Diffusion and Directionality of Charged Nanoparticles on Lipid Bilayer

Diffusion and Directionality of Charged Nanoparticles on Lipid Bilayer Membrane Pengyu Chen,†,# Zihan Huang,†,# Junshi Liang,† Tianqi Cui,† Xinghua Zhang,‡ Bing Miao,*,§ and Li-Tang Yan*,† †

Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, China School of Science, Beijing Jiaotong University, Beijing 100044, China § College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China ‡

S Supporting Information *

ABSTRACT: Diffusion dynamics of charged nanoparticles on the lipid membrane is of essential importance to cellular functioning. Yet a fundamental insight into electrostaticsmediated diffusion dynamics of charged nanoparticles on the membrane is lacking and remains to be an urgent issue. Here we present the computational investigation to uncover the pivotal role of electrostatics in the diffusion dynamics of charged nanoparticles on the lipid membrane. Our results demonstrate diffusive behaviors and directional transport of a charged nanoparticle, significantly depending on the sign and spatial distribution of charges on its surface. In contrast to the Fickian diffusion of neutral nanoparticles, randomly charged nanoparticles undergo superdiffusive transport with directionality. However, the dynamics of uniformly charged nanoparticles favors Fickian diffusion that is significantly enhanced. Such observations can be explained in term of electrostatics-induced surface reconstruction and fluctuation of lipid membrane. We finally present an analytical model connecting surface reconstruction and local deformation of the membrane. Our findings bear wide implications for the understanding and control of the transport of charged nanoparticles on the cell membrane. KEYWORDS: diffusion, charged nanoparticle, Saffman−Delbrück theory, lipid membrane, surface reconstruction

T

electrostatic interaction in the diffusion dynamics of charged nanoparticles on the cell membrane. In fact, it has been well established that the surface charge of nanoparticles plays a critical role in modulating membrane potential and subsequent downstream intracellular events.17,18 A great deal of experimental evidence has also suggested that the electrostatic adsorption of a charged nanoparticle on a charged lipid membrane can evidently perturb the membrane.19−23 The sign and spatial distribution of charges over the surface of the charged nanoparticle are thereby expected to have profound implications for its motion on the membrane consisting of lipids with charged termini. However, a fundamental insight into electrostatics-mediated diffusion dynamics of nanoparticles in the plane of membrane is lacking, and this is the focus of this work. We herein describe previously unreported diffusive dynamics of a charged nanoparticle on the fluid membrane of zwitterionic lipids. We show that the in-plane diffusion of a charged

he diffusive dynamics of nanoscale particles on cell membranes is essential to their potential applications ranging from drug delivery1,2 to disease diagnosis3 and biosensing4 as well as abundant cellular activity5 and ligand− receptor binding.6 The theoretical investigation of diffusion of nanoparticles on membranes has been studied widely going back to Saffman and Delbrück (SD).7 They developed a continuum hydrodynamic model of lateral and rotational Brownian diffusion of nanoparticles on lipid membrane. This model predicts a logarithmic dependence of diffusion coefficient on the nanoparticle size, which has been confirmed for some in vitro experiments on membranes containing nanoparticles.8−10 However, it was also found to fail in some other experiments,11 triggering a number of experimental and theoretical studies systematically going beyond the SD model by including additional effects, such as membrane-fluctuationinduced drag exerted on the nanoparticle and the effect of membrane curvature.12−15 Indeed, understanding the diffusive behaviors of such systems is a topic of fundamental significance in broad fields, but is far from complete.16 One important aspect of the questions that remain to be addressed and could be of great relevance concerns the role of © 2016 American Chemical Society

Received: November 9, 2016 Accepted: December 8, 2016 Published: December 8, 2016 11541

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

www.acsnano.org

Article

ACS Nano

Figure 1. Typical states of the interactions between lipid bilayer membrane and nanoparticles with different surface charges: β = −0.8 (a), −0.5 (b), 0 (c), 0.5 (d), 0.7 (e), and 0.8 (f). Solvent and counterion beads are not shown for clarity.

nanoparticle significantly depends on the sign and spatial distribution of charges on its surface. In contrast to the Fickian diffusion of neutral nanoparticle, we find that randomly charged nanoparticles undergo superdiffusive transport (see following section) with statistical directionality. However, the dynamics of uniformly charged nanoparticles favors Fickian diffusion that is significantly enhanced. Such enhancement leads to the invalidity of the SD theory for charged nanoparticles. Through examining the surface organization and fluctuation of lipid membrane, we discuss the molecular mechanism of the electrostatics-mediated diffusion dynamics of charged nanoparticles, where an analytical model connecting surface reconstruction and local deformation of the membrane is presented. Our findings suggest principles for the control of many important biophysical processes regarding the transport of charged nanoparticles on the cell membrane.

RESULTS AND DISCUSSION Binding States and Diffusion Trajectories. The models of lipid, membrane, and charged nanoparticles are displayed in Figure S1, and the details description of them are presented in the Methods. For the initial simulations, a nanoparticle with the diameter 3.6 nm is positioned in close proximity above the surface of the bilayer membrane of zwitterionic lipids with saturated acyl chains.24 All systems are pre-equilibrated for the first 5 μs to confirm the equilibrium of the binding states, while the production trajectories are obtained from succeeding 45 μs simulations. The typical binding states of nanoparticles on the membrane are depicted in Figure 1 and are summarized in Figure 2(a). For the neutral nanoparticle, it stays at the embedded pore (Figure S2) of the lipid bilayer due to the hydrophobic surface of the nanoparticle, in agreement with previous simulation results.25 However, inducing charges into the nanoparticle surface evidently distorts the local shape of the bilayer into a bent configuration. What is striking is that the orientation of the membrane deformation crucially depends on the sign of the surface charges. That is, the protrusion is concave up toward wrapping a negatively charged nanoparticle whereas it is concave down for a positively charged nanoparticle. Such a charge dependent membrane deformation will be quantified and be rationalized through a theoretical analysis in the last section of the letter. In the next section we first explore the implications of these local membrane deformations for the diffusion dynamics of charged nanoparticles. The typical trajectories of randomly charged nanoparticles diffusing in the plane of the lipid bilayer are illustrated in Figure 2(b) and (c) where β = 0.8 and −0.8. β denotes the fraction of surface charges and is defined as the ratio of charged beads to total surface beads, with plus and minus indicating positively and negatively charged nanoparticles, respectively. We observe a tendency for the transport of these charged nanoparticles to adopt nontrivial directionality, especially for the nanoparticle

Figure 2. (a) Schematic diagram of a lipid bilayer membrane with bound neutral and randomly charged nanoparticles. (b−e) Representative trajectories and distributions of turning angles for the nanoparticles with randomly (b, c) and uniformly (d, e) distributed surface charges, where β = 0.8 (b, d) and −0.8 (c, e). Color bar denotes the time lapse of each trajectory.

with positive charges [Figure 2(b)]. To further confirm this observation, we calculate the turning angle of the trajectories. As illustrated in Figure S3, the distribution of turning angle will concentrate on the values near 0° or 360° for a directional trajectory, no matter what orientation the trajectory prefers. Indeed, the images of turning-angle distribution, which are obtained based on five independent simulations for each case, in these panels confirm the statistical directionality for the randomly charged nanoparticles (for more results, see Figure S4). In sharp contrast, the diffusion of uniformly charged nanoparticles becomes isotropic, as confirmed by the stochastic trajectories and the statistical distributions of the tuning angles [Figure 2(d) and (e)]. Normally, the diffusion of the neutral nanoparticle on the membrane is statistically isotropic (Figure S5). The transition from isotropic to considerably directional diffusion signifies that the spatial distribution of charges on nanoparticle surface is essentially important for the diffusion dynamics of nanoparticles on the lipid membrane. Diffusion Dynamics and Mechanism. To provide a detailed insight into the diffusion dynamics of charged nanoparticles on the membrane, the mean-square displacement (MSD) ⟨Δr2(t)⟩ = ⟨|r(⃗ t) − r(⃗ 0)|2⟩ and the self-part of the van Hove correlation function Gs(r,t) = ⟨δ{r ⃗ − [r(⃗ t) − r(⃗ 0)]}⟩ are calculated using equilibrated configurations from DPD simulations.26,27 Here, ⟨...⟩ denotes an ensemble average and r(⃗ t) is the position vector of the monomer bead at time t. Figure 3(a) and (b) display the ensemble-averaged MSD for 11542

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

ACS Nano

For the Fickian diffusion with random displacement, the translational diffusion coefficient, D, can be calculated by Einstein relation.34 Figure 4 presents D as a function of R for

Figure 4. Lateral diffusion coefficient D of membrane-bound nanoparticles as a function of nanoparticle radius R. The solid red line shows the data fit using the SD model. Vertical dashed line denotes the critical radius Rc for the SD fitting.

Figure 3. (a) Mean-square displacement ⟨Δr2(t)⟩ for nanoparticles, with randomly (a) and uniformly (b) distributed surface charges. The inset in (a) shows the |β| dependence of diffusion exponent at long time scale, α. (c) Gs(r,t) at β = 0.8 for nanoparticles with randomly distributed charges and uniformly distributed charges (inset). (d) Azimuthal angle, ϕ and θ, of a nanoparticle surface versus time in a directed and persistent motion taking the insetting trajectory. Insetting graph: definition of ϕ and θ.

the neutral nanoparticle and the uniformly charged ones. We find that either positively or negatively charged nanoparticles possess larger values of D than the neutral one. This demonstrates that the surface charges can evidently accelerate the diffusion of nanoparticles, resulting in enhanced diffusion of charged nanoparticles. As indicated by the solid red line in Figure 4, the translational diffusion coefficients of the neutral nanoparticle are fitted to the SD model with a P value of 4.36,38,39 For water with ηw ≈ 10−3 Pa·s, the critical size obeying this condition is R ∼ 100 nm, much larger than the particle sizes used in the present work. However, the electrostatic interaction can remarkably enlarge the local deformation of the membrane around a charged nanoparticle, as demonstrated in Figure 1 and measured in Figure 5. Consequently, this fluctuation field can exert random forces and torques on the particle coupled to those originating from thermal collisions with the fluid lipids, which can be interpreted as enhanced diffusion. Such a “passive” random motion is significantly larger in magnitude than would be expected from purely thermal fluctuations, giving rise to random fluctuating motion that dominates over thermal

the randomly and uniformly charged nanoparticles. We fit MSD to the scaling tα, yielding the diffusion exponent, α. At short time scales, the lines overlap well with one another and scale as t2, indicating that all nanoparticles diffuse via ballistic motions with few collisions with lipids. However, at long time scales, randomly charged nanoparticles show superdiffusive transport where diffusion exponent α > 1,28−30 while the neutral and uniformly charged nanoparticles enter the Fickian regime with α = 1. A natural one-body consequence of superdiffusion is an anomalous long-range drift of particles.31,32 Indeed, the considerably persistent directed motion of randomly charged nanoparticles can be confirmed from their trajectories [Figure 2(b) and (c)] and, particularly, from Gs(r,t) where a bias in the probability of moving can be definitely identified, in contrast to the Gaussian displacement for the isotropic diffusion of uniformly charged nanoparticles [Figure 3(c) and inset]. To understand the persistent directed motion of randomly charged nanoparticles, we measure the rotational diffusion coefficient Dr using an exponential fit for the orientational correlation function.33 This yields Dr = (1.5 ± 0.3) × 105 s−1 and (1.3 ± 0.2) × 106 s−1 for a randomly charged nanoparticle on the membrane and within the pure solvent. For the uniformly charged and neutral nanoparticles on the membrane, Dr = (3.6 ± 0.2) × 105 s−1 and (3.2 ± 0.1) × 105 s−1, respectively. Clearly, the rotation diffusion of randomly charged nanoparticle on the membrane is dramatically retarded. Furthermore, the electrostatic interaction between randomly distributed charges and charged membrane surface is more prone to exert asymmetric forces and specific torques on the nanoparticle, which leads to instantaneously preferred direction. The retarded rotation diffusion significantly delays the “relaxation” of such a bias, resulting in the persistent directed diffusion. This can be rationalized through calculating the azimuthal angles of a certain point in the nanoparticle, which is virtually independent of the time within a section of persistent trajectory [Figure 3(d)]. 11543

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

ACS Nano

What molecular mechanism underpins such an enlarged fluctuation of the membrane? Binding charged nanoparticles can alter the tilt angle of the head of zwitterionic lipids, i.e., an electric dipole of positive and negative head termini.19 As illustrated by the schematic diagrams in Figure 6(a) and (b), positively charged nanoparticle interacts preferentially with the negative head bead, reducing the tilt angle; conversely, negatively charged particle raises the angle of the dipole. We calculate area per bead, Ah, for the head beads through a Voronoi tessellation (Figure 7).44 The points in Figure 6(a)

Figure 5. Fluctuation of lipid bilayer membrane in the presence of bound nanoparticles with β = 0.8 (a), 0 (b), and −0.8 (c), where black circles mark the positions of nanoparticles. (d) The distance of the contact line between nanoparticle and membrane to the membrane plane, l, as a function of |β| for the nanoparticles with uniformly distributed surface charges. Inset: the schematic for the definition of l.

fluctuations and results in the invalidity of the SD model. In fact, a similar effect has been observed in random motion within the cytoplasm undergoing constant agitation caused by the activity of molecular motors and other nonequilibrium cellular processes.40 It should be emphasized that here enhanced diffusion of charged nanoparticles is fundamentally caused by the enlarged fluctuation of the membrane. In a previous experimental work based on the measurement by Förster resonance energy transfer (FRET), adsorption of negatively charged nanoparticles to giant unilamellar vesicles (GUVs) can induce local gelation of their zwitterionic lipid membrane.19 However, it can be noted that these measurements focus on the mobility of local lipid molecules, instead of the nanoparticles. Moreover, these experiments demonstrated that adsorption by negatively charged nanoparticles should cause liposomes to shrink (Figure S1 of ref 19), which is much likely to induce lateral tension on the membrane of the vesicles.41,42 Thus, in contrast to the lipid patchy concerned in the present work, the membrane fluctuation in the vesicle can be considerably inhibited,43 penalizing the possible enhanced diffusion of the nanoparticles on it.

Figure 7. Area per bead for positive head bead (green point) and negative head bead (pink point) of lipids interacting with nanoparticles of negative and positive surface charges: β = −0.8 (a, b) and 0.8 (c, d). In each panel, area per bead is determined using a Voronoi tessellation of the coordinates of the head beads.

clarify that positively charged nanoparticle induces positive head beads to increase in area, as opposed to the decrease for the negative head beads [Figure 7(c, d)], which prompts the formation of a concave-down protrusion becoming higher for a larger β [Figure 5(d)]. As to the negatively charged nanoparticle, absolutely inverse changes can be identified for the positive and negative head beads of lipids [Figure 6(b) and

Figure 6. |β| dependence of area per bead, Ah, for positive head bead (green) and negative head bead (pink) of lipids interacting with nanoparticles of positive (a) and negative (b) surface charges. The insetting schematic diagrams in (a) and (b) illustrate the binding-induced reorientation of the charged head beads. The local membrane shapes from the analytical model are also presented in the dashed rectangles inset in (a) and (b). 11544

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

ACS Nano

where x = |x − x0| denotes the distance from the nanoparticle, K1(x) is the first-order modified Bessel function of the second kind. We plot the equilibrium shape in the insets of Figure 6 (a) and (b) for the case of c0 < 0 and c0 > 0, respectively. This illustrates the response of the membrane shape to the charged nanoparticle. As illustrated by the schematic diagrams in Figure 6, the membrane bends as a result of the electrostatic interactions between the negatively charged inner-layer, positively charged outer-layer and the charged nanoparticle. For a nanoparticle of positive charge, the repulsions to the outer-layer beads lead to an optimal area per lipid Σ larger than the area per lipid for a flat membrane, Σ0; the spontaneous curvature c0 ∼ Σ0 − Σ in our convention, therefore c0 < 0; the equilibrium membrane shape is thereby concave down. For a negatively charged nanoparticle, c0 > 0 due to Σ < Σ0, the corresponding equilibrium membrane shape is thus concave up.

Figure 7(a, b)], and the membrane deformation turns to a concave-up configuration [Figure 5(d)]. These observations highlight electrostatics-induced surface reconstruction and local deformation of the lipid membrane, which depends heavily on the charge sign of nanoparticles. Consequently, the relations of diffusion exponents and coefficients to β and R are different for positively and negatively charged nanoparticles, as shown in the inset of Figure 3(a) and Figure 4. Theoretical Analysis. To pinpoint the mechanism of enhanced diffusion of charged nanoparticles on the membrane, we propose an analytical model connecting surface reconstruction and local deformation of the membrane. An extended description of the model can be found in Supporting Information. For brevity, the membrane shape is described as h(x) = h(x,y) in the Monge parametrization, where x = (x,y) is a two-dimensional vector and h denotes the height of the membrane. Under the small gradient approximation, the fluctuation of the membrane around the flat shape is subject to the modified Helfrich free energy F[h(x)] =

CONCLUSION In summary, we have presented the investigation to uncover the pivotal role of electrostatics in the diffusion dynamics of charged nanoparticles on the zwitterionic lipid membrane. We demonstrate that the lateral diffusion of a charged nanoparticle significantly depends on the sign and spatial distribution of charges on its surface. A central finding is that, unlike the Fickian diffusion of neutral nanoparticle, randomly charged nanoparticles undergo superdiffusive transport with statistical directionality, whereas the dynamics of uniformly charged nanoparticles favors Fickian diffusion that is significantly enhanced. Such enhancement results in the invalidity of the SD theory for charged nanoparticles, and can be ascribed to electrostatics-generated surface reconstruction and fluctuation of the membrane. Furthermore, we propose a model relating surface reconstruction to local deformation of membrane. Bearing in mind that chemical composition in these singlecomponent lipid bilayers is the same everywhere, the findings will certainly be useful for the understanding and control of many important biophysical processes regarding the transport of charged nanoparticles on the cell membrane.

⎡

∫ d2 x⎢⎣ 12 γ(∇h)2 + 12 k(∇2 h)2 − cW (x − x 0) ⎤ ∇2 h⎥ ⎦

(1)

The first two terms are the original Helfrich free energy of a free membrane with γ and k being the surface tension and the bending modulus, respectively. The last term is a coupling term which describes the effect of the nanoparticle locating at x0 on the membrane shape. This term can be understood as a generalization of the energy term due to the spontaneous curvature of a nonhomogeneous membrane. Specifically, in the present model, the positively charged outer-layer beads and the negatively charged inner-layer beads in the membrane have different responses to the charged nanoparticle as the result of the electrostatic interaction. This asymmetric coupling of the nanoparticle with respect to the membrane plane leads to an effective spontaneous curvature of the membrane. By this generalization, we have the coupling strength c = 2πkR2c0 with R and c0 standing for the nanoparticle radius and the effective spontaneous curvature; the weighting function W(x − x0) characterizes the distribution of this coupling effect through the membrane. Note that W is normalized, namely, ∫ d2xW = 1. The Euler−Lagrange equation satisfied by the equilibrium membrane shape is derived by the minimization of the free energy with respect to h(x), which reads k∇2 (∇2 − ξ −2)h0(x) − c∇2 W (x − x 0) = 0

METHODS Computer simulations use the dissipative particle dynamics (DPD) technique which extends the simulation scales of time and space to be appropriate to the study of nanoparticle−membrane systems with explicit water.45−49 This method captures the hydrodynamic effect that plays an important role in the translation diffusion of membrane inclusions.37 The models of lipid, membrane, and charged nanoparticles are displayed in Figure S1 in Supporting Information. Each amphiphilic lipid consists of a headgroup and two tails. The headgroup contains three connected hydrophilic beads and the top two of them carry the charges of +1 and −1 respectively. Each tail includes three connected hydrophobic beads. Initially, 2500 lipids self-assemble into a tensionless bilayer membrane spanning the simulation box. Each nanoparticle is modeled as a cluster of frozen DPD beads grouped into a rigid body with fcc (face-centered cubic)-arranged interior beads and uniformly distributed surface beads.50 The radius of nanoparticles is set as R = 2.6rc except where noted otherwise (rc: the length unit of DPD). To consider the effect of the spatial distribution of charges, randomly or uniformly selected surface beads are changed into charged beads, each bead carrying one unit charge. To preserve charge neutrality, the randomly selected solvent beads, with the same number of the charged beads in the nanoparticle, are changed into the counterions with opposite charges. Solvent particles are represented by a single bead. The present simulations are carried out using five different interaction forces between beads i.e., the conservative interaction force FC, dissipative force FD, random force FR, bond

(2)

It admits the general solution c h 0 (x) = − d 2x′G(x − x′)W (x′ − x 0) k

∫

(3) −2

where the Green’s function G satisfies (−∇ + ξ )G(x − x′) = δ(x − x′). In two dimensions, G(x − x′) = K0(|x − x′|/ξ)/2π, where K0(x) is the zeroth-order modified Bessel function of the second kind, ξ = κ−1 = k/γ is the correlation length of the membrane fluctuation. By choosing the weighting function W = ξ−2G of a characteristic range ξ, the equilibrium membrane shape is solved as 2

h 0 (x) = −

R2c0 κxK1(κx) 2

(4) 11545

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

ACS Nano force FS (including harmonic bond force and bond angle force) and the electrostatic force FE, i.e., fi = ∑j ≠ i (FCij + FijD + FijR + FSij + FijE) where the sum runs over all beads j.49 These forces, excluding the electrostatic one, are pairwise additive, depend on the coordinate differences, and are truncated at a certain cutoff distance rc. The conservative force is a soft, repulsive force given by FCij = aij(1 − rij)r̂ij, where aij is the maximum repulsion between beads i and j, rij = |ri − rj|/ rc, and r̂ij = rij/|rij| . In the present simulations, the interaction parameters aij used in FC are similar to those provided by the MARTINI force field,51,52 and have been successfully used in our previous works regarding lipid membranes.46,47 Particularly, the uncharged surface beads of nanoparticles are hydrophobic, so we take the particle−solvent and particle-lipid tail interactions to be 50 kBT and 30 kBT, while the interaction between charged beads of particle and charged lipid heads is set to 20 kBT for an adhesive interaction. The dissipative force FD and random force FR act as heat sink and source, respectively, so that their combined effect is a thermostat.49 The drag force is FDij = −γωD(rij)(r̂ij·vij)r̂ij, where γ is a simulation parameter related to viscosity, ωD is a weighting function that goes to zero at rc, and the relative velocity is vij = vi − vj. The random force is FRij = σωR(rij)ξijr̂ij, where ξij is a zero-mean Gaussian random variable of unit variance and σ2 = 2kBTγ.Here, kB is the Boltzmann constant and T is the temperature of the system. We select weighting functions to take the following form: ωD(rij) = ωR(rij)2 = (1 − rij)2 for rij < rc. Hookean spring with the potential Us(i,i + 1) = (1/2)Ks(|ri,i+1| − l0)2 is used to construct lipids, where i, i + 1 represent connecting beads in the molecules. The spring constant, Ks = 64 kBT, and unstretched length, l0 = 0.5rc, are chosen so as to fix the average bond length to a desired value. A three-body potential acting between adjacent bead triplets in each tail of lipids, Ua(i − 1,i,i + 1) = Ka[1 − cos(φ − φ0)] is selected to model the chain stiffness, where the angle φ is defined by the scalar product of the two bonds connecting beads i − 1, i, and i, i + 1.53,54 The electrostatic interaction among charged beads is included based on a modified particle−particle-particle-mesh (P3M) algorithm in which the electrostatic field is solved by smearing the charges over lattice grid.55 This approach has been widely used in the simulations of the bilayer membrane of charged lipids with proper mechanical properties.42,43 Moreover, the electrostatic interaction between charged nanoparticles and the bilayer membrane of zwitterionic lipids has also been successfully captured by this approach.43,46 The simulation box is 40 × 40 × 40r3c in size and with periodic boundary condition in all directions, which is large enough to avoid the finite size effects. The time step of Δt = 0.02τ is chosen ensuring the accurate temperature control over the simulation system.56 We choose our basic length and time scales to match the experimentally observed area per dipalmitoylphosphatidylcholine (DPPC) molecule and the typical diffusion coefficient of lipids.24 Then we get rc ≈ 0.70 nm and τ ≈ 7.70 ns.

Author Contributions #

P. C. and Z. H. contributed equally.

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are thankful for stimulating discussions with Ye Yang, and Guolong Zhu. L.T.Y. acknowledges financial support from Ministry of Science and Technology of China (Grant No. 2016YFA0202500). We acknowledge support from NSFC (Grant Nos. 21422403, 51273105, 21104094, 21544007, and 51633003). B.M. acknowledges support from the Youth Innovation Promotion Association, CAS (No. 2012316). REFERENCES (1) Davis, M. E.; Chen, Z. G.; Shin, D. M. Nanoparticle Therapeutics: An Emerging Treatment Modality for Cancer. Nat. Rev. Drug Discovery 2008, 7, 771−782. (2) Ghosh, P.; Han, G.; De, M.; Kim, C. K.; Rotello, V. M. Gold Nanoparticles in Delivery Applications. Adv. Drug Delivery Rev. 2008, 60, 1307−1315. (3) Doane, T. L.; Burda, C. The Unique Role of Nanoparticles in Nanomedicine: Imaging, Drug Delivery and Therapy. Chem. Soc. Rev. 2012, 41, 2885−2911. (4) 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. (5) Anderson, R. G.; Jacobson, K. A. A Role for Lipid Shells in Targeting Proteins to Caveolae, Rafts, and Other Lipid Domains. Science 2002, 296, 1821−1825. (6) Forstner, M. B.; Yee, C. K.; Parikh, A. N.; Groves, J. T. Lipid Lateral Mobility and Membrane Phase Structure Modulation by Protein Binding. J. Am. Chem. Soc. 2006, 128, 15221−15227. (7) Saffman, P. G.; Delbrück, M. Brownian Motion in Biological Membranes. Proc. Natl. Acad. Sci. U. S. A. 1975, 72, 3111−3113. (8) Peters, R.; Cherry, R. J. Lateral and Rotational Diffusion of Bacteriorhodopsin in Lipid Bilayers: Experimental Test of the Saffman-Delbrück Equations. Proc. Natl. Acad. Sci. U. S. A. 1982, 79, 4317−4321. (9) Ramadurai, S.; Holt, A.; Krasnikov, V.; van den Bogaart, G.; Killian, J. A.; Poolman, B. Lateral Diffusion of Membrane Proteins. J. Am. Chem. Soc. 2009, 131, 12650−12656. (10) Vaz, W. L. C.; Criado, M.; Madeira, V. M. C.; Schoellmann, G.; Jovin, T. M. Size Dependence of the Translational Diffusion of Large Integral Membrane Proteins in Liquid-Crystalline Phase Lipid Bilayers. A Study Using Fluorescence Recovery after Photobleaching. Biochemistry 1982, 21, 5608−5612. (11) Gambin, Y.; Lopez-Esparza, R.; Reffay, M.; Sierecki, E.; Gov, N. S.; Genest, M.; Hodges, R. S.; Urbach, W. Lateral Mobility of Proteins in Liquid Membranes Revisited. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 2098−2102. (12) Reister-Gottfried, E.; Leitenberger, S. M.; Seifert, U. Diffusing Proteins on a Fluctuating Membrane: Analytical Theory and Simulations. Phys. Rev. E 2010, 81, 031903. (13) Naji, A.; Atzberger, P. J.; Brown, F. L. Hybrid Elastic and Discrete-Particle Approach to Biomembrane Dynamics with Application to the Mobility of Curved Integral Membrane Proteins. Phys. Rev. Lett. 2009, 102, 138102. (14) Démery, V.; Dean, D. S. Drag Forces in Classical Fields. Phys. Rev. Lett. 2010, 104, 080601. (15) Petrov, E. P.; Schwille, P. Translational Diffusion in Lipid Membranes beyond the Saffman-Delbrück Approximation. Biophys. J. 2008, 94, L41−L43. (16) Bae, S. C.; Granick, S. Molecular Motion at Soft and Hard Interfaces: From Phospholipid Bilayers to Polymers and Lubricants. Annu. Rev. Phys. Chem. 2007, 58, 353−374.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b07563. Additional simulation results (PDF) Video S1 (AVI) Video S2 (AVI) Video S3 (AVI)

AUTHOR INFORMATION Corresponding Authors

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

Li-Tang Yan: 0000-0002-6090-3039 11546

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547

Article

ACS Nano

(39) Hormel, T. T.; Kurihara, S. Q.; Brennan, M. K.; Wozniak, M. C.; Parthasarathy, R. Measuring Lipid Membrane Viscosity Using Rotational and Translational Probe Diffusion. Phys. Rev. Lett. 2014, 112, 188101. (40) Brangwynne, C. P.; Koenderink, G. H.; MacKintosh, F. C.; Weitz, D. A. Cytoplasmic Diffusion: Molecular Motors Mix It Up. J. Cell Biol. 2008, 183, 583−587. (41) Shillcock, J. C.; Lipowsky, R. Tension-Induced Fusion of Bilayer Membranes and Vesicles. Nat. Mater. 2005, 4, 225−228. (42) Yan, L. T.; Yu, X. Charged Dendrimers on Lipid Bilayer Membranes: Insight through Dissipative Particle Dynamics Simulations. Macromolecules 2009, 42, 6277−6283. (43) Yan, L. T.; Yu, X. Complexes Comprised of a Dendrimer and a Vesicle: Role of Vesicle Size and the Surface Tension of the Vesicle Membrane. Nanoscale 2011, 3, 3812−3818. (44) Murtola, T.; Róg, T.; Falck, E.; Karttunen, M.; Vattulainen, I. Transient Ordered Domains in Single-Component Phospholipid Bilayers. Phys. Rev. Lett. 2006, 97, 238102. (45) Grafmüller, A.; Shillcock, J.; Lipowsky, R. Pathway of Membrane Fusion with Two Tension-Dependent Energy Barriers. Phys. Rev. Lett. 2007, 98, 218101. (46) Yan, L. T.; Yu, X. Enhanced Permeability of Charged Dendrimers across Tense Lipid Bilayer Membranes. ACS Nano 2009, 3, 2171−2176. (47) Guo, R.; Mao, J.; Yan, L. T. Unique Dynamical Approach of Fully Wrapping Dendrimer-Like Soft Nanoparticles by Lipid Bilayer Membrane. ACS Nano 2013, 7, 10646−10653. (48) Liu, Z.; Guo, R.; Xu, G.; Huang, Z.; Yan, L. T. EntropyMediated Mechanical Response of the Interfacial Nanoparticle Patterning. Nano Lett. 2014, 14, 6910−6916. (49) Groot, R. D.; Warren, P. B. Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423−4435. (50) Yong, X. Modeling the Assembly of Polymer-Grafted Nanoparticles at Oil-Water Interfaces. Langmuir 2015, 31, 11458−11469. (51) Gurtovenko, A. A.; Anwar, J.; Vattulainen, I. Defect-Mediated Trafficking across Cell Membranes: Insights from in Silico Modeling. Chem. Rev. 2010, 110, 6077−6103. (52) Tieleman, D. P.; Leontiadou, H.; Mark, A. M.; Marrink, S. J. Simulation of Pore Formation in Lipid Bilayers by Mechanical Stress and Electric Fields. J. Am. Chem. Soc. 2003, 125, 6382−6383. (53) Shillcock, J.; Lipowsky, R. Equilibrium Structure and Lateral Stress Distribution of Amphiphilic Bilayers from Dissipative Particle Dynamics Simulations. J. Chem. Phys. 2002, 117, 5048−5061. (54) Yan, L. T.; Schoberth, H. G.; Böker, A. Lamellar Microstructure and Dynamic Behavior of Diblock Copolymer/Nanoparticle Composites under Electric Fields. Soft Matter 2010, 6, 5856−5964. (55) Groot, R. D. Electrostatic Interactions in Dissipative Particle Dynamics-Simulation of Polyelectrolytes and Anionic Surfactants. J. Chem. Phys. 2003, 118, 11265−11277. (56) Vattulainen, I.; Karttunen, M.; Besold, G.; Polson, J. M. Integration Schemes for Dissipative Particle Dynamics Simulations: From Softly Interacting Systems Towards Hybrid Models. J. Chem. Phys. 2002, 116, 3967−3979.

(17) Arvizo, R. R.; Miranda, O. R.; Thompson, M. A.; Pabelick, C. M.; Bhattacharya, R.; Robertson, J. D.; Rotello, V. M.; Prakash, Y. S.; Mukherjee, P. Effect of Nanoparticle Surface Charge at the Plasma Membrane and Beyond. Nano Lett. 2010, 10, 2543−2548. (18) Leroueil, P. R.; Hong, S.; Mecke, A.; Baker, J. R.; Orr, B. G.; Banaszak Holl, M. M. Nanoparticles Interaction with Biological Membranes: Does Nanotechnology Present a Janus Face. Acc. Chem. Res. 2007, 40, 335−342. (19) Wang, B.; Zhang, L.; Bae, S. C.; Granick, S. NanoparticleInduced Surface Reconstruction of Phospholipid Membranes. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 18171−18175. (20) Li, Y.; Gu, N. Thermodynamics of Charged Nanoparticle Adsorption on Charge-Neutral Membranes: A Simulation Study. J. Phys. Chem. B 2010, 114, 2749−2754. (21) 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 Bilayer. Nano Lett. 2013, 13, 4060−4067. (22) Van Lehn, R. C.; Alexander-Katz, A. Membrane-Embedded Nanoparticles Induce Lipid Rearrangements Similar to Those Exhibited by Biological Membrane Proteins. J. Phys. Chem. B 2014, 118, 12586−12598. (23) Van Lehn, R. C.; Ricci, M.; Silva, P. H. J.; Andreozzi, P.; Reguera, J.; Voïtchovsky, K.; Stellacci, F.; Alexander-Katz, A. Lipid Tail Protrusions Mediate the Insertion of Nanoparticles into Model Cell Membranes. Nat. Commun. 2014, 5, 4482. (24) Smith, K. A.; Jasnow, D.; Balazs, A. C. Designing Synthetic Vesicles That Engulf Nanoscopic Particles. J. Chem. Phys. 2007, 127, 084703. (25) Li, Y.; Gu, N. Computational Investigation of Interaction Between Nanoparticles and Membranes: Hydrophobic/Hydrophilic Effect. J. Phys. Chem. B 2008, 112, 16647−16653. (26) Hansen, J.; McDonald, I. Theory of Simple Liquids; Elsevier Academic Press: London, 2006. (27) Guo, R.; Liu, Z.; Xie, X. M.; Yan, L. T. Harnessing Dynamic Covalent Bonds in Patchy Nanoparticles: Creating Shape-Shifting Building Blocks for Rational and Responsive Self-Assembly. J. Phys. Chem. Lett. 2013, 4, 1221−1226. (28) Liu, B.; Goree, J. Superdiffusion and Non-Gaussian Statistics in a Driven-Dissipative 2D Dusty Plasma. Phys. Rev. Lett. 2008, 100, 055003. (29) Baskaran, A.; Marchetti, M. C. Enhanced Diffusion and Ordering of Self-Propelled Rods. Phys. Rev. Lett. 2008, 101, 268101. (30) Tang, S.; Wang, M.; Olsen, B. D. Anomalous Self-Diffusion and Sticky Rouse Dynamics in Associative Protein Hydrogels. J. Am. Chem. Soc. 2015, 137, 3946−3957. (31) Codling, E. A.; Plank, M. J.; Benhamou, S. Random Walk Models in Biology. J. R. Soc., Interface 2008, 5, 813−834. (32) Yan, L. T.; Xie, X. M. Wetting-Layer Formation Mechanisms of Surface-Directed Phase Separation under Different Quench Depths with Off-Critical Compositions in Polymer Binary Mixture. J. Chem. Phys. 2007, 126, 064908. (33) Zöttl, A.; Stark, H. Hydrodynamics Determines Collective Motion and Phase Behavior of Active Colloids in Quasi-TwoDimensional Confinement. Phys. Rev. Lett. 2014, 112, 118101. (34) Einstein, A. Ü ber Die Von Der Molekularkinetischen Theorie Der Wärme Geforderte Bewegung Von in Ruhenden Flüssigkeiten Suspendierten Teilchen. Ann. Phys. 1905, 17, 549−560. (35) Herold, C.; Schwille, P.; Petrov, E. P. DNA Condensation at Freestanding Cationic Lipid Bilayers. Phys. Rev. Lett. 2010, 104, 148102. (36) Guigas, G.; Weiss, M. Size-Dependent Diffusion of Membrane Inclusions. Biophys. J. 2006, 91, 2393−2398. (37) Stone, H. A.; Masoud, H. Mobility of Membrane-Trapped Particles. J. Fluid Mech. 2015, 781, 494−505. (38) Sickert, M.; Rondelez, F.; Stone, H. A. Single-Particle Brownian Dynamics for Characterizing the Rheology of Fluid Langmuir Monolayers. Europhys. Lett. 2007, 79, 66005. 11547

DOI: 10.1021/acsnano.6b07563 ACS Nano 2016, 10, 11541−11547