Free Energy of PAMAM Dendrimer Adsorption onto Model Biological Membranes Yongbin Kim, Yongkyu Kwak, and Rakwoo Chang* Department of Chemistry, Kwangwoon University, Seoul 139-701, Republic of Korea S Supporting Information *

ABSTRACT: We investigated the thermodynamic, structural, and dynamics changes in dendrimer−membrane systems during dendrimer adsorption to biological membrane systems by combining atomistic molecular dynamics simulations with umbrella sampling techniques to understand the atomistic interactions between the dendrimer and biological membranes. An ethylenediamine core polyamidoamine dendrimer (generation 3) with amine terminal groups and both zwitterionic dipalmitoyl-phosphatidyl-choline (DPPC) and anionic palmitoyl-oleoyl-phosphatidyl glycerol (POPG) lipid bilayer membranes were used as the model dendrimer and biological membranes, respectively, in this study. The free energy of the dendrimer adsorption onto two model membranes with different charge states was quantitatively determined. For the zwitterionic DPPC membrane, the dendrimer has a minimum free energy of approximately 50 kcal/mol, which is 15 kcal/mol higher than that observed in previous studies. The dominant contribution to the adsorption potential energy is the van der Waals attraction between the dendrimer and the DPPC membrane. However, the anionic POPG membrane pulls the positively charged dendrimer with an attractive mean force of about 200 pN, finally positioning the dendrimer in the membrane headgroup region. As a result of these strong attractive dendrimer and membrane interactions, the dendrimer structurally undergoes the transition from spherical to a pancake conformation, which slows its lateral mobility, especially in the presence of the POPG membrane. The bilayer lipid membranes are also perturbed by the dendrimer adsorption.

INTRODUCTION Dendrimers are regularly branched macromolecules that consist of a central core, branched building blocks, and terminal groups. Their molecular properties such as size, charge state, and cytotoxicity, can be systematically controlled by changing the number of branching processes (called generations) and introducing various functionalized terminal groups.1−4 Because of their versatility, their capacity as drug and gene carriers or antitumor therapeutics under biological environments has been of special interest. For these applications, understanding the interactions between dendrimers and biological membranes with atomistic detail is essential. The interactions between dendrimers and biological membranes have been extensively experimentally investigated.5−16 It was reported that amine-terminated polyamidoamine (PAMAM) dendrimers can cause hole formation or expansion depending on the dendrimer’s size, both in aqueous supported lipid bilayers and in vitro in cells.6−9 Efficient crossmembrane transport and membrane disruption were also observed, depending strongly on dendrimer size, charge state, and chemical structure as well as the model membrane composition.12,13 This dendrimer-induced hole formation or dendrimer cytotoxicity could be reduced via acetylation or PEGylation of the terminal amine groups in the dendrimer.6,16 However, how dendrimers translocate through the cell membrane without the help of membrane proteins is still controversial. Recently, Åkesson et al. reported that the passive © XXXX American Chemical Society

translocation of a PAMAM dendrimer through both zwitterionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and anionic palmitoyl-oleoyl-phosphatidyl glycerol (POPG) bilayer membranes is not likely.17 Instead, they suggested that the strong electrostatic interactions between positively charged PAMAM dendrimers with terminal amine groups and the negatively charged POPG membrane induce a lamella phase with alternating membrane and dendrimer layers. On the other hand, computer simulations also play an important role in understanding dendrimers and cell membrane interactions.18−25 Most previous theoretical studies employed simplified PAMAM dendrimer or biological membrane models. Lee and Larson investigated dendrimer-induced pore formation for differing dendrimer sizes, dendrimer charge states, temperatures, dendrimer concentrations, molecular shapes, membrane fluidities, and salt concentrations using a series of coarsegrained (CG) molecular dynamics (MD) simulations,18−23 summarizing that the pore formation is facilitated by large charged dendrimers with spherical shape and fluidic membranes in high dendrimer but low salt concentrations. These results were qualitatively consistent with experimental observations.6,8,9,16,26 PAMAM dendrimers in an implicit solvent were also simulated near a negatively charged plane, which was Received: February 19, 2014 Revised: May 17, 2014

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intended to be a simple mimic of a negatively charged bilayer surface. These simulations indicated that the dendrimer flattens as it adsorbs to the plane.27 Dissipative particle dynamic (DPD) simulations of CG models have also been used to study the translocation of charged PAMAM dendrimers into zwitterionic lipid bilayer membranes, and it was observed that the dendrimer is flattened and strongly adsorbed into the headgroup region of the membrane.24,25 However, as will be discussed later, the positively charged dendrimer energetics and structure on zwitterionic lipid bilayer membranes using CG models differ qualitatively from the atomistic simulation results. The dendrimer equilibrium location is well above the zwitterionic membrane headgroup region; furthermore, its shape is not significantly changed upon adsorption. These findings imply the attractive interactions between the dendrimer and membrane are overestimated in the CG model. Only a few computational studies of PAMAM dendrimers in biological membranes have had atomistic detail. Kelly et al. recently adopted atomistic models for both the third generation (G3) PAMAM dendrimers and 1,2-dimyristoyl-sn-glycero-3phosphocholine (DMPC) bilayer membranes to study the dendrimer−membrane binding process.28,29 Using umbrella sampling30,31 and weighted histogram analysis methods (WHAM),32 they calculated the free energy for the binding of three PAMAM dendrimers with different terminal groups (G3−NH3+, G3−Ac, and G3−COO−) to zwitterionic DMPC bilayer membranes. However, they treated water molecules implicitly using distance-dependent dielectric constants (ϵ(r) = 4r) and Langevin dynamics because of the limitations in the computational resources. Because water molecules would significantly affect both macromolecular structure and the dynamics of macromolecules, it is essential to study how the adsorption behavior of PAMAM onto biological membranes is affected by the presence of explicit water molecules. Hence, in this study, we investigated the adsorption of PAMAM dendrimers onto two model biological membranes using atomistic MD simulations with explicit water molecules. A G3 PAMAM dendrimer with an ethylenediamine (EDA) core and protonated amine terminal group (G3−NH3+) was used as the model dendrimer, and both the neutral dipalmitoylphosphatidylcholine (DPPC) and negatively charged POPG lipid bilayer membranes were used as model biological membranes with different charges. Typical bacterial membranes contain major lipid components such as zwitterionic phosphatidylethanolamine (PE), negatively charged cardiolipin (CL), and phosphatidylglycerol (PG).33 Therefore, the two model membranes used in this study can be considered to be the limiting cases for studying the effects that positively charged PAMAM dendrimers have on differently charged biological membranes. This paper is organized as follows. Methods describes in detail the molecular models and computer simulation methods used in this study. The structural, dynamic, and thermodynamic analyses are presented in Results and Discussion; a summary and the conclusions together with limitations of the present study are given in Summary and Conclusions.

Figure 1. Molecular description of (a) PAMAM generation 1, (b) DPPC, and (c) POPG. The number schemes for the heavy atoms in the two lipid head groups are also shown in (b) and (c).

each terminal amine functional group. Therefore, the G3 PAMAM dendrimer contains 60 amidoamine molecules and one ethylenediamine molecule. At a neutral pH, the terminal amine groups are protonated, and the net charge of the G3 PAMAM dendrimer is +32 e. The GROMOS86 force field for the PAMAM dendrimer was obtained from the Dundee PRODRG2 Server ( prodrg).34 To verify the validity of the force field parameters for the G3 PAMAM dendrimer, we performed 10 ns equilibrium MD simulations of the dendrimer in water at T = 300 K. The resulting radius of gyration shows reasonable agreements with previous studies as given in Table 1. In addition, radial atom distribution and radial pair distribution of the primary amines to the oxygen of water were also calculated and were also in reasonable agreements with results from Yang et al.35 (Please see Figure S1 in the Supporting Information.) It is also noted that because the model G3 PAMAM dendrimer has 32

METHODS Molecular Models. The model dendrimer used in this study is the EDA-core G3 PAMAM dendrimer. The molecular structure for generation 1 of the PAMAM dendrimer is shown in Figure 1a. The next PAMAM dendrimer generation is formed by connecting additional amidoamine side chains to B | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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with equal 0.1 nm intervals along the reaction coordinates from 1.8−5.8 nm, and the harmonic potential force constants for each window were first set to 120 kcal/(mol·nm2) and MD simulations of each window were run for 20 ns (G3-DPPC) or 18 ns (G3-POPG). The resulting final configuration at each window was used as the initial configuration for the subsequent production PMF calculation, where the harmonic potential was raised to 500 kcal/(mol·nm2) for better statistics. At each window, a 1 ns MD simulation was run during each PMF calculation and analyzed by WHAM to generate the PMF curve along all of the reaction coordinates. The umbrella sampling simulations were continued until the PMF curve converged. The total simulation time for the production run was 15 and 10 ns for the G3-DPPC and G3-POPG systems, respectively. The error bars of the data points were obtained using the block average of the converged PMF data (the last 5 ns). To verify the equilibration of the dendrimer−membrane system, we plotted the distance between dendrimer and membrane center, radius of gyration, and membrane thickness as a function of simulation time at the free-energy minimum (ξ = 2.3 nm) (see Figure S2 in the Supporting Information). During the umbrella sampling run, all the results seem to fluctuate around a mean value have reached a plateau. Especially, the normal component Rg,z of the radius of gyration is much smaller than the other component Rg,xy, which implies that the dendrimer flattens significantly when it is adsorbed onto the membrane.

Table 1. Comparison of Radius of Gyration (Rg) of the G3 PAMAM Dendrimer with Previous Experiments and Simulations experiments Rg (nm) a



all-atom models 1.04−1.97


CG models 1.31

this study 1.50 ± 0.01


Values from SANS and SAXS experiments.48−51 atomistic MD simulations.4,35,52,53 cFrom ref 18.


Values From

positively charged amine groups, its size and structure depend on the simulation box size (or the dendrimer concentration). The two model bilayer membrane systems investigated in this study consist of DPPC and POPG lipid molecules as shown in Figure 1b,c. The force fields for both lipids were obtained from previous studies by Elmore et al.,36 and the initial bilayer membrane configurations for both lipids, each consisting of 512 lipids, were obtained from the Tieleman group ( and http://www.softsimu. org/downloads.shtml).37 For water, the simple point charge (SPC) model38 was used for all of the simulations. The G3 PAMAM dendrimer−DPPC bilayer membrane system (G3-DPPC) consists of a single G3 PAMAM dendrimer, 512 DPPC lipids, 41 861 water molecules, and 32 Cl− ions in a simulation box size of approximately 12 × 12 × 12 nm3. The G3 PAMAM dendrimer−POPG bilayer membrane system (G3-POPG) consists of a single G3 PAMAM dendrimer, 512 POPG lipids, 31 441 water molecules, 657 Na+ ions, and 177 Cl− ions. Additional NaCl was added to mimic physiological conditions (150 mM). The GROMACS simulation software package (version 4.5.3)39 with the NPT ensemble was used with a Nose− Hoover thermostat for temperature control (323 K for G3DPPC; 310 K for G3-POPG)40 and a Parrinello−Rahman barostat for pressure control (1 bar).41 The temperatures were chosen to ensure the liquid-crystalline phase of the lipid bilayer membranes. The pressure coupling was isotropic in the directions parallel to the membrane plane but different in the z direction, which is normal to the membrane plane. The time step was 2 fs. The SHAKE algorithm was used to constrain the bond lengths in the system. A 1 nm cutoff was used for the Lennard-Jones potential. In addition, the particle-mesh Ewald summation (PME)42,43 electrostatic scheme was used to handle long-range electrostatic interactions with a real space cutoff of 1 nm. Equilibrium MD simulations were run for a total of 5 ns to equilibrate each system with the dendrimer position fixed in the water phase until the thermodynamic and structural variables, such as system energy, dendrimer size, and membrane area per lipid, converged. Umbrella Sampling and Weighted Histogram Analysis Method. The umbrella sampling method30,31 combined with a weighted histogram analysis32 are standard methods for obtaining the potential mean force (PMF) for a given reaction coordinate and have been successfully used for several nanoparticle−membrane systems.28,44−46 In this study, the reaction coordinate ξ in the PMF calculation was set to the z distance between the center of masses for the dendrimer and the membrane with the z direction defined as the direction normal to the membrane plane. The initial umbrella sampling configuration for each window was obtained by pulling the equilibrated dendrimer configuration from the neighboring window at a speed of 0.01 nm/ps with a spring force constant of 120 kcal/(mol·nm2) and starting from the equilibrated system. A total of 41 windows were used

RESULTS AND DISCUSSION Free Energy of G3 PAMAM Dendrimer Adsorption onto Model Biological Membranes. The PMF curves for both membrane systems are shown in Figure 2a as a function of the reaction coordinate ξ. Note that the average location d of P atoms in the lipid head groups from the upper leaflet for the equilibrated bilayer membranes is shown as dashed lines: d = 1.88 nm for DPPC (red) and 2.23 nm for POPG (blue) membranes, respectively. Several interesting points deserve mention. First of all, an attractive interaction regime exists between the dendrimer and the DPPC membrane up to approximately 3 nm from the membrane surface, despite the membrane surface charge being neutral (or zwitterionic). As will be discussed in a later section, the attractive interaction is mainly due to the van der Waals interaction between the dendrimer and the membrane. This attractive behavior between the positive dendrimer and zwitterionic membrane was also reported in previous atomistic MD simulations that treated water molecules implicitly and made lipid tails fixed.28 Our PMF results have attractive behavior similar to that of the Kelly group’s observations but with an approximately 15 kcal/mol larger adsorption free energy and a free-energy minimum location 0.5 nm closer to the membrane surface. These discrepancies can be attributed to how both water molecules and the DPPC tails were treated in previous studies. The presence of explicit water molecules significantly effects the adsorption thermodynamics. First, the free energy of dendrimer adsorption onto the biological membrane is stronger for explicit water molecules because these water molecules gain more space (more entropy) by pushing the dendrimer out of the water phase (toward the membrane surface). Second, hydrogen bonding between water and the dendrimer (and membrane), which is essential to biological environments, is missing in the implicit water model. C | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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symmetric. However, in the case of the G3-POPG system, it shows a bimodal distribution, indicating that the image POPG membrane attracts some branches of the dendrimer with the long-range electrostatic interaction. In addition to this strong adsorption, the free-energy minimum for the G3-POPG system was much closer to the membrane surface than was that for the G3-DPPC system. This difference indicates the electrostatic attractions between the positive dendrimer and negative POPG membrane induces strong adsorption that results in a large perturbation in the lipid bilayer membrane and supports the observation of Åkesson et al.17 Both dendrimer−membrane systems have similar repulsive barriers when the dendrimer approaches the center of the bilayer membrane, which implies this repulsive barrier is caused by van der Waals repulsion between the dendrimer and membrane (see the next subsection). To understand the nature of the dendrimer and model biological membrane interactions, the mean force Fξ was calculated and is shown in Figure 2b. Fξ is defined as

Fξ ≡ −

d G (ξ ) dξ


where G(ξ) is the potential mean force (PMF). The G3 PAMAM dendrimer feels an approximately 100 pN attractive force when approaching the neutral DPPC membrane; however, well before its core approaches the lipid head groups, the dendrimer is subject to van der Waals repulsion, which prevents it from penetrating the membrane. In contrast, the anionic POPG membrane attracts the dendrimer with up to a 200 pN force until the dendrimer core deeply penetrates the POPG membrane headgroups. Interestingly, the repulsive force of the anionic POPG membrane is much stronger than that of the neutral DPPC membrane, which indicates that the PAMAM dendrimer penetration through a charged POPG membrane is more difficult than that through a neutral membrane, even though the adsorption free energy of the amine-terminated dendrimer for the POPG membranes is much stronger than that for the DPPC membranes. To check the temperature effect on the adsorption free energy of the dendrimer, we performed additional umbrella sampling simulations (10 ns total) for the G3-POPG system at T = 323 K, the results of which are shown in the free-energy and force curves as green solid triangles in Figure 2a,b. Although the overall behavior is similar to that at the lower temperature, the free-energy minimum at T = 323 K is lowered by about 20 kcal/mol. This implies that the entropic contribution by salt ions to the adsorption free energy is significant in the G3-POPG system. The charge density distributions at two different temperatures and at ξ = 2.3 nm are also plotted in Figure S4 in the Supporting Information. The most noticeable change is in the distribution of salt ions, which screen the electrostatic interaction between the dendrimer and the membrane. With increasing temperature, some Na+ and Cl− ions are released from the membrane surface to the water phase, which leads to the increase of the effective charge of both the dendrimer and the membrane, and as a result, the enhanced dendrimer adsorption onto the POPG membrane. Figure 3 displays representative snapshots of both systems at various reaction coordinates. The PAMAM dendrimer maintains its spherical shape until it contacts the membrane

Figure 2. (a) Potential mean forces (PMF) and (b) corresponding forces as a function of their reaction coordinate ξ for the two dendrimer−membrane systems. The average location d of the P atoms in the lipid head groups of the upper leaflet of equilibrated bilayer membranes are shown as dashed lines: d = 1.88 for DPPC (red) and 2.23 nm for POPG (blue) membranes. The reaction coordinate ξ is defined as the distance in the z direction between the dendrimer and membrane centers of mass.

The lipid mobility also affects the dendrimer adsorption mechanism of the membrane, as shown in Figure 2a. As the dendrimer approaches the membrane, lipid molecules near the adsorption site rearrange themselves to minimize the lipid membrane and dendrimer interactions. This rearrangement was manifest in our simulation results, where the free-energy minimum was located closer to the membrane surface than in previous studies.24,25,28 In contrast, the dendrimer is strongly attracted to the anionic membrane over long distances because of electrostatic attractions. The resulting adsorption free energy was approximately −88 kcal/mol; however, this value should be considered to be a lower bound for the adsorption free energy of the system because the dendrimer also feels long-range attractive interactions from periodic image membranes. As shown in Figure 3b, some branches of the dendrimer are pointing toward the opposite direction at ξ = 5.8 nm. This indicates that the upper image membrane also attracts the dendrimer, counterbalancing the attractive interaction from the original membrane. To examine the effects of the attraction due to the image membrane on the dendrimer structure, we plotted the average density distribution of the dendrimer at ξ = 5.8 nm (Figure S3 of the Supporting Information). At this distance, the dendrimer does not have significant attractive interaction with the DPPC membrane, and as a result, the distribution is D | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 3. Representative snapshots from several umbrella sampling simulation windows for (a) G3-DPPC and (b) G3-POPG systems.

surface; however, near the membrane but as far as ξ = 4.0 nm, several dendrimer branches reach toward the surface. However, even at the free-energy minimum (ξ = 2.3 nm), the dendrimer is not completely submerged in the membrane region, with half of the dendrimer dangling in the water phase. In contrast, in the presence of the negatively charged POPG membrane, the PAMAM dendrimer branches spread out in two directions before contacting the membrane (ξ = 5.8 nm): one branch spreads toward the membrane and the other branch spreads away from the membrane. This trend results from the periodic boundary conditions imposed on the simulation box, causing the dendrimer to feel additional anionic membranes in the opposite direction as discussed above.

As the dendrimer approaches the membrane (ξ = 4.0 nm), the dendrimer seems to pull the membrane by reaching out its side chains toward the membrane surface, which induces a slight curvature of the membrane. At the free-energy minimum (ξ = 2.3 nm), the dendrimer nearly flattens onto the membrane surface. These findings are consistent with the experimental results by Åkesson et al.17 Åkesson et al. observed that the passive translocation of the dendrimer is not likely regardless of membrane charge state and that the highly cationic dendrimers interact with anionic membranes more strongly than with zwitterionic membranes by disturbing the membrane and even inducing stacks of bilayer patches. From the free-energy and force calculation, we observed strong repulsive force built up as E | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 4. Relative energy contributions as a function of the reaction coordinate ξ for (a) G3-DPPC and (b) G3-POPG systems. The major group contributions from the Lennard-Jones potential energy for the G3-DPPC system and Coulombic potential energy for the G3-POPG system are plotted in (c) and (d), respectively. ⟨E⟩bulk is the average energy when the PAMAM dendrimer is in bulk water phase (ξ = 5.5−5.8 nm). Notably, the Coulombic energy is calculated with a cutoff of 5 nm.

energetic penalty from other components, including salt ions. Hence, the large free energy of the dendrimer adsorption onto the anionic membrane results from not only direct electrostatic interaction between the dendrimer and membrane but also interplays between salt ions and the dendrimer (and membrane), which include the entropy increase of the salt ions upon adsorption. This is consistent with the temperature dependence of the free energy, as shown in Figure 2. It is also noted that the water contribution is not negligible in either system. Structural Changes during the Adsorption Process. The global G3 PAMAM dendrimer shape change when adsorbing to the biological membranes is characterized by the mass-weighted radius of gyration Rg,and its lateral (Rg,xy) and normal (Rg,z) components, which are defined as follows:

the dendrimer approaches the membrane core regardless of the membrane charge state, which supports the difficulty of passive translocation. We also observed that the dendrimer interacts with the anionic membrane much more strongly than with the zwitterionic membrane (by about 100 pN). This strong interaction induces large structural perturbation of both dendrimer and anionic membrane, which will be discussed from structural analyses in later sections. Decomposition of the Adsorption Potential Energy. To better understand the interactions between the amineterminated G3 PAMAM dendrimer and biological membranes, the potential energy contributions to the adsorption energy are shown in Figure 4. Figure 4a shows the potential energy (Epot), intramolecular (Eintra), intermolecular (Einter), Lennard-Jones (ELJ), and Coulombic (ECoul) contributions relative to their bulk values ⟨E⟩bulk as a function of the reaction coordinate ξ for the G3DPPC system. ⟨E⟩bulk is obtained for ξ = 5.5−5.8 nm. As expected, the intramolecular contribution is nearly constant throughout the adsorption; however, the intermolecular potential energy, especially the Lennard-Jones contribution ELJ, stabilizes significantly as the dendrimer approaches the membrane. The three major contributions to the ELJ are also plotted in Figure 4c. The dominant contribution clearly comes from the G3 PAMAM dendrimer and DPPC membrane interactions. In contrast, the potential energy and its components for the G3-POPG system do not significantly change upon adsorption (see Figure 4b). Interestingly, the Coulombic contribution becomes positive (or E − ⟨E⟩bulk > 0) as the dendrimer approaches the membrane, which is counterbalanced by the Lennard-Jones contribution. The further decomposition of the Coulombic contribution shown in Figure 4d indicates that the strong electrostatic attractive interactions between the cationic dendrimer and anionic membrane is compensated by the

Rg ≡

R g, xy =

2R g, xy 2 + R g, z 2 1 4MP 2



∑ {(mixi − mjxj)2 + (miyi − mjyj )2 } i,j


R g, z =

1 2MP 2


∑ {(mizi − mjzj)2 } i,j


where MP and NP are the total mass and number of PAMAM dendrimers, respectively, and mi is the atomic mass of atom i in the dendrimer. Figure 5a,b shows Rg (and its components) as a function of ξ for G3-DPPC and G3-POPG systems. For both systems, the overall dendrimer size Rg does not significantly change upon adsorption, which implies the dendrimer density remains constant during adsorption. The same uncharacteristic behavior F | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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which is well before the adsorption free-energy minimum (ξ = 2.3 nm). The atomic number density profiles for molecular species in both systems during adsorption are also shown in Figure 6a,b. The water and membrane densities were obtained from the snapshots at ξ = 5.0 nm and scaled down by a factor of 1/10 to be compared with other densities. Interestingly, when the dendrimer is in the aqueous phase (ξ = 4.0 and 5.0 nm), the density of both systems is bimodally distributed, which is reminiscent of the spread conformation of the dendrimer observed in Figure 3 and indicates that the dendrimer branches and biological membrane already interact at these distances. The salt concentration in the water phase (z = 3−7 nm) for the G3-POPG system ranged from approximately 350−390 mM depending on the dendrimer location. This salt concentration is higher than the intended ionic strength (150 mM) because salt ions are excluded from the membrane region. Figure 6c,d displays the corresponding charge density profiles for G3-DPPC and G3-POPC systems, respectively, at several reaction coordinates. For the G3-DPPC system, the zwitterionic DPPC membrane shows a dipolar distribution for each leaflet that is compensated by water dipoles arranged near the membrane surface. For the G3-POPG system, the anionic membrane forms a large negative charge density in the headgroup region, which is mostly neutralized by Na+ salt ions. The water molecules have similar arrangements near the G3-DPPC membrane surface despite having limited charge neutralizing effects. Structural and Dynamic Properties at the Free-Energy Minimum. The model biological membranes are subjected to structural changes via dendrimer adsorption. Figure 7 shows the average density maps for both the dendrimer and membrane upper leaflet (where the dendrimer is adsorbed)

Figure 5. Radius of gyration Rg for the G3 PAMAM dendrimer and its lateral (Rg,xy) and normal (Rg,z) components as a function of the reaction coordinate ξ for G3-DPPC and G3-POPG systems.

was observed for the Rg component in the G3-DPPC system, which qualitatively disagrees with previous CG simulation results.24,25 However, in the G3-POPG system, the z-directional component Rg,z undergoes dramatic structural changes from a spherical to a pancake shape starting at ξ = 3.0 nm,

Figure 6. Atomic number density and charge density profiles for the molecular species in the z direction at ξ = 2.3, 3.0, 4.0, and 5.0 nm for both G3DPPC (panels a and c) and G3-POPG (panels b and d) systems. Notably, both the membrane and water number densities are at ξ = 5.0 nm and scaled down by a factor of 10. G | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 7. Two-dimensional number density maps (in nm−3) of the dendrimer and membrane upper leaflet in the interfacial region (z = 0.0−4.0 nm) at the free-energy minimum location (ξ = 2.3 nm) for both G3-DPPC (panels a and c) and G3-POPG (panels b and d) systems.

relation (D = limt→∞ (MSD)/(4t)) by fitting data in the time range of 500−800 ps. This figure shows the dendrimer mobility slows by a factor of 3.4 at the anionic POPG membrane surface relative to the zwitterionic DPPC membrane surface. In addition, the relative mobility of the dendrimer compared with the corresponding lipids is 0.71 and 0.53 for the G3-DPPC and G3-POPG systems, respectively. It indicates that the slowdown of the dendrimer mobility in the POPG membrane is partly due to the slow mobility of the POPG lipid. The dendrimer adsorption onto the membrane surface also depletes the lipids near the dendrimer, as shown in Figure 7c,d. The strong dendrimer adsorption to the POPG membrane pushes neighboring lipids away, which leads to the local accumulation of lipids over long distances. For the G3-DPPC system, lipid depletion and accumulation near the dendrimer is weak and short-ranged. The lipid deuterium order parameters SCD show the behavior similar to that in the density map. The perturbation range SCD is short (1 nm) for the DPPC lipids but much longer (3−4 nm) for the POPG lipids (see Figure S5 in the Supporting Information). Specific interactions between the G3 PAMAM dendrimer and membrane can also be identified via the radial distribution functions g(r) for each atomic pair. Figure 9a plots the radial distribution functions between the terminal amine groups (NT) of the dendrimer and several heavy atoms in the DPPC lipid headgroups of the G3-DPPC system at the free-energy minimum (ξ = 2.3 nm). The dominant peaks at approximately 0.26 nm correlate to oxygen atoms (O7 and O11) bonded to both C and P atoms in the DPPC headgroup, and the broad peak near 0.35 nm correlates to the P atoms. Interestingly, the other oxygen atoms (O9 and O10) bonded to only a P atom show relatively weak, broad dual peaks near 0.37 and 0.47 nm. Because the relatively free oxygen atoms (O9 and O10) have

in the interfacial region (z = 0.0−4.0 nm) at the free-energy minimum location (ξ = 2.3 nm) for G3-DPPC (Figure 7a,c) and G3-POPG systems (Figure 7b,d). The dendrimer density spreads out smoothly in a circular area approximately 6 nm in diameter for the G3-DPPC system, whereas the dendrimer density in the G3-POPG system is branch-like, which implies it is bound to the membrane surface more strongly than in the G3-DPPC system. This difference in dendrimer mobility is clearly observed in the lateral mean square displacement (MSD) data (see Figure 8). Each MSD curve value is the diffusion coefficient (in square nanometers per picosecond) obtained from the Einstein

Figure 8. Lateral mean square displacements (MSD) of the dendrimer and lipids at the free-energy minimum (ξ = 2.3 nm) for both the G3DPPC and G3-POPG systems. The value for each MSD curve is the diffusion coefficient (in nm2/ps) obtained from the Einstein relation (D = limt→∞ (MSD)/(4t)) using the MSD data across the time range of 500−800 ps. H | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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the two model membranes with different charge states was quantitatively determined. For the zwitterionic DPPC membrane, the dendrimer has a minimum free energy of approximately 50 kcal/mol, which is 15 kcal/mol larger than the minimum free energy observed in previous studies that used implicit solvent and fixed membrane tail models. The freeenergy minimum location is also closer to the membrane lipid headgroup than in previous studies by approximately 0.5 nm. The dominant adsorption potential energy contribution comes from the van der Waals attraction between the dendrimer and membrane. In contrast, the anionic POPG membrane pulls the positively charged dendrimer via an attractive mean force of approximately 200 pN to a final position in the membrane headgroup region. However, the electrostatic attraction between the dendrimer and membrane is counterbalanced by interactions between the dendrimer (or membrane) and salt (or water), which increases the electrostatic interactions during the adsorption process. This finding indicates that small salt ions and water molecules arrange themselves to effectively screen the electrostatic interactions between the dendrimer and membrane. As a result of the strong attractive interaction with the membrane, the dendrimer structurally undergoes the transition from a spherical to a pancake conformation and reduces in mobility, especially for the POPG membrane. The membranes are also perturbed by the dendrimer adsorption: lipids are depleted and disordered near the dendrimer adsorption site, especially for the negatively charged membranes. At this point, we should discuss the limitations of our model. First, our study regarding dendrimer adsorption to biological membranes is only the first stage of dendrimer translocation through biological membranes. To induce the membrane pore formation, we would need a much larger membrane system, which is bounded by limited computational resources. Nonetheless, this quantitative and atomic level information regarding the dendrimer adsorption onto biological membranes is still invaluable for understanding and developing new dendritic materials for drug and gene delivery. Second, the surface tension felt by each membrane leaflet is not symmetric because only one dendrimer exists within the rectangular simulation box. For example, the membrane leaflet through which the dendrimer translocates would feel more tension than the other leaflet, which would induce a curve to release the tension. However, the membrane curvature is not allowed in the simulation setup because of the small membrane size and periodic boundary conditions. However, in this study, the dendrimer does not deeply penetrate the membrane. We expect this asymmetric tension effect would not be significant. This effect can be relieved in two ways. The most conventional way is to introduce dendrimer molecules to each membrane leaflet with sufficient distance between them not to interact with each other. However, in this case, the simulation system should be much larger than the current system. The second method is to introduce a clever boundary condition P21, where the lipid can migrate between the two leaflets via symmetry.47 We are currently working on the dendrimer penetration process using the boundary condition.

Figure 9. Three-dimensional radial distribution functions g(r) between the terminal amine (designated as NT) of the dendrimer and headgroup atoms of the (a) DPPC or (b) POPG lipids at the freeenergy minimum (ξ = 2.3 nm for both G3-DPPC and G3-POPG systems). The radial distribution function between the NT and the oxygen atom (OW) of the water molecules is also shown. Please refer to Figure 1 for the atom numbering.

more water accessible space, they tend to form hydrogen bonds with water rather than contact the dendrimer (data not shown). The similar correlation behavior is also observed for the G3POPG system, as shown in Figure 9b with the dominant peak near 0.27 nm corresponding to oxygen (O12) bonded to both P and C atoms. However, unlike G3-DPPC, the dendrimer terminal amine (NT) shows highly damped and broad correlation with O12 but strong correlations with the two alcohol groups (O2 and O5) in the headgroup. This strong correlation to the two alcohol groups seems to play an important role in the strong dendrimer adsorption to the POPG membrane surface.

SUMMARY AND CONCLUSIONS We investigated dendrimer adsorption to biological membrane systems using atomistic MD simulations combined with umbrella sampling techniques. The model dendrimer and biological membranes used in this study were an EDA core G3 PAMAM dendrimer with an amine terminal group and both zwitterionic DPPC and anionic POPG lipid bilayer membranes, respectively. The thermodynamic, structural, and dynamical changes in the dendrimer−membrane systems during the process were calculated and analyzed to understand the atomistic interaction details between the dendrimer and biological membranes. Importantly, the free energy of the dendrimer adsorption onto I | J. Phys. Chem. B XXXX, XXX, XXX−XXX

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S Supporting Information *

Force field verification, system equilibration, density profiles, and order parameters. This material is available free of charge via the Internet at


Corresponding Author

*E-mail: [email protected]. Phone: +8229405243. Fax: +8229420108. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We acknowledge support from National Research Foundation Grant funded by the Korean government (MEST) (2013R1A1A1A05009866) and Research Grant of Kwangwoon University in 2013.


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Free energy of PAMAM dendrimer adsorption onto model biological membranes.

We investigated the thermodynamic, structural, and dynamics changes in dendrimer-membrane systems during dendrimer adsorption to biological membrane s...
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