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Design of Amphiphilic Polymers via Molecular Dynamics Simulations Arjun Sharma,† Lixin Liu,‡ Sreeja Parameswaran,† Scott M. Grayson,§ Henry S. Ashbaugh,‡ and Steven W. Rick*,† †

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

‡

ABSTRACT: Extensive all-atom molecular dynamics simulations were carried out on three novel amphiphilic homopolymers in explicit polar and nonpolar solvent environments. These nonlinear polymers have potential applications in drug delivery and consisted of 32 repeating bifurcated amphiphilic side chains bound to an alkynyl functionalized cyclic framework. All of the polymer systems investigated have the same backbone and hydrophobic dodecyl side chains and differ only in the nature of the hydrophilic side chains. This report focuses on the solvent polarity induced conformational changes exhibited as a result of the different hydrophilic modifications. Our simulations of polymer microenvironment provides useful information about the amphiphilic phase segregation that drives the formation of normal micelle-like and reverse micelle-like nanostructures that are expected to occur in response to solvents of varying polarities.

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INTRODUCTION Polymeric micelles are promising drug delivery agents1 owing to their potential to form stable structures with well-defined sizes. Traditional micelles consist of multiple surfactants that exhibit amphiphilic structures with two distinct parts: a hydrophilic headgroup and a hydrophobic tail. In polar solvents, such surfactants exist as monomers in true solution at low concentration, but above their critical micelle concentration (CMC) they favor thermodynamic selfassembled aggregates with their hydrophobic tails partitioned to the core and their hydrophilic heads forming a threedimensional shell that segregates the hydrophobic tails from the solvent. Polymer-based micelles typically exhibit lower CMCs compared to common low molecular weight surfactant micelles,2 because of the greater effective concentration of hydrophobic moieties down the macromolecular backbone and lower entropic penalty for association compared to monomeric surfactants. In some exceptional cases for highly branched amphiphilic polymers, a single unaggregated macromolecule can act alone as an effective micelle, i.e., a “unimolecular micelle”, and therefore exhibit no CMC.3−6 Although amphiphilic block copolymers (those with a series of hydrophobic repeating units followed by a series of hydrophilic repeating units) have been the subject of thorough investigation, amphiphilic homopolymers (those with one hydrophobic and one hydrophilic side chain on each repeating unit) remain less studied and therefore less well-understood.25 Each of these types of polymer micelles have potential advantages over the conventional small-molecule micelles, making them attractive options for the micelle-based transdermal drug delivery systems. © 2016 American Chemical Society

Amphiphilic homopolymers, with hydrophobic dodecyl and hydrophilic tetraethylene glycol (TEG) side chains attached via click chemistry to a functionalized cyclic polymer backbone, have been developed by Laurent and Grayson7 to successfully encapsulate and release water-soluble dyes, in response to changing solvent polarity, which can serve as a trigger to affect delivery. The oligoethylene glycol and alkyl groups were selected as side chains for amphiphilic homopolymers because they both remain uncharged regardless of pH, yet this set of side chains has demonstrated the ability to form both reverse micelles in nonpolar solutions, and normal micelles in polar solutions.24,26−29 However, molecular simulations showed that rather than exhibiting a complete structural inversion, the TEG arms appeared to be equally solvated in both the polar and the nonpolar solvents and the predominant change in the polymer configuration was traced to reordering in the alkyl arms distribution.8 The simulations also found a small population of alkyl arms residing within the polymer core irrespective of solvent polarity. In order to understand how different polymer designs influence their structural response to solvent, three different hydrophilic arms were examined, while keeping the rest of the polymer unchanged. These three are a TEG arm, as studied previously,8 an analogous 3,6,9,12-tetrahydroxytridecyl (THT) arm, which has alcohol groups that can both accept and donate hydrogen bonds, and an oxyammonium-terminated TEG arm (OATEG), which adds a charged group (see Figure 1). The Received: August 2, 2016 Revised: September 21, 2016 Published: September 22, 2016 10603

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The Journal of Physical Chemistry B

Partial atomic charges for the cyclic polymers were calculated from quantum mechanical calculations using the GAUSSIAN 09 package10 at the MP2 level11 with a cc-pVTZ basis set. The electrostatic potential (ESP) fitting methods were used to obtain these charges. The general AMBER force field (GAFF)12 was used for all other parameters. Simulations were performed using either the sander or pmemd module of AMBER. All structures were energy minimized in vacuum prior to solvation. To mimic hydrophilic and hydrophobic environments, the polymers were solvated in a truncated octahedral box of water (TIP4P/2005 model)13 and toluene (GAFF parameters) respectively. For the OATEG polymer, additional chloride ions were added to maintain system neutrality. The simulations used a single polymer with 9317, 7590, and 9021 water molecules and 2828, 2502, and 2780 toluene molecules for the TEG, THT, and OATEG polymers, respectively. The polymer structures were minimized using 10 000 steps of steepest descent algorithm followed by 3000 steps of conjugate gradient. The minimized structures were kept fixed using a harmonic restraint with a force constant of 25 kcal/mol· Å2 and heated at constant volume, changing the temperature linearly from 0 to 300 K over 100 ps time frame. This was followed by a 100 ps run at 300 K with no positional restraints. A short preproduction run for 1 ns at isobaric−isothermal ensemble (NPT) was performed using the Langevin dynamics to stabilize the system density, by allowing reorganization of solvent molecules around the polymer. Polymer systems were then subjected to NPT production run. Long-range electrostatic interactions were evaluated using the particle mesh Ewald14,15 method, using a real space cutoff of 9 Å. The molecular dynamics simulations were performed over hundreds of nanoseconds using GPUs.

Figure 1. Chemical structure of the TEG, THT, and OATEG polymers consisting of the same cyclic backbone (red) attached to hydrophobic dodecyl side chains (green) with different hydrophilic tetra(ethylene glycol) (TEG), [3,6,9,12-tetrahydroxytridecyl] (THT), and oxyammonium-terminated TEG (OATEG) side chains (blue), respectively.

idea was to render the hydrophilic arms more water-soluble than the TEG arms in order to enhance the incompatibility between hydrophobic and hydrophilic segments of the amphiphilic side chains in the polymer, while keeping the size of the arms constant. For this study, a cyclic core was selected for detailed investigation because this unique form of amphiphilic polymer had not been previously reported,30 and subsequently its solvent-dependent conformations remain unclear. The primary goal of this study is to understand how modifications to the hydrophilic side chains in the cyclic amphiphilic homopolymers change their behavior in solvents of differing polarity. As in our previous work,8 an all-atom molecular dynamics simulation was used to study polymer structures in water and toluene as high and low polarity solvents, respectively. These simulations utilize Graphics Processing Units (GPUs) for long time scale simulations to overcome challenges in conformational changes due to large free energy barriers rather than using enhanced sampling techniques. This investigation should help inform the future design of macromolecules for drug-delivery through clarifying the role of solvent interactions, hydrophilic functional groups and structural flexibility in determining the conformation of amphiphilic homopolymers.

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RESULTS AND DISCUSSION Figure 2 shows representative configurations of the TEGpolymer in water and toluene after 300 ns of simulations at 300

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MATERIALS AND METHODS All amphiphilic homopolymers were prepared using the tleap module in AmberTools 14 program suite.9 Each polymer consists of 32 bifurcated monomeric units. The bifurcated amphiphilic unit incorporates hydrophobic dodecyl and hydrophilic tetra(ethylene glycol) monomethyl ether moieties covalently attached via a triazole linker to a cyclic polymer core7 henceforth referred to as the TEG-polymer (Figure 1a). All of the polymers investigated share the same cyclic core and hydrophobic arms; however, the other two polymer types exhibit modified hydrophilic side chains of the amphiphilic block. In the THT polymer (Figure 1b), hydroxyl functionalities on the THT polar side chains replace the ether units of the TEG-polymer, while a terminal charged oxyammonium group on the hydrophilic TEG arms is incorporated into the polar side chains of the final polymer, the OATEG polymer (Figure 1c). The three different hydrophilic arms have the same length, but have different hydrogen bond capability.

Figure 2. Simulation snapshots of the TEG-polymer in water (left) and toluene (right). The TEG arm atoms are represented in blue, the alkyl arm atoms in green, and the backbone atoms in red.

K. In water, one can see that the TEG-polymer adopts noticeably compact conformation, suggesting that neither the TEG nor the alkyl chains exhibit high solubility in water. However, in this configuration the TEG chains appear preferentially at the surface, with the hydrophobic alkyl side chains predominantly buried underneath. In contrast, the overall polymer conformation in toluene is relatively extended. The alkyl side chains extend beyond the TEG side chains into the solvent which is consistent with our previous simulations of amphiphilic homopolymers8 and other polymer−solvent studies.16,17 The more extended structure implies a more soluable polymer in nonpolar solvents, as has been observed 10604

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The Journal of Physical Chemistry B experimentally.7 The snapshots of the THT and the OATEGpolymers in polar and nonpolar solvents illustrate attributes qualitatively similar to the TEG-polymer (data not shown). The radii-of-gyration (Rg) and its probability distributions provide a quantitative estimate of the polymer size and the relative positioning of its constituents. For a polymer with N atoms, the mean-square radius of gyration is given by ⟨Rg2⟩ = (1/M)⟨[ΣNi=1mi|ri − r|2]⟩, where r is the center-of-mass of the polymer, ri and mi are the position and mass of the ith atom, and M is the total mass of the polymer. The radius of gyration can be calculated for the polymer separated into three parts (the backbone, which includes the cyclic backbone and the linker regions, the alkyl chains, and the hydrophilic chains). The radius of gyration values of the polymers as a function of total simulation time in different solvents are shown in Figures 3−5. The three polymers in each of the two solvents all start

Figure 4. Time evolution of the radius of gyration for the backbone atoms (red lines), alkyl side chains (green lines), hydrophilic side chains (blue lines), and the total polymer (black lines) for the THTpolymer in water (A) and toluene (B).

Figure 3. Time evolution of the radius of gyration for the backbone atoms (red lines), alkyl side chains (green lines), hydrophilic side chains (blue lines), and the total polymer (black lines) for the TEGpolymer in water (A) and toluene (B).

with similar structures, as described in the Materials and Methods in which the alkyl arms have a Rg around 23 Å, larger than the Rg of the hydrophilic arms, which is somewhere between 19 and 21 Å. In water, there is a rapid decrease in the Rg of the alkyl arms to 19 Å in about 2 ns, followed by a slower contraction of the alkyls arms over the following ∼100 ns. On this time scale there is a slow increase in the Rg of the hydrophilic arms. In toluene, there is no large change apparent in the Rg values, except for a small increase in the Rg of the alkyl arms. After 150 ns the polymer conformation in both solvents appears stable. Subsequently, the final 100 ns were used to compile thermodynamic averages for the analyses presented below. The hydrophilic arms show the largest extension in water in the case of the OATEG polymer, which includes a charged ammonium group at the end of each side chain. This suggests that the presence of the charged end causes a more extended conformation of the hydrophilic arms.

Figure 5. Time evolution of the radius of gyration for the backbone atoms (red lines), alkyl side chains (green lines), hydrophilic side chains (blue lines), and the total polymer (black lines) for the OATEG-polymer in water (A) and toluene (B).

The equilibrations shown in Figures 3−5 start from the userconstructed structure as described in the Methods section, which are not necessarily physically meaningful. Taking the structure equilibrated in one solvent and placing it in a different solvent allows for the determination of the time scales involved in the transition between two equilibrium structures. The structures of the TEG-polymer after 300 ns were put into the different solvent. Switching the water equilibrated structure to 10605

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The Journal of Physical Chemistry B toluene flips the alkyl and TEG position in about 30 ns (Figure 6A). The alkyl arms take longer than the TEG arms to

Figure 6. Time evolution of the radius of gyration for the backbone atoms (red lines), alkyl side chains (green lines), hydrophilic side chains (blue lines), and the total polymer (black lines) for the TEGpolymer (A) beginning with the water equilibrated structure in toluene and (B) beginning with the toluene equilibrated structure in water.

equilibrate, perhaps because the response is larger. When the toluene equilibrated structure is put in water (Figure 6B) there is a rapid response in the first 2 ns of the alkyl arms and in the first 5 ns of the TEG arms, followed by a longer time scale (50 ns) response. This is roughly similar to the TEG equilibration (Figure 3). The average Rg of the polymers and its subunits are shown in Table 1. Each configuration of the simulation can have a different Rg, so in addition to calculating its average value, the distribution is calculated. Figure 7 shows the probability distributions of Rg for the polymers and its constituent parts as a function of distance from the center-of-mass position. For all three polymers, the total Rg increases from about 17 Å in water to about 19 Å in toluene. The Rg distributions of the backbone for the three polymers in both solvents are similar, with a small increase when in toluene. In water, the Rg of the hydrophilic side chains TEG and THT are both around 19.4 Å, while that of the OATEG increases by over an Angstrom. In toluene, both the TEG and the OATEG side chains have a

Figure 7. Probability distributions of the radius of gyration for the backbone atoms (red lines and circles), alkyl side chains (green lines and triangles), hydrophilic side chains (blue lines and squares), and the total polymer (black lines with no symbols). The solid lines are for the polymer in water and the dashed lines are for the polymer in toluene.

smaller Rg, while the THT retains the same value it has in water. The alkyl side chains demonstrate a large shift as the solvent changes. In water, the Rg of the alkyl chains is near the value for the whole polymer and less than the Rg of the hydrophilic chains. The structure is reversed for the polymers in toluene, when the Rg is much larger than the other groups. The changes in the Rg values indicate that the alkyl arms change structure more significantly than the hydrophilic arms in response to solvent. The Rg of the alkyl arms also shows a broader distribution when in toluene than the other parts of the

Table 1. Average Radii of Gyration and Standard Deviation of the Three Polymers, the Backbones, the Hydrophobic Alkyl Arms, and the Hydrophilic Arms in Water and Toluene after 300 ns of Simulationa polymer (Å) TEG THT OATEG

a

water toluene water toluene water toluene

16.6 18.7 17.4 19.4 17.1 19.2

± ± ± ± ± ±

0.4 0.4 0.3 0.3 0.5 0.2

backbone (Å) 14.4 14.8 14.7 15.4 14.9 15.3

± ± ± ± ± ±

0.1 0.2 0.1 0.1 0.2 0.2

alkyl arms (Å) 16.7 23.0 18.0 23.2 16.6 23.6

± ± ± ± ± ±

0.4 0.5 0.3 0.5 0.5 0.5

hydrophilic arms (Å) 19.2 18.3 19.5 19.7 20.5 18.6

± ± ± ± ± ±

0.1 0.2 0.1 0.2 0.1 0.2

Error estimates show the standard deviations from breaking the last 100 ns of data into five 20 ns blocks. 10606

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The Journal of Physical Chemistry B polymers in either solvent, as a consequence of the extension of the alkyl arms into the toluene solvent (Figure 7). The polymer center-of-mass density distributions are shown in Figures 8−10. For all three polymers in both solvents, the

Figure 10. Density of atoms relative to the polymer center-of-mass for the backbone atoms (red lines), alkyl side chains (green dashed lines), hydrophilic side chains (blue dotted lines), and the solvent (black dotdashed lines) for the OATEG-polymer in water (A) and toluene (B). Figure 8. Density of atoms relative to the polymer center-of-mass for the backbone atoms (red lines), alkyl side chains (green dashed lines), hydrophilic side chains (blue dotted lines), and the solvent (black dotdashed lines) for the TEG-polymer in water (A) and toluene (B).

the second at ∼15 Å in water and ∼20 Å in toluene. Only atoms from the alkyl arms partition to the polymer micelle center in both solvents for all three polymers, possibly resulting from association with the hydrophobic backbone. The densities of the hydrophilic atoms do not change position as much as that of the alkyl arms, consistent with the Rg data. In water the distributions shift slightly outward to extend beyond the alkyl densities. In toluene, the reverse is true where the alkyl arm atoms tend to be farthest from the center. Toluene is found closer to the center than is water, likely due to the solubility of the backbone in toluene. This explains why the polymers have a larger radius of gyration in toluene, since more of the interior space is occupied by the solvent. The amount of solvent inside the region of the polymer can be found by integrating the density. The water density becomes a constant beyond 27 Å, so that distance provides one upper limit to the polymer region. Integrating out to this limit gives roughly the same number of water molecules for all three polymers (1580, 1520, and 1620 water molecules for TEG, THT, and OATEG respectively). The amount of water deeper inside the polymer micelle (at a distance less than 17 Å, the Rg of the polymers) is 28, 53, and 51 water molecules per polymer for the TEG, the THT, and the OATEG polymers, respectively, so by this measure there is less water inside the TEG polymer. For the OATEG-polymer, there are chloride counterions paired with each oxyammonium end group. The range of the chloride ions distribution overlaps with the OATEG side chains as expected (data not shown in Figure 10). In water, there are about 12 chloride ions within 27 Å of the center and in toluene, all the counterions are within this distance, toluene being a much poorer solvent for the chloride anion. As expected, the vast majority of chloride ions condense onto the positively charged oxyammonium moieties on the OATEG side chains in toluene. The three polymers studied here all possess repeat units of oxygen-containing functional moieties in TEG, THT, and

Figure 9. Density of atoms relative to the polymer center-of-mass for the backbone atoms (red lines), alkyl side chains (green dashed lines), hydrophilic side chains (blue dotted lines), and the solvent (black dotdashed lines) for the THT-polymer in water (A) and toluene (B).

backbone atoms are largely located between 2 to 12 Å from the center with a broad shoulder out to 25 Å. The alkyl arms distribution is bimodal with a peak near the center-of-mass and 10607

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The Journal of Physical Chemistry B OATEG, each of which can form hydrogen bonds with water. The THT and OATEG side chains can both donate and accept hydrogen bonds, while TEG can only accept. The number of hydrogen bonds were quantified by calculating the radial distribution function of all water atoms around each functional group in all polymer arms (Table 2). The total number of water Table 2. Hydrogen Bonds Involving the Hydrophilic Side Chains, with Water Molecules (a 3.5 Å Cutoff between the Water Oxygen and Side Chain Oxygen) and Atoms on the Same and Different Side Chains side chainwater TEG THT

165 ± 1 205 ± 6

OATEG

200 ± 5

same side chain 4.0 ± 0.4 (in water)/ 7.0 ± 0.8 (in toluene)

different side chain 7.0 ± 0.2 (in water)/ 24 ± 2 (in toluene)

molecules within the first-neighbor shell. We take as our hydrogen bond definition a distance between oxygen atoms less than 3.5 Å, with no additional angular criteria. This gives 165, 205, and 200 water-side chain hydrogen bonds for TEG, THT, and OATEG polymers, respectively. Given that there are 128 functional groups (4 repeats on each hydrophilic arm times 32 hydrophilic arms in the whole polymer) on each polymer, each polymer oxygen atom has on average 1.3, 1.6, and 1.6 water molecules for the TEG, the THT, and the OATEG-polymers. The THT side chains can both accept and donate hydrogen bonds and so side chain atoms can form hydrogen bonds with other side chain atoms. There are small amounts of hydrogen bonding between atoms on the same side chain, about 4 in water and 7 in toluene, and more hydrogen bonds between atoms on different side chains. In toluene, the amount of intraand interchain hydrogen bonds (about 31) is less than the number of alcohol groups on the side chains (32 times 4), so not all possible hydrogen bonds are made. Another analysis reveals how the structure looks relative to the solvent rather than the center of mass. For this analysis the position of the solvent surface that surrounds the polymer is determined using the instantaneous interface method.18 The probability of the position of the heavy atoms of the polymer relative to the nearest point on the instantaneous Willard− Chandler interface is shown in Figure 11. (The probabilities are ∞ normalized so that ∫ p(r ) dr = 1). For the TEG-polymer, 0 the probabilities are similar to the results published previously.8 This analysis gives a different perspective than represented by Figures 8−10, from the outside in rather than the inside out. All three polymers have a number of features in common. The positions of the alkyl arms change the most in response to the solvent change, as seen in the difference between the green solid and green dot-dashed lines. The alkyl arms move from being closest to the solvent in toluene to being further than the hydrophilic arms in water. This is consistent with the radius of gyration data and the density relative to the center of mass. For the alkyl arms in water, the distribution is bimodal, while in toluene there is a just a single peak near the solvent. This is different from the data in Figures 8−10, which shows a bimodal distribution for the alkyl arms both in water and in toluene. The differences between looking at the structures relative to the center of mass and relative to the solvent interface reveals the extent of solvent exposure for the polymers. For the TEG arms,

Figure 11. Probability distribution of the distance between heavy atoms and the instantaneous surface for the alkyl side chains in water (green solid lines) and in toluene (green dot-dashed line) and hydrophilic side chains in water (blue dashed line) and in toluene (blue dotted line).

there is more solvent exposure in toluene (blue dotted line) than there is in water (blue dashed line). For the other polymers, the amount of solvent exposure is either about the same, for the THT side chains, or slightly more, for the OATEG side chains, for water compared to toluene. Making the side chains more hydrophilic increases the tendency to be near water. The changes in the hydrophilic arms are not as large as those of the alkyl arms, so that for all polymers, there is more solvent exposure in toluene than there is in water (see also Figure 2). The OATEG polymer, with the positively charged end, shows a larger structural change in the different solvents, as can be seen in Figures 5 and 7. For this polymer the polar arms are extended out into water much more than the other two polymers, indicating that a design strategy that places strongly hydrophilic groups at the ends leads to larger conformational changes. Charge repulsion between the ends would also promote more extended arms, but the average distance between ends for the TEG and OATEG polymers are similar, suggesting that the interaction with the water is the primary driving force for the extended structure. 10608

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CONCLUSIONS The three polymers with different hydrophilic arms demonstrate similar structural changes upon shifting solvent polarity from water to toluene, consistent with our previous study.8 In toluene, the structures are more open and more solvent exposed than in water. This can be seen from the single snapshot from the simulations (Figure 2) as well as the radius of gyration (Table 1 and Figure 7). The enhanced solvent exposure in toluene is evident from the instantaneous surface analysis (Figure 11) which shows that the alkyl arms are much closer to the toluene than they are to water, but the proximity of the hydrophilic arms does not change much for the two solvents. The response of the polymer is largely due to the alkyl arms, as the backbone and hydrophilic arms do not show a large change in structure (Figure 7). As the hydrophilic arms become more hydrophilic, there is more solvent exposure, so that the OATEG arms show the most exposure to water and also the biggest response to the solvent change. Pure TEG shows good solubility in water as well as in toluene,8 has tendency to self-associate,19 and is the least hydrophilic among the three arms studied. The THT-arms are intermediate between the TEG and OATEG arms in terms of solvent response. Pure THT like poly(vinyl) alcohol, PVA, is expected to be soluble in water,20−22 and not in any nonaqueous medium, but as part of the amphiphilic polymer the THT arms have significant contact with the toluene solvent. The polymer geometry, the lengths of the polymer arms, and number of subunits impose constraints on the solvent response. Huynh et al.23 in their study on star copolymer micelles observed that longer PEO segments would have larger shielding effect on the hydrophobic core. The length of hydrophilic arms (4 repeat units) in our polymers might be too short to completely cover the polymer surface and to minimize contact of polar solvent with the hydrophobic backbone and the alkyl arms. The time scales for the structural changes were determined by taking a polymer structure equilibrated in one solvent and switching it to the other solvent (Figure 6). For the TEGpolymer, there is quick response within the first 5 ns, followed by a longer response of about 30 ns. The initial fast response is more rapid in water than in toluene like a result of the smaller size and mobility of water, but the longer response to equilibrium happens on about the same time scale as a result of larger-scale restructuring of the polymer conformation. These studies confirmed a number of experimentally observed trends,7,24 including the limited solubility of the TEG polymers in water, and provide a valuable insight for designing future amphiphilic polymers.

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tional support. L.L., H.S.A., and S.M.G. also acknowledge NSFCHE 1412439 for funding.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported fully or in part by the National Science Foundation’s Experimental Program to Stimulate Competitive Research (EPSCoR) under Cooperative Agreement No. IIA1430280. The Louisiana Optical Network Initiative is gratefully acknowledged for providing computa10609

DOI: 10.1021/acs.jpcb.6b07791 J. Phys. Chem. B 2016, 120, 10603−10610

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DOI: 10.1021/acs.jpcb.6b07791 J. Phys. Chem. B 2016, 120, 10603−10610