Molecular Dynamics Simulations of PAMAM Dendrimer-Induced Pore

(DPPC) bilayers with explicit water using the coarse-grained (CG) model developed by .... bead, and the head group is represented by two beads, one fo...
8 downloads 0 Views 391KB Size
Download PDF
18204

J. Phys. Chem. B 2006, 110, 18204-18211

Molecular Dynamics Simulations of PAMAM Dendrimer-Induced Pore Formation in DPPC Bilayers with a Coarse-Grained Model Hwankyu Lee† and Ronald G. Larson*,‡ Department of Biomedical Engineering and Department of Chemical Engineering, Biomedical Engineering, Mechanical Engineering, and Macromolecular Science and Engineering Program, UniVersity of Michigan, Ann Arbor, Michigan 48109 ReceiVed: May 19, 2006; In Final Form: July 23, 2006

We have performed 0.5-µs-long molecular dynamics (MD) simulations of 0%, 50%, and 100% acetylated third- (G3) and fifth-generation (G5) polyamidoamine (PAMAM) dendrimers in dipalmitoylphosphatidylcholine (DPPC) bilayers with explicit water using the coarse-grained (CG) model developed by Marrink et al. (J. Phys. Chem. B 2004, 108, 750-760), but with long-range electrostatic interactions included. Radii of gyration of the CG G5 dendrimers are 1.99-2.32 nm, close to those measured in the experiments by Prosa et al. (J. Polym. Sci. 1997, 35, 2913-2924) and atomistic simulations by Lee et al. (J. Phys. Chem. B 2006, 110, 4014-4019). Starting with the dendrimer initially positioned near the bilayer, we find that positively charged un-acetylated G3 and 50%-acetylated and un-acetylated G5 dendrimers insert themselves into the bilayer, and only un-acetylated G5 dendrimer induces hole formation at 310 K, but not at 277 K, which agrees qualitatively with experimental observations of Hong et al. (Bioconj. Chem. 2004, 15, 774-782) and Mecke et al. (Langmuir 2005, 21, 10348-10354). At higher salt concentration (∼500 mM NaCl), un-acetylated G5 dendrimer does not insert into the bilayer. The results suggest that with inclusion of long-range electrostatic interactions into coarse-grained models, realistic MD simulation of membrane-disrupting effects of nanoparticles at the microsecond time scale is now possible.

Introduction Polyamidoamine (PAMAM) dendrimers consist of a central core, regularly branched monomeric building blocks, and many surface terminal groups. Due to their controlled mass, surface valency, and surface functionality, they are considered to be good candidate nanoparticles for use as antitumor therapeutics and drug delivery.1-4 For these applications, the dendrimers need to interact with cell membranes, and thus it is important to understand the interactions between the dendrimer and lipid bilayers in the cell. Using atomic force microscopy (AFM) and enzyme assays, Hong et al. found that un-acetylated dendrimers can cause hole formation or expansion both in aqueous supported lipid bilayers and in vitro in cells, whereas acetylated dendrimers do not cause hole formation, suggesting that terminalacetylation plays an important role in the interactions between the dendrimer and lipid bilayers.5 Mecke et al. observed that the dendrimer size also influences the interactions between the dendrimer and the bilayer, and proposed that large dendrimers extract lipids from the membrane to form dendrimer-filled vesicles.6 They also found that when the bilayer is brought into the gel phase through decreasing the temperature to 6 °C, hole formation by dendrimers is suppressed, suggesting that the dendrimer interacts selectively with the liquid-crystalline bilayer phase and not with the gel phase.7 While AFM, enzyme assays, flow cytometry, fluorescence microscopy, and other experimental probes provide vital infor* Address correspondence to this author. E-mail: [email protected]. † Department of Biomedical Engineering. ‡ Department of Chemical Engineering, Biomedical Engineering, Mechanical Engineering, and Macromolecular Science and Engineering Program.

mation on the interaction between dendrimers and lipid bilayers, results from these are not always easy to interpret at the level of individual molecules or specific interactions between the dendrimer and lipids. On the other hand, molecular-level phenomena can be visualized in detail by atomistic molecular dynamics (MD) simulations, which offer insights into structure and dynamics, assuming that these simulations can be validated by successful comparisons to available experimental results. In addition to atomistic MD simulations, which are very limited in the range of system size and time scale they can reach, coarsegrained molecular dynamics simulations have been recently used to study the insertion and assembly of simple mimics of membrane proteins and polymers in the lipid bilayer.8-10 Atomistic molecular dynamics simulations have yielded predictions of the size and structure of PAMAM dendrimers. The Goddard group has performed molecular dynamics simulations of PAMAM dendrimers in explicit water, showing the structure of the dendrimer and the thermodynamic and dynamic properties of water near the dendrimer.11,12 We have also simulated G5 PAMAM dendrimers atomistically in explicit water and methanol and found that the predicted internal structure compared favorably with experimental findings.13 However, atomistic models are restricted to small simulation time and length scales, and large systems that include both a G5 dendrimer and a lipid bilayer as well as solvent are difficult to capture in atomistic simulations. To overcome these limitations, we here will employ a coarse-grained (CG) model of the dendrimer-lipid bilayer system. Although several CG dendrimer models have been proposed, the beads in early CG models were too simple to represent with any accuracy the properties of dendrimers.14-16 Recently, Gurtovenko et al. developed an improved CG model of a PAMAM dendrimer by adjusting the

10.1021/jp0630830 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/31/2006

Dendrimer-Induced Pore Formation in DPPC Bilayers coarse-grain parameters so that the radius of gyration of the CG model dendrimer matched the experimental value.17 This new CG model could represent both charged and un-charged dendrimers, showing good agreement with experimental radii of gyration in both cases. However, in Gurtovenko’s CG model, all the beads in the interior of the dendrimer were made identical, which may not properly represent the internal structure of the dendrimer because of hydrogen bonding interactions between branches in the dendrimer interior, which we observed in our previous work.13 Therefore, we here extend the CG lipid model of Marrink et al.18 to the case of dendrimers. This new model distinguishes nodes and branches in interior parts of the dendrimer, and hence beads representing branches can be given the capability of hydrogen bonding, which is not possible for the nodes, and thus we can simulate dendrimers more accurately with the coarse-grained model of Marrink et al. than with other CG models. Although the interactions between dendrimers and lipid bilayers have been investigated experimentally,5-7 no simulations of these interactions with a realistic membrane have been performed and compared with experimental results. Mecke et al. simulated PAMAM dendrimers in implicit solvent near a negatively charged plane, consisting of a two-dimensional hexagonal array of beads, which was intended as a simple mimic of a negatively charged surface, such as a mica surface, or, less realistically, the top surface of a bilayer. These simulations showed that dendrimers flattened as they were attached to the plane.19 However, because the surface beads were held fixed, these simulations could not show dendrimer-induced hole formation. Here, we develop a model of a CG PAMAM dendrimer and perform 0.5-µs-long molecular dynamics simulations of G3 and G5 PAMAM dendrimers acetylated to different extents in dipalmitoylphosphatidylcholine (DPPC) bilayers and explicit water to investigate the effect of different sizes of dendrimers and the extent of terminal-acetylation, temperature, and salt concentration on the interactions between the dendrimer and the lipid bilayer, and to test the ability of CG models to predict experimentally measured dendrimer-bilayer properties. Methods All the simulations and analyses were performed with the GROMACS3.2 simulation package20 with the coarse-grained (CG) force field developed by Marrink et al.,18 which was downloaded from http://md.chem.rug.nl/∼marrink/coarsegrain.html. We used the CG DPPC, water, and ion (Na+ and Cl-) force field models, which are given in detail by Marrink et al.18 For the CG DPPC, four methylene units are lumped into each tail bead, and the head group is represented by two beads, one for the phosphate and one for the choline. For the CG water, each water bead represents four water molecules. For the CG ion, a reduced charge of 0.7 is used to mimic the implicit screening of the first hydration shell, as described in ref 18. Using the CG force field, we developed CG models for G3 and G5 PAMAM dendrimers with different levels of acetylation. Equilibration of a Coarse-Grained DPPC Bilayer. The simulated bilayer consists of 512 CG DPPC molecules and ∼5800 CG water molecules in a periodic box of size 12 × 13 × 9 nm3. Several bilayers were constructed at temperatures 277 and 310 K, and salt concentrations 0 and ∼500 mM NaCl. After energy minimization, equilibration runs were performed for 0.1 µs with a time step of 32-40 fs. The center of mass motion of each monolayer in the bilayer was removed every time step for correct calculation of the lipid lateral diffusion coefficient. The temperature was maintained by applying a

J. Phys. Chem. B, Vol. 110, No. 37, 2006 18205

Figure 1. (a) Mapping of dendrimer chemical moieties into coarsegrained dendrimer beads. The dendrimer is composed of four different types of chemical moiety, each represented by a single bead type. N0 stands for a neutrally charged group; Qd represents a charged group with hydrogen-bond donors; Nda indicates a neutrally charged group with a hydrogen-bond donor and an acceptor. (b) Schematic illustration of the topology of the G1 dendrimer. The interior portion consists of N0 and Nda moieties, respectively, for nodes and branches, and the surface consists of Nda and Qd groups, respectively, for acetylated and un-acetylated surface terminals. Higher generations can be described by extending this topology. The harmonic bonding and angle potentials are used to connect these beads.

Berendsen thermostat21 in an NPT ensemble. A cutoff of 12 Å was used for van der Waals interactions. With use of the standard shift function of GROMACS20 in which both the energy and force vanish at the cutoff distance, the LJ potential was smoothly shifted to zero between 0.9 and 1.2 nm to reduce the cutoff noise. For electrostatic interactions, both a cutoff of 12 Å and particle mesh Ewald summation (PME) were used and compared.22 With a cutoff of 12 Å, the Coulombic potential was also smoothly shifted to zero from 0 to 1.2 nm. The final DPPC configurations were analyzed for the effect of different electrostatics and temperature on bilayer properties and then used as the starting states for simulations of dendrimers in bilayers. Equilibration of a Coarse-Grained Dendrimer Model. The force field of Marrink et al. was used to develop the CG model for differently acetylated G3 and G5 dendrimers.18 Figure 1a illustrates our CG model. Each dendrimer has symmetrically repeated branches, and is composed of four different chemical moieties, each of which we represent by a single bead, yielding 122 and 506 CG beads in G3 and G5 dendrimers, respectively. To make the four different bead types distinguishable, the four main types of beadsspolar (P), nonpolar (N), apolar (C), and charged (Q)sof the CG model of Marrink et al. are used. The four CG bead types are further discriminated to represent groups having no hydrogen bonding capabilities (0), having hydrogen bond donors (d), having hydrogen bond acceptors (a), and having both hydrogen bond donors and acceptors (da). Therefore, N0 and Nda are respectively used for nodes and branches in the interior parts of the dendrimer, and Nda and Qd are respectively used for acetylated and un-acetylated surface terminals of dendrimers. The Lennard-Jones parameters of these bead types are specified by Marrink et al.18 Realistic masses of 56.1, 72, and 29 computed by summing the masses of the atoms in each chemical moiety are respectively assigned to beads of type N0, Nda, and Qd. Figure 1b shows a schematic picture of a coarse-grained G1 PAMAM dendrimer, and CG G3 and G5

18206 J. Phys. Chem. B, Vol. 110, No. 37, 2006

Figure 2. (a) A snapshot at the beginning (0 ns) of the simulation of system G5-1 (100% acetylated). Snapshots at the end (0.5 µs) of simulations of systems (b) G5-1, (c) G5-2 (50% acetylated), (d) G5-3 (un-acetylated), (e) G5-4 (un-acetylated, 500 mM NaCl), (f) G5-5 (unacetylated, low temperature), (g) G3-1 (100% acetylated), and (h) G3-2 (un-acetylated). Black dots represent dendrimers, and blue dots represent headgroups of the DPPC bilayer. The explicit water and ions are omitted for clarity. The images were created with VMD.23

dendrimers can be described by repeating the same bonding interactions. Initial atomic coordinates of well-defined G3 and G5 PAMAM dendrimers with no folding were generated with the Insight II software package (Accelrys Inc., San Diego, CA), followed by several steps of energy minimization. The atomic coordinates of the nitrogen atom in each moiety were used to specify the initial position of each CG bead. Beads of the CG dendrimer that represent chemically bonded moieties are connected by a weak harmonic potential Vbond(R) with an equilibrium distance Rbond ) 0.5 nm (Vbond(R) ) 1/2Kbond(R - Rbond)2), and a weak harmonic angle potential with an equilibrium angle θ0 ) 120° or 180° (Vangle(θ) ) 1/2Kangle{cos(θ) - cos(θ0)}2).18 To parametrize force constants of the harmonic bonding potential and angle potential, we performed 70-ns-long molecular dynamics simulations of CG dendrimers in CG water at 310 K with various force constants. The equilibrated radius of gyration of the CG dendrimer was compared with that predicted by atomistic simulations and with experimental results, and details of this comparison will be discussed below. The force constant of the bonding potential Kbond ) 1250 kJ mol-1 nm-2 was the same as that used in the CG lipid model. The force constant of the angle potential, Kangle ) 150 kJ mol-1 rad-2, was chosen to be higher than that of the CG lipid model, for

Lee and Larson which Kangle ) 25 kJ mol-1 rad-2, to maintain a realistic rigidity of the CG dendrimer. Dendrimers equilibrated in CG water were analyzed to determine their size and then used as starting configurations for simulations of dendrimers in bilayers. Equilibration of a Dendrimer with a DPPC Bilayer. Equilibrated dendrimers were then added to the bilayer systems obtained from previous equilibration runs. The center of mass of each dendrimer was positioned a distance of 4 nm above the center of the bilayer. Water molecules and ions were added to achieve electroneutrality and to add salt. The final configuration included a G3 or G5 dendrimer, 512 DPPC lipids, ∼13 000 water molecules, and Na+ and Cl- ions in a box of dimensions 12 ×13 × 14 nm3, shown in Figure 2a. The various dendrimerbilayer systems are defined in Table 1. After several steps of energy minimization, the dendrimer was position-restrained with a force constant of 1000 kJ mol-1 nm-2, and an equilibration run of 10-20 ns was performed. After restrained runs, unrestrained equilibration runs were performed for 0.5 µs with a time step of 25-32 fs. The temperature was maintained at 277 or 310 K by applying a Berendsen thermostat21 in NPT ensemble. A cutoff of 12 Å was used for van der Waals interactions, and both a cutoff of 12 Å and particle mesh Ewald summation (PME) for electrostatic interactions.22 With use of the standard shift function of GROMACS20 in which both the energy and force vanish at the cutoff distance, the LJ potential was smoothly shifted to zero between 0.9 and 1.2 nm to reduce the cutoff noise. The Coulombic potential was also smoothly shifted to zero from 0 to 1.2 nm. The coordinates were saved every 100 ps for analysis. Results and Discussion Simulations of a Coarse-Grained Dendrimer. To verify CG models for G3 and G5 dendrimers, the radii of gyration Rg were calculated and compared with values from experiments and from previous atomic simulations. Rg was measured by using electron densities from SAXS by Prosa et al.,24 and thus we modified the normal equation for Rg by using electron numbers instead

of mass. (Here Rg) x∑i||ri||2ei / ∑iei, where ei is the electron number and ri is the position of atom i with respect to the center of mass of the molecule.) Figure 3 shows that Rg values for dendrimers drastically decrease as functions of time after the beginning of the simulations and then reach steady-state values at around 30 ns. After 30 ns, Rg values fluctuate a bit but do not change much, suggesting that dendrimers are equilibrated within the simulated time scales. Table 2 shows that the values of Rg from our simulations compare favorably with those from experiments and atomistic simulations. Note that the more acetylated G5 dendrimers show lower values of Rg compared to un-acetylated dendrimers, which agrees with experimental and atomic simulation results, suggesting that our CG dendrimer models successfully represent the effect of terminal-acetylation on the size of

TABLE 1: List of Simulations no. of surface groups name

generation

NH3+

acetylation (NHCOCH3)

no. of DPPC molecules

NaCl concn (mM)

temp (K)

simulation time (µs)

G5-1 G5-2 G5-3 G5-4 G5-5 G3-1 G3-2

5 5 5 5 5 3 3

0 64 128 128 128 0 32

128 64 0 0 0 32 0

512 512 512 512 512 512 512

0 0 0 500 0 0 0

310 310 310 310 277 310 310

0.5 0.5 0.5 0.5 0.5 0.5 0.5

Dendrimer-Induced Pore Formation in DPPC Bilayers

Figure 3. Radii of gyration (Rg) for differently acetylated G3 and G5 PAMAM dendrimers.

J. Phys. Chem. B, Vol. 110, No. 37, 2006 18207

Figure 4. Order parameters of DPPC tails in pure DPPC bilayers at different temperatures. GLYC designates the bead for glycerol in DPPC, and C1 through C4 are beads for the tail.

TABLE 2: Average Values of Radius of Gyration (Rg) of Differently Acetylated Atomistic (Lee et al.) and Coarse-grained (this work) G3 and G5 PAMAM Dendrimers over the Last 20 ns of the Simulations, Compared with Experiments radius of gyration (nm) experiment

un-acetylated G5 50% acetylated G5 100% acetylated G5 un-acetylated G3 100% acetylated G3

simulation

Prosa et al.24

Choi et al.25

Lee et al.13

2.41

2.50

2.51

2.35

2.11

this work 2.32 ( 0.01 2.20 ( 0.01 1.99 ( 0.01 1.31 ( 0.01 1.32 ( 0.01

TABLE 3: Area per Lipid for CG DPPC Bilayers With and Without Long-Range Electrostatic Interactions, Compared with Experimental Results simulation (310 K)

experiment28 area per lipid of DPPC bilayer (nm2)

0.48 (293 K) 0.64 (323 K)

cutoff (1.2 nm)

long-range electrostatics (PME)

0.61 ( 0.001

0.64 ( 0.001

dendrimers. For G3, acetylation of the surface does not affect the dendrimer size. The Effect of Long-Range Electrostatic Interactions on a Pure DPPC Bilayer. Hong et al. and Mecke et al. performed their dendrimer-bilayer experiments with dimyristoylglycerophosphocholine (DMPC) lipids. In the CG models of Marrink et al., the transition temperature of the DPPC bilayer between the rippled gel phase and liquid-crystalline phase is 295 ( 5 K, which lies between the experimental transition temperature for DMPC (297 K) and that for DPPC (314 K).26,27 Note that because lipid “beads” each contain four methylene groups, the CG model cannot distinguish lipids with a difference of only one or two methylene units. Since the transition temperature of the CG DPPC model is closer to the experimental value for DMPC than to that for DPPC, as Marrink et al. suggested in their paper,26 it is reasonable to use the CG DPPC model to mimic DMPC bilayers in dendrimer-bilayer experiments. The CG lipid models of Marrink et al. have been parametrized for short-range electrostatic interactions by using a cutoff of 1.2 nm with a shift function from 0 to 1.2 nm.18 However, longrange electrostatic interactions may be important for the interactions between dendrimers and lipid bilayers because the radius of the dendrimer is larger than the typical cutoff value. In pure DPPC-bilayer systems, we applied both cutoff and particle mesh Ewald (PME) summation and analyzed the effect of PME summation on the properties of bilayers. Table 3 shows

Figure 5. Order parameters of DPPC tails in the G5 dendrimer-bilayer systems. GLYC designates the bead for glycerol in DPPC, and C1 through C4 are beads for the tail.

the area per lipid of the pure DPPC-bilayer systems obtained from experiments and simulations. Since the dendrimer-bilayer experiments were performed at physiological temperature, 310 K, our simulations on pure bilayers were performed at 310 K, which cannot be compared directly with experiments at the same temperature. However, the area per lipid from the simulation with an electrostatic cutoff is 0.61 nm2, which is between the experimental results at 293 and 323 K, showing that the cutoff method represents experimental results well. Using it, Marrink et al. achieved excellent agreement of various properties of CG lipid bilayers with experimental results at different temperatures.18 For the system with PME summation, we find an area per lipid of 0.64 nm2, which is higher than with a cutoff, indicating that use of a cutoff might better represent the bilayer properties than does the PME method, probably because Marrink et al. tuned their CG bead potentials to give accurately an area per lipid with cutoff electrostatic interactions. However, the difference in the area per lipid between the simulations with a cutoff and those with PME is within 5%, suggesting that the PME method can be used if a rigorous match of the area per lipid is not essential. In addition to the area per lipid, the lipid lateral diffusion coefficient was measured from the slope of the mean-squared displacement, showing that diffusion coefficient in the simulation with PME is 0.78 ((0.00) × 10-6 cm2/s, which is similar to that in the simulation with a cutoff of 0.76 ((0.02) × 10-6 cm2/s, suggesting that inclusion of PME does not affect the dynamics of lipid molecules. Also, in our simulations with an electrostatic cutoff, we do not observe insertion of dendrimer into the bilayer, whereas using the PME method, we do observe that some un-acetylated dendrimers insert into the bilayers and induce pore formation, as occurs in experiments. Therefore, we here incorporate long-range electrostatic interactions using the PME method. To understand the phase behavior of lipid bilayers at different temperatures, the pure DPPC bilayer was also simulated at 277 K and compared with the results at 310 K. The DPPC

18208 J. Phys. Chem. B, Vol. 110, No. 37, 2006

Lee and Larson

Figure 6. Mass density profiles of (a) G5-1 (100% acetylated), (b) G5-2 (50% acetylated), (c) G5-3 (un-acetylated), (d) G3-2 (un-acetylated), and (e) charged beads in G5-3.

tail conformational order is quantified by the order parameter Scc ) 3/2〈cos2θz〉 - 1/2, where θz is the angle that the vector connecting beads Cn-1 to Cn+1 makes with the z axis. The bracket indicates averaging over time and over all molecules in the simulation. Order parameters can vary between 1 (perfect orientation in the interface normal direction) and -1/2 (perfect orientation perpendicular to the normal).29 In Figure 4, DPPC lipids at 277 K are much more ordered than that at 310 K, suggesting that lower temperature induces a more condensed lipid phase, which was also observed in the simulations by Marrink et al.26

Insertion of the Dendrimer into a DPPC Bilayer. We performed 0.5-µs-long CG-molecular dynamics simulations of G3 and G5 PAMAM dendrimers in a DPPC bilayer with different acetylation of the dendrimer surface, and different temperatures and salt concentrations. Here, these dendrimerbilayer systems are designated “G5-1”, “G5-2”, “G5-3”, “G5-4”, “G5-5”, “G3-1”, and “G3-2”, and described in Table 1. Figure 2 shows snapshots from the beginning (a) and end (b-h) of the simulations with PME long-range electrostatics. Although the simulations were performed over a run time of 0.5 µs, the average properties were analyzed only over

Dendrimer-Induced Pore Formation in DPPC Bilayers the last 200 ns when the system was in its most equilibrated state. Experimentally, Hong et al. and Mecke et al. found that unacetylated G5 PAMAM dendrimers remove lipids from the bilayer and expand holes mostly from the edges of existing bilayer defects, whereas acetylated G5 and un-acetylated and acetylated G3 dendrimers are only attracted to the edges of existing bilayer defects, but do not cause the formation or expansion of defects in the lipid bilayer.5-7 Also, they studied un-acetylated and acetylated G5 dendrimers in vitro with KB and Rat2 cell membranes, showing that only un-acetylated G5 can induce membrane permeability. Those experimental results suggest that the size of the dendrimer and the extent of terminalacetylation play important roles in hole formation and expansion in lipid bilayers. From our simulations, snapshots b-d of Figure 2 show that 100% acetylated dendrimers do not insert into the bilayer, whereas 50% acetylated and un-acetylated dendrimers do insert, which is analogous to experimental results showing that terminal-acetylation reduces dendrimer interactions with the membrane. In addition, snapshots g and h of Figure 2 show that only un-acetylated G3 dendrimers insert into the bilayer, similar to the results of G5 dendrimers. To further analyze the effect of terminal-acetylation on disruption of lipid bilayer, order parameters of DPPC tails in the bilayers with 0%, 50%, and 100% acetylated dendrimers were measured. Each dendrimer interacts with the lipids close to it, and thus only DPPC molecules within 2 nm from the center of mass of the dendrimer in the x,y-direction were considered for the analysis of order parameters. With use of this criterion, 56-61 DPPC lipids per system were analyzed. Figure 5 shows tail order parameters of the pure DPPC bilayer with different G5 dendrimers. Although 100% acetylated G5 dendrimer disorders the DPPC bilayer, the extent of disorder is relatively smaller than that of other G5 dendrimers. Both 50% acetylated and un-acetylated dendrimers show significant disordering of lipid bilayers, suggesting that the extent of acetylation is important for the interactions between the dendrimer and the lipid bilayer, which corresponds to experimental results and our findings of the dendrimer insertion into the bilayer. In addition to considering the dendrimer size and the extent of terminal-acetylation, systems with different temperatures and salt concentrations were simulated and compared with experimental results. Experimentally, Hong et al. observed unacetylated G5 dendrimer-induced enzyme leakage from cells in vitro at 310 K, but not at 279 K.5 Mecke et al. also observed that un-acetylated G5 dendrimers interact selectively with the fluid phase lipid bilayer and not with the gel phase lipid bilayer. Over our simulation time scales (Figure 2f), the un-acetylated G5 dendrimer does not insert into the bilayer at 277 K, which is consistent with the experimental finding. Insertion may be blocked because DPPC lipids at 277 K are more condensed than those at 310 K as discussed above. With added salt, the simulations (Figure 2e) show that un-acetylated G5 does not insert into the bilayer probably because electrolyte weakens the electrostatic interactions between surface charges of dendrimers and the headgroups of lipids. Dendrimer-Induced Pore Formation in DPPC Bilayers. In Figure 6a-d, mass densities of the dendrimer, DPPC, and water are plotted for the simulations G5-1, G5-2, G5-3, and G3-2. G5-1 (100% acetylated), G5-4 (un-acetylated, but with salt), G5-5 (un-acetylated, at low temperature), and G3-1 (100% acetylated) do not show any dendrimer mass in the bilayer region, whereas G5-2, G5-3, and G3-2, which are all charged dendrimers with no added electrolyte, show dendrimer penetra-

J. Phys. Chem. B, Vol. 110, No. 37, 2006 18209

Figure 7. Radial distribution functions for (a) terminals of dendrimer with respect to DPPC headgroups and (b) counterions with respect to DPPC headgroups, averaged over the last 200 ns.

tion through the bilayer. Although G3-2 and G5-2 show insertion of dendrimers into the bilayer, the dendrimer region is too small to be recognized in these plots. However, G5-3, which is completely un-acetylated, shows a relatively large concentration of the dendrimer throughout the bilayer, reinforcing our finding that the size of the dendrimer and its extent of terminalacetylation are important for the extent of dendrimer insertion into the bilayer. Figure 6e shows mass densities of headgroups of DPPC, terminals of the dendrimer, and counterions in the system G5-3. Terminals of the dendrimer are observed in the region of DPPC headgroups of both leaflets of the bilayer, but not in the DPPC tail region, showing that the terminal groups cross the bilayer to interact with headgroups in the opposite leaflet of the DPPC bilayer. In Figure 7a, the radial distribution function (RDF) of the dendrimer terminals around the phosphate groups of DPPC has a much higher peak at ∼0.5 nm than does that around the choline groups, showing that the positively charged terminals strongly interact with negatively charged phosphate groups of DPPC, indicating that this interaction is important for the insertion of the dendrimer and for pore formation. In addition to the charged groups of DPPC and the dendrimer, mass densities and the RDF of the counterions were calculated. Figure 6e shows that counterions are observed near the headgroups of DPPC as well as the terminal groups of the dendrimer. Figure 7b shows that the RDF of the counterions around the DPPC choline groups has a higher peak at ∼0.5 nm than does that around the phosphate groups, suggesting that negatively charged counterions strongly interact with the positively charged choline groups of DPPC. Panels a-c of Figure 8 show a top view of the DPPC bilayer at the end of simulations G3-2, G5-2, and G5-3, respectively, which show the insertion of charged dendrimers into the bilayer, although the pores formed by G3-2 and G5-2 are too small to be recognized in Figure 8a,b. However, in Figure 8c, G5-3 shows a relatively large hole, which is consistent with the mass density profiles. Parts a and b of Figure 9 show the time

18210 J. Phys. Chem. B, Vol. 110, No. 37, 2006

Lee and Larson bilayer. In Figure 9a, G5-3 has many more dendrimer particles inside the bilayer than G5-2 and G3-2 do, confirming that dendrimer size affects the extent of insertion of the dendrimer. Also, Figure 9b shows that these dendrimers have roughly the same number of water beads (roughly 1-7) inside the bilayer, indicating that water molecules can be transported through the pore in the bilayer. These results show, again, that the larger and less acetylated dendrimer increases the pore formation tendency, in agreement with experimental results. After hole formation by G5-3, the dendrimer was removed, and then the simulations of the now pure DPPC bilayer continued. Figure 8d shows that the removal of the dendrimer results in disappearance of the hole, and recovery of the undisturbed lipid bilayer structure. This result is similar to the experimental finding of Hong et al., that cells recover their membrane integrity upon removal of a dendrimer solution. These simulation and experimental results suggest that the G5 PAMAM dendrimer may not be cytotoxic in the cell. Conclusions

Figure 8. Top view of the DPPC bilayer at the end (0.5 µs) of simulations (a) G5-2, (b) G3-2, and (c) G5-3. The dendrimer, water, and ions are omitted for clarity. (d) Top view of the DPPC bilayer after removing the dendrimer from the simulation G5-3.

Figure 9. Number of beads of (a) dendrimer and (b) water within a distance of 1 nm from center of mass of the bilayer along a direction normal to the bilayer as a function of time.

Coarse-grained molecular dynamics simulations of differently acetylated G3 and G5 PAMAM dendrimers in DPPC bilayers were performed for 0.5 µs under various conditions to understand the effect of dendrimer size, extent of terminal-acetylation, temperature, and salt concentration on dendrimer-lipid bilayer interactions and to test the ability of CG models to predict experimentally measured dendrimer-bilayer properties. The radii of gyration of the equilibrated CG G5 dendrimers were found to be 1.99-2.32 nm for G5 dendrimers, corresponding closely to the atomic simulations and experimental results.13,24,25 The simulations with long-range electrostatic interactions (PME) yield an area per lipid in the pure DPPC bilayer that compares reasonably well with the results of simulations with the cutoff method. Also, un-acetylated dendrimers insert into the bilayers and induce pore formation, similar to what is seen in experiments, but only in the simulations that use long-range particle mesh Ewald (PME) electrostatics rather than a short-range electrostatic cutoff. Starting with the dendrimer initially positioned near the bilayer, final configurations after 0.5 µs show that acetylated G3 and G5 dendrimers are not inserted into bilayers, whereas un-acetylated G3, and 50% acetylated and unacetylated G5 dendrimers are inserted. Only un-acetylated G5 induces significant pore formation, which corresponds qualitatively to experimental results that show that un-acetylated G5 can expand bilayer holes, but acetylated G5 and G3 dendrimers cannot.5-7 After removal of un-acetylated G5 dendrimer, the hole formed in the simulation heals, which was also observed in the experiment. At 277 K, un-acetylated G5 is not inserted into the bilayer due to the condensed (gel) lipid bilayer, which again corresponds to the experimental results. Insertion of unacetylated G5 into the bilayer does not occur at higher salt concentration, which is probably the result of weakened electrostatic interactions between the dendrimer and the bilayer. Acknowledgment. We gratefully acknowledge the help of Senthil Kandasamy and Susan Duncan, members of our research group, and Seungpyo Hong in the Nanotechnology institute for Medicine and Biological Sciences for valuable discussions. References and Notes

dependence of the number of the dendrimer and water beads inside the bilayer, where beads “inside the bilayer” are taken to be those within 1 nm of the center of mass of the bilayer where this distance is measured along a direction normal to the

(1) Baker, J. R.; Quintana, A.; Piehler, L. T.; Holl, M. M. B.; Tomalia, D. A.; Raczka, E. Biomed. MicrodeVices 2001, 3, 61-69. (2) Tomalia, D. A.; Naylor, A. M.; Goddard, W. A. Angew. Chem., Int. Ed. Engl. 1990, 29, 138-175.

Dendrimer-Induced Pore Formation in DPPC Bilayers (3) Malik, N.; Evagorou, E. G.; Duncan, R. Anti-Cancer Drugs 1999, 10, 767-776. (4) Choi, Y.; Thomas, T.; Kotlyar, A.; Islam, M. T.; Baker, J. R. Chem. Biol. 2005, 12, 35-43. (5) Hong, S.; Bielinska, A. U.; Mecke, A.; Keszler, B.; Beals, J. L.; Shi, X.; Balogh, L.; Orr, B. G.; Baker, J. R.; Banaszak Holl, M. M. Bioconj. Chem. 2004, 15, 774-782. (6) Mecke, A.; Lee, D. K.; Ramamoorthy, A.; Orr, B. G.; Banaszak Holl, M. M. Langmuir 2005, 21, 8588-8590. (7) Mecke, A.; Majoros, I. J.; Patri, A. K.; Baker, J. R.; Banaszak Holl, M. M.; Orr, B. G. Langmuir 2005, 21, 10348-10354. (8) Bond, P. J.; Sansom, M. S. P. J. Am. Chem. Soc. 2006, 128, 26972704. (9) Lopez, C. F.; Nielsen, S. O.; Ensing, B.; Moore, P. B.; Klein, M. L. Biophys. J. 2005, 88, 3083-3094. (10) Nielsen, S. O.; Ensing, B.; Ortiz, V.; Moore, P. B.; Klein, M. L. Biophys. J. 2005, 88, 3822-3828. (11) Maiti, P. K.; Cagin, T.; Lin, S. T.; Goddard, W. A. Macromolecules 2005, 38, 979-991. (12) Lin, S.; Maiti, P. K.; Goddard, W. A. J. Phys. Chem. B 2005, 109, 8663-8672. (13) Lee, H.; Baker, J. R.; Larson, R. G. J. Phys. Chem. B 2006, 110, 4014-4019. (14) Timoshenko, E. G.; Kuznetsov, Y. A.; Connolly, R. J. Chem. Phys. 2002, 117, 9050-9062. (15) Gotze, I. O.; Likos, C. N. Macromolecules 2003, 36, 8189-8197. (16) Freire, J. J.; Rodriguez, E.; Rubio, A. M. J. Chem. Phys. 2005, 123, 154901.

J. Phys. Chem. B, Vol. 110, No. 37, 2006 18211 (17) Gurtovenko, A. A.; Lyulin, S. V.; Karttunen, M.; Vattulainen, I. J. Chem. Phys. 2006, 124, 094904. (18) Marrink, S. J.; de Vries, A. H.; Mark, A. E. J. Phys. Chem. B 2004, 108, 750-760. (19) Mecke, A.; Lee, I.; Baker, J. R.; Banaszak Holl, M. M.; Orr, B. G. Eur. Phys. J. E. 2004, 14, 7-16. (20) Lindahl, E.; Hess, B.; van der Spoel, D. J. Mol. Model. 2001, 7, 306-317. (21) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Dinola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684-3690. (22) Essmann, U. L.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577-8592. (23) Humphrey, W.; Dalke, A.; Schulten K. J. Mol. Graphics 1996, 14, 33-38. (24) Prosa, T. J.; Bauer, B. J.; Amis, E. J.; Tomalia, D. A.; Scherrenberg, R. J. Polym. Sci. 1997, 35, 2913-2924. (25) Choi, Y.; Mecke, A.; Orr, B. G.; Banaszak Holl, M. M.; Baker, J. R. Nano Lett. 2004, 4, 391-397. (26) Marrink, S. J.; Risselada, J.; Mark, A. E. Chem. Phys. Lipids 2005, 135, 223-244. (27) Koynova, R.; Caffrey, M. Biochim. Biophys. Acta 1998, 1376, 91145. (28) Nagle, J. F.; Tristram-Nagel, S. Biochim. Biophys. Acta 2000, 1469, 159-195. (29) Egberts, E.; Berendsen, H. J. C. J. Chem. Phys. 1988, 89, 3718-3732.