Molecular Dynamics Simulations of Linear and Cyclic Amphiphilic

Jan 6, 2014 - For these studies, we use all atom molecular dynamics computer simulations to study the stable conformations of Laurent and Grayson's cy...
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Molecular Dynamics Simulations of Linear and Cyclic Amphiphilic Polymers in Aqueous and Organic Environments Lixin Liu,† Sreeja Parameswaran,‡ Arjun Sharma,‡ Scott M. Grayson,§ Henry S. Ashbaugh,† and Steven W. Rick*,‡ †

Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148, United States § Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States ‡

ABSTRACT: We have studied the conformational changes of two novel amphiphilic homopolymers in water and toluene relevant to delivery applications using molecular dynamics simulations supplemented with enhanced sampling techniques. The individual homopolymer repeating units are amphiphilic with a hydrophobic dodecyl chain and a hydrophilic tetra(ethylene glycol) chain attached via ether linkages to each repeating unit of the polymer backbone. Two polymer topologies were examined: one cyclic and one an exact linear analog. Here we show that these polymers exhibit highly dynamic conformations with the side arm orientations driven by the solvent polarity. In water these polymers exhibit a compact conformation with the hydrophobic arms retracted toward the backbone core, whereas in toluene the hydrophobic arms extended into the solvent. Different from the hydrophobic arms, the hydrophilic ethylene glycol chain orientations and backbone conformations are largely unperturbed by the solvent polarity. Probing the polymer microenvironment in different solvents to examine solute uptake supports the hypothesis that these polymers can selectively encapsulate/release guest molecules depending on the solvent polarity, highlighting the potential of these polymers as drug delivery vehicles.

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INTRODUCTION Polymer-based micelles have attracted significant interest as potential drug delivery vehicles.1 More common surfactant micelles are amphiphilic structures that self-assemble to shield their hydrophobic tail groups away from water to form an oily interior microenvironment, while keeping the assembly soluble by exposing their hydrophilic head groups outward toward the bulk water. At low concentrations surfactants exist as monomers as a result of the translational entropy of the individual surfactants. Above their critical micelle concentration (CMC), however, surfactants assemble into micelles due to the hydrophobic driving force overwhelming the translational entropy. Polymeric micelles, on the other hand, can exhibit vastly reduced CMCs, and in the case of some branched structures, even overcome this concentration dependent assembly behavior. They can make unimolecular micelles as a result of the significant local concentration of hydrophobic and hydrophilic groups to yield a micellar structure without aggregating with any other polymer molecules. The more robust nature of polymer micelles makes them attractive for a range of applications from drug delivery vehicles and oil dispersants to nanoreactors and emulsifiers Laurent and Grayson recently reported the synthesis of novel amphiphilic homopolymer architectures that form dynamic micelle structures that have the capability for selective encapsulation and responsive release of guest molecules depending on the solvent polarity.2 These amphiphilic homopolymers were synthesized with either a linear and cyclic © XXXX American Chemical Society

topology by attaching a bifurcated amphiphilic unit, consisting of a dodecyl hydrophobic side chain and a tetra(ethylene glycol) hydrophilic side chain onto preformed linear and cyclic backbones using copper-catalyzed azide−alkyne cycloaddition chemistry (Figure 1).2 These polymers were shown to readily dissolve water-soluble dyes in toluene, demonstrating their potential for the encapsulation and subsequent release of watersoluble drugs when transported across nonpolar barriers like the skin.2 Although 1H NMR, SEC, and MALDI-TOF mass spectroscopy measurements confirm the chemical architecture of these polymers, questions remain concerning the molecularlevel conformation and structure of these polymers in various solvents and their inversion upon transfer from a polar solvent to a nonpolar solvent, and vice versa.2 The vast majority of nonlinear amphiphilic polymers are structurally biased toward the formation of either micelles or unimolecular micelles.3 For example, amphiphilic star block copolymers are covalently attached in such a way that the core is attached to either the hydrophilic half or the hydrophobic half of the block copolymer arms. The cyclic amphiphilic homopolymers that were reported for the first time recently are of particular interest because they are assembled in such a way Special Issue: William C. Swope Festschrift Received: December 12, 2013 Revised: January 2, 2014

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Figure 2. Schematic illustration of the side chain distribution about the cyclic amphiphilic polymer in water and toluene. The top figure shows the complete inversion model in which the position of the polar (red) and nonpolar (cyan) side chains completely switch their orientations relative the polymer backbone (yellow) in the differing solvents. The bottom figure shows the observed conformations in which the polar chains are relatively swollen in both water and toluene, while the nonpolar chains retreat in water and swell in toluene. In both solvents the central ring of the cyclic polymer is observed to be filled with a pool of alkyl chains.

Figure 1. Chemical structure of the linear and cyclic homopolymer amphiphilic monomers.

that both the polar and nonpolar side chains exhibit equal proximity to the core and to the periphery. As such, they are expected to reversibly form both micellar and reverse micellar configurations, depending upon external stimuli. The extent to which one conformation is favored over the other is independent of the architecture, but rather dependent upon the nature of the side chains and that of the external environment. For the cyclic polymers, Laurent and Grayson hypothesized that in nonpolar solvents the hydrophilic ethylene glycol chains would orient themselves inward to minimize solvent interactions while the hydrophobic alkyl arms would orient outward into the solvent, forming a “reverse micelle-like” configuration as depicted in Figure 2.2 In polar solvents the expectation is that the hydrophilic and hydrophobic arms would invert orientations and provide a “normal micelle-like” configuration (Figure 2).2 This inversion from micellar to reverse micellar configurations has also been reported for linear amphiphilic homopolymers.4,5 This polarity driven conformation change can potentially be exploited for selective encapsulation and the stimulus-responsive release of guest molecules. Herein, we seek to understand the exact placement of polar and nonpolar side chains during this reversible behavior. In the simplest model for the reversibility of cyclic amphiphilic homopolymers, one could imagine the nonpolar side chains being extended outward in nonpolar solutions with the polar side chains buried near the core and the polymer backbone located at the interface. In polar solvents, because of the architectural symmetry between the polar and nonpolar side chains, one might expect a complete inversion of this conformation, with nonpolar side chains at the core, and polar ones at the periphery (Figure 2). For these studies, we use all atom molecular dynamics computer simulations to study the stable conformations of Laurent and Grayson’s cyclic amphiphilic homopolymers in polar and nonpolar environments and use linear homopolymer analogs to help clarify the effect of the cyclic architecture on solvent-dependent

conformations. Water and toluene are used as the high and low polarity solvents. This particular study focuses on the conformational analysis of a singular polymer chain, and therefore it most accurately correlates with a model of amphiphilic polymers as unimolecular micelles. Conformational changes can be challenging for simulations to explore due to large free energy barriers between conformations, so we use the replica exchange with driven scaling (REDS2)6 method to enhance sampling of polymer conformations of these dense, structured polymers. From knowledge of the solvent dependence of the polymer configurations we investigate whether the solvent induced conformational changes support the encapsulation and release of guest molecules.

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MATERIALS AND METHODS The linear and cyclic amphiphilic homopolymers were prepared using the LEaP module in AMBER.7 The amphiphilic unit of the linear and cyclic polymer includes a dodecane chain and a tetra(ethylene glycol) chain attached to a tris-alcohol core (Figure 1).2 There are 115 atoms in the monomeric unit and the linear polymer model consists of 40 monomeric units whereas the cyclic polymer consists of 32 monomeric units. Quantum mechanical calculations were conducted to obtain the charges for the polymer systems using the GAUSSIAN 09 package8 at the MP2 level9 with a cc-pvtz basis set. The atomic partial charges for the molecules were obtained through electrostatic potential fitting methods. All other parameters for the polymers were taken from the general AMBER force field (GAFF).10 The GAFF force field was chosen because it has been demonstrated to be accurate in simulations of organic liquids,11,12 membranes,13 and polymers.14 Simulations were performed in water and toluene. Explicit water molecular dynamics simulations were performed with TIP4P/2005 water model.15 The toluene parameters were taken from GAFF. Both B

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the linear and the cyclic polymers were solvated using 8000 water molecules. In the case of toluene 1500 toluene molecules were used to solvate the polymer systems. The replica exchange with driven scaling (REDS2)6 method implemented within AMBER 11 was used for all simulations. Replica exchange methods generally enhance sampling of conformational space by simulating a number of replicas over a wide temperature range and permitting exchanges between neighboring replicas to overcome free energy barriers between distinct conformations. The REDS2 method is a variation on the REDS method.16 In both methods the potential energies of selected replicas are modified, according to ⎡ T T ⎤ E(r ,λ) = ⎢λ M + (1 − λ) M ⎥E(r ) TB ⎦ ⎣ TA

(1)

where TM is the temperature of the scaled replica, TA and TB are the temperatures of the neighboring unscaled replicas, and E(r) is the standard potential energy of the system. The scaling parameter λ varies from 0 to 1, allowing for high probabilities of accepted exchanges with the replica at temperature TA when λ is near 1 and the TB replica when λ is near 0. This allows for a single replica to span a wide range of energies and to replace a number of conventional replicas. In the REDS2 method, λ is made to change from 0 to 1 over a time scale τ as λ(t) = sin2(πt/τ). Over the range of replica temperatures, scaled replicas are alternated with conventional replicas. These simulations were performed on the Louisiana Optical Network Initiative high performance computing environment. Molecular dynamics simulations were performed in the canonical ensemble. Before initiating replica exchange moves, each replica was pre-equilibrated for 1 ns. The production simulations were run for 20 ns. Twelve replicas were used in our simulations spanning from 300 to 500 K, with temperatures equal to 300, 314, 328, 344, 359, 376, 393, 411, 429, 447, 464, and 482 K. Of these 12 replicas, we used six unscaled replicas (T = 300, 328, 359, 393, 429, and 464 K) and six scaled replicas (T = 314, 344, 376, 411, 447, and 482 K). The Hamilton scaling time τ was set to 120 ps, which ensures the scaled replica remains in equilibrium.6 To check that the system is in equilibrium, the energy components of the system are compared to the results of conventional simulations at the appropriate temperature.

Figure 3. Representative simulation snapshots of the linear and cyclic amphiphilic polymers in water and toluene at 300 K after 20 ns. The polymer backbone, alkyl side chains, and oligomeric PEO side chains are illustrated as the yellow, cyan, and red van der Waals surfaces. Connecting units attaching the side chains to the backbone are illustrated as dark sticks.

temperature,18 above which the polymer phase separates from aqueous solution. The relative polymer sizes and positioning of their constituent units can be characterized by their radii-of-gyration (Table 1) and radii-of-gyration probability distributions Table 1. Average Radii of Gyration of the Linear and Cyclic Amphiphilic Polymers, Their Backbones, the Hydrophobic Alkyl Arms, and the Hydrophilic PEO Arms in Water and Toluene at 300 K

linear linear cyclic cyclic

in in in in

water toluene water toluene

polymer (Å)

backbone (Å)

alkyl arms (Å)

PEO arms (Å)

21.6 25.7 16.5 18.9

18.0 22.0 9.1 9.2

21.1 27.8 16.4 23.8

23.1 25.8 19.2 19.4

(Figures 4 and 5). The instantaneous radius-of-gyration (Rg) of a polymer, or subset of constituent polymer atoms, is determined by the expression Rg2 = (∑i=atoms|r̃i − r̃com|2)/N, where the sum extends over the N atoms of the polymer, or subset of atoms, and r̃com is the center-of-mass position. In both water and toluene, the cyclic polymer has a smaller radius than its linear counterpart, resulting from the internal constraints imposed to create a macrocycle (Table 1). Indeed, although the backbone Rg distribution for the linear polymer shifts to greater radii upon transfer from water to toluene (Figure 4), reflecting the fact that toluene is a better solvent for the backbone than water, the backbone distribution of the cyclic polymer barely changes (Figure 5). Nevertheless, the overall dimensions of both polymers swell in toluene compared to water (Table 1), suggesting that on average toluene is a better solvent than water for these polymers and their constituent units. In water the Rg distribution of the PEO arms of the linear and cyclic polymers are greater than those of the alkyl arms (Figures 4 and 5). As expected, the relative positioning of the PEO and alkyl arms switch in toluene, with the radii of the alkyl arms being greater than PEO. In addition, the radii of the side chains are greater than that of the backbone, indicating the

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RESULTS AND DISCUSSION Structure of Linear and Cyclic Polymers in Solvents of Varying Polarity. Representative simulation snapshots after 20 ns of the linear and cyclic polymers in water and toluene at 300 K are provided in Figure 3. The linear polymer adopts a relatively extended conformation in both solvents, whereas the cyclic polymer is more compact as a result of its internal topological constraints. The peripheries of both polymers in water appear to be more compact than in toluene. Specifically, the oligomeric PEO side chains appear to lie on top of an alkyl arm core in water for both the linear and cyclic polymers (Figure 3), while the polymer backbone is buried beneath the alkyl layer. Rather than switching positions, in toluene (Figure 3) both the PEO and alkyl side chains appear to swell, giving the polymers a “hairier” appearance. This observation suggests the PEO arms are more soluble in toluene than the alkyl side chains are in water. Indeed, PEO sits on the edge of solubility in water, exhibiting surface activity17 and a lower critical solution C

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Figure 4. Radius-of-gyration probability distributions for the linear polymer and its constituent groups in water (a) and toluene (b) at 300 K. The figure symbols are defined in the legend provided in (a). The probability distributions are normalized as ∫ ∞ 0 p(Rs) dRs = 1. Figure 6. Heavy atom density as a function of distance from the cyclic polymer center-of-mass for the polymer backbone, alkyl arm, PEO arm units in water (a), toluene (b), and water/toluene mixed (c) solvents at 300 K. Figure symbols are defined in the inset legends.

smeared densities over a wider range of separations. In water, the PEO arm carbon and oxygen atoms predominantly reside on the surface of the assembly (Figure 6a), with a single peak in the neighborhood of the PEO arm Rg (Table 1). The alkyl arms, on the other hand, exhibit two peaks, an outer peak at a separation comparable to the alkyl arm Rg and a more prominent inner peak near the center-of-mass. This inner alkyl peak lies inside the backbone density distribution, suggesting that some of the alkyl chains do fill the core, though the majority are outside the average radius of the backbone. This makes the center of the polymer a significantly nonpolar environment. Water is repelled by the polymer core and its density falls to essentially zero below the layer of PEO side chains. The PEO arm density distribution is only weakly perturbed upon transfer to toluene. There is a presence of PEO chains inside the average backbone radius, however, only to a limited extent when compared to the alkyl rich core when observed in water. The outer alkyl arm density peak swells to a separation outside the PEO distribution when in toluene (Figure 6b). This observation is consistent with the changes in the Rg of the constituent polymer units upon transfer from water to toluene reported above. The swelling of the outer alkyl peak is supplied in part by the pool of alkyl units at the polymer center, resulting in a slight depression of the inner peak density. In difference to water, toluene is able to penetrate the core of the cyclic polymer. Although Figures 4−6 take an inside-out center-of-mass based perspective on polymer structure, an alternate outside-in perspective can be achieved by determining an instantaneous surface encapsulating the polymer at each moment during the simulation and evaluating the alkyl and PEO arm distributions relative to that interface. The instantaneous polymer−solvent interface is determined here using the definition of Willard and Chandler.19 This interface is defined by coarse-graining the

Figure 5. Radius-of-gyration probability distributions for the cyclic polymer and its constituent groups in water (a) and toluene (b) at 300 K. The figure symbols are defined in the legend provided in (a). The probability distributions are normalized as ∫ ∞ 0 p(Rs) dRs = 1.

backbone is enshrouded beneath the side chains. Upon transfer from water to toluene, the PEO arm Rg for the linear polymer slightly swells whereas it barely moves for the cyclic polymer (Table 1). The swelling of the PEO chains for the linear polymer likely reflects the swelling of the linear backbone in toluene, which is absent in the case of the cyclic polymer. Indeed, the PEO Rg distributions for the cyclic polymer in water and toluene are nearly superimposable on one another (Figure 5). The largest dimensional change upon transfer is observed for the alkyl side chains, which significantly extend into toluene. The solvent and polymer unit density distributions about the center-of-mass of the cyclic polymer in water and toluene are plotted in Figure 6. We only plot density distributions for the cyclic polymer because it has a more compact, spherical structure than the linear polymer (Figure 3), which exhibits D

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solvent by placing a normalized Gaussian function, (2πλ2)−3/2 exp(−r2/2λ2), where λ is the smearing length, at each heavy atom site of the solvent and determining the surface at which the smeared density is equal to half the bulk solvent density. This approach has been previously applied to determine the dynamic interfacial properties of protein assemblies in water.19 Here we assign a value of λ = 2.4 Å to the smearing length, which is comparable to the correlation length for water. The instantaneous interface-side chain heavy atom distance distribution functions for the alkyl and PEO arm side chains of the linear and cyclic polymers in water and toluene are reported in Figure 7. We note that short distances in these distributions

the capture and release of hydrophobic/hydrophilic guests in differing solvent environments? Capacity To Deliver Hydrophobic and Hydrophilic Moieties. To assess the capacity of these polymers to deliver hydrophobic guests from an aqueous to an organic environment, we have evaluated the potential-of-mean force (PMF) between argon these polymers in water and toluene. PMFs were evaluated by determining the excess chemical potential of argon as a function of distance from the polymer center-of-mass out into the bulk solvent using the test particle insertion method. The distance dependent excess chemical potential, μex Ar(r), is evaluated as ex μAr (r ) = −kT ln⟨exp[−φsolvent ‐ Ar(r )/kT ]⟩0

(2)

where kT is the product of Boltzmann’s constant and the temperature, φsolvent‑Ar(r) is the total solvent-argon interaction energy r away from the polymer center-of-mass, and the brackets ⟨...⟩0 indicate a canonical ensemble average over configurations obtained in the absence of a guest.20 In these calculations argon was modeled as a Lennard-Jones particle with σArAr = 3.415 Å and εArAr = 1.0393 kJ/mol.21 The PMF between argon and the cyclic polymer in water (Figure 8) shows a distinct preference for the polymer interior.

Figure 7. Instantaneous solvent interface-side chain heavy atom distance distribution functions for the PEO and alkyl heavy arms for the linear (a) and cyclic (b) polymers in water and toluene at 300 K. Figure symbols are defined in the inset legends. The probability distributions are normalized as ∫ ∞ 0 p(Rs) dRs = 1. Figure 8. Argon excess chemical potential as a function of distance from the cyclic polymer center-of-mass in water and toluene at 300 K. Figure symbols are defined in the inset legend.

correspond to the heavy atoms being closest to the solvent interface and further away from the polymer center. In water the PEO arms sit closest to the interface, as indicated by the prominent peak at ∼1 Å, while the alkyl side arm atoms are spread out further from the interface. In toluene both the alkyl and PEO heavy atoms reside approximately 0.5 Å from the interface; however, the alkyl atoms display a larger, more prominent peak than the PEO atoms. Most interestingly, the distributions of the alkyl and PEO arms for the linear and cyclic polymers in both water and toluene are practically identical, barring minor differences. So although distinct differences in the structures of the linear and cyclic amphiphilic polymers based on a center-of-mass analysis are observed, from the outside-in the polymers are nearly identical. We conclude then that the major structural differences observed during the centerof-mass based analysis result from polymer backbone topology effects, and that the impact of the solvent on the ordering of the alkyl and PEO arms is largely independent of that topology. The structural analysis indicates that the primary response to the difference solvent environments involves movement of the alkyl arms. The asymmetric redistribution of the alkyl and PEO side chains in water and toluene begs the question, are the observed conformational changes significant enough to impact

Specifically, the excess chemical potential of argon drops from a very unfavorable 8.6 kJ/mol in bulk water to a more favorable plateau of ∼4 kJ/mol in the polymer between separations of 5− 15 Å in the periphery of the assembly structure where the water density has dropped to nearly zero (Figure 6a). Between 0 and 5 Å the PMF exhibits an even higher affinity well in the vicinity of the alkyl arm enriched center of the polymer. Though not shown here, the PMF between argon and the linear polymer in water is essentially the same as that for the cyclic polymer, except it does not exhibit the deeper inner minimum because the center-of-mass for the linear polymer is occluded by the polymer backbone. In toluene the PMF displays a broad plateau of ∼4 kJ/mol inside the cyclic polymer assembly that drops to 2.5 kJ/mol in the bulk solvent. On the basis of these PMFs, then we expect model hydrophobic species, like argon, to partition into the amphiphilic polymer’s hydrophobic interior in water and into the bulk solvent in toluene. The test particle method (eq 1) is not practical for modeling delivery of a hydrophilic guest as a result of added electrostatic interactions and orientational degrees-of-freedom that reduced the probability of successful insertions. In this case then we E

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passively examine the affinity of water as a model polar guest for the cyclic polymer interior in an organic solvent by adding 75 water molecules to our simulations in 1500 molecules of toluene solvent. The local density of water as a function of distance from the center-of-mass for the cyclic polymer in water is shown in Figure 6c, after 20 ns of simulation. The water density shows a prominent peak that coincides with the PEO arm density between the backbone and alkyl arm peaks, corresponding to the highest polarity portion of the polymer in toluene. This is distinct to simpler ideas that envision hydrophilic guests settled into the hydrophilic center. Integrating the polymer density from the center-of-mass out to the periphery at 25 Å, we find the polymer soaks up 72 of the 75 added water molecules, indicating both a strong preference of the model hydrophilic guest for the polymer in toluene and a significant carrying capacity. The observed preferential uptake of argon in water followed by release in toluene, and the uptake of water in toluene and de facto release in water supports the capacity for these amphiphilic polymers to act as delivery vehicles triggered by changes in solvent polarity. More importantly, the ability of our simulations to capture this experimentally documented capability lends evidence that the REDS2 enhanced sampling technique is capturing relevant conformational changes essential to model delivery from a molecular perspective.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents. The Louisiana Optical Network Initiative is gratefully acknowledged for providing computational support, and additional support was provided by BP/The Gulf of Mexico Research Initiative (RFP-II-798). S.P. acknowledges access to computational resources at University of California Irvine funded by NSF Grant CHE-0840513.

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CONCLUSIONS Our structural analysis indicates that the most basic model that the cyclic chain inverts when transferred between a polar and nonpolar solvent is too simple (Figure 1). The structural analysis was based on the radius-of-gyration of the different parts of the polymers (Figures 4 and 5), the density distribution relative to the polymer center of mass (Figure 6), and the distribution of atomic distances from the instantaneous surface (Figure 7). Rather than a large structural inversion, the PEO chains appear to be equally solvated in both solvents and that the predominant changes in the polymer structure can be traced to changes in the alkyl arm distributions. In water the alkyl arms retreat beneath the PEO chain layer, whereas in toluene the alkyl arms swell beyond the PEO layer. For the cyclic polymer a small pool of alkyl arms resides in the assembly core near the similarly hydrophobic polymer backbone no matter the solvent polarity. The structural results of this study may provide guidance for the design of other amphiphilic polymers. Perhaps larger structural changes would be observed by substituting the oligomeric PEO with more hydrophilic (e.g., charged) side chains. Our results indicate the ability of the polymers to bind either hydrophobic or hydrophilic guests. Argon, a model hydrophobic guest, can bind to a variety of positions inside the polymer when in water and in toluene there is no free energy gain to bind relative to the solvent (Figure 8). Water molecules, as prototypes for hydrophilic guests, bind to positions close the PEO arms (Figure 6c) when in toluene solvent and not in the center. Near the center is the polymer backbone, which is hydrophobic. A more hydrophilic backbone might bring polar guests into the center. The conclusion that proposed drug delivery polymers may in fact bind drug molecules away from the center of the polymer was also reached in a simulation study by Swope et al.22 for star polymers with diblock arms, consisting of hydrophobic and hydrophilic segments. These results also suggest design strategies, as the side chains not only help to determine the polymer structure but also bind guests. F

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