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Nanoparticles of Various Degrees of Hydrophobicity Interacting with Lipid Membranes Chan-Fei Su,*,†,‡ Holger Merlitz,†,§ Hauke Rabbel,† and Jens-Uwe Sommer*,†,‡ †

Leibniz-Institut für Polymerforschung Dresden, 01069 Dresden, Germany Institute of Theoretical Physics, Technische Universität Dresden, D-01069 Dresden, Germany § Research Institute for Biomimetics and Soft Matter, Fujian Provincial Key Laboratory for Soft Functional Materials Research, Department of Physics, Xiamen University, Xiamen 361005, China ‡

S Supporting Information *

ABSTRACT: Using coarse-grained molecular dynamics simulations, we study the passive translocation of nanoparticles with a size of about 1 nm and with tunable degrees of hydrophobicity through lipid bilayer membranes. We observe a window of translocation with a sharp maximum for nanoparticles having a hydrophobicity in between hydrophilic and hydrophobic. Passive translocation can be identified as diffusive motion of individual particles in a free energy landscape. By combining direct sampling with umbrella-sampling techniques we calculate the free energy landscape for nanoparticles covering a wide range of hydrophobicities. We show that the directly observed translocation rate of the nanoparticles can be mapped to the mean-escape-rate through the calculated free energy landscape, and the maximum of translocation can be related with the maximally flat free energy landscape. The limiting factor for the translocation rate of nanoparticles having an optimal hydrophobicity can be related with a trapping of the particles in the surface region of the membrane. Here, hydrophobic contacts can be formed but the free energy effort of insertion into the brush-like tail regions can still be avoided. The latter forms a remaining barrier of a few kBT and can be spontaneously surmounted. We further investigate cooperative effects of a larger number of nanoparticles and their impact on the membrane properties such as solvent permeability, area per lipid, and the orientation order of the tails. By calculating the partition of nanoparticles at the phase boundary between water and oil, we map the microscopic parameter of nanoparticle hydrophobicity to an experimentally accessibly partition coefficient. Our studies reveal a generic mechanism for spherical nanoparticles to overcome biological membrane-barriers without the need of biologically activated processes. translocate through the lipid bilayer by passive diffusion.12−14 Apart from the size of the NP, shape and initial orientation can play a role for translocation and cellular uptake.15,16 The self-assembly of lipids into bilayers is driven by the hydrophobic interaction, i.e., the demixing of the hydrophobic tails of the lipids from the aqueous solution. The hydrophobicity of the NP is therefore an essential parameter controlling on the interaction with the membrane. Monte Carlo (MC) simulations of homogeneous/amphiphilic NPs interacting with a lipid bilayer show that NPs having a certain degree of hydrophobicity could induce a dramatic increase of the permeability of lipid bilayers for water and small molecules.17 Similar results have been reported in recent studies of homopolymers/copolymers of tunable hydrophobicity.18−20 The analysis of disruption of supported membranes, induced by semihydrophobic NPs, demonstrates that surface hydrophobicity, concentration and size of the NPs control the formation of pores in the membrane. This is

1. INTRODUCTION Self-assembled lipid bilayers are the protective barriers of living cells but allow for exchange of substances and information between the cell and its surroundings. Identifying the mechanisms of interactions of synthetic NPs with cell membranes is the key for understanding potential NP cytotoxicity1−3 and for developing efficient applications such as nanocarriers for targeted drug delivery.4,5 Particularly, it is of great interest to design NPs to breach the free energy barrier imposed by the membrane and to control the translocation of NPs through lipid bilayers. Experimental and simulation approaches have been implemented to study the interaction of NPs with biosystems on various time scales, focusing on the effects of NPs’ properties, i.e., size, shape, as well as surface chemistry. In recent studies, it is shown that the size of the NP is crucial for cell uptake6−8 and translocation.9 Molecular dynamics simulation studies of NPs in the range of 1−6 nm interacting with dipalmitoylphosphatidylcholine (DPPC)10 and human skin11 demonstrate that the free energy barrier of translocation through membranes increases with the size of the NPs and small hydrophobic particles as well as small solute molecules can directly © 2017 American Chemical Society

Received: July 21, 2017 Accepted: August 10, 2017 Published: August 10, 2017 4069

DOI: 10.1021/acs.jpclett.7b01888 J. Phys. Chem. Lett. 2017, 8, 4069−4076

Letter

The Journal of Physical Chemistry Letters offering insights into the design of biofunctional NPs with a reduced potential of cytotoxicity.21 Neutral or negatively charged, polymer-coated AuNPs exhibit an increased rate of crossing the Caco-2 monolayer (of human colon adenocarcinoma cells). These AuNPs were also capable of inducing an elevated cellular monolayer permeability (up to 4 times) for small molecules.9 Apart from that, other strategies have been approached to modify the surface chemistry, e.g., through the implementation of hydrophobic/hydrophilic patterns on the surface of the NP. Stellacci et al. designed NPs coated with alternating hydrophobic and hydrophilic ligands that could penetrate the membrane without inducing membrane disruption, while NPs randomly decorated with hydrophilic and hydrophobic components got trapped in endosomes.22 In turn, Gkeka et al. performed coarse-grained molecular simulations to study the effect of various hydrophobic−hydrophilic surface patterns on the permeation of NPs through lipid membranes. In particular, homogeneously distributed hydrophobic−hydrophilic surface patterns have been demonstrated to flatten the translocation free-energy profiles.23 As it is difficult to obtain microscopic information about NPs interacting with lipid membranes in experiments, molecular simulation provides a valuable physical insight into the interaction of NPs with lipid membranes. However, there still exists a lack of knowledge about the mechanisms behind the translocation process. This concerns, in particular, passive transport, which does not involve consumption of energy, such as ATP-hydrolysis. In our present study, we investigate self-assembled lipid bilayers interacting with spherical NPs under variation of hydrophobicity and concentration of the NPs using a simplified version of the MARTINI model,24 as explained in Section 2. The distributions of NPs of different degrees of hydrophobicity are analyzed in Section 3.1. In Section 3.2 we study the translocation of NPs through lipid membranes in terms of the potential of mean force and Kramers theory. In Section 3.3, the degree of hydrophobicity of the NP is classified in terms of a hydrophobicity scale, which is accessible experimentally. We then discuss the effects of hydrophobicity and concentration of NPs on the perturbation of membranes in Section 3.4. Our findings are summarized and discussed in Section 4.

Figure 1. Sketch of the coarse-grained model for lipids (h,t), solvent (s), and NPs.

our model, we obtained equilibrium values of the area per lipid (61.00 Å2), membrane thickness (44 Å), membrane compressibility (400 mN/m), and water permeability coefficient (7.5 × 10−3 cm/s), which are in the range of experimental values. The membrane compressibility was calculated with a Nose−Hoover barostat. The water permeability coefficient obtained in our model is higher than the result from the Martini model, but agrees with the magnitude of water permeation rate in experimental measurements regarding DPPC vesicles.25,26 This shows that our simplified model reproduces essential properties of real systems. Our goal was, however, to study the generic effect of relative hydrophobicity on the interaction of NPs with lipid bilayers. Charge effects, although substantially screened under physiological conditions, can be investigated as an additional parameter in later studies and can be important for charged particles. The effective interaction potentials between NPs of various hydrophobicities and components of the system are implemented as follows (the interaction constants are illustrated in the right panel of Figure 1): ⎡⎛ σij ⎞12 ⎛ σij ⎞6 ⎤ ULJ(r ) = 4ϵij⎢⎜ ⎟ − ⎜ ⎟ ⎥ , ⎝r ⎠⎦ ⎣⎝ r ⎠ σi , j = (Di + Dj)/2, ϵh , h = ϵs , s = ϵh , s = 5 kJ/mol, ϵt,t = 3.4 kJ/mol,

2. COARSE-GRAINED MODEL AND SIMULATION DETAILS We implement a simplified version of the MARTINI model of DPPC molecules24 to construct lipid membranes interacting with NPs. MARTINI represents a coarse-grained model that is based on the mapping of four atoms into single beads with four different interaction characteristics: polar, nonpolar, apolar, and charged. Our simplification consists of a reduction to only two different neutral bead-species, namely, apolar lipid tails and polar lipid heads. Minimal models of this type have been successfully applied in recent bond-fluctuation-based MC simulations.18−20 Figure 1 presents the structure of the lipid molecule, as used in our present work (left panel), as well as the interaction sites for NPs of tunable degree of hydrophobicity H (right panel). The precise meaning of the hydrophobicity scale H is going to be analyzed and discussed in Section 3.3. Lipid head monomers and solvent beads are identical in terms of hydrophobic interactions. Details regarding the Lennard-Jones pair potential, the bond potential, and the choices for the bond angles are described in the literature about MARTINI.24 With

ϵt,h = ϵt,s = 1.8 kJ/mol, ϵNP,NP = ϵs,s + (ϵt,t − ϵs,s) × H , ϵNP,h = ϵNP,s = ϵs,s + (ϵt,s − ϵs,s) × H , ϵNP,t = ϵs,t + (ϵt,t − ϵs,t) × H

(1)

Here, lipid head monomers, tail monomers, and solvent beads are denoted by h, t, and s, respectively. When the NP is hydrophilic (H = 0), its interactions are identical with those of the solvent beads and the lipid head monomers. Vice versa, interactions of hydrophobic (H = 1) NPs are indistinguishable from lipid tail monomers. This allows the hydrophobicity of NPs to be defined as follows: ϵNP,NP − ϵs,s ϵNP,h − ϵs,s ϵNP,t − ϵs,t H= = = ϵt,t − ϵs,s ϵt,s − ϵs,s ϵt,t − ϵs,t (2) For hydrophilic NPs, the NP−NP interaction equals the solvent−solvent interaction (ϵNP,NP = ϵs,s = 5 kJ/mol), while the 4070


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umbrella sampling simulation results for different values of z0 by weighted histogram analysis method (WHAM). For the analysis with WHAM, a bin of 0.5 Å and convergence threshold of 0.1 were implemented. Then, we shift all the potential of mean forces of NPs with different hydrophobicities to zero in the region far outside the membrane. We note that in this procedure, the bias potential should not perturb the system. As a consequence the biased samples, subtracting the harmonic bias from the resulting free energy should lead to the identical result as an unbiased sample, where the histogram of particle positions, ρ(z), has been recorded. We made use of this fact by combining biased and unbiased results in overlapping windows of the reaction coordinate, z, whenever this was possible.

interaction between hydrophobic NPs is the same as the interaction between hydrophobic lipid tails (ϵNP,NP = ϵt,t = 3.4 kJ/mol). Therefore, the bare interaction between NPs also varies when their hydrophilicity is shifted. We note that the effective interaction between NPs is always the result of bare interactions and those between the NPs and the other components. Also realistic particles will differ in this respect. Therefore, it is important to introduce a hydrophobicity scale which can be directly applied to experiments regardless of the details of the microscopic interactions. This is done in Section 3.3. Our simulation model is able to interpolate between maximum degrees of lipophilicity and hydrophilicity, and thus serves to study these effects in general using a single parameter, H. It should be noted that in our study the size of NP is small. The diameter of a NP (DNP = 9.4 Å) is twice the diameter of a coarse-grained lipid monomer (Ds,h,t = 4.7 Å) or a coarsegrained water bead, which is mapped by four water molecules.24 Thus, it corresponds roughly to the volume of 32 water molecules and is in the order of 100 atoms (such as Au). Therefore, the effective interaction lengths of the LennardJones potentials of NP−NP and NP−other components are σNP,NP = 9.4 Å and σNP, (s,h,t) = 7.05 Å, respectively. The simulations were conducted with the open source LAMMPS molecular dynamics package,27 using highly parallelized code. The temperature of the system was coupled to a Langevin thermostat (temperature 323 K), and the pressure was coupled to a Berendsen barostat28 (water pressure 1 bar, with a bulk modulus of the membrane of 3333.3 bar). Note that the barostat was coupled to the x−y plane of the membrane, to respond to its stress, while in the z-direction (normal to the membrane) the barostat secured a constant solvent pressure. An (initially) cubic simulation box of 120 Å and periodic boundary conditions in all directions were implemented. In the initial configurations, 450 lipid molecules were arranged into a planar lipid bilayer in the x−y plane, while solvent beads and NPs were distributed outside the lipid membrane. For systems of 50 and 100 NPs, 8653 and 8253 solvent beads were simulated, respectively. A run of 300 ns (107 MD steps) was conducted for equilibration, with a constant time step of 30 fs, followed by a production run of 2700 ns (9 × 107 MD steps). In order to obtain the free energy profile of the NPs as a function of their distances to the membrane’s center, we also apply umbrella sampling techniques.29,30 The general idea of umbrella sampling is to obtain the relative weight of a state of the system which is hardly accessible (very improbable) in direct simulations. This is typically related to high free energy differences of about 10 kBT and more. In our case we are interested in the free energy function F(z), where z denotes the distance perpendicular to the membrane with respect to the membrane center of mass. The variable of the free energy profile, z, is called the reaction coordinate in the following. We run a series of umbrella sampling simulations conducted with the LAMMPS package.27 For umbrella sampling the NP is constrained by the bias potential to a target position z0 using the harmonic potential Ub = (1/2) K(z − z0)2. The spring constant has been chosen as K = 0.2 kcal/(mol Å2) here. This is similar to a tweezer-type experiment, but instead of measuring the force, we record the distribution of the particle, ρ(z), under the harmonic constraint. As the center of mass of the membrane is not fixed in the simulations, we update the relative distance between the membrane’s center and constrained harmonic particle during sampling. We combined these

3. RESULTS AND DISCUSSION 3.1. NP Distribution in the Membrane. Snapshots of lipid membranes, together with 50 NPs are shown in Figure 2

Figure 2. Snapshots: Lipid membranes interacting with 50 NPs, at different values of the hydrophobicity (H = 0, 0.5, 0.8, 1). Solvent beads are not shown to improve visibility. The solid lines displayed for H = 0.5 indicate the thresholds for calculating translocation events.

for different values of the hydrophobicity H. The corresponding density profiles of all components (Figure 3) show that hydrophilic NPs H = 0 remain outside the lipid bilayer. We further note that in the distributions of hydrophilic NPs (H = 0,0.2), a depletion zone at the water−membrane interface is observed. This observation is consistent with previous simulations of membranes and NPs of small diameters, as summarized in a recent review.31 Upon a further increase of the NPs’ hydrophobicity to H = 0.5, an adsorption of NPs on the membrane surface takes place, specifically in the head−tail interface. When increasing the hydrophobicity to H = 0.8, a trimodal distribution of NPs is clearly discernible in Figure 3 (red curves): A certain fraction of NPs are absorbed in the core of the membrane, while others are located at the head−tail interface. The observation that NPs prefer the layers in between the two leaflets has some similarities with the uptake/repulsion of NPs by polymer brushes.32−35 We note that in previous studies,17 using the bond fluctuation method (BFM), the distribution of NPs turned out to be homogeneous throughout the membrane profile. The difference emerges due to the fact that the membrane, as modeled in the BFM, was less stiff, which allowed NPs to distribute inside the leaflet. It should be noted that the three-population structure of NPs represents a dynamic 4071


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Figure 4. Translocation rates of NPs as a function of hydrophobicity, in the presence of 50 (black curve, circle symbols) and 100 NPs (red curve, diamond symbols). Brown line with triangle symbols presents the results calculated from Kramers theory. Note that Tc in the last plot is in the scale of diffusion coefficient of NP (D).

Figure 3. Density profiles of the various components of the lipid membrane, as well as the NPs at different degrees of hydrophobicity (H = 0, 0.2, 0.4, 0.8, 1). Tail groups (black), head groups (green), lipid molecules (blue), NPs (red), and solvent beads (purple) are presented as functions of distance from the center plane of the membrane, z.

is sufficiently high. In order to understand the cooperative effect we note that for H = 0.5 both the solvent (water) and lipid core act as a poor solvent, i.e., a repulsive environment, which induces the formation of clusters of NPs for larger densities. It is worth noting that the bare interaction between the NPs in our model is less important, and the same effect can be observed if the particles have athermal pair interactions between each other for all values of the hydrophobiticy (see also ref 17). The membrane is destabilized at places where many particles are absorbed due to filling-up the states of the free energy minima (interfaces in this case; see Figure 5). Furthermore, particles can also form bridges through the membrane at higher densities, thus forming gates for other

equilibrium, and that NPs were able to jump between these three different layers, i.e., upper leaflet, core of membrane, and lower leaflet. When discussing the potential of mean force (Section 3.2), and the membrane perturbations (Section 3.4), we are going to pick up this issue once again in a rather quantitative manner. Fully hydrophobic NPs H = 1 are stabilized in the core of lipid membrane. It is remarkable that such a split up into three populations is still visible for H = 1, as shown in Figure 3. Overall, with increasing hydrophobicity from H = 0 to H = 1, the lipid membranes change from a potential NP barrier to a potential NP trap. 3.2. NPs Translocation and Potential of Mean Force. Figure 4 shows the frequency of NP translocation events obtained from the simulations in the presence of 50 and 100 NPs, respectively. Here we define a translocation event if a NP translocates from the solvent phase on one side of the membrane to the solvent phase on the other side, while passing through the core of the membrane (defined as the region z = zcenter ± 15 Å, with zcenter being the center of mass of the lipid membrane). For a translocation event to be completed, the NP has to arrive at the boundary defined as zcenter ± 40 Å. Translocations of hydrophilic NPs with H ≤ 0.4 were absent in our simulations. About hydrophobicity values of H = 0.5, a pronounced peak of membrane permeability for NPs occurs. A further increase of hydrophobicity to H = 1 leads to a decrease of translocations of NPs though the lipid membrane. We demonstrate that the peak in the translocation rate is due to the fact that the role of the lipid membrane changes from a potential barrier to a potential trap. It is worth to note that translocation events in the presence of 100 NPs increase up to 10-fold when compared to 50 NPs, indicating an cooperative effect when the concentration of NPs

Figure 5. Free energy profiles as a function of the distance from the membrane center, in the presence of 50 NPs, and at different hydrophobicities, H. 4072


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essential to map our microscopic model, characterized by the parameter H, to a hydrophobicity scale that is uniquely accessible in experiments. We achieved this hydrophobicity scale for NPs by measuring the free energy of partitioning of NPs at the boundary between the two phases: water and lipophilic solvent, the latter corresponding to a melt of oligomers (oil). This phase is composed of 1125 hydrophobic chains that are made of five tail monomers. The water phase contains 5827 beads. In order to measure the free energy difference between water and oil phases for NPs of various hydrophobicities, we conducted umbrella sampling simulations. Here the reaction coordinate is chosen as the distance from the center of the oil phase in the direction perpendicular to the water/oil interface. The details of umbrella sampling simulations are the same as described in Section 2, except that the pressure allows for changes in the box size only in z-direction. A run of 30 ns (106 MD steps) was conducted for equilibration, followed by a production run of 600 ns (2 × 107 MD steps) in each sampling window. The results are displayed in Figure 6. The upper part of the figure shows the free energy profiles as a function of reaction

particles. It is worth noting that the cooperative effect can be reduced and even eliminated if the particles are patchy in terms of the hydrophobicity effect.17 The general physical mechanism of passive translocation of particles through self-organized amphiphilic membranes could be depicted as passing through a free energy barrier. Therefore, it is of great importance to study the free energy profile of these systems. Once known, the theory of stochastic processes may be applied to calculate the mean first escape times of NPs from the lipid bilayer, which might turn out to be much larger than the accessible simulation time. In a straightforward approach, the free energy profiles defined as the potential of mean force (PMF) could be directly derived from the density profiles, ρ(z), of the NPs: F(z) = −kBT ln[ρ(z)]

(3)

Here, the reaction coordinate, z, denotes the distance of the NP from the center of mass-plane of the membrane. If the free energy differences are too high, the density of NPs is virtually zero during the simulation run. Whenever such a case emerges, we conducted umbrella sampling simulations as described in Section 2. We note that the free energy corresponds to the Gibbs free energy in our case, since the pressure is constant. Results for the PMF of NPs with different hydrophobicity are shown in Figure 5, which are obtained from unbiased MD simulations of 50 NPs combined with umbrella sampling simulations of single NP. As shown in Figure 5, for rather hydrophilic particles (H = 0.4), the lipid membrane acts as a potential barrier, while being a potential trap for hydrophobic NPs. For hydrophobic NPs, which form the three-population structure seen in Figure 3, the potential of mean force also reveals three energy minima, in the center of the membrane as well as at the two head−tail interfaces. For H = 0.5, the energy difference to the free NP along the free energy surface nowhere exceeds a value of 8 kBT, and thus allows for a direct translocation through the membrane, as observed above. Using the potential of mean force as shown in Figure 5, we calculated the translocation rate using the solution for the mean first passage time of the one-particle diffusion equation in a free energy landscape.36 This is sometimes noted as Kramers theory:37,38 τ=

1 D

∫z

z+ −

e F(z ′)/ kBT dz′

∫z

z′ −

e−F(z ″)/ kBT dz″

(4)

Here, τ denotes the average time it takes for the diffusing particle to reach the layer z+ on the trans-site of the membrane for the first time, if the particle was placed in the layer z− on the cis-side of the membrane at the beginning. The location of z+ and z− has been chosen as zcenter ± 40 Å, which are the same thresholds used for direct calculation of the translocation rate and located well outside the membrane’s profile (see also in Figure 2). We assume that the diffusion coefficient D of the NPs is constant along the direction perpendicular to the membrane (z coordinate) . The translocation rate, TC = τ−1, of the NP through the lipid membrane as a function of hydrophobicity is displayed in Figure 4 (brown line, triangle symbols). A pronounced peak of the membrane permeability for NPs is distinguishable at H = 0.5, which is in excellent agreement with our observations of translocation events during the simulations. 3.3. Hydrophobicity Scale. We note that the effective hydrophobic effect is a result of the interplay of all microscopic interactions that take place in the real system. Therefore, it is

Figure 6. Free energy profiles of NPs as a function of the distance from the center of the oil phase (upper panel). The location of the interface between the water and the oil phase is indicated as a dashed vertical line. Here black, blue, green, red, yellow, brown lines denote H = 0, 0.3, 0.45, 0.5, 0.7, 1. Hydrophobicity scale for the NPs (lower panel): Free energy difference between water and oil phases for NPs at different degrees of hydrophobicity H.

coordinate as obtained from sampling. In the lower part the differences between the free energies in the bulk of the two phases are shown for the various values of the microscopic hydrophobicity, H. These results show that for NPs close to the critical point of hydrophobicity (H = 0.5), the free energy difference between the phases vanishes, indicating that water and oil are indistinguishable for NPs. The simulation data can be fitted by the following linear equation 4073


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The Journal of Physical Chemistry Letters ΔF = 52.781·H − 24.736 = ln(c H/c P) kBT

phobic NPs or hydrophobic polymers, led to an increase of the membrane thickness that, contrary to our results, reduced the permeability. In our study, the observed 4.5% increase of membrane thickness (2 Å) did not have any significant effect on the membrane’s permeability with respect to solvent. Let us recall the scenario of NPs interacting with the lipid membrane in Section 3.1: Hydrophobic NPs distribute into three layers inside the membrane, i.e., the core of the membrane and the two head−tail interfaces of the leaflets. This three-population structure of NPs is dynamic, which implies that NPs move between these three layers, thereby inducing a considerable degree of membrane perturbation. We note the correlation between the solvent permeability and the area per lipid, which will be discussed further below. The presence of interacting NPs also changes the order parameter of lipid tails. To quantify the tail orientation, we have defined the orientational order parameter P2 as follows:

(5)

This linear relationship allows for a mapping of the parameter H to experimental quantities. In eq 5 the density of NPs on the hydrophobic/hydrophilic side is given by c H and c P , respectively, and the partition coefficient is defined by K = cH/cP. Since the free energy difference ΔF is directly related to the partitioning coefficient, this linear relationship can be used to map the parameter H to relevant experimental observations, such as immune response to NPs.39 3.4. Solvent Permeation and Perturbation of the Lipid Membrane Induced by NPs. Due to the interaction with NPs, the membrane itself changes its properties, depending on the degree of hydrophobicity and concentration of the NPs. The upper part of Figure 7 shows the membrane permeability

P2 = ⟨3 cos2 θ − 1⟩/2

(6)

where θ is the angle between the end-to-end vector of the lipid tail and the z-axis. By definition, P2 = 0 denotes random orientation, while P2 = 1 indicates alignment parallel to zcoordinate (normal to the bilayer plane). The results are displayed in the center panel of Figure 7. A minimum of the orientational order parameter close to H = 0.5 is visible, indicating a maximum of membrane perturbation induced by NPs. This is correlated with the fact that, around H = 0.5, NPs frequently penetrate in and detach from the membrane. Another feature characterizing the state of the lipid bilayer is the area per lipid. The corresponding results are displayed in the lower panel of Figure 7. For H = 0, the area per lipid does not change compared with the pure lipid membrane system. With increasing hydrophobicity, NPs get absorbed by the lipid membrane. Once the dynamic three-population structure of NPs is formed inside the membrane, NPs are pushing the lipid monomers away to occupy the space between these layers, which expands the lipid membrane to some extent. With a further increase of hydrophobicity of NPs, the majority of NPs stay put inside the core layer of the membrane, leading to weaker membrane perturbation induced by NPs, and a decrease of its area per lipid.

Figure 7. Relative membrane permeability for solvent (upper panel), order parameter of lipid tails (center panel), and area per lipid (lower panel), as a function of the hydrophobicity H, and in the presence of 50 (black curves, open circle) and 100 (red curves, open diamond) NPs.

4. CONCLUSIONS Self-organized amphiphilic membranes in the liquid state may be regarded either as potential traps or potential barriers with respect to NPs, depending on their hydrophobicity. This is examined in the present study by calculating the potential of mean force of the NPs which have a size of about 1 nm. Using these results, we relate the passive translocation of NPs, as observed in the simulations, with the mean first-passage time of a diffusing particle in the potential of mean force. Both results coincide, displaying a narrow window of high translocation rates for NPs with a balanced hydrophobicity close to H = 0.5, thus verifying the potential model of the lipid membrane. At this point the free energy landscape is maximally flat and the remaining barrier can be associated with the entropy reduction of the tails by accommodating the particle. The latter is of the order of a few kBT only which explains the high translocation rates. In order to relate the microscopic definition of hydrophobicity of NPs, which is based on the coarse-grained interaction model, we simulated a water/oil system and calculated the free energy difference of the NP distributed in

for water versus hydrophobicity of the NPs at two concentrations of NPs. Here we scale the membrane permeability in the presence of NPs with its solventpermeability in the absence of NPs. The permeability is generally increased whenever H differs from zero. Even in situations in which the NPs do not yet enter the membranes, they are capable of disturbing the molecular order and thereby affecting membrane permeability for water. At high NP concentrations, a clear maximum of the permeability is visible at about H = 0.7. A similar effect is discussed in the study of amphiphilic NPs interacting with membranes,17 in which the amphiphilic NPs do not form any aggregation inside the membrane. It should be noted that Figure 7 shows that, for H = 1, the permeability is slightly higher than for the case of H = 0. According to previous studies conducted with the bond fluctuation model,17 a stabilization effect, induced by hydro4074



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the two phases. The results show a linear relation between our microscopic parameter H and the partition coefficient on the passage of the NP between the two phases. At intermediate hydrophobicity, the NPs are distributed inside the membrane. This distribution is not homogeneous, but displaying an effective three-population pattern: NPs are preferentially located in the regions between the head and tail groups, and in between the leaflets of the two lipid layers. The preference for the location between the leaflets is increased with increasing hydrophobicity. This leads to different kinetic pathways of translocation at different hydrophobicities as sketched in Figure 8. For balanced hydrophobicity, at H =

Letter

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01888. Nanoparticles with balanced hydrophobicity interacting with a lipid bylayer (H = 0.5) (AVI) Hydrophobic nanoparticles interacting with a lipid bylayer (H = 1) (AVI) Hydrophilic nanoparticles interacting with a lipid bylayer (H = 0) (AVI)

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AUTHOR INFORMATION

Corresponding Authors

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

Chan-Fei Su: 0000-0003-3891-9672 Hauke Rabbel: 0000-0002-9387-3999 Jens-Uwe Sommer: 0000-0001-8239-3570

Figure 8. Sketch of the kinetic pathways of NPs for H = 0.5 (blue) and H = 0.8 (red) based on the analysis of the free energy landscape. The states of NPs are indicated as solvent (s), interface (i), and core, i.e., between leaflets (c). The arrows indicate the rate of the processes.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by Marie Curie Actions under EU FP7 Initial Training Network SNAL 608184. The authors thank the ZIH, TU Dresden as well as Peter Friedel for technical support. Insightful discussions with Marco Werner and with Markus Koch regarding the implementation of the umbrella sampling method are gratefully appreciated. We also thank Olivier Benzerara in Institute Charles Sadron, Strasbourg, France for his support.

0.5 in our notation, the NPs are mostly located at the membrane boundary where they can frequently enter or leave. The probability to cross the membrane, i.e., to jump between the two interface states is of the same order (see the free energy profile Figure 5). This translocation pathway is basically a 2 + 1-state process (2 states dominate the behavior inside the membrane; 1 state corresponds to solvated state) with essential events being: (1) to enter/leave the interface region from/to the solvated state, and (2) to jump between the two interface states. This is indicated by the blue double-headed arrows in Figure 8. For higher hydrophobicities such as H = 0.8, a 3 + 1state process becomes more dominant where NPs jump between the interface regions and the interleaflet core positions. This is indicated by the red double-headed arrows in Figure 8. At the same time, the “check-out” events become very rare and dominate the translocation time. The free energy barrier for leaving the membrane exceeds the order of 10 kBT already for H = 0.8. Different kinetic pathways can be expected for many NPs where collective effects play a role. Here, the free energy landscape for individual particles becomes flatter (results not shown here) and bridging of the membrane by clustered particles can further facilitate the translocation process. The detailed analysis of these phenomena needs further simulation studies. The uptake of NPs modifies the properties of the lipid bilayer too. As observed in previous studies, partially hydrophobic NPs, i.e., 0 < H < 1, enhance the permeability of the membrane for water considerably. Our simulation results display a correlation between the area per lipid and the NP-induced permeability of the membrane. We note that these effects are not related to any pore formation of the membrane, but rather being a consequence of the fact that the lipid layer is a self-organized liquid state representing just a free-energy barrier/landscape for nano-objects. Our investigation provides an improved understanding of the influence of various degrees of hydrophobicity and concentrations of uncharged NPs on lipid membranes.

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REFERENCES

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