Fusion of Ligand-Coated Nanoparticles with Lipid Bilayers - American

Article pubs.acs.org/JPCA

Fusion of Ligand-Coated Nanoparticles with Lipid Bilayers: Effect of Ligand Flexibility Reid C. Van Lehn and Alfredo Alexander-Katz* Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: Amphiphilic, monolayer-protected gold nanoparticles (AuNPs) have recently been shown to insert into and fuse with lipid bilayers, driven by the hydrophobic effect. The inserted transmembrane state is stabilized by the “snorkeling” of charged ligand end groups out of the bilayer interior. This snorkeling process is facilitated by the backbone flexibility of the alkanethiol ligands that comprise the monolayer. In this work, we show that fusion is favorable even in the absence of backbone flexibility by modeling the ligands as rigid rods. For rigid ligands, snorkeling is still accommodated by rotations of the ligand with respect to the grafting point, but the process incurs a more significant free energy penalty than if the backbone were fully flexible. We show that the rigid rod model predicts similar trends in the free energy change for insertion as the previous flexible model when the size of the AuNPs is varied. However, the rigidity of the ligand backbone reduces the overall magnitude of the free energy change compared to that of the flexible model. These results thus generalize previous findings to systems with hindered backbone flexibility due to either structural constraints or low temperature.

■

INTRODUCTION Monolayer-protected gold nanoparticles (AuNPs) have recently emerged as an important new class of nanomaterial for use in a variety of biological applications such as drug delivery, biosensing, or bioimaging.1−5 AuNPs are particularly useful because their chemical and surface properties can be tuned by grafting a protecting ligand monolayer to the surface using wellestablished chemical techniques.6,7 Such monolayers typically consist of alkanethiol ligands, possibly end-functionalized with hydrophilic moieties to confer aqueous solubility, or other biological molecules such as DNA or polymers. The versatile surface properties achievable via the selection of particular protecting ligands allows AuNPs to be tailored for a large set of applications.7−9 One particularly interesting class of monolayer-protected AuNPs was recently developed by Jackson and co-workers.10−13 These AuNPs are protected by a binary monolayer consisting of a purely hydrophobic alkanethiol ligand and an anionic endfunctionalized alkanethiol ligand, with the charged end groups of the latter “hydrophilic” component permitting aqueous solubility.14 The combination of the charged end groups and the hydrophobic alkane backbones of both the hydrophobic and hydrophilic ligands yields an amphiphilic surface reminiscent of membrane proteins. Surprisingly, these AuNPs were found to penetrate into cells via a nondisruptive process even under conditions when endocytosis was blocked.15,16 This nonendocytic transport mechanism was shown to be related to both the ratio of the hydrophilic and hydrophobic components in the monolayer and the nanoscale arrangement of the two ligands in the mixed monolayers.15 Although cationic AuNPs © 2014 American Chemical Society

and peptides have been previously shown to penetrate into cells via nonendocytic mechanisms, their mechanism of entry may involve transient poration or disruption of the membrane that can affect cell viability.17−21 In contrast, the anionic monolayerprotected AuNPs previously studied were able to bypass the membrane without allowing the passage of a membraneimpermeable dye, indicating a novel pathway that does not involve bilayer poration or endocytosis yet still enables the highly charged AuNPs to access the cytosol.15,16 Gaining an understanding of the nondisruptive penetration mechanism of anionic AuNPs may lead to a new generation of targeted drug delivery vehicles or biosensors capable of bypassing the membrane without being trapped in endosomal compartments and without harming cells. Indeed, recent work has already demonstrated the efficacy of monolayer-protected anionic AuNPs for both drug delivery and biosensing;22,23 however, despite several theoretical studies on similar systems,24−32 the full mechanism of penetration is still poorly understood. In recent work, we described the hypothesis that these monolayer-protected AuNPs first fuse with the hydrophobic core of the membrane as a critical intermediate step in the full mechanism of penetration.33−35 We used an implicit solvent, implicit bilayer model to calculate the free energy change associated with translocating AuNPs from aqueous solvent into Special Issue: Energetics and Dynamics of Molecules, Solids, and Surfaces - QUITEL 2012 Received: November 27, 2013 Revised: March 26, 2014 Published: April 29, 2014 5848

dx.doi.org/10.1021/jp411662c | J. Phys. Chem. A 2014, 118, 5848−5856

The Journal of Physical Chemistry A

Article

the hydrophobic core of a pure lipid bilayer.34,35 In this model, the driving force for insertion is the hydrophobic effect associated with shielding the hydrophobic surface area from water by sequestering it in the bilayer core.36 The primary penalty for AuNP fusion is the strong electrostatic penalty associated with exposing charged end groups to the hydrophobic core, a penalty that is partially alleviated if the flexible alkanethiol ligands “snorkel” charges to the nearest aqueous interface via a deformation of the alkane backbone.37−39 The results of this model suggest that insertion is favorable for AuNPs with diameters smaller than a monolayer compositiondependent size cutoff. For particles larger than the cutoff, the lack of free volume in the monolayer strongly inhibits the snorkeling process and thus prevents favorable insertion.34,35 Predictions from the model were shown to agree with experiments on model lipid bilayers, multilamellar vesicles, and cells, providing verification for the fusion hypothesis and its importance in the membrane penetration mechanism.34 Furthermore, membrane insertion has been recently observed in related systems with similar AuNP coatings.40,41 However, an open question is the role of molecular flexibility in enabling such behavior. The alkanethiol ligands considered in the previous study were modeled as having flexible alkane backbones that excluded volume but were unconstrained by bond angle restrictions, effectively maximizing chain flexibility.34,35 This simplifying assumption is adequate in the limit of high temperature or highly flexible ligands. For more rigid ligands, such as DNA, unsaturated alkanethiols, ligands containing alkane rings, fluorescent dyes, or alkanethiols at low temperature,42 the flexible backbone assumption is likely a poor representation of the physical system and may overestimate the ease of the snorkeling process. A variety of such ligands have already been reported for use in biological applications.43−46 In addition, cell penetration was experimentally observed at 4 °C,15 a temperature chosen to block endocytosis that may also bias ligands toward more rigid backbone structures. It is thus important to understand how backbone flexibility may influence AuNP-bilayer fusion. In this work, we explore the role of molecular flexibility in determining the free energy change for the insertion of AuNPs with rigid ligands. Taking the opposite extreme from the previous flexible backbone assumption, here the ligands are modeled as rigid rods with ligand flexibility only possible at the grafting site. Our results show that ligand backbone flexibility is not necessary for snorkeling to still be a mechanism for charge removal from the hydrophobic core. Consistent with our previous findings, sufficiently small AuNPs always experience a strong driving force for embedding driven by favorable hydrophobic interactions.34,35 By directly comparing results of the rigid rod ligand model with the flexible backbone model, we show that ligand rigidity does significantly penalize snorkeling for larger particle diameters, further decreasing the previously described size thresholds. This work thus indicates that ligand rigidity is another design parameter that may be considered in constructing AuNPs for interactions with lipid bilayers. Furthermore, the use of two opposite extremes of molecular flexibility provides upper and lower bounds on the true free energy change expected of physical systems.

a lipid bilayer.34,35 Figure 1 schematically illustrates that the initial state of the system is an AuNP in solution that then

Figure 1. Schematic illustration of the fusion of a monolayer-protected AuNP with a lipid bilayer. In all simulations, a 150 mM salt solution is assumed as illustrated. AuNP insertion depends on the snorkeling of charges out of the bilayer accompanied by the deformation of the bilayer at the AuNP interface. The inset shows the chemical structures of hydrophilic MUS and hydrophobic OT, the two ligands assumed in most simulations unless otherwise noted.

inserts into the bilayer as the system’s final state. The inset box illustrates the chemical structures of the two typical components, 11-mercapto-1-undecanesulfonate (MUS) and 1octanethiol (OT). MUS is end-functionalized with an anionic sulfonate group and is thus the “hydrophilic” ligand, whereas OT is purely hydrophobic. These ligands are chosen on the basis of their use in previous theoretical and experimental studies.15,16,33,34 The total free energy change for insertion is decomposed into the sum of five terms: ΔGtotal = ΔGphobic + ΔGinsert + ΔEelec + ΔEthick − T ΔSconf

(1)

Here, ΔGphobic is the magnitude of the hydrophobic effect associated with shielding exposed hydrophobic surface area in the core of the hydrophobic bilayer core and is calculated from simulations. Within the implicit solvent, implicit bilayer model, this term is calculated by computing the solvent-accessible surface area (SASA) of the system.34,35 The free energy for transferring organic solutes into aqueous solvent scales approximately linearly with the hydrophobic SASA,47,48 so we assume that the change in the free energy of hydrophobic solvation can be approximated by multiplying the change in the SASA by a phenomenological parameter, γ. In this work, γ is set to 4.7 (kcal/mol)/nm2 on the basis of findings from our previous work and estimates in the literature.34,35,48−51 The magnitude of the hydrophobic driving force is then related to the decrease in the SASA upon exposing hydrophobic surface area to the bilayer core rather than solvent, with additional

■

SIMULATION METHODS In this work, we use the previously described implicit solvent, implicit bilayer model to calculate the free energy change for the insertion of a monolayer-protected AuNP into the center of 5849



Article

represents the difference between the flexible backbone and RR models, including example simulation snapshots.

details of this methodology discussed in the Supporting Information. ΔGinsert is the total penalty for the insertion of charged end groups into the bilayer from the aqueous environment and is calculated in simulations by applying a potential adapted from all-atom simulations of anion partitioning into lipid bilayers.52,53 This penalty implicitly includes free energy changes of the system associated with related effects such as localized bilayer deformation, the cost of forming a water defect, and electrostatic interactions with the bilayer itself. Additional details of how this free energy contribution is calculated are in the Supporting Information. ΔEelec is the change in the electrostatic energy between endfunctionalized groups in the system and is calculated from simulations using a screened Coulombic potential assuming that Debye−Hückel theory is valid as has been previously shown for small charged nanoparticles.54−56 The Debye length of the system is set to 0.8 nm assuming a 150 mM aqueous salt solution. ΔEthick penalizes changes in the thickness of the bilayer in the vicinity of the AuNP assuming in-plane radial symmetry around the embedded particle. Unlike the preceding three terms, this contribution to the free energy is calculated analytically for a given value of λ, a coupling parameter described below, using a continuum model of membrane deformation.57,58 ΔSconf is the change in the conformational entropy of the ligand monolayer upon insertion into the bilayer and is calculated using the Bennett acceptance ratio (BAR) method.59 The entropy change is related to the decrease in the number of accessible system configurations as the effects of the bilayer are introduced. To calculate this term, a coupling parameter, λ, is used to represent the perturbed thickness of the bilayer in the vicinity of the embedded AuNP. Each of the other terms in the free energy decomposition in eq 1 is then made a function of λ as described in the Supporting Information. A value of λ = 0.0 corresponds to the initial state with no bilayer whereas λ = 1.0 corresponds to a bilayer at its unperturbed thickness. Simulations were conducted by first setting λ = 0.0 to sample configurations from a baseline state using a Monte Carlo methodology described below. λ was then slowly increased to a final value of λ = 1.2, representing the slow increase in thickness of the implicit bilayer. Ligand conformations were biased as λ increased due to the penalties for charge insertion into the bilayer and the exposure of SASA that both depend on bilayer thickness. System configurations sampled for each value of λ were saved and the free energy change between consecutive λ values was calculated using BAR as described further in the Supporting Information. The overall free energy change of the system relative to the baseline state at λ = 0 was calculated by summing the free energy change between consecutive values of λ to find both the global free energy minimum and corresponding λ value that represents the preferred bilayer thickness after AuNP fusion.

Figure 2. Schematic illustrating the distinction between the flexible backbone (FB, left) and rigid rod (RR, right) approaches to treating ligand flexibility. In the FB model, bond angle constraints are ignored. For the RR model, the alkane backbone is fixed in the all-trans configuration and treated as a cylinder. Simulation snapshots further illustrate this distinction.

For both the FB and RR models, united atom beads were used to represent each gold atom, sulfur atom, end-functionalized group, and CH2 or CH3 groups. Each united atom bead was treated as a hard sphere with a radius adapted from the van der Waals radii of the constituent atoms.60 Each Monte Carlo time step consisted of selecting a single bead (or ligand in the case of the RR model, as described below) and attempting a trial move. Moves were first tested to see if they obeyed the bonding/excluded volume criteria enforced by each model. In the FB model, bonded atoms were subject to fixed bond lengths but no bond angle restrictions. Excluded volume effects were taken into account by rejecting moves that led to hard sphere overlap between beads unless they were within two bonds of each other. Thus, near- and next-near-neighbor atoms were able to freely fluctuate without bonding constraints, allowing a significant amount of molecular flexibility, whereas beads within the same ligand were only constrained by hard sphere interactions with neighbors at least two bonds away. In the RR model, the entire alkane backbone of the chain was approximated as a cylinder of uniform diameter. Rather than move individual beads, the entire backbone cylinder was rotated around the fixed grafting point for each trial move. Given the collective nature of the RR moves, the algorithm was computationally more efficient than the flexible backbone model, with a speed up of approximately 2.5−4 times depending on the system. If a move was valid, the change in

■

FLEXIBLE BACKBONE VERSUS RIGID ROD APPROXIMATIONS A Monte Carlo simulation methodology was used to generate configurations of the system and calculate ΔGtotal. Two different approximations were used to model constraints between beads in the same ligand chain. These two approximations will be referred to as the flexible backbone (FB) and rigid rod (RR) models. Figure 2 schematically 5850



Article

the system energy was calculated according to the potentials defined in eq 1 for both models. Specifically, the change in the system SASA, and thus hydrophobic energy, was computed for each move along with the change in the insertion energy and electrostatic interaction energy between charged end groups. Trial moves were then accepted with a probability given by

1 N

N

∑ (xi − ⟨x⟩)2 i=1

(3)

■

where N is the number of system configurations sampled per bead, xi is the position of a particular bead for configuration i, and ⟨x⟩ is the average position of that bead. In the RR model, the MSF is calculated for the entire ligand by averaging over each bead in the ligand. The MSF values indicate that fluctuations are greatest for the long end-functionalized ligands in the FB model because the effective free volume available to the end beads is small. In comparison, these fluctuations are eliminated by the RR approximation so that only ligands near the edges of clusters have pronounced fluctuations whereas ligands on the cluster interior were highly constrained. This lack of end group fluctuations in the RR model limits the ability of charges to be removed from the implicit bilayer, effectively penalizing the snorkeling process to a greater extent than in the FB model as will be discussed below. Figure 4 shows simulation snapshots of AuNPs inserted into the bilayer using both the FB (top) and RR (bottom) models.

Figure 3. Simulation snapshots and average positions of 2.5 nm diameter 1:1 MUS:OT particles in the baseline state for both FB and RR particles. Beads in the snapshots are colored by the mean square fluctuations of each individual bead (FB model) or the average fluctuations of each bead in the ligand (RR model).

Figure 4. Simulation snapshots of 1:1 MUS:OT, 2.5 nm gold core diameter AuNPs with the FB (top) and RR (bottom) models. The implicit bilayer is drawn as a guideline to the eye. The snapshots illustrate the increased flexibility of the FB model that enhances ligand snorkeling and incurs less exposure of charged end groups to the bilayer than in the RR model.

0). Both snapshots are taken for AuNPs with 2.5 nm gold core diameters and 1:1 MUS:OT surface compositions. All diameters reported are the diameter of the gold core only, excluding the length of the ligand layer. The snapshots illustrate the more pronounced tendency for ligand clustering in the RR model, reflecting the lessened entropic penalty for clustering due to fewer ligand degrees of freedom. Such clustering has been observed previously in atomistic simulations of monolayer-protected AuNPs,42,61 indicating that the RR model may be appropriate even for systems that have flexible ligands. Figure 3 further shows the same particles with ligand positions averaged over the simulation trajectory and colored by the mean squared fluctuations (MSF) of each bead during the simulation, with the same color scale applied to both models. The MSF per bead is calculated as

Both snapshots are taken for the same 2.5 nm AuNPs with 1:1 MUS:OT surface compositions shown in Figure 3. The snapshots illustrate the qualitative effect of the RR approximation: in comparison to the FB model, the RR model leads to increased unfavorable insertion of the charged end groups into the bilayer due to the lack of end group flexibility. This inhibited flexibility effectively acts as a barrier to snorkeling and would thus be expected to increase ΔGinsert, the primary free energy term opposing insertion. Figure 5 shows a breakdown of the total free energy change for insertion into each of the components identified in eq 1 as a function of gold core diameter for both the FB (left) and the RR (right) models. The surface composition for both particles was 2:1 MUS:OT. Each point is plotted for the value of λ that minimizes the overall free energy change for that gold core diameter. The same qualitative trends are observed for both models. First, the dominant terms in both models are the

P = e−ΔE / kT

(2)

where ΔE is the change in system energy for moving the bead/ ligand. The temperature was set to 300 K for all simulations. A total of 50 000 Monte Carlo timesteps were performed for equilibration and then another 100 000 Monte Carlo timesteps were performed for production for each value of λ. Fifteen values of λ were simulated for each simulation, incrementing from an initial value of λ = 0.0 to a maximum value of λ = 1.2 All simulations were performed ten times to obtain averages and corresponding error bars.

RESULTS AND DISCUSSION As a first comparison of the RR and FB models, Figure 3 shows simulation snapshots of both models in the baseline state (λ =

5851



Article

Figure 5. Breakdown of free energy terms from (1) into individual components plotted as a function of the gold core diameter for a AuNP with a 2:1 MUS:OT surface composition. The plot indicates the dominance of the hydrophobic driving force, ΔGphobic, and charge insertion penalty, ΔGinsert, over other free energy terms.

hydrophobic driving force, ΔGphobic, and the penalty for charge insertion, ΔGinsert. The penalty for bilayer thickness deformations, ΔEthick, and the change in conformational entropy, ΔSconf, contribute weakly whereas the electrostatic interactions between end groups, ΔEelec, are largely negligible although larger in the FB model than in the RR model. The small conformational entropy change and electrostatic energy change are both related to the pronounced domain formation in the baseline state. Bilayer insertion effectively requires these domains to reorient, but because the ligands in the domains are already constrained prior to insertion, there is no significant entropy change and the electrostatic energy is effectively the same because end groups do not significantly change position with respect to each other. The overall nonmonotonic shape of the total free energy change leads to a cutoff diameter above which insertion is unfavorable, in agreement with previous studies using the FB model.34,35 The primary quantitative distinction between the two models lies in the value of ΔGinsert. As the gold core diameter increases, the free volume per ligand decreases and ligand fluctuations are reduced. The FB model permits end group and backbone deformations that aid snorkeling and enable the removal of end group charges from the bilayer even for small ligand free volumes. For the RR model, charges are forced to be exposed to the bilayer by the inability of ligands to flexibly snorkel, increasing ΔGinsert, decreasing the overall free energy change Gtotal, and decreasing the size cutoff relative to the FB model. The same lack of flexibility slightly decreases the magnitude of the hydrophobic effect, ΔGphobic, although the change is less pronounced than the effect on charge insertion. From the change in the value of ΔEthick, it is apparent that there is a change in the preferred bilayer thickness when the overall free energy change is minimized. Figure 6 shows the preferred bilayer thickness as a function of the gold core diameter for the 2:1 MUS:OT AuNPs used in Figure 5. Each value of λ reported in Figure 6 is the value that minimizes the corresponding total free energy change of insertion in Figure 5. The deformed bilayer thickness is also shown in nanometers on the basis of an experimentally measured unperturbed thickness of 4.53 nm for DOPC.62 The results show that NP incorporation induces local bilayer thinning for both the FB

Figure 6. Preferred bilayer thicknesses for both the FB model and RR model as a function of gold core size for 2:1 MUS:OT AuNPs. Each value of λ is the value that minimizes the total free energy change of insertion for that core size (Figure 5). The bilayer thickness in nanometers is based on an unperturbed thickness of 4.53 nm.

and RR models, consistent with the schematics of Figure 1 and Figure 4. The RR model predicts slightly larger thickness changes consistent with higher values of ΔEthick in Figure 5. The change in bilayer thickness reflects the principle of hydrophobic matching, in which the bilayer thickness locally deforms to maximize hydrophobic interactions with exposed hydrophobic area in the AuNP monolayer.63 The reduction in bilayer thickness induces negative mismatch conditions and may give rise to membrane-mediated interactions that trigger AuNP aggregation,64,65 especially given the large thickness deformations predicted by both models. Having established that the RR approximation inhibits ligand fluctuations in the baseline state, Figure 7 shows the effect of the RR approximation on the total free energy change for bilayer fusion in comparison to the FB approximation. Parts A and B of Figure 7 show plots of the FB and RR models, respectively, for all-MUS, 2:1 MUS:OT, and 1:1 MUS:OT monolayer compositions. As previous work has suggested that the nanoscale morphology of the grafting monolayer may play an important role in cell penetration,15 striped, random, and 5852



Article

mixed morphologies were also tested.66 Images of these three morphologies and a description of how they were generated are given in the Supporting Information. The free energy curves for all compositions and all morphologies have a cutoff diameter above which the free energy change is negative, as previously discussed. The plot shows that this cutoff diameter is composition-dependent, with monolayers containing more OT exhibiting a larger cutoff diameter. In contrast, no morphology dependence is observed as the curves for the striped, random, and mixed morphologies are all identical within the error bars, agreeing with previous studies on model bilayers.34,35 The same general trends are observed for both the FB and RR models. However, comparing the two models clearly shows that the reduced molecular flexibility imposed by the RR model greatly inhibits bilayer insertion as the magnitude of the free energy change decreases for all three surface compositions leading to smaller size thresholds, consistent with the breakdown in Figure 5. Figure 7C shows the area bounded by the RR and FB results. The FB and RR models can be thought of as opposite extremes of molecular flexibility, so the insertion free energy change for a real system with some restrictions on bond rotation should lie within the areas bounded by these two extremes. The previous analysis demonstrates that the FB and RR approximations predict quantitatively distinct free energy profiles and corresponding size thresholds for stable insertion. One question might be what differences the models predict as the grafting density of ligands on the surface increases, leading to a decrease in the free volume of each ligand and an effective increase in chain rigidity for the FB model due to steric interactions. Figure 8 shows free energies of insertion for 2:1 MUS:OT particles for three different grafting densities corresponding to 100%, 110%, and 120% of the 4.77 ligands/ nm2 density assumed elsewhere. The FB model profiles are drawn with solid lines whereas the RR profiles are drawn with

Figure 7. Comparison of the overall free energy change for AuNP insertion between the FB (A) and RR (B) models for three different monolayer compositions and three different monolayer morphologies. Data from (A) are taken from ref 34. The plot in (C) shows the areas bounded by both models.

Figure 8. Insertion free energies for 2:1 MUS:OT AuNPs for three different ligand densities. Predictions from the FB model are drawn with solid lines, and predictions from the RR model are drawn with dashed lines. 5853



Article

interactions between charged peptides and membranes, it is possible that such charge translocation requires pre-existing bilayer defects or the transient poration of the bilayer,17,19,20,38 both behaviors that cannot be captured with the implicit bilayer approach. Similarly, the effect of the embedded AuNP on the surrounding membrane cannot be fully described with an implicit bilayer model. In this work, a single term, ΔEthick, is used to penalize thickness deformations of the bilayer around an embedded AuNP in the free energy decomposition presented in eq 1. In principle, thickness deformations alone are insufficient to fully describe changes in the surrounding lipid annulus as lipid tilt angles could change as well64,67 which are not accounted for in this model. Moreover, cooperative effects, such as the membrane-mediated aggregation of AuNPs,64,65 cannot be modeled on the basis of the study of a single AuNP in isolation. In this work, we sought to only model the thermodynamics associated with the membrane insertion process and believe that the computationally efficient implicit bilayer, implicit solvent model is suitable for this calculation, especially given the size of the AuNPs studied (up to 10 nm in core diameter). In future work, we will expand this study to focus on the kinetics of insertion and the deformation of the surrounding bilayer using an explicit model for the bilayer to gain additional physical insight into these processes.

dashed lines. As in Figure 7, both models predict similar qualitative features, with both the magnitude of the free energy well and the insertion cutoff decreasing as the grafting density increases. Both models predict a change of approximately 1 nm in the size cutoff as the grafting density is increased by 10%. Similar responses of both models show that the inability of end groups to fluctuate in the RR model always leads to a greater penalty for insertion than for the FB model independent of whether backbone fluctuations are inhibited by larger grafting densities. A final question is what effect changing ligand lengths has in the RR approximation. Figure 9 shows the free energy change

■

CONCLUSIONS In this work, we probe the role of backbone flexibility in determining the free energy change for the fusion of monolayer-protected AuNPs with lipid bilayers. We compare two extremes of backbone flexibility: in the flexible backbone model, ligand backbones are fully flexible subject only to the constraint of excluded volume interactions, whereas in the rigid rod model, ligand backbones are fixed in an all-trans configuration and can only rotate around the grafting point. With these two representations, the free energy change for the insertion of AuNPs into a bilayer was calculated by using a previously described implicit solvent, implicit bilayer model.34,35 Both models show a composition-dependent size threshold for insertion, a result previously confirmed experimentally.33,34 Comparing the flexible backbone and rigid rod modes shows that the reduced backbone flexibility in the rigid rod model, and particularly the lack of end group fluctuations, inhibits ligand deformations that remove charge from the bilayer, leading to a stronger barrier to insertion than in the flexible case. The resulting size threshold for penetration for the rigid rod model shifts to smaller sizes than in the flexible backbone model. As a true physical system will have bond constraints subject to various restrictions on bond angles or dihedral angles that result in backbone flexibilities somewhere in between the rigid and fully flexible regimes, the free energy curves for these two models provide upper and lower bounds on the true free energy change for a physical system. This work thus shows that AuNP fusion can be favorable even for rigid ligands and provides bounds on the size threshold expected for AuNP insertion.

Figure 9. Insertion free energies for 2:1 hydrophilic/hydrophobic monolayer compositions for several different ligand lengths using the RR model. Curves are labeled by the number of carbon atoms in the alkane backbone of the hydrophilic/hydrophobic components, respectively.

for insertion for ligands of varying lengths specified by the number of carbon atoms in the ligand’s alkane backbone. A MUS:OT composition thus corresponds to 11:8 on the plot. Ligand ratios were also fixed as 2:1 hydrophilic:hydrophobic with a mixed morphology. The plot indicates that modifying the relative length difference of the hydrophilic and hydrophobic ligands has a negligible effect the overall insertion free energy change as is evident by comparison of the 11:5, 11:8, and 11:11 curves. As the end groups are unable to fluctuate, the change in the length difference does not afford more effective free volume to the ligands so no difference is observed. Changing the overall length of the hydrophilic ligand, however, leads to significant changes in the free energy profiles as is evident by comparison of the 8:5, 11:8, and 14:11 curves. Choosing longer ligand lengths permits easier snorkeling and increases the amount of hydrophobic surface area that can be shielded in the bilayer, both factors that drive fusion and increase the size threshold for favorable penetration. This analysis indicates that increasing the ligand length sufficiently can drive bilayer insertion, even for rigid ligands. It is important to acknowledge several limitations of the implicit bilayer, implicit solvent model. First, treating the bilayer implicitly does not allow the full dynamical pathway for NP translocation from solution to the bilayer center to be modeled. This kinetic pathway likely requires that charged end groups translocate across the bilayer to achieve a transmembrane configuration. On the basis of previous studies of

■

ASSOCIATED CONTENT

S Supporting Information *

Additional simulation methods and description of flexible backbone and rigid model implementation and morphologies. Images of different morphologies and a plot of scaling functions applied to represent implicit bilayer. This material is available free of charge via the Internet at http://pubs.acs.org/. 5854



■

Article

(17) Herce, H. D.; Garcia, A. E. Molecular Dynamics Simulations Suggest a Mechanism for Translocation of the HIV-1 TAT Peptide Across Lipid Membranes. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 20805−20810. (18) Leroueil, P. R.; Berry, S. A.; Duthie, K.; Han, G.; Rotello, V. M.; McNerny, D. Q.; Baker; Orr, B. G.; Banaszak Holl, M. M. Wide Varieties of Cationic Nanoparticles Induce Defects in Supported Lipid Bilayers. Nano Lett. 2008, 8, 420−424. (19) Almeida, P. F.; Pokorny, A. Mechanisms of Antimicrobial, Cytolytic, and Cell-Penetrating Peptides: From Kinetics to Thermodynamics. Biochemistry 2009, 48, 8083−8093. (20) Yesylevskyy, S.; Marrink, S.-J.; Mark, A. E. Alternative Mechanisms for the Interaction of the Cell-Penetrating Peptides Penetratin and the TAT Peptide with Lipid Bilayers. Biophys. J. 2009, 97, 40−49. (21) Chen, J.; Hessler, J. A.; Putchakayala, K.; Panama, B. K.; Khan, D. P.; Hong, S.; Mullen, D. G.; DiMaggio, S. C.; Som, A.; Tew, G. N.; Lopatin, A. N.; Baker, J. R.; Holl, M. M. B.; Orr, B. G. Cationic Nanoparticles Induce Nanoscale Disruption in Living Cell Plasma Membranes. J. Phys. Chem. B 2009, 113, 11179−11185. (22) Leduc, C.; Jung, J.-M.; Carney, R. R.; Stellacci, F.; Lounis, B. Direct Investigation of Intracellular Presence of Gold Nanoparticles via Photothermal Heterodyne Imaging. ACS Nano 2011, 5, 2587−2592. (23) Jewell, C. M.; Jung, J.-M.; Atukorale, P. U.; Carney, R. P.; Stellacci, F.; Irvine, D. J. Oligonucleotide Delivery by Cell-Penetrating “Striped” Nanoparticles. Angew. Chem., Int. Ed. 2011, 50, 12312− 12315. (24) Lee, H.; Larson, R. G. Multiscale Modeling of Dendrimers and Their Interactions with Bilayers and Polyelectrolytes. Molecules 2009, 14, 423. (25) Li, Y.; Gu, N. Thermodynamics of Charged Nanoparticle Adsorption on Charge-Neutral Membranes: A Simulation Study. J. Phys. Chem. B 2010, 114, 2749−2754. (26) Van Lehn, R. C.; Alexander-Katz, A. Penetration of Lipid Bilayers by Nanoparticles with Environmentally-Responsive Surfaces: Simulations and Theory. Soft Matter 2011, 7, 11392. (27) Lin, J.; Zhang, H.; Chen, Z.; Zheng, Y. Penetration of Lipid Membranes by Gold Nanoparticles: Insights into Cellular Uptake, Cytotoxicity, and Their Relationship. ACS Nano 2010, 4, 5421−5429. (28) Prates Ramalho, J. P.; Gkeka, P.; Sarkisov, L. Structure and Phase Transformations of DPPC Lipid Bilayers in the Presence of Nanoparticles: Insights from Coarse-Grained Molecular Dynamics Simulations. Langmuir 2011, 27, 3723. (29) Ting, C. L.; Wang, Z.-G. Interactions of a Charged Nanoparticle with a Lipid Membrane: Implications for Gene Delivery. Biophys. J. 2011, 100, 1288−1297. (30) Li, Y.; Li, X.; Li, Z.; Gao, H. Surface-Structure-Regulated Penetration of Nanoparticles Across a Cell Membrane. Nanoscale 2012, 4, 3768−3775. (31) Pogodin, S.; Werner, M.; Sommer, J.-U.; Baulin, V. A. Nanoparticle-Induced Permeability of Lipid Membranes. ACS Nano 2012, 6, 10555−10561. (32) Ting, C. L.; Frischknecht, A. L. Activated Pathways for the Directed Insertion of Patterned Nanoparticles into Polymer Membranes. Soft Matter 2013, 9, 9615−9623. (33) Carney, R. P.; Astier, Y.; Carney, T. M.; Voïtchovsky, K.; Jacob Silva, P. H.; Stellacci, F. Electrical Method to Quantify Nanoparticle Interaction with Lipid Bilayers. ACS Nano 2013, 7, 932−942. (34) Van Lehn, R. C.; Atukorale, P. U.; Carney, R. P.; Yang, Y.-S.; Stellacci, F.; Irvine, D. J.; Alexander-Katz, A. Effect of Particle Diameter and Surface Composition on the Spontaneous Fusion of Monolayer-Protected Gold Nanoparticles with Lipid Bilayers. Nano Lett. 2013, 13, 4060−4067. (35) Van Lehn, R. C.; Alexander-Katz, A. Free Energy Change for Insertion of Charged, Monolayer-Protected Nanoparticles into Lipid Bilayers. Soft Matter 2014, 10, 648−658. (36) Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly. Nature 2005, 437, 640−647.

AUTHOR INFORMATION

Corresponding Author

*A. Alexander-Katz: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS R.C.V. and A.A.K. acknowledge support by the MRSEC Program of the National Science Foundation under award number DMR-0819762. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI1053575. Some of the computations in this paper were run on the Odyssey cluster supported by the FAS Sciences Division Research Computing Group.

■

REFERENCES

(1) Ghosh, P.; Han, G.; De, M.; Kim, C. K.; Rotello, V. M. Gold Nanoparticles in Delivery Applications. Adv. Drug Deliver. Rev. 2008, 60, 1307−1315. (2) Sardar, R.; Funston, A. M.; Mulvaney, P.; Murray, R. W. Gold Nanoparticles: Past, Present, and Future. Langmuir 2009, 25, 13840− 13851. (3) Wang, Z.; Ma, L. Gold Nanoparticle Probes. Coord. Chem. Rev. 2009, 253, 1607−1618. (4) Doane, T. L.; Burda, C. The Unique Role of Nanoparticles in Nanomedicine: Imaging, Drug Delivery and Therapy. Chem. Soc. Rev. 2012, 41, 2885. (5) Jiang, S.; Win, K. Y.; Liu, S.; Teng, C. P.; Zheng, Y.; Han, M.-Y. Surface-Functionalized Nanoparticles for Biosensing and ImagingGuided Therapeutics. Nanoscale 2013, 5, 3127−3148. (6) You, C.-C.; De, M.; Rotello, V. M. Monolayer-Protected Nanoparticle-Protein Interactions. Curr. Opin. Chem. Biol. 2005, 9, 639−646. (7) Moyano, D. F.; Rotello, V. M. Nano Meets Biology: Structure and Function at the Nanoparticle Interface. Langmuir 2011, 27, 10376−10385. (8) Nel, A. E.; Mädler, L.; Velegol, D.; Xia, T.; Hoek, E. M. V.; Somasundaran, P.; Klaessig, F.; Castranova, V.; Thompson, M. Understanding Biophysicochemical Interactions at the Nano−Bio Interface. Nat. Mater. 2009, 8, 543−557. (9) Verma, A.; Stellacci, F. Effect of Surface Properties on Nanoparticle-Cell Interactions. Small 2009, 6, 12−21. (10) Jackson, A. M.; Myerson, J. W.; Stellacci, F. Spontaneous Assembly of Subnanometre-Ordered Domains in the Ligand Shell of Monolayer-Protected Nanoparticles. Nat. Mater. 2004, 3, 330−336. (11) Jackson, A. M.; Hu, Y.; Silva, P. J.; Stellacci, F. From Homoligand- to Mixed-Ligand- Monolayer-Protected Metal Nanoparticles: A Scanning Tunneling Microscopy Investigation. J. Am. Chem. Soc. 2006, 128, 11135−11149. (12) DeVries, G. A.; Brunnbauer, M.; Hu, Y.; Jackson, A. M.; Long, B.; Neltner, B. T.; Uzun, O.; Wunsch, B. H.; Stellacci, F. Divalent Metal Nanoparticles. Science 2007, 315, 358−361. (13) Carney, R. P.; DeVries, G. A.; Dubois, C.; Kim, H.; Kim, J. Y.; Singh, C.; Ghorai, P. K.; Tracy, J. B.; Stiles, R. L.; Murray, R. W.; Glotzer, S. C.; Stellacci, F. Size Limitations for the Formation of Ordered Striped Nanoparticles. J. Am. Chem. Soc. 2007, 130, 798−799. (14) Uzun, O.; Hu, Y.; Verma, A.; Chen, S.; Centrone, A.; Stellacci, F. Water-Soluble Amphiphilic Gold Nanoparticles with Structured Ligand Shells. ChemComm 2008, 196. (15) Verma, A.; Uzun, O.; Hu, Y.; Hu, Y.; Han, H.-S.; Watson, N.; Chen, S.; Irvine, D. J.; Stellacci, F. Surface-Structure-Regulated CellMembrane Penetration by Monolayer-Protected Nanoparticles. Nat. Mater. 2008, 7, 588−595. (16) Carney, R. P.; Carney, T. M.; Mueller, M.; Stellacci, F. Dynamic Cellular Uptake of Mixed-Monolayer Protected Nanoparticles. Biointerphases 2012, 7, 17. 5855



Article

(37) Strandberg, E.; Killian, J. A. Snorkeling of Lysine Side Chains in Transmembrane Helices: How Easy Can It Get? FEBS Lett. 2003, 544, 69−73. (38) Dorairaj, S.; Allen, T. W. On the Thermodynamic Stability of a Charged Arginine Side Chain in a Transmembrane Helix. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 4943−4948. (39) Bond, P. J.; Sansom, M. S. P. Bilayer Deformation by the Kv Channel Voltage Sensor Domain Revealed by Self-Assembly Simulations. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 2631−2636. (40) Lee, H.-Y.; Shin, S. H. R.; Abezgauz, L. L.; Lewis, S. A.; Chirsan, A. M.; Danino, D. D.; Bishop, K. J. M. Integration of Gold Nanoparticles into Bilayer Structures via Adaptive Surface Chemistry. J. Am. Chem. Soc. 2013, 135, 5950−5953. (41) Tatur, S.; Maccarini, M.; Barker, R.; Nelson, A.; Fragneto, G. Effect of Functionalized Gold Nanoparticles on Floating Lipid Bilayers. Langmuir 2013, 29, 6606−6614. (42) Ghorai, P. K.; Glotzer, S. C. Molecular Dynamics Simulation Study of Self-Assembled Monolayers of Alkanethiol Surfactants on Spherical Gold Nanoparticles. J. Phys. Chem. C 2007, 111, 15857− 15862. (43) Chabane Sari, S. M.; Debouttiére, P. J.; Lamartine, R.; Vocanson, F.; Dujardin, C.; Ledoux, G.; Roux, S.; Tillement, O.; Perriat, P. Grafting of colloidal stable gold nanoparticles with lissamine rhodamine B: an original procedure for counting the number of dye molecules attached to the particles. J. Mater. Chem. 2004, 14, 402. (44) Rosi, N. L.; Giljohann, D. A.; Thaxton, C. S.; Lytton-Jean, A. K. R.; Han, M. S.; Mirkin, C. A. Oligonucleotide-Modified Gold Nanoparticles for Intracellular Gene Regulation. Science 2006, 312, 1027−1030. (45) Lund, T.; Callaghan, M. F.; Williams, P.; Turmaine, M.; Bachmann, C.; Rademacher, T.; Roitt, I. M.; Bayford, R. The influence of ligand organization on the rate of uptake of gold nanoparticles by colorectal cancer cells. Biomaterials 2011, 32, 9776−9784. (46) Yeh, Y.-C.; Creran, B.; Rotello, V. M. Gold nanoparticles: preparation, properties, and applications in bionanotechnology. Nanoscale 2012, 4, 1871−1880. (47) Chothia, C. Hydrophobic Bonding and Accessible Surface Area in Proteins. Nature 1974, 248, 338−339. (48) Sharp, K. A.; Nicholls, A.; Fine, R. F.; Honig, B. Reconciling the Magnitude of the Microscopic and Macroscopic Hydrophobic Effects. Science 1991, 252, 106. (49) Nicholls, A.; Sharp, K. A.; Honig, B. Protein Folding and Association: Insights from the Interfacial and Thermodynamic Properties of Hydrocarbons. Proteins 1991, 11, 281−296. (50) White, S. H.; Wimley, W. C. Membrane Protein Folding and Stability: Physical Principles. Annu. Rev. Biophys. Biomol. Struct. 1999, 28, 319−365. (51) Van Lehn, R. C.; Alexander-Katz, A. Ligand-Mediated ShortRange Attraction Drives Aggregation of Charged Monolayer-Protected Gold Nanoparticles. Langmuir 2013, 29, 8788. (52) MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Partitioning of Amino Acid Side Chains into Lipid Bilayers: Results from Computer Simulations and Comparison to Experiment. J. Gen. Physiol. 2007, 129, 371−377. (53) MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Distribution of Amino Acids in a Lipid Bilayer from Computer Simulations. Biophys. J. 2008, 94, 3393−3404. (54) Guo, P.; Sknepnek, R.; Olvera de la Cruz, M. ElectrostaticDriven Ridge Formation on Nanoparticles Coated with Charged EndGroup Ligands. J. Phys. Chem. C 2011, 115, 6484−6490. (55) Huißmann, S.; Likos, C. N.; Blaak, R. Explicit Vs Implicit Water Simulations of Charged Dendrimers. Macromolecules 2012, 45, 2562− 2569. (56) Heikkilä, E.; Gurtovenko, A. A.; Martinez-Seara, H.; Häkkinen, H.; Vattulainen, I.; Akola, J. Atomistic Simulations of Functional Au144(SR)60 Gold Nanoparticles in Aqueous Environment. J. Phys. Chem. C 2012, 116, 9805−9815.

(57) Nielsen, C.; Goulian, M.; Andersen, O. S. Energetics of Inclusion-Induced Bilayer Deformations. Biophys. J. 1998, 74, 1966− 1983. (58) Nielsen, C.; Andersen, O. S. Inclusion-Induced Bilayer Deformations: Effects of Monolayer Equilibrium Curvature. Biophys. J. 2000, 79, 2583−2604. (59) Bennett, C. H. Efficient Estimation of Free Energy Differences from Monte Carlo Data. J. Comput. Phys. 1976, 22, 245−268. (60) Bondi, A. van der Waals Volumes and Radii. J. Phys. Chem. 1964, 68, 441−451. (61) Lane, J. M. D.; Grest, G. S. Spontaneous Asymmetry of Coated Spherical Nanoparticles in Solution and at Liquid-Vapor Interfaces. Phys. Rev. Lett. 2010, 104, 235501. (62) Tristram-Nagle, S.; Petrache, H. I.; Nagle, J. F. Structure and interactions of fully hydrated dioleoylphosphatidylcholine bilayers. Biophys. J. 1998, 75, 917−925. (63) Jensen, M. O.; Mouritsen, O. G. Lipids Do Influence Protein Function - The Hydrophobic Matching Hypothesis Revisited. Biochim. Biophys. Acta 2004, 1666, 205−226. (64) Schmidt, U.; Guigas, G.; Weiss, M. Cluster Formation of Transmembrane Proteins Due to Hydrophobic Mismatching. Phys. Rev. Lett. 2008, 101, 128104. (65) Parton, D. L.; Klingelhoefer, J. W.; Sansom, M. S. P. Aggregation of model membrane proteins, modulated by hydrophobic mismatch, membrane curvature, and protein class. Biophys. J. 2011, 101, 691−699. (66) Van Lehn, R. C.; Alexander-Katz, A. Communication: Lateral Phase Separation of Mixed Polymer Brushes Physisorbed on Planar Substrates. J. Chem. Phys. 2011, 135, 141106. (67) May, S. Theories on structural perturbations of lipid bilayers. Curr. Opin. Colloid Interface Sci. 2000, 5, 244−249.

5856


Fusion of Ligand-Coated Nanoparticles with Lipid Bilayers - American

Recommend Documents