, 0.7. For details about the PLC sequences with varying composition, refer to Figure S1 in the Supporting Information document. The multichain PLC system consists of 8000 solute molecules and 20 100-mer PLCs containing H and P monomers with xH = 0.5. The sequence of all of the 20 100mers PLCs is identical for a specific xH in the multichain PLC system. In both the single-chain and multichain PLC systems, the voids (V) or unoccupied lattice sites play the role of an implicit solvent. The values of the various interaction energies εij between segments of type i and j are listed in Table 1. Table 1. Matrix of Interaction Parametersa εij V H P S a

V 0

H 0.3 −1.0

P −0.3 0.0 0.0

S 0.3 εHS varied 0.0 εSS varied

V, void; H, hydrophobic; P, hydrophilic; and S, solute.

Interaction energies εVV, εVH, εVP, εHH, εVP, and εPP are held fixed; their values are closely related to those used in the work of Khokhlov et al. on generating PLCs.20,21 To account for the fact that the solute molecules are hydrophobic in an aqueous medium, we set εVS = 0.3 and choose only negative values for εSS. The εHS and εSS interaction energies are varied. To calculate the energy of the system, we need to decide on a range of interactions; this is usually reported in terms of the number of nearest neighbors to any site that experiences an interaction. 3519

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are performed for 2 million Monte Carlo steps (MCS). In each MCS, all beads in the system are moved once on average. To gauge the encapsulation effectiveness of different PLC− solute systems and understand the role of various parameters, the following measures are used: (1) visual inspection of simulation snapshots, (2) composition profiles of the hydrophobic (H), hydrophilic (P), solute (S), and implicit solvent or void (V) segments within the PLC globule that is formed, and (3) solute encapsulation efficiency, which is defined as the fraction of solutes encapsulated by the PLC. A visual analysis of simulation snapshots, although empirical, allows us to identify situations in which PLC encapsulates solute molecules. The PLCs, which are effective at encapsulating solutes, typically adopt a globular conformation with a dense solute-containing hydrophobic core and a surrounding hydrophilic corona. To evaluate the composition profiles and solute encapsulation efficiency, we carry out cluster analysis. A cluster is a collection of beads that are arranged spatially relatively close to each other when compared to the members of another cluster. The algorithm to identify all of the clusters and their member beads that are present in the single-chain PLC system is described as follows: (1) Let j denote a bead in the single-chain PLC system which takes on positive integer values from 1 through N, where N is the total system size. N = 500 for the single-chain PLC system as it has a 100-mer PLC and 400 solute molecules. (2) Let n denote a cluster in the single-chain PLC system which takes on positive integer values from 1 through N. Initially we assume that the nth cluster contains only the nth bead as its member, and hence all of the clusters initially are of size one. All of the clusters and their members are updated as described in the following steps. (3) For each j, we construct an initial neighbor list which contains its nearest 26 neighbors. Let k denote one of the possible 26 nearest neighbors of j such that k > j. We impose the restriction k > j to enhance the computational efficiency and also to avoid double counting the nearest neighbors of j. (4) We update the nth cluster by adding the nearest neighbors of the nth bead to the existing members of the nth cluster, and this update process is carried out for all of the N clusters. (5) Starting from the last cluster (n = 500), we proceed to the second cluster (n = 2) sequentially and carry out the following analysis: For the nth cluster, an attempt is made to find the first cluster m (m varies sequentially from n − 1 to 1) for which any of the members of nth cluster are also existing members of the mth cluster. If we are able to find m, then all of the members of the nth cluster are merged into the existing members of the mth cluster and the nth cluster is deleted because its members are now a part of the mth cluster. In this framework for the single-chain PLC system, the cluster which contains both the hydrophobic and solute beads as its members is of key interest as it implies that the solute has been encapsulated by the hydrophobic core of the PLC chain. For such a cluster, we quantify the number of H/P/S/V segments that are its members. To quantify the performance of PLCs as encapsulants for solutes, we evaluate the composition profiles for H, P, S, and V segments within the PLC globule that is formed during the coilto-globule transition in the presence of solute molecules at low PLC concentration. The composition profile of any component across a PLC-chain/solute cluster is determined by locating the cluster’s center of mass (COM), calculating the number of component sites in a spherical shell at evenly spaced distances from the COM, and then dividing by the total number of sites

Three different interaction ranges are considered, assuming one of the segments is located at (0,0,0): (1) short-ranged (the 6 vectors obtained by all of the sign inversions and permutations of the vector family P(1,0,0) between segments), (2) mediumranged (the 18 vectors obtained by all of the sign inversions and permutation of the two vector families P(1,0,0) and P(1,1,0), and (3) long-ranged (the 26 vectors obtained by all of the sign inversions and permutation of the vector families P(1,0,0), P(1,1,0), and P(1,1,1). Once one of the three aforementioned interaction ranges is chosen, it remains the same across all of the possible segment-type pairs. The MC simulations are based on the 3D BFM30 performed on a cubic lattice (L × L × L lattice sites) in the NVT ensemble. In the BFM, monomers, which represent either a Kuhn segment or a solute molecule, occupies eight sites on the lattice. Successive monomers along the chain are connected via a predetermined set of bond vectors. To avoid bond crossing and monomer overlap, the bond vectors are derived from all possible permutations and sign inversions of the following six vector families: P(2,0,0), P(2,1,0), P(2,1,1), P(2,2,1), P(3,0,0), and P(3,1,0). For example, all possible permutations and sign inversions of the vector family P(2,0,0) yield the following six distinct bond vectors: (2,0,0), (−2,0,0), (0,2,0), (0,−2,0), (0,0,2), and (0,0,−2). Repeating this process for all 6 vector families leads to a total of 108 bond vectors and 87 bond angles. Thus, the BFM offers the flexibility associated with an off-lattice model while maintaining the advantages associated with working on a lattice, such as integer arithmetic and parallelization.31 We chose the BFM over an off-lattice coarse-grained model with a realistic force field primarily because of its simplicity and computational efficiency. Khokhlov et al.21−23,29 previously used it to study the singlechain PLC thermodynamic behavior. We cannot state how our lattice model compares to an off-lattice model for our ternary system. We acknowledge, however, that compressibility and solvent excluded-volume effects may lead to differences in the self-assembly behavior of lattice and off-lattice models, especially in the strongly aggregating regime.32 In addition, the discretized dynamics in a lattice model could also lead to slow relaxation within the dense globule.33 The MC algorithm is executed in the following manner. First, a segment is chosen at random and translated by one lattice move in a direction chosen randomly out of the 6 possible directions within the lattice. Next, a check is made to verify that the resulting move does not violate the excluded volume and bond constraints set forth by the BFM. If it does, the move is rejected and the unit is restored to its original position. If all of the BFM constraints are satisfied, then the Metropolis sampling rule is applied, i.e., the move is accepted with a probability equal to min(1,exp(−ΔE/(kBT))), where ΔE is the energy change due to the move, kB is the Boltzmann constant, and T is the temperature. In a typical simulation, we set the box length at L = 50 for both single-chain and multi-PLC chain systems. The volume fraction, ϕ = N/L3, for the single PLC chain system is set to ϕ = 0.004, and for the multi-PLC chain system it is set to ϕ = 0.08, where N is the total number of segments including solute molecules in the simulation box. Periodic boundary conditions are imposed in all three directions (x, y, and z) to overcome the limitation of finite system size. The simulations commence in a random configuration at the desired volume fraction. The appropriate interactions are switched on, and MC simulations 3520

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PLCs and solute molecules are randomly mixed. Figures 1b through 1d display the PLC−solute system at the end of the simulation with various interaction ranges: (1) short-ranged (6 nearest neighbors, Figure 1b), (2) medium-ranged (18 nearest neighbors, Figure 1c), and (3) long-ranged (26 nearest neighbors, Figure 1d). Comparisons of Figures 1b through 1d provides insight into how the interaction range affects the ability of the PLCs to undergo a coil-to-globule transition while encapsulating solutes. The short-ranged interaction (cf. Figure 1b) does not lead to the collapse of the PLC chain; as a result, no solute encapsulation takes place. Although the mediumranged interaction (cf. Figure 1c) collapses the PLC chain, the solute encapsulation efficiency, defined as the fraction of solute molecules encapsulated by the PLC, is poor at ∼0.017. The long-ranged interaction (cf. Figure 1d) results in the strong collapse of the PLC chain and efficient solute encapsulation. The single-chain PLC system shown in Figure 1d can be considered to be an ideal solute encapsulant as it succeeds in encapsulating a relatively large amount of solute, with ∼0.069 solute encapsulation efficiency in its hydrophobic core. Figure 2 displays the composition profiles of H, P, S, and V for a single-chain PLC−solute system with xH = 0.5, interaction

within the shell. The composition profiles are averaged over time after reaching steady state. Ideally the system’s free energy should be calculated to ensure that it has attained true thermodynamic equilibrium and is not stuck in a metastable state. However, calculating the system’s entropy and hence the free energy is computationally expensive and nontrivial. We do, however, monitor the system’s potential energy and use it as a proxy for the system’s free energy to detect a steady state. For both the single-chain and multichain systems, the potential energy declines rapidly at the start of the MC simulation and later stabilizes at around 1 million MCS, and we let the simulations run for another 1 million MCS. Starting at 1.9 million MCS, the composition profiles are calculated once every 500 MCS and later are time-averaged over the 200 samples once the simulation runs to completion. The composition profiles and solute encapsulation efficiencies for a single-chain PLC system are also averaged over five independent MC runs starting from uncorrelated random initial configurations and over three PLC sequences for a given initial configuration. Thus, the two aforementioned calculated properties are effectively averaged over 15 independent MC runs. The errors, which represent the sample standard deviations of the properties calculated, are within 3%. We chose not to represent the errors bars for clarity.

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RESULTS AND DISCUSSION We first report the results on the PLC−solute systems involving a single 100-mer PLC chain. Figure 1 depicts simulation snapshots for a single-chain PLC−solute system with xH = 0.5, εHS = −1, and εSS = −1. Figure 1a shows a snapshot of a typical initial configuration in which both the

Figure 2. Composition profiles of the hydrophobic (H), hydrophilic (P), solute (S), and implicit solvent or void (V) segments for the PLC−solute system (with xH = 0.5) with (a) medium-ranged and (b) long-ranged interactions.

strengths εHS = −1 and εSS = −1, and (a) medium- and (b) long-ranged interaction potentials. The volume fraction of solute segments within the PLC−solute globule is higher for the long-ranged interaction than for the medium-ranged interaction. The volume fraction of the void (or implicit solvent) segments within the PLC−solute globule is higher for the medium-ranged interaction than for the long-ranged

Figure 1. Simulation snapshots of the single 100-mer PLC chain with xH = 0.5 in the presence of solute (a) initially and at the end of the simulation with (b) short-ranged, (c) medium-ranged, and (d) longranged interactions. The hydrophobic (H), hydrophilic (P), and solute (S) segments are depicted in blue, red, and green, respectively. 3521

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efficiency (∼0.038 for xH = 0.3, ∼0.069 for xH = 0.5, and ∼0.1 for xH = 0.7) increases with increasing hydrophobic content in the PLC. Because the single-chain 100-mer PLC solute system with long-ranged interaction and PLC composition of xH = 0.5 exhibits efficient solute encapsulation, we now examine its behavior in more depth as a function of the interaction strength ratios εHS/εHH and εSS/εHS. Figure 4 shows examples of

interaction. These trends indicate a strong collapse of the PLC chain to a globule with more efficient solute encapsulation for long-ranged interaction than for medium-ranged interaction. The composition profile shown in Figure 2b (i.e., longranged interaction) corresponds to the case when the PLC chain (simulation snapshot shown in Figure 1d) undergoes a coil-to-globule transition while successfully encapsulating solutes in its hydrophobic core. The volume fractions for the H and S segments are very high near the center of the PLC− solute aggregate and tail off at distances away from the aggregate’s center. The volume fraction of P at distances near the aggregate’s center is negligible and it increases, goes through a maximum, and eventually decays with increasing distance from the aggregate’s center. The volume fraction of V at distances near the aggregate’s center is negligible and increases monotonically with increasing distance from the aggregate’s center and eventually becomes 1 at distances far away from the PLC−solute aggregate. These behaviors are what one would expect. Figure 3 presents simulation snapshots for a single-chain 100-mer PLC−solute system with εHS = −1, εSS = −1, and

Figure 4. Simulation snapshots for the single-chain 100-mer PLC solute (S, green) system (with xH = 0.5) for various values of εHS/εHH and εSS/εHS at the end of the simulation. The hydrophobic (H) and hydrophilic (P) segments are depicted in blue and red, respectively.

simulation snapshots, Figure 5 depicts the solute encapsulation efficiency, and Figure 6 displays the H, P, S, and V composition profiles for this single-chain 100-mer PLC solute system at

Figure 3. Simulation snapshots of the single 100-mer PLC chain solute system at the end of the simulation at various PLC compositions and the corresponding composition profiles of the hydrophobic (H, blue), hydrophilic (P, red), solute (S, green), and implicit solvent or void (V, black) segments at (a) xH = 0.3, (b) xH = 0.5, and (c) xH = 0.7.

long-ranged interaction at (a) xH = 0.3, (b) xH = 0.5, and (c) xH = 0.7. The corresponding composition profiles of H, P, S, and V are also shown. The volume fractions of the H and S segments within the PLC−solute globule increase, while the volume fractions of P and V segments decrease, with increasing hydrophobic content of the PLC. The solute encapsulation

Figure 5. Solute encapsulation efficiency for the single-chain 100-mer PLC solute system with composition xH = 0.5 and long-ranged interaction for various values of εHS/εHH and εSS/εHS. 3522

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Figure 6. Composition profiles of the hydrophobic (H, blue), hydrophilic (P, red), solute (S, green), and implicit solvent or void (V, black) segments for the PLC−solute system with xH = 0.5 and varying interaction strength ratios εHS/εHH and εSS/εHS.

selected values of the interaction strength ratios εHS/εHH and εSS/εHS. The simulation snapshots for εHS/εHH = 0.25, εSS/εHS = 1, εHS/εHH = 0.5, εSS/εHS = 1 shown in Figure 4 indicate that the PLC chain adopts a globular conformation when εHS/εHH < 1 but fails to encapsulate the solute efficiently regardless of the value of εSS/εHS. We find this to be the case generally. The solute encapsulation efficiency is ∼0.005 and ∼0.01 for εHS/εHH = 0.25 and εHS/εHH = 0.5, respectively, irrespective of the value of εSS/εHS. Figure 5 suggests that to achieve high solute encapsulation efficiency the condition εHS/εHH ≥ 1 must be satisfied. Moreover, for a given εHS/εHH the solute encapsulation efficiency generally increases with increasing εSS/εHS except when εHS/εHH = 1.25, εSS/εHS = 2; εHS/εHH = 1.5, εSS/εHS = 2; and εHS/εHH = 2, εSS/εHS ≥ 1.5. In these cases, the interaction among solute molecules εSS is so strong that it causes the solute to form multiple distinct pure solute aggregates that the PLC fails to encapsulate efficiently, as shown in the simulation snapshots in Figure 4. Although the condition εHS/εHH ≥ 1 is necessary to achieve a high solute encapsulation efficiency, focusing just on the encapsulation efficiency is insufficient. Specifically, to obtain

complete information about the system behavior, one also needs to explore the composition profiles and simulation snapshots to gain a deeper understanding of the performance of a single-chain PLC−solute system. When εHS/εHH ≥ 1, εSS/εHS plays an important role in determining the behavior of the PLC−solute system. Figures 6a through 6b show the composition profiles for the PLC−solute system with εHS/ εHH = 1 and 0 ≤ εSS/εHS ≤ 2. When εSS/εHS ≤ 1, the volume fraction of H is dominant compared to the volume fractions of the other components within the PLC−solute aggregate. When εSS/εHS>1, the volume fraction of S is dominant compared to the volume fractions of the other components within the PLC− solute aggregate. The condition εSS/εHS>1 implies that the εSS interaction among the solute molecules is stronger than the hydrophobic/solute interaction (εHS), which causes the solute to form a large aggregate around which the PLC chain wraps instead of collapsing to a well-defined globular conformation. These trends are also verifiable in the simulation snapshots in Figure 4. Thus, when εHS/εHH = 1, εSS/εHS = 1 acts as a threshold above which the solute volume fraction becomes dominant within the PLC−solute aggregate. Similar behavior is observed for εHS/εHH = 1.25 (with threshold εSS/εHS = 0.5), 3523

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Figure 7. Simulation snapshots of the multichain 100-mer PLC solute (S) system (with xH = 0.5) at the end of the simulation with the interaction being (a) short-, (b) medium-, or (c) long-ranged.

Figure 8. Simulation snapshots of the multichain 100-mer PLCs solute (S) system (with xH = 0.5) at the end of the simulation with interaction strengths of (a) εHS = εSS = −0.5, (b) εHS = εSS = −0.75, and (c) εHS = εSS = −1.0.

εHS/εHH = 1.5 (with threshold εSS/εHS = 0.5), and εHS/εHH = 2 (with threshold εSS/εHS = 0). To understand the trends better, refer to Figures 4 and 6, which depict the simulation snapshots and the composition profiles, respectively. It is also important to note that the threshold value of εSS/εHS above which the volume fraction of S becomes dominant within the PLC−solute aggregate decreases with increasing εHS/εHH. In summary, a single PLC chain encapsulates solute molecules successfully by collapsing to a well-defined globular conformation when εHS/ εHS ≥ 1 and εSS/εHS ≤ 1, with the threshold value given by εSS/ εHS depending upon the value of εHS/εHH. We now report the results for PLC−solute systems involving multi-100-mer PLC chains in an effort to learn what would happen at higher PLC concentrations. We point out that our results on the multi-chain PLC−solute system are not exhaustive, and more work on this system will be a part of our future research. In the multichain system we have three possibilities: (1) individual chains undergo a coil-to-globule transition while encapsulating solutes, (2) many PLCs aggregate to form large clusters with solutes encapsulated, or (3) both phenomena take place simultaneously. This makes the analysis of the composition profiles more complex than that of the single-chain case. Figure 7 displays snapshots at the end of the simulation for the multi-chain 100-mer PLC−solute system with xH = 0.5 and interaction strengths εHS = −1 and εSS = −1 with various interaction ranges: (a) short, (b) medium, and (c) long. Comparisons of Figures 7a through 7c offer insights into how the interaction range affects the ability of the system to encapsulate solutes. The short-ranged interaction (cf. Figure 7a) does not collapse the PLCs to globular conformations; no solute encapsulation takes place. In contrast, both the medium (cf. Figure 7b) and long-ranged (cf. Figure 7c) interactions cause the PLCs to aggregate and form large clusters which encapsulate solutes. Hence, unlike the single-chain PLC system where long-ranged interactions are necessary, satisfactory solute encapsulation in the multichain PLC system requires either

medium- or long-range interactions to be in place. Although we do not have a concrete reason for the difference between the desirable interaction range of the multi- and single-chain PLC systems, the difference in the overall system density between the two systems could partially explain the differences observed in the desirable interaction range of the two systems. Figure 8 displays simulation snapshots for a multichain 100mer PLC−solute system with xH = 0.5, a medium-ranged interaction, and εSS/εHS = 1 at the end of the simulation for interaction strength ratios of (a) εHS/εHH = 0.5, (b) εHS/εHH = 0.75, and (c) εHS/εHH = 1.0. In Figure 8a, the solutes are dispersed uniformly, unlike in the other two systems which possess stronger hydrophobic/solute interactions. The multichain PLC−solute system (unlike the single-chain PLC−solute system) succeeds in encapsulating solutes even when the condition εHS/εHH ≤ 1 holds; however, lower values of the interaction strengths εHS and εSS favor uniform solute dispersion. Because the PLC chain length was fixed at 100-mer for all of our simulations, we cannot currently address the effect of the variation in chain length on our results for the single-chain PLC system; this will be a part of our future research. With increasing PLC chain length, we expect the PLC to encapsulate more solute and undergo the coil-to-globule transition at higher temperatures with faster kinetics based on the previous work on PLCs by Khokhlov et al.21−23 and regular multiblock copolymers by Wang et al.34

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CONCLUSIONS

We presented the results of Monte Carlo (MC) simulations aimed at supporting the development of proteinlike copolymers comprising hydrophobic (H) and hydrophilic (P) units as soft nanoparticles for the encapsulation of solute (S) molecules. We considered both the single-chain and multichain PLC systems to mimic low and high PLC concentrations, respectively. Unoccupied lattice sites (or voids, V) played the role of an implicit solvent for both the single-chain and multichain PLC 3524

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The results of our current work cannot be applied directly to applications such as drug delivery via PLCs without incorporating significant changes in our model. Specifically, the solute molecules must be larger in size than a single solvent unit and more realistic force fields than what we currently use should be employed in order to accurately model real drug molecules. The solute (or drug) release process and solute release rate need to be studied in detail to understand completely the potential of PLCs as drug-delivery agents.

systems. We explored the impact of the interaction range, PLC chemical composition, interaction strength between hydrophobic segments on the PLC and solute particles, and interactions among solute molecules on the behavior of the PLC−solute system and solute encapsulation efficiency. We performed visual inspection of the simulation snapshots to determine if the PLCs succeeded at encapsulating solutes. To gain a quantitative understanding of the PLC−solute systems, we carried out cluster analyses to evaluate the composition profiles of the H, P, S, and V segments within the PLC−solute aggregate. For single-chain PLC−solute systems, the interaction range extending to the 26 nearest neighbors is desirable for encapsulation whereas for multichain PLC−solute systems the interaction ranges extending to 18 or to 26 nearest neighbors is desirable for solute encapsulation. The solute encapsulation efficiency increases with increasing hydrophobic content of the PLC. A single PLC chain successfully encapsulates solute by collapsing to a globular conformation when the hydrophobic/solute interaction strength is at least as strong as the interaction among hydrophobic units and when the interaction strength acting among solute molecules is at most as strong as the hydrophobic/solute interaction strength. The optimal value of the interaction strength among solute molecules depends on the hydrophobic/solute interaction strength. Very strong interaction among solute units causes the solute to form solute clusters, around which the PLC chain wraps. Unlike the single-chain PLC−solute system, the multichain PLC−solute arrangement succeeds in encapsulating solutes even when the hydrophobic/solute interaction strength is not as strong as the interaction strength among hydrophobic units. However, lower values of the hydrophobic/solute and solute/solute interaction strengths favor uniform solute dispersion. We have seen that PLCs form unimolecular micelles by adopting a hydrophobic-core/hydrophilic-shell architecture in an aqueous medium while successfully encapsulating hydrophobic small-solute molecules that exhibit an affinity for the hydrophobic core of the PLC. PLCs could also prove useful in encapsulating solutes at low polymer concentrations where polymeric-micelle-based solute encapsulants might become unstable because they are below the critical micelle concentration. In a nutshell, PLCs possess potential as nanoparticles for solute encapsulation. Alternate routes to solute encapsulation via PLCs would be the subject of future publications. It is challenging to validate our work due to the lack of prior experimental and theoretical research on PLCs as nanoscale solute encapsulants. In this article, we have mainly discussed the solute encapsulation process by the PLCs. The release of solutes could be accomplished by altering the pH or solubility of the solution or changing the temperature, which would cause the PLC globules to undergo either inversion or expansion to a coil-like conformation. Alternate routes to solute encapsulation via PLCs exist, which we have not explored in this article. As an example, complementary PLC polyelectrolyte sequences can be used to form ionic complexes with the solute molecules. We can also utilize the coil-to-globule transition of a homopolymer below the theta temperature (poor-solvent conditions) to encapsulate solutes first and then use the coloring process suggested by Khokhlov and coworkers to create modified PLCs with enhanced solubility in solution.

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ASSOCIATED CONTENT

S Supporting Information *

PLS sequences used in the simulations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

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

(R.M.) Advanced Analytics Modeling (GBS), Air Products and Chemicals, Inc., Allentown, Pennsylvania 18195-1501, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Office of Basic Sciences, Chemical Science Division of the U.S. Department of Energy under grant DE-FG05-91ER14181 awarded to C.K.H. We thank the National Science Foundation for financial support through grants nos. DMR-0353102 (to J.G.) and OISE0730243 (to J.G.) and CBET 123603 (to C. H.) and DMR 1206943 (to C. H.). This work was also supported by the NSF’s Research Triangle MRSEC (DMR-1121107). We thank Professor Andrew Ng for his “Coursera” course on machine learning, which provided deep insight into nonhierarchical clustering algorithms and helped us develop our own algorithm for cluster analysis. We thank Professor Erik Santiso for his help with molecular visualization. Finally, we thank David Latshaw for his outstanding help with the computer laboratory system administration and other system administrators Dave Rutkowski, Emily Curtis, and Lauren Ridge.

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DOI: 10.1021/acs.langmuir.5b00032 Langmuir 2015, 31, 3518−3526