Membrane Pore Formation Induced by Acetylated and Polyethylene

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Membrane Pore Formation Induced by Acetylated and Polyethylene Glycol-Conjugated Polyamidoamine Dendrimers Hwankyu Lee*,† and Ronald G. Larson‡ † ‡

Department of Chemical Engineering, Dankook University, Yongin 448-701, South Korea Department of Chemical Engineering, Biomedical Engineering, Mechanical Engineering, and Macromolecular Science and Engineering Program, University of Michigan, Ann Arbor, Michigan 48109, United States ABSTRACT: We performed molecular dynamics (MD) simulations of 36 copies of unmodified (charged), acetylated, and polyethylene glycol (PEG)-conjugated G4 dendrimers in dimyristoylphosphatidylcholine (DMPC) bilayers with explicit water using coarse-grained (CG) lipid and PEG force fields (FF). Attachment of small PEG chains to the dendrimer leads to the same reduction in membrane permeability as does attachment of acetyl groups, while a larger PEG size or a higher degree of PEGylation induces even fewer pores. This indicates that PEGylation is more efficient than acetylation in reducing membrane permeability and cytotoxicity, in qualitative agreement with experimental findings (Kim et al. Bioconjugate Chem. 2008, 19, 1660). Attachment of larger PEG chains makes the dendrimer-PEG complex larger and more spherical. Although a larger size and a more spherical shape are usually conducive to pore formation, a thick PEG layer on the dendrimer surface blocks the charge interaction between cationic dendrimer terminals and anionic lipid phosphate groups, and thus inhibits pore formation, despite the increased dendrimer size. Large PEG chains also keep the dendrimer-PEG complexes far from each other, suppressing interparticle aggregation.

’ INTRODUCTION Polyamidoamine (PAMAM) dendrimers have been considered promising possible drug transporters because of their controlled mass, uniformly branched structure, surface functionality, and good water solubility.1-5 Many interesting ligands, such as targeting, imaging, and therapeutic molecules, can be attached to the dendrimer surface and delivered to specific cancer cells.6-9 For these applications, the interaction between dendrimers and cell membranes needs to be understood. Experiments have shown that larger dendrimer size and higher charge density, as well as higher dendrimer concentration, increase cytotoxicity and membrane permeability.10-13 Recently, Ramamoorthy and co-workers have performed solid-state NMR experiments and showed that PAMAM dendrimers stably insert into lipid membranes.14 In particular, they found that the strong hydrophobic interaction between the lipid tail and the interior of the dendrimer induces dendrimer insertion after binding and restricts the motion of bilayer lipid tails. Dendrimer insertion may be significantly influenced by membrane compositions, as observed in NMR experiments of antimicrobial peptides in model membranes.15 Because cationic charges on the dendrimer terminals strongly interact with membranes and thereby increase dendrimer toxicity, the surface of the dendrimer needs to be modified for the specific targeting. To reduce nonspecific binding, dendrimers have been acetylated, which reduces their surface charge, and these show less pore formation and cytotoxicity.10 Alternatively, r 2011 American Chemical Society

polyethylene glycol (PEG) or polyethylene oxide (PEO) has been attached to the dendrimer surface, and this is called PEGylation.16,17 PEGylation not only reduces the toxicity of the dendrimer, but it also improves water solubility and shields drug molecules for longer circulation lifetime. Therefore, PEGylated dendrimers have been experimentally studied both in vivo and in vitro.18-24 Experimentally, Kim et al. found that relatively low degrees of PEGylation (25% or less) and small PEG size (Mw = 550, 750) may be enough to reduce cytotoxicity of amine-terminated G3 PAMAM dendrimers while retaining good water solubility.19 In particular, as compared to acetylated dendrimers, less surface modification was needed in the case of PEG, indicating that PEGylation is more efficient than acetylation in reducing cytotoxicity. However, this efficiency of PEGylation has not been explained in terms of size and shape of the dendrimer-PEG complex, especially because PEGylation increases particle size, which, when achieved by increasing size of the underlying PAMAM dendrimer, has been shown to increase cytotoxicity. They also showed that longer PEG (Mw = 2000) induces higher toxicity than does shorter PEG (Mw = 550), which runs opposite to the general effect of PEGylation on toxicity. This result was explained by hypothesizing an interparticle entanglement of large Received: October 20, 2010 Revised: January 10, 2011 Published: March 04, 2011 5316

dx.doi.org/10.1021/jp1100285 | J. Phys. Chem. C 2011, 115, 5316–5322

The Journal of Physical Chemistry C PEG chains at high concentration of dendrimers,19,25 but this assumption has not been explained in any detail. Molecular dynamics (MD) simulations have been able to explore the dendrimer properties26-28 and their effects on membrane permeability. In all-atom MD simulations, free energy calculations showed that charged dendrimers interact more favorably with lipid bilayers than do neutral dendrimers.29-31 To understand the effects of the dendrimer size, concentration, and shape, multiple copies of dendrimers with lipid bilayers were simulated using a coarse-grained (CG) molecular model.32-35 Pore formation induced by differently sized, charged, shaped, and concentrated dendrimers was observed, in qualitative agreement with experimental findings. Also, CG simulations showed that spheroidal dendrimers are more efficient than linear polymers in increasing membrane permeability because spheroidal dendrimers that hold their shape must penetrate the membrane and contact both leaflets of the membrane, to exploit favorable electrostatic interactions with a large fraction of the membrane surface area. Although mesoscale simulations have revealed the effects of dendrimer properties on interactions with lipid bilayers,36,37 the interactions of PEGylated dendrimers with lipid bilayers have not yet been simulated. To understand the effects of PEGylation on dendrimerinduced membrane permeability, we here describe CG-MD simulations of 36 copies of PEG (Mw = 550, 2000)-attached G4 dendrimers with lipid bilayers and water. Bilayer pores induced by differently charged acetylated and PEGylated dendrimers are compared by calculating number of pores and the amount of dendrimer material inside pores. To help understand these results, the size and shape of the dendrimer-PEG complex, the density profiles of PEG grafts on dendrimer terminals, and the radial distribution functions of dendrimer terminals with respect to PEG and lipid head groups are computed. Last, the effect of the PEG size on interparticle interaction is discussed.

’ METHODS Simulations and analyses were performed using the GROMACS4.0.5 simulation package38,39 with the MARTINI CG force field (FF).40,41 CG PEG and dendrimer FFs, and the interactions of PEG with dendrimers and lipids, were previously parametrized within the framework of the MARTINI CG FF by our group.32,42,43 For the CG dendrimer, four CG bead types were used to represent chemical moieties with different charges and hydrogen-bonding properties, and bond and angle potentials were parametrized.32 For the CG PEG, the monomer unit (C-O-C) was modeled as a CG bead, and their bond, angle, and dihedral potentials were parametrized.42 For PEG-PEG interaction, the CG bead type “SNda” was used (σij = 4.3 Å and εij = 3.375 kJ/mol for the LJ potential, VLJ(rij) = 4εij[(σij/rij)12 (σij/rij)6]). Following the framework of the MARTINI model, the SNda type yields σij = 4.7 and εij = 4.0 for the PEG-water interaction. For PEG-lipid and PEG-dendrimer interactions, the less attractive CG type “SN0” was used only for PEG, which has LJ parameters σij = 4.7 and εij = 3.5.43 The actual mass for each chemical moiety was assigned to each CG bead. All parametrizations were performed by comparing densities, conformations, and hydrodynamic properties from CG and all-atom simulations, experiments, and polymer theories, as described in our previous work.32,42,43 Equilibrated charged, acetylated, PEGylated G4 dendrimers, and dimyristoylglycerophosphocholine (DMPC) lipid bilayers from our previous work were used as the initial configura-

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tions.33,42,44 For dendrimer-PEG complexes, 16 and 32 copies of PEG chains with Mw of 550 (12 mers) or 2000 (45 mers) were connected to the terminals of G4 dendrimers by a weak harmonic potential with a bond length of 3.3 nm at the minimum energy. PEG chains were evenly distributed on the dendrimer surface to spread cationic charges. PEGylated terminals of the dendrimer become neutral, leading to net charges of þ48 and þ32, respectively, for 16- and 32-PEGylated dendrimers. 36 copies of charged, acetylated, or PEGylated dendrimers were evenly distributed above the lipid bilayer with distances of 5-7.5 nm between the bilayer and dendrimer centers (Figure 1). The final simulation system consists of 36 dendrimer complexes, 8192 DMPC lipids, ∼310 000 water beads (∼1 240 000 water molecules), and 1152-2304 counterions (Cl-) in a periodic box of size 50 50 19 nm3. The LJ potential was smoothly shifted to zero between 9 and 12 Å. Our previous work showed that long-range electrostatics must be considered to observe insertion of dendrimers into lipid bilayers,32 and hence the shortrange electrostatic cutoff of 12 Å was supplemented by a particle mesh Ewald summation (PME) for electrostatic interactions.45 Temperature and pressure were maintained at 310 K and 1 bar by applying a Berendsen Thermostat in the NPT ensemble.46,47 After 1 ns-long simulations with the position restraint on dendrimer complexes and lipid bilayers, simulations were performed without the position restraint for 100 ns with time steps of 8 and 20 fs, respectively, for dendrimer-PEG and dendrimer systems. The last 20 ns was averaged for analyses. To obtain more extensive sampling, two replicate simulations were performed for charged, 25%-acetylated and -PEGylated dendrimer systems, where pore formation was observed.

’ RESULTS AND DISCUSSION The 36 copies of charged, acetylated, and PEGylated G4 dendrimers were simulated in DMPC bilayers with explicit water. These simulation systems are named “G4”, “G4A-16”, “G4A-32”, “G4P550-16”, “G4P550-32”, and “G4P2000-16”, where the second initial “A” designates acetylation, and “P” designates PEG. The first and last numbers describe the dendrimer generation and the number of acetyl or PEG chains, respectively. The number after the initial “P” represents the PEG molecular weight; see Table 1. Duplicate simulations were performed for G4, G4A16, G4P550-16, and G4P2000-16, where lipid bilayer pores were observed. Pore Formation Induced by PEGylated Dendrimers. Figure 1 shows snapshots at the beginning (0 ns; top) of G4 and end (100 ns; 2-7 rows) of all simulations. Side and top views with dendrimer-PEG complexes are shown in the left side, while top views without complexes are shown in the right side to show clearly the lipid bilayer pores. 36 copies of the dendrimer-PEG complex were initially located above the lipid bilayer for all simulations. G4, G4A-16, G4P550-16, and G4P2000-16 show lipid bilayer curvature and pore formation, while more highly acetylated and PEGylated dendrimer systems, G4A-32 and G4P550-32, show no pore formation. This indicates that charges on the dendrimer terminal play an important role in increasing membrane permeability, although membrane permeability is also affected by other factors, such as particle size, shape, and concentration, as observed in many experiment and simulation studies.10,13,33,34,48 Each pore is occupied by one dendrimerPEG complex, and these complexes remain free of aggregation in all simulations. 5317

dx.doi.org/10.1021/jp1100285 |J. Phys. Chem. C 2011, 115, 5316–5322

The Journal of Physical Chemistry C

Figure 1. Snapshots of the side view (left, top), the top view (left, bottom), and the top view without dendrimer or dendrimer-PEGs (right) at the beginning (0 ns; top row) and end (100 ns; 2-7 rows) of simulations. The initial configuration is shown only for G4. Gray, red, and green dots, respectively, represent dendrimers, PEG, and DMPC headgroups. For clarity, water molecules, DMPC tails, and ions are omitted. The images were created with VMD.53

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Figure 2 shows an expanded view of PEGylated dendrimerinduced pores in bilayers, similar to the “toroidal pore” observed in our previous work with dendrimers.33 Although both G4P55016 and G4P2000-16 show pore formation, the G4P550-16 complex inserts nearly completely into the bilayer, whereas only a fraction of G4P2000-16 inserts. For G4P2000-16, the PEG chains almost fully cover the dendrimer surface outside the pore, which may block the dendrimer insertion into the lipid bilayer. To quantitatively compare these pores from different simulations, the number of pores and the number of CG beads inside the pores were calculated. Because of the significant fluctuation in the shape of the lipid bilayer, the bilayer surface plane (x,y plane of the system) was equally divided into 400 voxels (20 20 grids), leading to an x,y area of approximately 2.5 2.5 nm2 for each voxel with a voxel height (z component) of ∼19 nm. For each voxel, the z-coordinate of the bilayer center was determined from the center of mass of the lipid glycerols. The dendrimer, water, and ion beads within a z-directional distance of 5 Å from this bilayer center were considered to be inside pores. In Table 2, both acetylated and PEGylated dendrimer systems show a significant decrease in the number of pores and the number of beads inside pores relative to the unconjugated dendrimer, again indicating the effect of charge on pore formation. G4P550-16 shows fewer pores than does G4A-16, but they have similar total numbers of beads in the pore. This result indicates that a PEG of this small length and low concentration causes the same extent of membrane permeability as do acetylated dendrimers with the same charge density. In experiments with G3 dendrimer, the same length (Mw = 550) and concentration (25% of dendrimer terminals) of PEG as used in our simulations were found to induce lower cytotoxicity than did acetylated dendrimers.19 This difference between simulations and experiment is probably because the G4 dendrimer used in the simulations is larger, and so tends to cause more membrane permeability and cytotoxicity than the G3 dendrimer used in the experiments, and thus a higher concentration or longer PEG chains are needed in the simulations to show a similar effect as seen for G3 in the experiments. In Table 2, G4P2000-16 shows many fewer pores and beads inside pores than do G4P550-16 and G4A-16. These results indicate that a dendrimer-PEG with a larger PEG is more efficient in reducing toxicity than is an acetylated dendrimer or a dendrimer-PEG with a smaller PEG, in qualitative agreement with experimental findings.19 Experiments showed that less PEGylation was needed to obtain a cell viability similar to that induced by acetylation, indicating that PEGylation is more efficient in reducing cytotoxicity, as observed in our simulations. Size and Shape of PEGylated Dendrimer. Besides surface charge density, particle size and shape are important factors controlling membrane permeability and toxicity. In Figure 3, radii of gyration (Rg) reach apparent steady-state values at ∼70 ns, indicating that the systems are well equilibrated. Table 3 shows that acetylated dendrimers are smaller than unacetylated dendrimers, similar to our previous work.49 Dendrimer-PEG complexes in G4P550-16 and G4P550-32 are larger than acetylated dendrimers in G4A-16 and G4A-32, indicating that PEGylation significantly increases the complex size. For G4P2000-16, the Rg value is much higher than for G4P550-16, indicating the large effect of PEG size on the complex size. To understand the effect of PEGylation on the complex shape, principal moments of inertia (Iz > Iy > Ix) were calculated for aspect ratios (Iz/Iy, Iz/Ix) and relative anisotropies (κ2 = 1 - 3I2/I12, where I1 = Ix þ Iy þ Iz and I2 = IxIy þ IyIz þ IxIz).50 In Table 3, aspect ratios and anisotropies for charged and acetylated dendrimers are seen to 5318



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Table 1. List of Simulations no. of G4 dendrimer terminals PEG (Mw)

no. of molecules dendrimers or

acetylation NH3þ

(NHCOCH3)

550

2000

DMPC lipids

time (ns)

no. of simulations

G4

64

36

8192

100

2

G4A-16

48

16

36

8192

100

2

G4A-32

32

32

36

8192

100

1

G4P550-16

48

16

36

8192

100

2

G4P550-32

32

32

36

8192

100

1

G4P2000-16

48

36

8192

100

2

16

Figure 2. Snapshots of the PEGylated dendrimer-induced pores in DMPC bilayers at the end (100 ns) of the simulations G4P550-16 and G4P2000-16. Gray, red, green, and yellow dots represent dendrimer, PEG, DMPC head groups, and tail groups, respectively. Water and ion molecules are omitted for clarity.

Table 2. Number of Pores and Total Number of Beads Inside All Pores, Averaged over the Last 20 nsa

Figure 3. Radii of gyration (Rg) averaged over all dendrimers or dendrimer-PEGs as a function of simulation time.

Table 3. Average Radii of Gyration (Rg), Aspect Ratios, and Relative Anisotropies Averaged over All Dendrimers or PEGylated Dendrimers of Each Simulation aspect ratio

no. of beads in pores

Rg (nm)

dendrimer or no. of pores dendrimer-PEG G4 G4A-16 G4P550-16 G4P2000-16 a

simulation

dendrimer-PEGs

11

302 ( 2

Iz/Iy

Iz/Ix

relative shape anisotropy

G4

2.2 ( 0.1

1.20

1.62

0.018

G4A-16

2.0 ( 0.1

1.15

1.60

0.018

water

ion

total

87 ( 2

13 ( 1

402

G4A-32

1.9 ( 0.1

1.21

1.73

0.023

G4P550-16

2.4 ( 0.1

1.16

1.51

0.014

G4P550-32 G4P2000-16

2.5 ( 0.1 3.5 ( 0.1

1.15 1.16

1.58 1.42

0.016 0.010

16 4

373 ( 4 142 ( 2

160 ( 8 56 ( 2

24 ( 2 6(1

557 204

2

81 ( 2

55 ( 2

4(1

140 191

2

113 ( 15

74 ( 16

4(2

1

15 ( 6

118 ( 14

2( 1

135

1

18 ( 3

102 ( 18

2(1

122

Duplicate simulations for each system show two values.

be higher than those for dendrimer-PEG complexes, indicating that PEGylation makes the complex more spherical. In particular, the larger PEG in G4P2000-16 significantly reduces aspect ratios and shape anisotropies. The Effect of PEGylation on the Dendrimer Interaction with Lipid Bilayer. Experiments and simulations have shown that larger particles induce greater lipid bilayer curvature and pore formation, if other properties of particles are the same.12,33 PEGylation makes the dendrimer-PEG complexes much larger and more spherical, but PEGylated complexes show less pore formation and membrane permeability than do acetylated dendrimers with the same charge density, which is opposite to the

general rule for the effect of particle size and shape. To understand this, the interactions of the dendrimer, PEG, and lipid headgroup were analyzed. Figure 4 shows that PEG chains in G4P550-16 are distributed close to the dendrimer terminals, but longer PEG chains in G4P2000-16 cover a much larger area outside the dendrimer surface up to 5-8 nm from the dendrimer center. In Table 4, the thickness of PEG on the dendrimer surface is compared to that calculated from polymer brush theory. In the simulations, this thickness is obtained as the difference between an “outer radius” and an “inner radius” of the PEG layer. The outer radius of the dendrimer-PEG complex was taken to be the root-mean-squared (rms) distance from the terminal bead of the PEG to the center of mass (COM) of the dendrimer-PEG complex. The inner radius was taken to be the rms distance from the dendrimer terminal (excluding the PEG) to the COM of the complex. Daoud and Cotton developed polymer brush theory,51 5319



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Figure 5. Radial distribution functions between dendrimer terminal beads and PEG beads from simulations of G4P550-16 and G4P2000-16.

Figure 4. Number of beads of dendrimers, charged dendrimer terminals, and PEG as a function of distance from center of mass (COM) of the dendrimer.

Table 4. Thickness of the PEG Layer on the Dendrimer Surface Directly Obtained from Simulations, and Calculated from the Polymer Brush Theory PEG thickness (nm) simulation

brush theory52

G4P550-16

0.6

0.6

G4P550-32

0.8

0.8

G4P2000-16

2.3

2.1

which was modified and used to obtain a simple analytic formula by Vagberg et al.,52 yielding the following analytic formula for the PEG thickness: R = [NEOl1/v(8f (1-v)/2v)/(3v41/v) þ Rd1/v]v Rd, where NEO is the number of EO monomers per chain (12 and 45 for PEG550 and PEG2000, respectively), l is the statistical length of the monomer (which is equivalent to the bond length of the CG bead, 3.3 Å), v is the Flory exponent (0.6 for a good solvent), f is the number of grafted chains, and Rd is the inner radius calculated from the simulation. Table 4 shows that thickness of PEG agrees well with those calculated from the brush theory, indicating that simulations can capture the theoretically predicted conformation of PEG grafted to the spherical particle. The thickness of PEG for G4P2000-16 is larger than that of G4P550-16 by 1.7 nm, showing that attachment of larger PEG chains significantly increases the thickness of the PEG layer as well as the size of the dendrimer-PEG complex. For the interactions between dendrimer and PEG, radial distribution functions (RDF) plotted in Figure 5 demonstrate that the dendrimer terminals in G4P2000-16 interact with PEG chains more strongly than in G4P550-16. These results indicate that larger PEG chains can block the charge interaction between the dendrimer surface and lipid headgroups. Figure 6 shows RDFs of anionic DMPC phosphate groups with respect to the cationic terminals of dendrimer-PEG complexes inserted into the pore. G4P55016 shows a higher peak at ∼0.5 nm than does G4P2000-16, indicating that longer PEG chain-conjugated dendrimers have relatively weaker charge interactions with lipid phosphate headgroups than do dendrimers with shorter chains. This result confirms that the thicker PEG layer on the dendrimer surface weakens charge interactions between dendrimer and lipid headgroups, which causes less pore formation and reduces toxicity,

Figure 6. Radial distribution functions of anionic DMPC phosphate groups with respect to the cationic dendrimer terminals in G4P550-16 and G4P2000-16.

Figure 7. Minimum distance between centers of mass of 36 dendrimers for each simulation as a function of time.

although the dendrimer-PEG complex is larger than the acetylated dendrimer. To understand the effect of the PEG layer on the interparticle interaction, the minimum value among all possible distances between centers of 36 dendrimers was calculated as a function of simulation time. In Figure 7, the minimum distances between dendrimers for G4, G4A-16, and G4P550-16 fluctuate around 4-6 nm, while those values for G4P2000-16 are always higher than 6 nm, indicating that the attached long PEG chains keep the dendrimer-PEG complexes far from each other. This result implies that there is no significant intermolecular entanglement between PEG chains from different dendrimer-PEGs. Experimentally, Kim et al. showed that larger PEG chains typically reduce toxicity, but when all terminals of the dendrimer are fully conjugated with PEG2000 at high dendrimer concentration, dendrimer-PEGs induce higher toxicity than do those with 5320


The Journal of Physical Chemistry C the shorter PEG550 or low levels of PEGylation.19 To explain this experiment result, intermolecular aggregation of large PEG chains at high concentration has been proposed. However, our simulations show no interparticle aggregation with longer PEG chains, although concentration and mass transport conditions of the simulation and experiments are different. Note that in the experiments, the high toxicity seen for PEG2000 was observed only at high dendrimer-PEG concentration. We are not yet able to explain this observation.

’ CONCLUSIONS Charged, acetylated, and PEGylated G4 dendrimers were simulated with different sizes and concentrations of PEG using the MARTINI CG lipid and PEG force fields.42,44 The dendrimer surfaces were acetylated or PEGylated at 25% and 50% of the dendrimer terminals. Calculation of the pore number and the bead number inside pore shows that 25%-acetylated and -PEGylated dendrimers produce fewer pores than do charged dendrimers, and 50%-acetylated and -PEGylated dendrimers show no pore formation, indicating the charge effect on membrane permeability, as observed in experiments and our previous work.19,32 For 25%-acetylated and -PEGylated dendrimers, attachment of PEG550 leads to comparable levels of pore formation as for acetylated dendrimers, but attachment of PEG2000 significantly reduces pore formation. These results indicate dependence of the membrane permeability on size and concentration of PEG, in qualitative agreement with experimental findings. The size and shape analyses of dendrimers and dendrimerPEG show that the dendrimer-PEG complexes are larger and more spherical than charged or acetylated dendrimers at the same surface charge density. Longer PEGs lead to thicker PEG layers on the dendrimer surface, in quantitative agreement with the polymer brush theory.52 Density profiles and radial distribution functions show that the longer PEG chains cover much more area on the dendrimer surface than do shorter PEG chains. Also, the larger PEGs cover cationic terminals of the dendrimer more completely, weakening their interactions with anionic lipid phosphate groups more than do shorter PEGs. These results indicate that, although attachment of a larger PEG yields a larger and more spherical particle that could in principle more effectively increase membrane permeability, the thicker PEG layer in fact weakens the charge interaction between dendrimer terminals and lipid head groups, leading to less membrane permeability and toxicity. Attachment of longer PEG chains enforces larger distances between the centers of dendrimer-PEG complexes, which should suppress interparticle aggregation. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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