Interactions of Amphiphilic Triblock Copolymers with Lipid Membranes

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Interactions of Amphiphilic Triblock Copolymers with Lipid Membranes: Modes of Interaction and Effect on Permeability Examined by Generic Monte Carlo Simulations Hauke Rabbel,*,† Marco Werner,† and Jens-Uwe Sommer*,†,‡ †

Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Str. 6, 01069 Dresden, Germany Technische Universität Dresden, Institute of Theoretical Physics, 01069 Dresden, Germany

‡

ABSTRACT: We investigate interactions of linear amphiphilic ABA triblock copolymers with lipid bilayer membranes by means of Monte Carlo simulations in a generic coarse-grained model. The polymers have hydrophilic A-blocks and B-blocks of varying hydrophobicity. The effect of different conformational states of the polymer on the induced permeability for solvent molecules is examined. We demonstrate that the local permeability of the membrane can be strongly increased in the transmembrane state, in particular for a mismatch in the hydrophobicity between the middle block and the membrane core, while the hairpin state has almost no effect on this property, especially for growing hydrophobic mismatch. We have investigated the relative stability of the two states using thermodynamic integration and have shown that only in a range of intermediate hydrophobic block lengths NB and hydrophobicities HB the transmembrane state is stable. Increasing mismatch of the B-block in terms of relative hydrophobicity and block length not only causes stronger perturbations in the membrane if the polymer is in the transmembane state but also renders this state metastable. Our studies support in particular previous experimental studies suggesting a two-state model of PEO−PPO−PEO copolymers.

1. INTRODUCTION

A widely used type of amphiphilic block copolymer is linear ABA triblock structures, the most prominent being poloxamers, known also under the commercial name Pluronics, a class of amphiphilic triblock copolymers made of polyethylene oxide (PEO) and polypropylene oxide (PPO). Numerous studies have shown the efficacy of these polymers as chemosensitizing agents in cancer treatment.10,11 Even though the mechanisms of interaction between such triblock copolymers and lipid bilayer membranes have been under investigation for some decades,12 the picture is not yet complete, owing to the complexity of the problem. Numerous experimental and simulation studies have been conducted, leading to sometimes seemingly contradictory conclusions depending on the model system under investigation. Setups differ for example in the type of lipids used, the polymer structure and composition,13−18 the use of lipid vesicles,16,18 lamellar membrane structures,14 or living cells.3 Similarly, molecular dynamics simulations have been performed on atomistic19 and coarse grained scales.20,21 Amphiphilic triblock copolymers have been demonstrated to be able to act as membrane sealants,3 as well as permeabilizers,16,18 or as protection against lipid peroxidation.22 Also, the conformations the polymers take with respect to the membrane are still under debate.20,22−24 Possible scenarios are insertion of the hydro-

Amphiphilic block copolymers consist of hydrophobic and hydrophilic chemical units. Their amphiphilic nature provides these molecules with remarkable properties and great potential for use in biomedical and pharmaceutical contexts.1,2 Possible applications are healing or protection of damaged cell membranes,3,4 or use as self-assembled drug delivery devices, where polymer micelles enclose a cargo in the water, and enhance the cellular uptake once contact with cell membranes is made.5,6 When in contact with lipid bilayer membranes, the hydrophobic blocks tend to interact favorably with the hydrocarbon core of the membrane, whereas the hydrophilic parts do the opposite. This heterogeneity enables amphiphilic polymers to alter membrane properties. Depending on the relative size, weight fractions, and hydrophobicities of the building blocks, the polymers can associate with the membrane in different ways, such as localization at the interface, partial, or full incorporation into the membrane structure. This polymer association can have diverse effects on membrane properties such as permeability, fluidity, or mechanical stability.7 Clearly, understanding the factors that cause these different, and sometimes seemingly opposing, effects is necessary for making the best use out of the potential of these molecules. A broad range of amphiphilic block copolymers with different chemical components and structures are being used in ongoing research.8,9 © XXXX American Chemical Society

Received: April 8, 2015 Revised: June 8, 2015

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DOI: 10.1021/acs.macromol.5b00720 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Schematic representation of the interaction model for lipids (h,t), solvent (s), and triblock copolymers (A,B). (t,B). The interaction potential is realized as a nearest neighbor contact interaction, where each contact between two monomers of species i and j contributes a contact energy of

phobic block into the hydrocarbon core of the membrane with the hydrophilic ends on opposing sides (transmembrane state) or the same side (hairpin state), or is only a loose attachment to the bilayer−solvent interface. The preferred configuration is, however, not clear. It is largely agreed on that the size of the hydrophobic block is a key determinant of the mode of polymer−membrane association. Only polymers with a sufficiently long hydrophobic block can adopt a transmembrane conformation. Wang et al. conclude from a series of experiments with giant unilamellar vesicles (GUVs) treated with Pluronics18,22 that the position of the polymer with respect to the membrane is a key to understanding the function as sealants or permeabilizers. Polymers adsorbed to the bilayer−water interface do not disrupt the membrane structure and can have a stabilizing or protective effect, whereas a deep insertion of the hydrophobic block into the bilayer core has a destructive effect on the GUVs. Their hypothesis is that it is the mismatch in size and hydrophobicity of the hydrophobic block compared with the membrane core that determines the destructive effect. On the other hand, a recent simulation study suggests that the hydrophobic block stabilizes the membrane, whereas the hydrophilic blocks lead to membrane distortion.19 Apart from a few exceptions,15 experiments have been mostly carried out with triblock copolymers of different block lengths, while the solubility of the chemical components was kept constant. Simulation studies have been focused on atomistic or coarse-grained studies of particular molecules, such as Pluronics interacting with DMPC lipid bilayers.20 A systematic simulation study of the influence of the relative hydrophobicity of the chemical units, in combination with varying block lengths, appears to be still missing. This article aims at closing this gap. We have carried out Monte Carlo simulations of linear amphiphilic triblock copolymers interacting with lipid bilayer membranes in a generic coarse-grained model. By varying the hydrophobic block length as well as the hydrophobicity of the chemical units, we analyze the influence of these parameters on induced membrane permeability and the modes of membrane− polymer association. We have calculated the potential of mean force acting on the polymer and determined the free energy difference between transmembrane and hairpin conformations by means of thermodynamic integration.

ϵij = |Hi − Hj|ϵ0 where ϵ0 = 0.8kBT and Hi∈[0,1] is the relative hydrophobicity of the i-th species (see Figure 1). The hydrophobicities used in this study are Hs = Hh = HA = 0.0, Ht = 1.0, and HB is varied as a parameter in the simulations in the range 0.5 ⩽ HB ⩽ 1.0. The choice of the parameters for the lipids have been shown to lead to self-assembly into stable bilayers.29 The simulation box has been chosen with the dimension (64a) 3 with periodic boundary conditions and a denoting the lattice constant of the simple cubic lattice. 300 lipids were preordered in the simulation box to form a bilayer membrane parallel to the x,y plane spread over the periodic boundaries. A single polymer chain was initially placed in the box in either the transmembrane or hairpin conformation. The simulation box was filled up with solvent (s) to achieve a total volume occupation of 0.5 corresponding to a dense state in the BFM. We have used polymer chains consisting of N = 64 and N = 128 repeat units with varying lengths NA, NB of the A- and Bblocks. Each simulation has been equilibrated for 107 Monte Carlo sweeps (MCS) and analyzed for at least 1 × 108 MCS. For nonionic amphiphiles such as poloxamers and other surfactants, the degree of hydrophobicity is commonly quantified by the “hydrophilic/lipophilic balance” (HLB).30−32 This parameter translates the overall hydrophobicity of a molecule to a value between 20 (hydrophilic) and 0 (hydrophobic) for nonionic surfactants. If we define a mean hydrophobicity H̅ as H̅ =

HANA + HBNB NA + NB

we can roughly estimate the HLB as31

HLB = 20(1 − H̅ ) According to this, the simulated polymers range between HLB = 10 and HLB ≈ 20, but these values have to be seen only as an approximation, as the calculation of the HLB from the structure of a molecule is not trivial.32 HLB values of some common Pluronics can be found in ref 1 (for example PEO9PPO32PEO9 has HLB = 11).

3. RESULTS 3.1. Mode of Polymer−Membrane Interaction: Transmembrane and Hairpin States. In order to characterize the polymer−membrane interaction we have calculated the potential of mean force F(z) acting on the hydrophobic middle monomer in the vicinity of the membrane. To this end, we recorded the probability distribution p(z) of finding the middle monomer at a distance z from the bilayer midplane in the simulations (Figure 2) . The potential of mean force can then be calculated via the relation

2. METHODS We use the bond fluctuation model25,26 (BFM) with an explicit repulsive solvent27,28 to simulate lipid bilayer membranes interacting with linear ABA-triblock copolymers. Figure 1 shows the structure of the molecules used in our simulation study. Lipids are formed by head (h) groups of three monomeric units and two tails (t) of five units. The hydrophobic effect is mediated by a short-range repulsive interaction between hydrophilic (h, s, A) and hydrophobic monomers

F(z)/kBT = −ln(p(z)) B


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the transmembrane conformation. For all chain lengths considered here the minimum of the potential is located in the center of the bilayer (Figure 3), which is clear by symmetry. For HB = 0.5 and a B-block length much larger than necessary to bridge the bilayer width D, the formation of droplets on the membrane surface is observed, while both hydrophilic ends are still on opposing sides of the membrane (Figure 5 bottom). It can be seen in all simulations that the free energy profile F(z) becomes softer with decreasing HB; i.e., the force driving the polymer back to the bilayer midplane becomes weaker. This trend can be explained in an idealized theoretical model, as shown in the next paragraph below. Transmembrane Configuration in an Ideal Chain Model. A simple model can be employed to explain the form of the potential of mean force acting on transmembrane triblock copolymers. The transmembrane part of the polymer is pictured as an ideal chain with the start and end points fixed on the membrane surface (Figure 4). For such a chain of length NB = n1 + n2 the distribution of the z-coordinate of the middle monomer can be calculated analytically. Here, n1 and n2 are the lengths of the subchains to either side of the middle monomer. The distribution can be written as

Figure 2. Simulation snapshot illustrating the coordinate z used in the calculations of the potential of mean force F(z): z is taken to be the distance of the middle monomer from the local bilayer midplane in the direction normal to the membrane. The local bilayer midplane was determined in a patch of radius R = 15 lattice units around the middle monomer.

As we aim to characterize the transmembrane and the hairpin states separately, two sets of simulations were carried out, in which the polymer was initially positioned in either a transmembrane or hairpin conformation. For each set, the hydrophobicities HB and length NB of the hydrophobic block were varied as parameters. In all simulations the polymer remained in the initially constructed transmembrane or hairpin state, except for the parameters HB = 0.64 and HB = 0.5 with N = 64. The question regarding which of the states, transmembrane or hairpin, is the more stable one was addressed by thermodynamic integration. The results for the potentials of mean force and from the thermodynamic integration are shown in the following. Potential of Mean Force for the Hairpin State. The calculated potentials for polymers of length N = 64 are shown in Figure 3 (lef t). The degree of incorporation of the hydrophobic block into the membrane is reflected by two major characteristics of the potential: First, the position of the minimum gives an indication of the penetration depth. Second, the difference between the potential minimum at the bilayer and the bulk solvent plateau shows the binding strength. Both quantities depend strongly on the hydrophobicity HB, as well as the block length NB. The length of the hydrophilic block NA did not have any significant influence (data not shown). Polymers with HB ⩽ 0.64 did not adsorb to the interface, irrespective of the length of the B-block. With growing hydrophobicities and block lengths NB, the development of (local) potential minima in the bilayer core, or at the interface, was observed. As can be concluded from Figure 3 (left), the threshold hydrophobicity Hads B , for which the adsorbed hairpin state becomes favorable as compared to the desorbed state, decreases with the length NB of the B-block. For the most hydrophobic polymers with HB = 1.0 and NB ⩾ 16, a desorption from the membrane could not be observed during the simulations. Potential of Mean Force for the Transmembrane State. The calculated potentials for transmembrane polymers of length N = 64 under variation of NB and HB are shown in Figure 3 (right). The potentials for polymers of total length N = 128 did not differ significantly and are therefore not shown. The only exception was the simulation with NB = 32, HB = 0.64, in which the polymer remained in the transmembrane state only for N = 128. In all other simulations with hydrophobicities in the range HB = 0.64−1.0, the polymers remained stable in

⎧ z2 ⎫ ⎬ G(z ; n1 , n2 , D) = C(n1 , n2 , D) exp⎨− 2 ⎩ 2n1b ⎭ ⎧ (D − z)2 ⎫ ⎬ exp⎨− 2n2b2 ⎭ ⎩

with the normalization factor ⎧1 ⎫ ⎛ 1 (n + n ) ⎞1/2 D2 1 2 ⎨ ⎬ ⎟ C(n1 , n2 , D) = ⎜ exp 2 2 ⎩ 2 (n1 + n2)b ⎭ ⎝ 2π n1n2b ⎠

Here, D is the membrane width and b an average bond length. Allowing the numbers n1,2 to fluctuate independently gives rise to the following expression for the distribution of the middle monomer: G(z ; D , HB) = Ω−1 ∑ G(z ; n1 , n2 , D) n1, n2

exp{−E(n1 , n2 , HB)}

Ω=

∑

exp{−E(n1 , n2 , HB)}

n1, n2

where the statistical weight exp{−E(n1,n2,HB)} stems from an energy penalty E(n1,n2,HB) on pulling hydrophilic monomers inside the membrane, or hydrophobic monomers into the solvent (Figure 4, right). In a simple picture this penalty can be modeled as a potential with three contributions ΔEins + ΔEA + ΔEB per monomer: • ΔEins = μins as a chemical potential for inserting an extra monomer into the bilayer29 due to effects such as a higher density and distortion of lipid order. • ΔEA = ϵ0Z for every additional hydrophilic (A) monomer that was inserted in the bilayer. • ΔEB = ϵ0Z(2HB − 1) for every hydrophobic monomer (B) that is not in the bilayer. Here, Z is an average coordination number taken from the simulations (Z ≈ 4−7, depending on HB), ϵ0 = 0.8kBT the energy scale as before, and μins ≈ 0.9kBT.27,29,33 C


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Figure 3. Potential of mean force for polymers in the hairpin (lef t) and transmembrane (right) conformation. Results are shown for different block lengths NB and hydrophobicities HB. The total length of the polymers is N = 64 for all data shown, except for the transmembrane configuration with NB = 32 and HB = 0.64, where N = 128. The vertical lines indicate the average position of the lipid−solvent interface. For the hairpin configurations the hydrophilic blocks are located on the right-hand side of the membrane and the potentials were shifted to F/kBT = 0 far away from the membrane as a reference value. Since the reference region was not sampled for some parameters (HB = 0.9,1.0 at NB = 32 and HB = 1.0 at NB = 16) the respective curves were shifted toward negative values by hand. For the transmembrane configurations the potentials were shifted to F/kBT = 0 at z/a = 0.

G(z;D,HB) . The resulting potentials are shown in Figure 5 together with simulation data for comparison. Essential features of the simulation results are reproduced despite the simplicity of the model, particularly the widening of the potential with decreasing hydrophobicity HB (Figure 5 top) and increasing hydrophobic block length (Figure 5, middle). Also, the development of local minima close to the interfaces for HB = 0.5 and longer chains is reproduced (Figure 5, bottom). Clearly, the model can by construction produce meaningful results only for coordinates z within the bilayer core and for a bilayer width D not much smaller than the size of the free Bblock. Interestingly the simulation data indicate a stronger localization of the middle monomer for HB = 1.0 as compared to the ideal model. The reason for this additional localization in the simulation may be a preference for conformations with the middle part of the polymer situated in the region between the leaflets of the bilayer due to smaller resulting bilayer perturbation.

Figure 4. Idealized model of a triblock copolymer trapped in the transmembrane state. The distribution of the position of the middle monomer is calculated by assuming an ideal chain starting and ending on the opposing membrane interfaces. The lengths n1, n2 of the subchains on either side of the middle monomer are allowed to fluctuate.

As in the simulations, the potential of mean force acting on the middle monomer can be calculated from the distribution D


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where the two integrated terms arise from independent simulation runs for each λ. Since an analytic expression for ∂H/∂λ can be derived directly from the energy Hλ, the averages ⟨∂H/∂λ⟩ can be measured in the simulations and only the integral has to be carried out numerically. The applied procedure assumes the two conformations to be quasi-stable, i.e. clearly separated from each other once interactions are switched on. Indeed, for all λ ≳ 0.1 the conformations prepared in the transmembrane state stayed in this state for the rest of the simulation. For λ ⩽ 0.02 the two states were well mixed in all simulations, such that this situation still provides a common reference. For 0.02 ≲ λ ≲ 0.1 the state occasionally changed in some simulations (from transmembrane to hairpin or vice versa), but these were relatively rare events. Therefore, this case was treated already as two separated states, and only simulations in which the initial state remained stable through the simulation were used (the others were repeated). The thus obtained differences in the free energy between the transmembrane and hairpin conformation are shown in Figure 6 (top) for different chain lengths as a function of the hydrophobicity HB. A corresponding phase diagram is shown in Figure 6 (bottom). To differentiate between polymers in adsorbed hairpin conformations and those with a hydrophobicity below the adsorption threshold Hads B , we have estimated Hads B for each chain length as the point of maximal fluctuations of the contact energy ΔE2 = ⟨E̅ 2⟩ − ⟨E̅⟩2 between Figure 5. Potential of mean force as calculated from the ideal chain model (lines) compared to simulation data (symbols). The model is able to reproduce essential features of the simulation data: The widening of the potential for lower hydrophobicity (top) and with increasing hydrophobic block length (middle). It also shows minima close to the interface for HB = 0.5 due to the fact that the middle block is pressed out of the membrane, but remains fixed by the hydrophilic blocks (bottom). This situation is shown in the inset snapshot.

Preferred Configuration. In order to judge whether the transmembrane state is stable or metastable we performed thermodynamic integration. To this end the interactions of the polymer with the rest of the system were tuned via a coupling parameter λ ∈ [0,1], such that for λ = 0 both excluded volume and hydrophilic−hydrophobic interactions were switched off, and for λ = 1 all interactions were fully present. The total energy thus reads H = H0 + Hλ Hλ =

1 2

∑ λϵijnijnn + i,j≠i

1 2

∑ (−ln(1 − λ) + λϵij)nijev) i,j≠i

where Hλ contains the interactions of the polymer and H0 is the remaining energy, which does not depend on the coupling ev parameter λ. Also, nnn ij and nij are the number of nearest neighbor contacts and excluded-volume contacts (i.e., overlaps) between types i and j, where i ∈ {A,B} are the polymer A-block and B-block types, and j runs over all types. The completely decoupled situation, λ = 0, provides a common reference state. By preparing transmembrane and hairpin conformations and measuring the derivative, ∂H/∂λ, one can thus find the free energy difference between the two conformational states by ΔF =

∫0

Figure 6. (Top) Free energy differences between transmembrane and hairpin conformations for different hydrophobic block lengths NB as a function of hydrophobicity HB. Positive values mean that hairpin is favored. (Bottom) Phase diagram of hydrophobicity vs block length. The dashed line approximately indicates the desorption line.

1

dλ( ∂Htrans /∂λ − ∂Hhairpin/∂λ ) E


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Macromolecules the B-block and lipid tails, as well as between the B-block and solvent (see dashed line in Figure 6, bottom). For moderate hydrophobicities HB ≲ 0.85 the transmembrane state is metastable. For more hydrophobic polymers, the situation depends on the length of the hydrophobic block NB. At hydrophobicities close to HB ≈ 1.0 and long hydrophobic blocks NB = 24, 32, there exists a coexistence region in which transmembrane and hairpin states are approximately equally favorable. For long and strongly hydrophobic B-blocks the placement of the hydrophilic ends should not matter in the range of chain lengths we have considered. The results for NB = 8, 16 display a region above HB ≈ 0.85 for which the transmembrane state is lower in free energy by a few kBT (ΔF < 0). Since for vanishing hydrophobic block length NB → 0 the transmembrane state must be unstable, we can conclude that there exists a finite range of hydrophobicities HB and block lengths NB for which the transmembrane state is stable as compared to both the desorbed and the hairpin state. The emergence of this region of stable transmembrane configurations is a consequence of the reduced depth of penetration into the bilayer core for small NB. If NB is large enough for the polymer to span the membrane, but too short to allow for a deep insertion of the hydrophobic block in a hairpin conformation, the transmembrane state is favored, because solvent contacts are avoided. On the other hand, this advantage vanishes for long hydrophobic blocks, which insert deeply into the bilayer core even in a hairpin state. At HB = 1.0 the contribution to the free energy difference between the two states resulting from solvent contacts can be estimated as ΔFcontact ≈ NBϵ0(Zhairpin − Ztrans), where the Z values are average numbers of contacts with solvent per hydrophobic monomer. For NB = 32 this contribution is close to zero, while for NB = 8 and HB = 1.0 it amounts to ΔFcontact ≈ −1.3kBT in favor of the transmembrane state. This is close to the measured total free energy difference of ΔF ≈ −1.8kBT between the two conformations for this polymer. An additional contribution favoring transmembrane conformations for small NB arises from the argument that a short hydrophobic block does not cause much perturbation in the lipid bilayer structure, because it is in a relatively stretched conformation parallel to the lipid order. Our simulations with NB = 8 and different total polymer lengths N = 64 and N = 128 did not lead to different profiles for the free energy F(z). From this we conclude that the conformational degrees of freedom for sufficiently long hydrophilic blocks do not play a major role in this context. 3.2. Membrane Permeability. In order to characterize the effect of the polymer on the membrane integrity, we have calculated the permeability of the membrane with respect to solvent monomers. As in previous studies of homopolymers27,29 and nanoparticles34 interacting with membranes, solvent translocation events were recorded during the simulation as a function of the distance d in the membrane plane between the center of mass of the hydrophobic block and the point at which the solvent enters the membrane (see Figure 7). Any solvent monomer that entered the membrane from one side, spent some time inside the bilayer core, and then left the membrane on the other side was counted as one translocation event. The boundaries of the membrane core were defined as a region of fixed width around the midplane of all lipid molecules. As before, separate simulations were performed for polymers in

Figure 7. Solvent monomer passing the membrane at distance d in the membrane plane from the center of mass of the hydrophobic block.

the transmembrane and hairpin conformations with varying NB and HB. Figure 8 shows plots of the normalized permeabilities PS/PS0, where PS0 is the permeability of the bare membrane without the polymer. We note that PS/PS0 is the factor by which the permeability is increased locally, i.e. in a unit area at distance d from the polymer. The conformational state of the polymer has a significant impact on the permeability. Triblock copolymers in the transmembrane state induced large changes of the local membrane permeability in their vicinity (right panel in Figure 8). The magnitude depends strongly on the hydrophobicity HB. Strongly hydrophobic polymers (HB = 1.0) slightly reduced the permeability, which can be interpreted as a stabilizing effect. With decreasing hydrophobicity the polymers induce a local increase in permeability by a large factor of up to PS/PS0 ≈ 5 (HB = 0.64) . The increase in permeability reaches a maximum not at the center of the polymer, but at a distance dmax around it. From there, it decreases back to the unperturbed value, i.e. PS/PS0 = 1. These results do not depend on the length NB of the hydrophobic block. Only the position of the maximum is slightly shifted due to the varying size of the hydrophobic block. This is consistent with observations made for homopolymers.29 It is worth noting that triblock copolymers in the transmembrane state increase the membrane permeability even below the adsorption threshold of HB ≲ Hads B due to the hydrophilic anchors keeping them fixed to the membrane. In contrast, triblock copolymers in the hairpin state, as well as homopolymers,29 do not associate with the membrane at such low hydrophobicities and have consequently no or little effect on the membrane permeability (left panel in Figure 8). However, also for parameters NB, HB above the adsorption threshold, HB > Hads B , the difference remains. Particularly, for HB < 1.0 and small NB, the hydrophobic block in the hairpin state is located close to the membrane surface, thus causing smaller perturbations and less permeability in the bilayer, as compared to the transmembrane state. Here, the difference in induced permeability between the states becomes smaller with increasing NB, as the hydrophobic block becomes large enough to disturb the structure of both membrane leaflets even in a hairpin state. This is illustrated in Figure 9, where the ratio of the induced permeabilities of the transmembrane and hairpin states is plotted. The barrier against solvent permeation was increased by the presence of the polymers for HB = 1.0, irrespective of the conformational state (Figure 8). The different effects of the transmembrane and hairpin conformations on membrane permeability reflect polymer induced permeability as a consequence of induced perturbations at the interface between a segregated B-block and the lipid F


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Figure 8. Induced permeability of the membrane to solvent monomers as a function of the radial distance d from the center of mass of the hydrophobic block for different block lengths NB, as well as hairpin (left) and transmembrane (right) conformations.

the adsorbed hairpin state. Polymers with a hydrophobicity that is lower than or equal to HB = 0.64 did not show any tendency for adsorption. This is in accordance with previous simulations in the same model, where homopolymers were shown to be expelled from the bilayer below a critial hydrophobicity of HB ≈ 0.68.29 Polymers in the transmembrane state remained in this state during the simulation even for HB < 0.68, although such configurations are metastable. Similar observations have been made in simulations of coarse-grained proteins.35 For HB = 0.5 and NB = 32 the hydrophobic block tends to form droplets on the membrane surface. These are caused by the fact that substantial parts of the hydrophobic block are expelled from the bilayer interior, while the polymer is held in the metastable transmembrane conformation by the hydrophilic blocks on either side of the membrane. We used thermodynamic integration to show that the transmembrane state is metastable with respect to the hairpin state for all simulated block lengths NB below HB ≈ 0.85. At higher hydrophobicities the two states are approximately equal in free energy, if the block length NB is long enough. For shorter hydrophobic blocks the transmembrane state is stable. Since for vanishing hydrophobic block length NB → 0 the transmembrane state cannot be stable, this means that there must be a finite range of NB and HB, in which the transmembrane configuration is favorable. This is displayed in the phase diagram in Figure 6. The largest energetic contribution leading to this effect can be understood to be a

tails. In the transmembrane state the interface ranges through the bilayer and topologically connects both bilayer−solvent interfaces. This is not the case for the hairpin state, leading to only marginally increased permeability, unless the hydrophobic block is very long. The density profiles of lipid tails and the Bblock depicted in Figure 10 illustrate this concept. We have carried out simulations with the same block lengths NB, but with the total polymer length N = 128 (results not shown). The longer hydrophilic blocks did not have any significant effect on permeability.

4. DISCUSSION The results obtained from the simulations are in accordance with observations made in experiments with lipid vesicles and amphiphilic triblock copolymers and can explain seemingly contradictory observations. When added to one leaflet of the bilayer, i.e. in a hairpin conformation, polymers with a sufficiently long and hydrophobic middle block insert deeply into the hydrocarbon core of the bilayer. Shorter hydrophobic blocks lead to a weaker binding,18,22 while decreasing the solubility (i.e., increasing HB) leads to stronger binding14,15 and deeper penetration into the bilayer. The simultaneous influence of the block length and hydrophobicity is intuitively clear, because the free energy gain due to adsorption at the interface can be estimated as ΔF ≈ NBZϵ0(2HB − 1) − (1/2)kBT ln(NB), where Z is again an average number of contacts between a hydrophobic monomer and solvent. The logarithmic term accounts for the formation of the loop, when the polymer is in G


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Figure 10. Average density profiles of lipid bilayer and hydrophobic Bblock with NB = 16 and hydrophobicities HB = 0.8 (top) and HB = 1.0 (bottom). The black lines are levels of equal density of lipid tails, representing 12.5%, 30%, 45%, and 60% of the maximum density. The colors represent the density of B-block monomers (arbitrary units). For the hairpin configurations, averages were taken for distances 0 < |z| < 5 of the B-block center of mass to the membrane midplane (left and middle column). While polymers in a transmembrane configuration (right column) provide an interface connecting the bilayer leaflets, the distortion of the membrane structure caused by polymers in the haipin state is clearly asymmetric and does not range continuously through the membrane.

Figure 9. Ratio of induced permeability in transmembrane state, PS(t), to induced permeability in hairpin state, PS(h), for hydrophobicities above the adsorption threshold (HB > Hads B ) and different B-block lengths NB. For small NB the hairpin state induces less permeability, because the hydrophobic block is located at the bilayer surface. The difference between the transmembrane and hairpin state becomes smaller for longer B-blocks and larger hydrophobicity HB.

to increase bilayer permeability. According to our findings, the “insertion state” corresponds to the transmembrane conformation. Even though the transmembrane and hairpin states are separated by a large free energy barrier, switching between the states can still be assumed to occur on long time scales. Thus, even though transmembrane states are metastable in many cases, they can still exist in considerable fractions, leading to the changes in bilayer stability as described above. It has been argued based on experimental results18,22 that the overall hydrophobicity of triblock copolymers, including the hydrophilic ends, determine their effect on membrane permeability, rather than just the size of the hydrophobic block. This can possibly be explained in the context of our model, as for shorter hydrophilic blocks it becomes increasingly likely for the polymer to switch its conformational state. In particular, this can explain why in the above-mentioned experiments18 vesicles had to be incubated with polymers for some time before a destabilizing effect could be observed, when the applied polymers were relatively hydrophilic. We have shown that slight changes in the hydrophobicity can change the effect of the polymer on the membrane in a dramatic manner, from a stabilizing effect to the formation of a pore. This can explain why experiments or simulations under different conditions (lipid type, temperature, assumed interaction potentials) can lead to different results, as discussed in the Introduction. Since the effective hydrophobicity of the middle block, as considered in our work, is defined relative to the hydrophobic properties of the membrane core and to the solvent, also changes in the solvent properties, such as pH or ionic strength, can influence the transition between the hairpin and transmembrane state and, as a consequence, can be decisive for the permeability and membrane integrity.

consequence of the reduced depth of penetration into the bilayer core for small NB. If the hydrophobic block is short, more solvent contacts are created in the hairpin state, as compared to the transmembrane state, clearly favoring transmembrane configurations. This advantage of the transmembrane configuration gradually becomes smaller for larger NB, as the hydrophobic block can completely insert into the bilayer core even in a hairpin conformation. Essential features of the transmembrane state can be understood using a Gaussian chain model in an idealized potential profile of the membrane. The bilayer permeability induced by the polymers is determined by the insertion state of the polymer in the membrane and the hydrophobicity of the B-block. Polymers in the transmembrane state can induce significant permeability changes, which become more pronounced with growing mismatch (1 − HB) in hydrophobicity between the hydrocarbon core of the membrane and the polymer. On the other hand, little or no effect can be observed if the polymer is in the hairpin configuration. This is mostly due to the fact that for the growing hydrophobic mismatch (1−HB) the polymer undergoes a desorption transition, or is located at the surface of the membrane, thus not being able to induce a pore. Our findings support the hypothesis of a two state model to explain disruptive effects of triblock copolymers on membranes, similar to what has been suggested by Wang et al.18 Based on flourecence leakage experiments with giant unilamellar vesicles treated with poloxamers, these authors propose an “adsorption state” and an “insertion state”, where only the latter is thought H


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We have used only the hydrophobicity of the middle block, HB, as a parameter in the simulations, while the hydrophilic ends of the polymer where kept at constant HA = 0.0 (i.e., completely hydrophilic). Changing the hydrophilic block length NA had only minor effects on the results. We note, however, that specific interactions of the hydrophilic blocks with the lipid head groups are not taken into account here.13,19

5. CONCLUSIONS We have examined single amphiphilic ABA triblock copolymers interacting with lipid bilayer membranes in a generic coarsegrained model, where the middle (B) block of the polymers is hydrophobic and the two end blocks (A) are hydrophilic. In particular we have analyzed the effect of varying hydrophobicity HB and length NB of the B-block. Hairpin and transmembrane states can be found as distinct modes of interaction of the triblock copolymer with the membrane, and their relative stability was analyzed using thermodynamic integration. The stability of both states can be triggered by slightly changing the relative hydrophobicity of the middle block. Also changing the length of the middle block leads to changes in stability. We have shown that in particular intermediate chain lengths lead to stable transmembrane conformations while a strong mismatch between the chain length and the thickness of the membrane core causes metastability of the transmembrane state. We note that the relative hydrophobicity of the middle block for a given copolymer such as PEO−PPO−PEO can be controlled by the specific lipid as well as the solvent environment. Both states, transmembrane and hairpin, can have a significantly different impact on the local permeability of the membrane with respect to the solvent: The transmembrane state is highly sensitive with respect to the hydrophobicity of the B-block. While strong hydrophobicity leads to an increase of the permeability barrier, a mismatch in hydrophobicity of the middle block leads to increased permeability. In the latter case, a polymer in the transmembrane state acts as a pore former. Polymers in the hairpin state, on the other hand, have only minor impact on the membrane permeability. This supports the hypothesis of a two state model for the effect of such polymers on bilayer membranes as suggested by Wang et al.,18 with an “insertion state” leading to an increased permeability, and an “adsorption state”, which does not have this effect (Figure 10). Our study shows that a slight modification of the interaction properties between the hydrophobic block and the lipid membrane can cause switching in the stability between the transmembrane and hairpin states with strong consequences for the permeability of the membrane, and offers a possible explanation for apparently contradicting experimental findings. Our study emphasizes again the dominant role of the relative hydrophobicity of membrane-active polymers.

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Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Fusco, S.; Borzacchiello, A.; Netti, P. J. Bioact. Compat. Polym. 2006, 21, 149−164. (2) Binder, W. H. Angew. Chem., Int. Ed. 2008, 47, 3092−5. I


Interactions of Amphiphilic Triblock Copolymers with Lipid Membranes

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