Theoretical Study of Binding and Permeation of ... - ACS Publications

Article pubs.acs.org/JPCB

Theoretical Study of Binding and Permeation of Ether-Based Polymers through Interfaces Susruta Samanta,† Samira Hezaveh,‡ and Danilo Roccatano* School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany S Supporting Information *

ABSTRACT: We present a molecular dynamics simulation study on the interactions of poly(ethylene oxide) (PEO), poly(propylene oxide) (PPO), and their ABA-type block copolymer, poloxamers, at water/n-heptane and 1,2-dimyristoyl-sn-glycero-3-phospatidycholine (DMPC) lipid bilayer/water interfaces. The partition coefficients in water/1-octanol of the linear polyethers up to three monomers were calculated. The partition coefficients evidenced a higher hydrophobicity of the PPO in comparison to PEO. At the water/n-heptane interface, the polymers tend to adopt elongated conformations in agreement with similar experimental ellipsometry studies of different poloxamers. In the case of the poloxamers at the n-heptane/ water interface, the stronger preference of the PPO block for the hydrophobic phase resulted in bottle-brush-type polymer conformations. At lipid bilayer/water interface, the PEO polymers, as expected from their hydrophilic nature, are weakly adsorbed on the surface of the lipid bilayer and locate in the water phase close to the headgroups. The free energy barriers of permeation calculated for short polymer chains suggest a thermodynamics propensity for the water phase that increase with the chain length. The lower affinity of PEO for the hydrophobic interior of the lipid bilayer resulted in the spontaneous expulsion within the simulation time. On the contrary, PPO chains and poloxamers have a longer residence time inside the bilayer, and they tend to concentrate in the tail region of the bilayer near the polar headgroups. In addition, polymers with PPO unit length comparable to the thickness of the hydrophobic region of the bilayer tend to span across the bilayer.

■

INTRODUCTION Polyether polymers based on poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) homopolymers have a wide range of applications in chemistry, biotechnology, and nanomedicine.1−9 PEO is an amphiphilic homopolymer with chemical formula X−O−[CH2−CH2−O]n−Y, where n is the number of monomers and X, Y indicate the terminal groups that can be of different types. PPO is hydrophobic homopolymer with a similar chemical formula as the PEO (X−O−[C*H(CH3)−CH2−O]n−Y) but with an chiral center due to an extra methyl group. PEO has very low toxicity,10 and it is completely soluble in water and in other organic solvents.11 It is also known that its chain length and composition are important for the stabilization of lipid bilayers.12 In addition, its peculiar property of being hydrophilic in high and hydrophobic in low degree of hydration9 determines its capability to permeate biological membranes. In fact, PEO dehydrates in a hydrophobic medium and can be transported on or through biomembranes.13 PPO is more hydrophobic than PEO due to the presence of an extra methyl group. In fact, only short PPO polymers (up to four monomers) are completely soluble in water. Further increase of polymer length rapidity decrease its solubility.14 Linear ABA-type triblock copolymers of PEO (outer block) and PPO (middle block) are known as poloxamers or with the commercial name of Pluronics. They have a broad range of © 2013 American Chemical Society

applications in biotechnology and biomedical sciences due to the combined properties of the PEO and PPO blocks.15,16 The accumulation and permeation of poloxamers have already been proven by X-ray and neutron scattering studies and differential scanning calorimetric studies.6,7 Though a good number of studies have already been done on the structural characteristics and interactions of poloxamers with biomembranes and lipid bilayers, the atomic details of permeation process of these polymers across lipid bilayers are not yet completely understood.6,7,17−19 Recently, we have published a molecular dynamics (MD) simulation study on the interaction of the shortest oligomer model of PEO, 1,2-dimethoxyethane (DME), and PPO, 1,2dimethoxypropane (DMP) with water/n-heptane and 1,2dimyristoyl-sn-glycero-3-phospatidycholine (DMPC) lipid bilayer/water interfaces.20 The permeation free energy barriers of the DME and DMP molecule from water to the interior of a DMPC lipid bilayer, estimated using umbrella sampling (US), provided the values of ∼20 and ∼6 kJ/mol at 310 K, respectively.20 The results of these simulations indicated a stronger preference of DME than DMP to the aqueous phase. In this work, we have extended the previous study by Received: March 24, 2013 Revised: November 8, 2013 Published: November 12, 2013 14723

dx.doi.org/10.1021/jp4028832 | J. Phys. Chem. B 2013, 117, 14723−14731

The Journal of Physical Chemistry B

Article

spline interpolation.31 Lennard-Jones interactions were truncated at 1.0 nm.31 The water/n-heptane interface consisted of two solvent layers of the same width (5.5 nm along the z-axis) containing 10 705 water and 1186 n-heptane molecules, respectively. The polymer molecules were located at the water/n-heptane interface, and after equilibration, the system was simulated for 50 ns. In Table 1, the list of simulated polymers is reported.

investigating the interaction of longer polymer and copolymer chains based on PEO and PPO units with interfaces. In particular, we have initially calculated the partition free energy of short polymer chain in water/1-octanal to measure their hydrophobicity and analyzed the effect of the polymer chain length and composition on interaction with a pure hydrophobic interface (n-heptane/water). This system was used as simple model to quantify the behavior of the polymers in the presence of pure hydrophobic surfaces and to dissect the contribution of the interior of the lipid bilayer (mimicked by the n-heptane interface) from the polar lipid headgroups. Hence, we have studied the interactions with a DMPC lipid bilayer patch. The study was conducted on PEO and PPO chain of different lengths (from 1 up to 43 monomers) and on three different poloxamers (L61, L64, and P85). Unrestrained MD simulations were conducted for analyzing the interactions of the polymer at the interfaces, and steered molecular dynamics and US methods were applied to estimate the height of permeation barriers. The paper is organized as follows. In the Methods section, all the details of the simulated systems, molecular models, and methods applied in this work are reported. In the Results and Discussion section, the partition coefficient for small polymers is calculated and the behavior of the polymers at the simple binary interface of water/n-heptane is analyzed. In the second part, the interactions of the polymers with a DMPC lipid bilayer are analyzed and compared with the results from our previous study on the interaction of DME and DMP with the same interfaces and the available experimental data. Finally, in the Conclusion section, the outcome of this study is summarized.

Table 1. List of Polymers Simulated for This Study at water/n-heptane interface (1) PEO7 (2) PEO20 (3) PEO43 (4) PPO7 (5) PPO20 (6) PPO43 (7) L61 (PEO2−PPO30− PEO2) (8) L64 (PEO13−PPO30− PEO13) (9) P85 (PEO25−PPO40− PEO25)

with DMPC bilayer (1) (2) (3) (4) (5) (6) (7)

PEO2 PEO3 PEO7 PEO20 PEO43 PPO2 PPO3

for PMF calculations (1) (2) (3) (4) (5)

PEO2 PEO3 PPO2 PPO3 Plu1

(8) PPO7 (9) PPO20 (10) PPO43 (11) Plu1 (PEO1−PPO1− PEO1) (12) L61 (13) L64 (14) P85

■

METHODS Force Field. For the DMPC lipids, the united atom model of Berger et al. was adopted.21 This model is a combination of GROMOS and OPLS parameters, optimized to reproduce the experimental physical properties of lipid bilayers. For PEO, PPO, and poloxamer chains, the force field models proposed recently by our group were used.22 In all these models, methyl groups are used for both X and Y chain terminal groups. Water molecules were modeled using the simple point charge (SPC) model. For 1-octanol and n-heptane molecules, OPLS united atom (OPLS-UA) models were used.23−25 Simulation Setup. All the simulations were performed using GROMACS (version 4.5.5) software package.26 The program VMD was used for the graphical representation of the molecular systems.27 The simulations of lipid bilayers were performed at 310 K, above the crystalline fluid/liquid phase transition temperature, using the V-rescale thermostat with a coupling constant of 0.1 ps.28 For comparison, the water/nheptane systems were simulated at the same temperature. All the simulations were performed by keeping the pressure constant at 1 bar using the Berendsen barostat with a coupling constant of 0.5 ps.29 For the lipid bilayer, the semi-isotropic barostat was used to take in account the difference in compressibility of the systems along the x, y, and z directions. For the water/n-heptane simulations, the systems were equilibrated under constant pressure and the production run was performed under NVT condition. The bond lengths were constrained using LINCS algorithm.30 An integration time-step of 2 fs was used for all the simulations. Electrostatic interactions were evaluated using the particle mesh Ewald method with a cutoff of 1.0 nm, grid spacing of 0.12 nm, and a fourth-order

The coordinates of a pre-equilibrated DMPC bilayer were obtained from the Web site of Prof. Peter Tieleman at University of Calgary (http://people.ucalgary.ca/∼tieleman/ download.html). Each layer consisted of 64 DMPC chains, making a total of 128 DMPC chains. The bilayer was put in a box of dimension 6.4 × 6.4 × 9.5 nm3 along with 8167 water molecules and further equilibrated for 20 ns. For the study of the polymer at the DMPC interface, two sets of simulations were run. In the first set, the polymer molecules were positioned 1−2 nm above the bilayer surface, and after equilibration, the system was simulated for at least 50 ns. In the second set, the simulations were started with the polymer molecule located inside the DMPC lipid bilayer. For these systems, simulations were run for at least 100 ns (in particular cases, the simulations were extended up to 200 ns as specified later). Calculation of the Free Energy of Solvation and Partition Coefficient. The partition coefficient water/1-octanol is used to measure the hydrophobicity of the polymers and their tendency to partition in the lipid phase. In fact, 1-octanol can be considered a simple model of the DMPC phospholipids since it has a polar head and a long aliphatic tail. The 1-octanol/water partition coefficients were calculated at 298 K following the same procedure as described in our recent publication and using the equation log P1‐octanol/water =

ΔG hyd − ΔGsol 2.303RT

(1)

where ΔGsol and ΔGhyd are the Gibbs solvation free energy in 1-octanol and water, respectively, and R is the universal gas constant.32 14724



Article

SMD Simulations. In our previous work we have shown that spontaneous diffusion of the DME and DMP molecule inside the bilayer does not occur within 50 ns.20 This result was also recently confirmed by coarse-grained simulations in which the spontaneous diffusion of poloxamers through the bilayer was not observed even after 2 μs.45 This is consistent with recent simulation study33 of the permeation of small molecules through DMPC bilayer have estimated the mean first passage time for DMSO and water molecules in the order of ∼16 and ∼1 μs, respectively. The time scale of these events is far beyond the length of unconstrained simulations performed in this study. Therefore, in order to speed up the permeation process of the order of several hundreds of nanoseconds time scale, we have used the steered molecular dynamics (SMD) method to pull the polymer molecules inside the bilayer. The SMD simulations were performed using a slow pulling regime to ensure operation in near-equilibrium conditions.34 The pulling parameters adopted by Pal et al.35 were used to study the permeation of a PEO chain through a DMPC lipid bilayer. The simulations were started with the polymer molecule in the water phase 1−2 nm away from the upper boundary of the bilayer. The center of mass (CoM) of the polymer molecule was harmonically restrained to a spring of force constant of 200 kJ/mol. The spring tip was pulled with constant velocity 5 × 10−4 nm/ps for 10 ns. Umbrella Sampling Simulations. Umbrella sampling method was used to calculate the free energy profiles for the permeation of the relatively smaller polymer molecules (PEO2, PEO3, PPO2, PPO3, and Plu1 as shown in Table 1) through DMPC layer. This method has been described in our previous paper.20 In the present work, we have adopted similar parameters. A harmonic restraint with a force constant 3000 kJ/(mol nm2) was applied to the distance between the center of mass (CoM) of the polymer molecule and the headgroups of the bottom DMPC layer, in the direction normal to the bilayer. Depending upon the system, 40−50 starting US configurations were taken from the path of one of the SMD trajectory. The first configurations were taken around 3 nm away from the bilayer center and the last one in the center. The difference of distances between the CoM of the DME/DMP molecules and reference group for two consecutive conformations was always less than 0.1 nm to ensure the correct calculation of PMF profile. Each frame was simulated for 10 ns. The weighted histogram analysis method (WHAM)36 was used to calculate the PMF profile. The free energy profiles obtained from the calculations were rescaled to assign a zero reference value to the profiles in the bulk water.

Table 2. Free Energy of Solvation and Partition Coefficient Values of the Short Polymers in Water and 1-Octanol polymer DMEa PEO2 PEO3 DMPa PPO2 PPO3 Plu1 a

ΔG(water) −22.1 −47.85 −64.97 −16.0 −31.74 −41.29 −44.95

± ± ± ± ± ± ±

0.80a 0.47 0.42 1.10a 0.45 0.58 0.33

ΔG(octanol) −20.5 −36.90 −51.55 −24.9 −55.04 −69.15 −49.21

± ± ± ± ± ± ±

1.30a 1.36 1.05 1.00a 0.20 1.18 0.64

log Poctanol/water −0.28 ± 0.30a −1.92 ± 0.29 −2.35 ± 0.22 +1.57 ± 0.30a +4.08 ± 0.10 +4.67 ± 0.26 +0.75 ± 0.14

Value obtained from our previous publication.1−3

Polymers at the Water/n-Heptane Interface. The polymer molecules were simulated at the water/n-heptane interface with the aim to understand the structural behavior of the polymers at a hydrophobic interface and compared it with the available experimental data. The oil interface can mimic the hydrophobic interior of a lipid bilayer; thus, it was used as comparative model though the liquid n-heptane molecules lack the orderly nature of the bilayer tails. Figure 1 shows the density distributions of the polymer molecules during the simulations. Though the molecules were initially placed at the interface, PEO diffuse into the water bulk phase and remains there for the rest of the simulation. A quite different trend is observed for PPO chains. The PPO chains tend to stay at the interface, resulting in a sharp peak in the density profile. The poloxamers show similar structural and distribution behavior. The PPO parts of the polymers remain at the interface, whereas the PEO units protrude into the water region forming a bottle-brush-shaped configuration. In such configurations, polymers consist of a long flexible main chain, at which side chains are densely grafted resulting in an overall shape of a wormlike cylindrical brush.38 The final configurations of the poloxamers and of the interface are shown in Figure 2. In Table 3, the radius of gyration (Rg) and the end-to-end distances (Dee) of the polymers, calculated for the last 30 ns of the simulations, are reported. For PEO the values of both Rg and Dee are similar to their respective values in pure water (Table S2 in the Supporting Information).22 The same occur to the PPO chain except for the longest one (PPO43) for which the Rg value at the interface, 1.69 ± 0.22 nm, is higher than the one in pure water (1.40 ± 0.08 nm)22 and in pure n-heptane (1.10 ± 0.05 nm).22 This difference suggests that the elongation of the PPO chain is favored by the presence of the water/n-heptane interface. This is consistent with our previous study showing that DME (that can be considered the shortest PEO oligomer) has a higher tendency than DMP (the shortest oligomer of PPO) toward the hydrophobic n-heptane phase.20 In fact, the potential of mean force (PMF) barrier for the permeation of DMP from water to n-heptane phase was found ∼12 kJ/mol less than that of DME.20 We also observed the presence of PMF minima in exact correspondence with the interface position.20 The results from the simulations of the longer polymers in this paper suggest a similar tendency. In addition, these results are in agreement with those reported by experimental studies of different poloxamers at similar water/oil interfaces.39−43 In a recent study, Ramirez et al. have performed ellipsometry studied of three poloxamers F68, L64, and P9400 at the water/hexane interface.39 The results of this study indicate a concentration dependence of the polymer structure at the interface. The experimental data suggest that at low

■

RESULTS AND DISCUSSION Water/1-Octanol Partition Coefficients. To understand the affinity of different polymer types and lengths for the water and lipid phase, the partition coefficient values (log Poct/wat) for the short polymers between water and 1-octanol were calculated and reported in Table 2. (The values of free energy of solvation used to derive these values are reported in Table S1 of the Supporting Information.) The decreasing (negative) values of log Poct/wat for the PEO chains denote an increasing affinity for the water than the 1octanol that depends on the polymer length. An opposite trend is observed for the PPO chains. The positive values of partition coefficient indicate better affinity toward 1-octanol than water. Interestingly, the simple poloxamer Plu1 has a borderline value with slightly higher affinity for the 1-octanol. 14725



Article

Figure 1. Density distributions of the PEO and PPO chains (left) and the PEO and PPO parts of the poloxamer molecules (right) during 50 ns unconstrained simulation in the water/n-heptane interface. Water is along the negative and n-heptane is along the positive coordinate of the x-axis.

Figure 2. Snapshot of poloxamers L61 (left), L64 (middle), and P85 (right) at the end of 50 ns unconstrained simulation in water/n-heptane interface. Water is shown in red and heptane in cyan. PEO and PPO parts of the polymers are shown in blue and green, respectively.

heptane phase. This tendency was also evidenced by our previous study of PEO and PPO chains in various solvent systems.22,44 PEO Polymers at the Interface and inside the DMPC Bilayer. The interaction of PEO and PPO chains of different lengths was studied by analyzing the behavior of the chains at the interface and in the interior of a DMPC lipid bilayer. The PEO polymers located at the water/lipid interface tend to diffuse during unconstrained simulation in the bulk water phase, and no specific interactions with the lipid bilayer were observed in the rest of the 50 ns simulations. Therefore, to study their effect inside the lipid bilayer, they were pulled inside the lipid bilayer using steered MD simulations. Once in the middle of the bilayer, the systems were first equilibrated using unconstrained MD and hence simulated for 100 ns. The Rg values were calculated in all the cases (shown in Table 3). As the polymer chains diffuse in the water phase, the values for each chain inside and outside the lipid bilayer have similar values, and those values are comparable with the values of Rg of PEO chains in water as reported in our previous work.21 In Figure 3, the density distribution of the polymers along the z-axis of the simulation box is shown in the left. Both the PEO oligomers diffused out of the bilayer into the water phase within 10 ns. The same behavior is observed for longer chains (7, 20, and 43 monomers) that diffuse out of the bilayer into the water phase within 50 ns. Interestingly, the PEO chains inside the lipid bilayers do not perturb significantly the lipid packing as

Table 3. Radius of Gyration (Rg) and End-to-End Distances (Dee) of the Polymers at the Water/n-Heptane Interface polymer PEO7 PEO20 PEO43 PPO7 PPO20 PPO43 L61 L64 P85

Rg (nm) 0.51 1.01 1.52 0.47 0.88 1.69 1.32 1.68 2.34

± ± ± ± ± ± ± ± ±

0.05 0.14 0.23 0.05 0.12 0.22 0.20 0.21 0.28

Dee (nm) 1.37 2.59 3.52 1.23 2.42 3.55 3.44 3.29 3.49

± ± ± ± ± ± ± ± ±

0.32 0.80 1.06 0.32 0.73 0.41 0.84 0.92 1.07

PEO/PPO concentration ratio the poloxamers assume a conformation with both PEO and PPO units in contact with the interface. As the ratio of PEO/PPO increases, the PEO parts tend to protrude into the water bulk phase forming a coiled structure. Finally, if the ratio is further increased, a mushroom-like conformation is observed in which PEO units reside in the water phase and the PPO unit coils up at the interface with a part in contact with both the solvent phases.39 The trend is similar to the results of our simulations. The smallest poloxamer, L61, assumes an extended conformation at the interface (Figure 2, left). The increased numbers of PEO and PPO monomers in the poloxamers L64 and P85 determine the protrusion of PEO chains in the water phase. In fact, PEO, being more hydrophilic than PPO, is expected to have a larger propensity for the water phase rather than the hydrophobic n14726



Article

Figure 3. Density distributions of smaller polymers chains (left) and the long PPO chains (right) inside the DMPC lipid bilayer. The position of the DMPC bilayer is shown in the background in gray.

Supporting Information). Finally, the PPO3 remained inside the bilayer for the whole course of the simulation. In this case, the simulation was further extended up to 200 ns without observing the diffusion of the polymer out of the bilayer even in this longer time frame. Longer chains of 7, 20, and 43 monomers stay inside the lipid bilayer during the simulation time, mainly localizing at the aliphatic tail group region of the bilayer. The density distributions of the PPO chains are shown in left profile of Figure 3. From the density distribution, it can be seen that the smallest PPO chain (with seven monomers) has a localized distribution near the bottom headgroup region of the lipid bilayer. In the case of PPO20, the density profile is more flat and well distributed throughout the bilayer. PPO43 stays more localized near the headgroup region but has a distribution ranging throughout the aliphatic region of the lipid bilayer. Also in this case Rg values of the PPO chains were calculated, and they are reported in Table 4. For PPO chains outside lipid bilayer the Rg values are similar to that of in bulk water.22 But for PPO chains inside the lipid bilayer, the Rg have smaller values for respective chains. The Rg values inside the bilayer has comparable values as for that in bulk n-heptane as reported in our previous study.22 On the contrary to PEO, the PPO chains inside the DMPC bilayer perturb the lipid organization determining AApL values higher than for those from simulations with PPO in the bulk phase. Moreover, the AApL values increase (up to ∼4%) with the length of the PPO chain (see Figure 3). Nevertheless, the lipid bilayer thickness, calculated using the peak-to-peak distance of the headgroup phosphorus atoms density

shown by the small variation of the average area per lipid (AApL) in Figure 4. In fact, the AApL values do not show significant differences for the simulation with polymers located at interface or inside the lipid bilayer.

Figure 4. Average area per lipid for the systems staring with PEO and PPO at the interface and inside the bilayer.

PPO at the Interface and inside the Bilayer. Similar to PEO, PPO does not show any preference to interact with the DMPC lipid bilayer and stays in the water phase outside the lipid bilayer. A set of simulations was run with the PPO chains inside the lipid bilayer using the procedure described in the previous paragraph. The PPO2 also diffused out of the bilayer, but the process occurred after 50 ns for it (Figure S3 in the

Table 4. Radius of Gyration Values of PEO and PPO Chains inside and outside DMPC Lipid Bilayer PEO inside outside

PPO

PEO7

PEO20

PEO43

PPO7

PPO20

PPO43

0.51 ± 0.05 0.51 ± 0.05

0.99 ± 0.14 1.00 ± 0.14

1.61 ± 0.25 1.59 ± 0.44

0.44 ± 0.04 0.48 ± 0.04

0.73 ± 0.08 0.90 ± 0.12

1.05 ± 0.09 1.62 ± 0.23

14727



Article

However, the kinetics of the process is quite different between the PEO and PPO chains. For the PPO containing chains, the spontaneous diffusion out of the lipid bilayer take longer time compared to PEO chains of the same length and for long chains, the process cannot be observed within the hundred(s) of nanoseconds of our simulations. It is likely that the process occur on time scale of microseconds as observed from coarsegrained simulations of same polymers and membrane models.45 The difference between the two polymer’s expulsion kinetic can be due of the larger steric hindrance of the PPO unit compared to the PEO one.20 Poloxamers at the Water/DMPC Bilayer Interface and inside DMPC Bilayer. Also for the case of the poloxamers studied in this paper, the atomistic simulations are too short to observe spontaneous diffusion of the polymers inside the lipid bilayer. Even in the case of the shortest possible model of a poloxamer (Plu1) studied in this paper, we did not observed spontaneous diffusion in the lipid bilayer within 50 ns. Instead, it spontaneously diffused out of the bilayer within 50 ns. Even with the current limitation of atomistic sampling, it is still useful and interesting to analyze the specific interaction occurring between the polymer and the lipid bilayer in the time scale of this study. In Figures 6 and 7, the values of AApL and bilayer thickness (i.e., the distance between the phosphorus atoms of the two

distributions, show no significant change for the all the simulated systems (Figure S2 in the Supporting Information). PMF Calculation of the Thermodynamics Percolations Barrier of Small Polymers in DMPC Lipid Bilayer. To thermodynamically quantify the results of the unconstrained simulations reported in the previous paragraphs and to analyze the effect of the chain length of the polymers on the permeation barriers, PMF’s through DMPC lipid bilayer of small polymers set have been calculated using the US method. The calculations were performed on the dimers and trimers of PEO and PPO and on Plu1. The PMFs for the single monomers, e.g., the DME and DMP molecules, have been reported in a previous publication.20 In Figure 5, different PMF

Figure 5. Comparison of PMF profiles of permeation of small polymers using umbrella sampling method. The position of the DMPC bilayer is shown as the gray background. The data for DME and DMP are included for comparison.20

profiles obtained from the US simulations, together with those from the DME and DMP, are shown. The curves are all referred to the same reference state (bulk water) for comparison. From the plot, as general trend, a gradual increase of the height of the energy barrier for permeation with the increase of the chain length of the polymers of same type is observed. The profiles are characterized by an steep rise in correspondence of the lipids headgroups followed by a plateau or a minimum when the polymer meet the tails region with a subsequent increase toward the center of the lipid bilayer. Though bulkier, the PPO chains have lower energy barriers than their corresponding PEO counterparts. For Plu1, the height of PMF of permeation is lower than the PEO or PPO chains of similar length. The relative difference between PEO and PPO can be attributed to the nonbonded and electrostatic energy contributions as explained in our previous work.20 Also, the loss of stability due to the loss of hydrogen bonds is much more extensive for DME/PEO. These effects result in a higher PMF barrier for PEO chains compared to their PPO counterparts. Interestingly, the poloxamer Plu1 has lower PMF barrier that both PEO3 and PPO3, though being of comparatively similar length. This suggests that in block copolymer the hydrophilic−lipophilic balance of the PEO and PPO blocks can facilitate the permeability in lipid bilayer than a PEO or PPO chain of similar length. The PMF profile suggests that thermodynamically the polymer favors the water phase than the lipid bilayer interior.

Figure 6. Average area per lipid for the polymers simulated.

lipid layers) are reported for L61, L64, and P85 outside and inside the bilayer. For values of the AApL with the polymers at the interface of the bilayer, the range of variation is quite small. When the simulations were started with the polymers inside the bilayer, the AApL value drops slightly below the normal value for pure DMPC bilayer, and they have quite similar values for all the poloxamers molecules. The distance between the phosphorus atoms of the top and bottom layer of DMPC bilayer was calculated to investigate any change in the width of the bilayer. Figure 7 shows the density distribution of the P atoms in both the layers. The dotted lines represent the density profile of the P atoms when the polymers were outside the bilayer at the water phase. No significant change in the membrane thickness was observed for this condition. On the contrary, when the simulations were started with the polymer molecules inside the bilayer, a significant increase in the distance between the P atoms was observed for L61 and L64. The absence of effects on 14728



Article

density distributions of the polymers along with its components are shown in the bottom row of Figure 8, and that also shows that in the case of L61 and L64 the PPO chain remains extended through the bilayer and forms a bridge while the PEO part stays in the headgroup region of the bilayer or in the water phase. The length of the PPO chain of L61 and L64 is shorter than P85, and the length is comparable to the width of the bilayer. Hence for L61, the hydrophobic PPO chain can extend throughout the width of the aliphatic region of bilayer, keeping the PEO parts in the polar and more favorable headgroup region. On the contrary, the PEO chains of the L64, being longer, extend into the water phase as well. In the both cases, the PPO block adopts a linear conformation inside the bilayer. In the case of P85, the length of the PPO chain is longer than the width of the bilayer and cannot extend along the width of the bilayer. Figure 9 shows the evolution of the radius of gyration (Rg) and end-to-end distance (Dee) of the polymers during the course of the simulations. In comparison, L61 has the lowest Rg value, and the other two polymers have similar Rg values after 10 ns of the simulation. The trend of Dee values is in order with the length of the polymer chains for L61 and L64. The P85 chain tends to assume a coiled conformation as shown in Figure 8. For that reason, despite the fact that P85 is the longest polymer among them, it still has the smallest Dee value.

Figure 7. P−P density profiles for systems B during the last 25 ns of simulation.

■

the thickness of the bilayer can be due to the limited extend of simulation time scale. Figure 8 shows the final conformations of the systems started with the polymers inside the lipid bilayer. For L61 and L64, the PPO part extends along the width of the bilayer and the PEO part resides in the lipid headgroup region. For P85, the PPO part remains coiled and the PEO parts localizes in the water interface by the upper headgroup region of the bilayer. The

CONCLUSIONS In this paper, structural properties of ether-based linear and block polymers in water/n-heptane and water/DMPC bilayer interfaces have been investigated with molecular dynamics simulations. The properties of PEO, PPO, and poloxamers were first investigated at the water/n-heptane interface. Our

Figure 8. Final conformation of poloxamers L61, L64, and P85 (left to right) at the end of 100 ns unconstrained simulations inside the DMPC lipid bilayer are shown on the top. In the bottom, the density distributions of the poloxamers during 100 ns unconstrained simulations inside the DMPC lipid bilayer are shown. The PEO part of the polymers is shown in blue, and the PPO part is shown in green. For the sake of clarity water is not shown. The density of the polymer in whole is shown in black, and the position of the DMPC bilayer is shown in orange. 14729



Article

Figure 9. Distribution of radius of gyration (left) and end-to-end distance (right) of the poloxamers L61, L64, and P85 during 100 ns unconstrained simulation inside a DMPC bilayer.

■

study shows that while PPO prefers to stay in the water/nheptane interface, PEO tends to diffuse to the water phase. This produces the bottle-brush type of structure for poloxamers molecules at the water/n-heptane interface. This observation is in agreement with available experimental results. The polymers at the water/DMPC interface did not render significant effects within 50 ns. Spontaneous diffusion of polymers inside lipid membrane is out of reach of atomistic simulations since the time scale for that can be as an order of microseconds.45 Hence, the properties of polymers inside lipid bilayer were studied by pulling them inside the bilayer using SMD simulations. PEO chains did not show any preference for the interior of the bilayer and diffused out of the bilayer. In comparison, the PPO chains tend to stay longer inside the lipid bilayer than the PEO chains. Relatively longer PPO20 and PPO43 tend to span across the width of the bilayer while the short PPO7 chain stayed in the tail region of the bilayer near the polar headgroups. Poloxamers L61 and L64 have PPO blocks with a length comparable to the width of the tail region of the bilayer. They spanned across the bilayer with the hydrophilic PEO blocks in the polar headgroup region and water in both sides. The PPO block length of P85 is longer than the width of the bilayer, and it assumed a conformation where the PPO block stays in the aliphatic tail group region of the bilayer and the PEO blocks stayed in the headgroup region and water phase in the same side of the bilayer. The findings are in order with the experimental results as reported by Firestone et al. from X-ray scattering studies.6,7 The PMF profiles of bilayer permeation were obtained using umbrella sampling method for small polymers. The energy barrier to transfer the polymers from water into the DMPC tail region was found to be smaller for PPO chains of all lengths than their PEO counterparts. For poloxamer Plu1, the energy barrier was found to be much lower than the homopolymers of similar length. This suggests that in block copolymer the hydrophilic−lipophilic balance of the block PEO and PPO blocks can facilitate the permeability in lipid bilayer than a PEO or PPO chain of similar length. In conclusion, the results of this study provide interesting insights into the mechanism of permeation of polyethers (PEO, PPO, and poloxamers) into the DMPC lipid bilayer at the atomistic level. Our results provide an accurate atomistic model on the partition behavior of hydrophilic PEO and hydrophobic PPO blocks of these polymers at a membrane interface.

ASSOCIATED CONTENT

* Supporting Information S

Density distribution of poloxamers outside DMPC bilayer, P−P density profiles, and comparison of PMF profiles of permeation of small polymers. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Fax +49 421 200-3249; Tel +49 421 200-3144; e-mail d. [email protected] (D.R.). Present Addresses †

S.S.: Dipartimento di Fisica, Università degli Studi di Cagliari, Monserrato, 09042 Cagliari, Italy. ‡ S.H.: Center of Smart Interfaces, Technische Universität Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This project is funded by the Deutsche Forschungsgemeinschaft (DFG) for the project “The study of detailed mechanism of polymers/biological membrane interactions using computer simulation” (RO 3571/3-1). The computational resources of the Computer Laboratories for Animation, Modeling and Visualization (CLAMV) at Jacobs University Bremen were used for the study.

■

REFERENCES

(1) Fusco, S.; Borzacchiello, A.; Netti, P. A. Perspectives on: PEOPPO-PEO Triblock Copolymers and their Biomedical Applications. J. Bioact. Compat. Polym. 2006, 21, 149−164. (2) Haag, R.; Kratz, F. Polymer Therapeutics: Concepts and Applications. Angew. Chem., Int. Ed. 2006, 45, 1198−1215. (3) Kodera, Y.; Matsushima, A.; Hiroto, M.; Nishimura, H.; Ishii, A.; Ueno, T.; Inada, Y. Pegylation of Proteins and Bioactive Substances for Medical and Technical Applications. Prog. Polym. Sci. 1998, 23, 1233− 1271. (4) Alarcon, C. D. H.; Pennadam, S.; Alexander, C. Stimuli Responsive Polymers for Biomedical Applications. Chem. Soc. Rev. 2005, 34, 276−285. (5) Chowdhary, R. K.; Sharif, I.; Chansarkar, N.; Dolphin, D.; Ratkay, L.; Delaney, S.; Meadows, H. Correlation of Photosensitizer Delivery to Lipoproteins and Efficacy in Tumor and Arthritis Mouse Models; Comparison of Lipid-Based and Pluronic P123 Formulations. J. Pharm. Pharm. Sci. 2003, 6, 198−204.

14730



Article

(6) Firestone, M. A.; Wolf, A. C.; Seifert, S. Small-Angle X-ray Scattering Study of the Interaction of Poly(ethylene oxide)-bPoly(propylene oxide)-b-Poly(ethylene oxide) Triblock Copolymers with Lipid Bilayers. Biomacromolecules 2003, 4, 1539−1549. (7) Firestone, M. A.; Seifert, S. Interaction of Nonionic PEO-PPO Diblock Copolymers with Lipid Bilayers. Biomacromolecules 2005, 6, 2678−2687. (8) Sahu, A.; Bora, U.; Kasoju, N.; Goswami, P. Synthesis of Novel Biodegradable and Self-Assembling Methoxy Poly(ethylene glycol)Palmitate Nanocarrier for Curcumin Delivery to Cancer Cells. Acta Biomater. 2008, 4, 1752−1761. (9) Melik-Nubarov, N. S.; Pomaz, O. O.; Dorodnych, T. Y.; Badun, G. A.; Ksenofontov, A. L.; Schemchukova, O. B.; Arzhakov, S. A. Interaction of Tumor and Normal Blood Cells with Ethylene Oxide and Propylene Oxide Block Copolymers. FEBS Lett. 1999, 446, 194− 198. (10) Smyth, H. F.; Weil, C. S.; Woodside, M. D.; Knaak, J. B.; Sullivan, L. J.; Carpente, Cp. Experimental Toxicity of a High Molecular Weight Poly(Ethylene Oxide). Toxicol. Appl. Pharmacol. 1970, 16, 442−445. (11) Zhou, P.; Brown, W. Static and Dynamic Properties of Poly(Ethylene Oxide) in Methanol. Macromolecules 1990, 23, 1131− 1139. (12) Liang, X.; Mao, G.; Ng, K. Y. S. Effect of Chain Lengths of PEOPPO-PEO on Small Unilamellar Liposome Morphology and Stability: An AFM Investigation. J. Colloid Interface Sci. 2005, 285, 360−372. (13) Israelachvili, J. The Different Faces of Poly(ethylene glycol). Proc. Natl. Acad. Sci. U. S. A. 1997, 94, 8378−8379. (14) Malcolm, G. N.; Rowlinson, J. S. The Thermodynamic Properties of Aqueous Solutions of Polyethylene Glycol, Polypropylene Glycol and Dioxane. Trans. Faraday Soc. 1957, 53, 921−931. (15) Granite, M.; Radulescu, A.; Pyckhout-Hintzen, W.; Cohen, Y. Interactions between Block Copolymers and Single-Walled Carbon Nanotubes in Aqueous Solutions: A Small-Angle Neutron Scattering Study. Langmuir 2011, 27, 751−759. (16) Xin, X.; Xu, G. Y.; Zhang, Z. Q.; Chen, Y. J.; Wang, F. Aggregation Behavior of Star-Like PEO-PPO-PEO Block Copolymer in Aqueous Solution. Eur. Polym. J. 2007, 43, 3106−3111. (17) Sevink, G. J. A.; Fraaije, J. G. E. M.; Huinink, H. P. Structure of Aqueous Pluronics Films: A Dynamics of Surface Directed Mesophase Formation. Macromolecules 2002, 35, 1848−1859. (18) Steve, O. N.; et al. Coarse Grain Models and the Computer Simulation of Soft Materials. J. Phys.: Condens. Matter 2004, 16, R481− R512. (19) Saiz, L.; Klein, M. L. Computer Simulation Studies of Model Biological Membranes. Acc. Chem. Res. 2002, 35, 482−489. (20) Samanta, S.; Hezaveh, S.; Milano, G.; Roccatano, D. Diffusion of 1,2-Dimethoxyethane and 1,2-Dimethoxypropane through Phosphatidycholine Bilayers: A Molecular Dynamics Study. J. Phys. Chem. B 2012, 116, 5141−5151. (21) Berger, O.; Edholm, O.; Jahnig, F. Molecular Dynamics Simulations of a Fluid Bilayer of Dipalmitoylphosphatidylcholine at Full Hydration, Constant Pressure, and Constant Temperature. Biophys. J. 1997, 72, 2002−2013. (22) Hezaveh, S.; Samanta, S.; Milano, G.; Roccatano, D. Molecular Dynamics Simulation Study of Solvent Effects on Conformation and Dynamics of Polyethylene Oxide and Polypropylene Oxide Chains in Water and in Common Organic Solvents. J. Chem. Phys. 2012, 136, 124901−124912. (23) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; Reidel: Dordrecht, 1981; p 331. (24) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. Optimized Intermolecular Potential Functions for Liquid Hydrocarbons. J. Am. Chem. Soc. 1984, 106, 6638−6646. (25) Garrido, N. M.; Queimada, A. J.; Jorge, M.; Macedo, E. A.; Economou, I. G. 1-Octanol/Water Partition Coefficients of n-Alkanes from Molecular Simulations of Absolute Solvation Free Energies. J. Chem. Theory Comput. 2009, 5, 2436−2446.

(26) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (27) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33−38. (28) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. J. Chem. Phys. 2007, 126, 14101−14107. (29) Berendsen, H. J. C.; Postma, J. P. M.; Vangunsteren, W. F.; Dinola, A.; Haak, J. R. Molecular-Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (30) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, 1463−1472. (31) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald - an N.Log(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089−10092. (32) Lin, J.; Novak, B.; Moldovan, D. Molecular Dynamics Simulation Study of the Effect of DMSO on Structural and Permeation Properties of DMPC Lipid Bilayers. J. Phys. Chem. B 2012, 116, 1299− 1308. (33) Samanta, S.; Roccatano, D. Interaction of Curcumin with PEOPPO-PEO Block Copolymers: A Molecular Dynamics Study. J. Phys. Chem. B 2013, 117, 3250−3257. (34) Park, S.; Khalili-Araghi, F.; Tajkhorshid, E.; Schulten, K. Free Energy Calculation from Steered Molecular Dynamics Simulations Using Jarzynski’s Equality. J. Chem. Phys. 2003, 119, 3559−3566. (35) Pal, S.; Milano, G.; Roccatano, D. Synthetic Polymers and Biomembranes. How Do They Interact?: Atomistic Molecular Dynamics Simulation Study of PEO in Contact with a DMPC Lipid Bilayer. J. Phys. Chem. B 2006, 110, 26170−26179. (36) Kumar, S.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A.; Rosenberg, J. M. The Weighted Histogram Analysis Method for FreeEnergy Calculations on Biomolecules. 1. The Method. J. Comput. Chem. 1992, 13, 1011−1021. (37) Samanta, S.; Hezaveh, S.; Milano, G.; Roccatano, D. Correction to “Diffusion of 1,2-Dimethoxyethane and 1,2-Dimethoxypropane through Phosphatidycholine Bilayers: A Molecular Dynamics Study”. J. Phys. Chem. B 2012, 116, 9286−9286. (38) Rathgeber, S.; Pakula, T.; Wilk, A.; Matyjaszewski, K.; Beers, K. L. On the Shape of Bottle-Brush Macromolecules: Systematic Variation of Architectural Parameters. J. Chem. Phys. 2005, 122, 124904−124913. (39) Ramirez, P.; Stocco, A.; Munoz, J.; Miller, R. Interfacial Rheology and Conformations of Triblock Copolymers Adsorbed onto the Water-Oil Interface. J. Colloid Interface Sci. 2012, 378, 135−143. (40) Holmqvist, P.; Alexandridis, P.; Lindman, B. Modification of the Microstructure in Block Copolymer−Water−“Oil” Systems by Varying the Copolymer Composition and the “Oil” Type: Small-Angle X-ray Scattering and Deuterium-NMR Investigation. J. Phys. Chem. B 1998, 102, 1149−1158. (41) Alexandridis, P.; Olsson, U.; Lindman, B. Phase Behavior of Amphiphilic Block Copolymers in Water-Oil Mixtures: The Pluronic 25R4-Water-p-Xylene System. J. Phys. Chem. 1996, 100, 280−288. (42) Alexandridis, P. Amphiphilic Copolymers and Their Applications. Curr. Opin. Colloid Interface Sci. 1996, 1, 490−501. (43) Gotchev, G.; Kolarov, T.; Khristov, K.; Exerowa, D. On the Origin of Electrostatic and Steric Repulsion in Oil-in-Water Emulsion Films from PEO-PPO-PEO Triblock Copolymers. Colloids Surf., A 2010, 354, 56−60. (44) Hezaveh, S.; Samanta, S.; Milano, G.; Roccatano, D. Structure and Dynamics of 1,2-Dimethoxyethane and 1,2-Dimethoxypropane in Aqueous and Non-aqueous Solutions: A Molecular Dynamics Study. J. Chem. Phys. 2011, 135, 164501−164511. (45) Hezaveh, S.; Samanta, S.; De Nicola, A.; Milano, G.; Roccatano, D. Understanding the Interaction of Block Co-Polymers with DMPC Lipid Bilayer Using Coarse-Grained Molecular Dynamics Simulations. J. Phys. Chem. B 2012, 116, 14333−14345.

14731


Theoretical Study of Binding and Permeation of ... - ACS Publications

Recommend Documents