Dendrimer Interactions with Lipid Bilayer: Comparison of Force Field

Article pubs.acs.org/JCTC

Cite This: J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

Dendrimer Interactions with Lipid Bilayer: Comparison of Force Field and Effect of Implicit vs Explicit Solvation Subbarao Kanchi,†,‡ Mounika Gosika,† K. G. Ayappa,*,‡ and Prabal K. Maiti*,† †

Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India Department of Chemical Engineering, Center for Biosystems Science and Engineering, Indian Institute of Science, Bangalore 560012, India

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‡

ABSTRACT: The understanding of dendrimer interactions with cell membranes has great importance in drug/gene delivery based therapeutics. Although molecular simulations have been used to understand the nature of dendrimer interactions with lipid membranes, its dependency on available force field parameters is poorly understood. In this study, we have carried out fully atomistic molecular dynamics (MD) simulations of a protonated G3 poly(amido amine) (PAMAM) dendrimer− dimyristoylphosphatidylcholine (DMPC) lipid bilayer complex using three different force fields (FFs) namely, CHARMM, GAFF, and GROMOS in the presence of explicit water to understand the structure of the lipid-dendrimer complex and nature of their interaction. CHARMM and GAFF dendrimers initially in contact with the lipid head groups were found to move away from the lipid bilayer during the course of simulation; however, the dendrimer remained strongly bound to the lipid head groups with the GROMOS FF. Potential of the mean force (PMF) computations of the dendrimer along the bilayer normal showed a repulsive barrier (∼20 kcal/mol) between dendrimer and lipid bilayer in the case of CHARMM and GAFF force fields. In contrast, an attractive interaction (∼40 kcal/mol) is obtained with the GROMOS force field, consistent with experimental observations of membrane binding observed with lower generation G3 PAMAM dendrimers. This difference with the GROMOS dendrimer is attributed to the strong dendrimer-lipid interaction and lowered surface hydration of the dendrimer. Assessing the role of solvent, we find that the CHARMM and GAFF dendrimers strongly bind to the lipid bilayer with an implicit solvent (Generalized Born) model, whereas binding is not observed with explicit water (TIP3P). The opposing nature of dendrimermembrane interactions in the presence of explicit and implicit solvents demonstrates that hydration effects play an important role in modulating the dendrimer-lipid interaction warranting a case for refinement of the existing dendrimer/lipid force fields.

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drazone (PPH) dendrimers to treat inflammatory diseases25 has recently been studied. There exists a wide body of experimental studies focusing on the interactions of PAMAM dendrimers with lipid membranes.26−30 At physiological pH (∼7) amine (NH2) terminated dendrimers are positively charged, and enhanced binding is observed with negatively charged lipids such as DPPG, POPG, and POPS when compared with zwitterionic or neutrally charged lipids.31 Studies with amine (positive), acetamide (neutral), and carboxylic acid terminated PAMAM dendrimers32 show that lower generation amine terminated G3 and carboxylic acid terminated G2.5 charged

INTRODUCTION

Dendrimers are three-dimensional hyperbranched polymeric nanoparticles having a central core connected by successive and uniform dendritic branching layers.1,2 The structure controlled parameters of dendrimers such as size, shape, surface chemistry, and architecture facilitate a wide range of applications in biomedicine,3−11 sensing,12 catalysis,13 and light harvesting.14 Dendrimers have potential applications in drug8,15−17 and gene delivery4,18−23 due to their versatility, flexibility, high drug loading capacity, and lowered toxicity.24 Understanding the interaction of dendrimers with the cell membrane is of fundamental importance for designing dendrimer based medical therapeutics and determining levels of toxicity. For example, the potential for polyphosphorhy© XXXX American Chemical Society

Received: February 3, 2018 Published: May 29, 2018 A

DOI: 10.1021/acs.jctc.8b00119 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

Article

Journal of Chemical Theory and Computation

tails was investigated on membrane binding, penetration, and pore formation with model G5-DPPC systems. Additionally, pore formation was found to occur on stretched membranes at sufficiently high interaction parameters strengths. The attraction between the dendrimer surface moieties and lipid head groups leads to flattening of the dendrimer along the membrane surface, while the interaction between the inner linkers of the dendrimer and lipid tails influences the insertion of the dendrimer into the bilayer membrane.38 Although coarse grained models at the level of MARTINI or DPD allow simulations at larger time and length scales, currently inaccessible with fully atomistic simulations, specific interactions such as hydrogen bonding and hydration effects are captured by modulating the specific interaction parameters between coarse grained beads. All-atom simulation studies by Kelly et al.44 using an implicit solvent model have shown that the interaction between the G3 PAMAM dendrimers and DMPC lipid membranes results in a free energy of binding of 36 kcal/mol for the charged amine and 47 kcal/mol for the carboxylic acid terminated dendrimers when compared with 26 kcal/mol for the neutral acetamide terminated case. While computing the free energy using umbrella sampling, the lipid tails were frozen with a 4 ns sampling at each window. Additionally, these simulations were carried out for a circular patch of lipids with a cylindrical hard wall imposed to constrain the area. Despite these simplifications, the results qualitatively agree with experimental data of Mecke et al.,26,43,45,46 which reveal binding of G3 PAMAM dendrimers on DMPC membranes. Area fluctuations and lipid mobility play an important role during binding of proteins and polymers to membranes47−49 and are expected to influence the final state of the dendrimer-membrane complex. While evaluating the free energy of transfer of the dendrimer into the hydrophobic region of the phospholipid bilayer, water bound on the dendrimer surface and interior must be removed to allow for interactions with the bilayer interior. Hydration of dendrimers also affects its structure50 and interactions51−53 with biomolecules and membranes. All atom simulations with explicit water models are expected to capture these effects with greater accuracy. In a recent all atom MD study54 with explicit water and a 20 ns sampling at each window, the free energy of binding for protonated G3 PAMAM dendrimers was obtained for both DPPC and anionic palmitoyl-oleoyl-phosphatidyl glycerol (POPG) using anisotropic pressure coupling to account for membrane areal changes. The binding free energies were about 50 and 120 kcal/mol for DPPC and POPG membranes, respectively. For DPPC membranes, the binding free energy was about 15 kcal/mol greater and located deeper in the membrane, than the values obtained in the study by Kelly et al.,44 for a G3-DMPC system. Although the pulling direction and simulation time at each window can influence the PMF during umbrella sampling, the difference in the PMFs observed in the above studies is largely attributed54 to the absence of desolvation and lipid areal rearrangements effects in the implicit solvent models.44 In other all-atom MD studies49 with explicit solvent, carried out with 5 dendrimers in contact with a DMPC bilayer, a single G4 poly(ether imine) (PETIM) dendrimer was found to insert into the bilayer, while the G3 dendrimers remained adsorbed on the surface of the bilayer. These results were in good agreement with AFM and SAXS data obtained in the same study. Clearly the manner in which the solvent is treated

dendrimers interact with DPPC vesicles despite having positive and negative zeta potentials, respectively. Their study further predicts partial penetration of the dendrimers into the bilayer interface. Using AFM with DMPC supported lipid bilayers26,27 in the Lα phase, G7 dendrimers were found to have a stronger propensity to form holes and remove lipids when compared with G5 dendrimers. This propensity for lipid removal was greater for amine terminated dendrimers when compared with acetamide (neutral) termination. Dendrimer binding for G7 and G5 was stronger at bilayer defects, and G3 dendrimers were found to bind both at defects and the surface of the bilayer without hole formation.26 In situ null ellipsometry and neutron reflection studies33 reveal penetration of the membrane with amine terminated PAMAM G2 and G4 dendrimers leaving the membrane intact and membrane disruption occurred only with G6 dendrimers. Hence smaller generation dendrimers have greater potential as transfection agents when compared with larger dendrimers. Similar dendrimer generation dependent binding trends are observed with liposomes which are largely devoid of defects.34 In other studies35 G2-COOH was found to increase POPC liposome leakage as the bulk dendrimer concentration was increased. In contrast, G5-COOH did not show any leakage, and this was attributed to intercalation of the G5-COOH within the bilayer core based on quartz crystal microbalance with dissipation (QCMD) studies. In addition to studies on model bilayer systems, interaction of dendrimers on different cell lines has also been investigated. Significant decrease in neural cell viability 36 occurred with G3−G7 PAMAM dendrimers, whereas G0−G2 dendrimers did not have any effect at similar bulk concentrations. Amine-terminated G5 PAMAM dendrimers had a greater disruptive effect on KB and Rat 2 cell lines when compared with their acetamide-terminated counterparts.27 It is clear that the dendrimer binding and pore forming efficacy with lipid membranes depends on the size, charge, bulk concentration, surface chemistry, and pH of the solvent.37−39 In general, higher generation PAMAM dendrimers have been observed to form pores and rupture the lipid membrane to a greater extent, while the smaller generation dendrimers remain adsorbed on the membrane surface or permeate without permanent rupture or pore formation. Although SAXS and IR spectroscopy can yield information about the bilayer thickness and extent of disorder in the lipid tails, accessing changes at the atomistic level during dendrimer-lipid complexation remains a challenging problem.34 Over the past decade, molecular dynamics simulations have played an important role in providing molecular level insight into the nature of dendrimer interactions with lipid membranes. Using coarse-grained (CG) MARTINI models, Lee and Larson37,40−42 showed that higher generation (G7, G5) PAMAM dendrimers can form pores in lipid membranes, and the pore formation efficacy is reduced for acetylated and PEGylated dendrimers in agreement with experimental observations.27,43 The nature of dendrimer interactions with lipid membranes strongly depends on the pH of the solvent. Using a MARTINI model, dendrimers were found to have an attractive interaction with negatively charged mixed (DPPC/ DOPG) lipid membranes and the free energy of binding is negative at low pH whereas the interaction becomes repulsive at high pH.39 Using dissipative particle dynamics, the influence of varying interaction strengths between the terminal and inner dendrimer groups with the lipid head groups and hydrocarbon B


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Journal of Chemical Theory and Computation Table 1. Details of Different Systems Simulated dendrimer (G3 PAMAM) FF

number of dendrimer atoms

lipid (DMPC) FF

number of atoms in (256 × 256) lipid patch

number of ions

number of water molecules

total number of atoms

CHARMM GAFF GROMOS

1124 1124 640

CHARMM Lipid14 GROMOS

60416 60416 23552

432 256 434

70818 (TIP3P) 40057 (TIP3P/SPC) 47497 (TIP3P/SPC)

274426 181967 167117

(explicit versus implicit) as well as the specific force field based on either an all-atom or united atom model is expected to modulate the interactions with phospholipid membranes. In a very recent study by Palazzesi et al.55 it has been shown that various all-atom force fields in combination with explicit solvents can generate different conformational ensembles. Given that several force fields are available while carrying out all atom simulations, the choice of an appropriate force field is a key factor. This dependency on the force field between dendrimer, lipids, and solvent models is poorly understood, and the choice of a force field would ultimately depend on agreement with available experimental data. In this study we carried out a detailed investigation on the binding of G3 protonated amine terminated PAMAM dendrimer with a DMPC bilayer membrane in the Lα phase using all-atom molecular dynamics simulations with explicit solvent. In order to evaluate the differences between available force fields, we have used three widely used force fields (CHARMM,56 GAFF,57 and GROMOS8658) for the dendrimer in combination with different membrane force fields (CHARMM36,59 LIPID14,60 and GROMOS56a61), respectively. To assess the differences with solvent models (explicit vs implicit), we have studied the G3 PAMAM-DMPC system in the presence of the Generalized Born (GB)62 implicit solvent. Potential of mean force computations using umbrella sampling is carried out to compare the binding free energy of the dendrimer with the membrane. Interestingly, both positive and negative binding free energies are obtained depending on the choice of the force field and solvent representation (explicit vs implicit) revealing a strong dependency on the specific force field used to model dendrimer-water interactions. The rest of the manuscript is organized as follows: In the “Methods” section, we explain the simulation protocols and different force fields used. In “Results and Discussions”, we discuss various results obtained from all-atom simulation of dendrimer-lipid systems. The structure and free energy of binding of dendrimer with lipid membrane using different available force fields and solvent models are discussed in this section. Finally, in “Summary and Conclusions”, we summarize all the results and highlights of the present study.

Unless stated otherwise, all reported simulations with the GAFF/GROMOS force fields are with SPC water. Initially, the dendrimer and lipid membranes are equilibrated separately in water for 50 ns. The equilibrated dendrimer is placed on the upper leaflet of the pre-equilibrated lipid membrane, and this combined system is solvated with 40 Å water layer on either side of the membranes using VMD.67 In the case of the positively charged (+32e) protonated G3 PAMAM dendrimer 32 Cl− counterions were added for charge neutralization. We have also added extra Na+ and Cl− ions to the systems to maintain a 0.15 M salt concentration which is close to the physiological conditions. The details of the simulated systems are given in Table 1. The simulations reported in this work are carried out using NAMD (version 2.9),68 AMBER14,69 and GROMACS 5.1.070 molecular dynamics packages. The solvated dendrimer-lipid complex is subjected to 1100 steps of conjugate gradient minimization to remove unfavorable contacts. The minimized systems are gradually heated from 0 to 303.15 K by using harmonic restraints with a force constant of 1000 kcal mol−1 Å−2. The systems are subjected to 1 ns of NVT equilibration with a time step of 2 fs for integration. During the NVT simulation, the head groups of the DMPC lipid bilayer are kept fixed at their initial positions using a harmonic restraint with a force constant of 1000 kcal mol−1 Å−2. Temperature is controlled using a Langevin piston71 with a damping coefficient of 1 ps. Subsequently, MD simulations are performed under constant temperature and constant pressure conditions (NPT) with periodic boundary conditions in all three directions. NoséHoover Langevin piston72 pressure control is used to apply an isotropic pressure of 1 atm with a piston period of 0.2 ps and damping time constant of 0.05 ps. A 12 Å cutoff is used for calculating the short-range part of nonbond interactions, and the long-range electrostatic interactions are calculated using particle mesh Ewald (PME)73 method. During the simulation the bond lengths involving hydrogen atoms are constrained using the SHAKE algorithm.74 MD simulations are performed for 200 ns in the NPT ensemble, and last 10 ns trajectory is used for analysis. Similar simulation protocol was used in our previous studies on systems11,24,49,75,76 involving dendrimer and lipid. Umbrella Sampling and Weighted Histogram Analysis Method. Umbrella sampling77,78 in combination with a weighted histogram analysis method (WHAM)79 is a standard method to compute the potential of the mean force (PMF) along a given reaction coordinate (ξ). This method has been successfully used in calculating the free energy of binding for nanoparticle−membrane systems.39,44,54 In this study, we have computed the PMF of the dendrimer as a function of distance along the membrane normal (z-axis) using the umbrella sampling method. The reaction coordinate (ξ) is defined as the distance between the center of mass of dendrimer and center of mass of the membrane along the membrane normal (z-axis). We have sampled the reaction coordinate starting from 60 to 20 Å using the force constant of 4.0 kcal mol−1 A−1 with a 1 Å bin width. Each bin is sampled for 10 ns, and the last 2 ns

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METHODS Initial structure of the protonated (P) ethylenediamine (EDA)core PAMAM dendrimer of generation three (G3) was built using the dendrimer building toolkit (DBT).63 A DMPC model membrane having 256 lipids in each leaflet was constructed using CHARMM-GUI.64 In this study, we have used three different force field parameters (CHARMM,56 GAFF,57 and GROMOS8658) for the dendrimer in combination with the following membrane force fields (CHARMM36,59 LIPID14,60 and GROMOS56a61), respectively. The TIP3P65 water is used as the solvent in the case of CHARMM dendrimer systems, whereas SPC66 water is used as solvent in the case of GAFF/ GROMOS dendrimer systems. A few simulations were carried with the GAFF/GROMOS force fields with TIP3P water. C


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Figure 1. Simulation snapshots of the G3 PAMAM dendrimer on the DMPC lipid membrane for different force field parameters: a) the CHARMM dendrimer-CHARMM membrane, b) the GAFF dendrimer-LIPID14 membrane, and c) the GROMOS dendrimer-GROMOS membrane. The GROMOS dendrimer binds to the lipid head groups, while the CHARMM and GAFF dendrimers move away from the surface of the lipid membrane.

⎛ I ⎞ δ = 1 − 3⎜ 22 ⎟ ⎝ I1 ⎠

trajectory is used to compute PMF profile of dendrimer. We have also computed various structural properties of dendrimer in this study to quantify its size, shape, and hydration as defined below. Radius of Gyration. The radius of gyration (Rg) which is a good measure of the size of the dendrimer is defined as ⎡N ⎤ R 2g = (1/M )⎢∑ mi |ri − R |2 ⎥ ⎢⎣ i = 1 ⎦⎥

(3)

where I1, I2, and I3 are defined as I1 = Ix + Iy + Iz

I2 = IxIy + IyIz + IzIx (1)

I3 = IxIyIz

th

where mi is the mass, ri is the position vector of the i atom, R is the position of the center of mass, and M is the total mass of the dendrimer. Aspect Ratios and Asphericity. To assess the shape anisotropy of the dendrimer as a function of dendrimer generation as well as changes due to their interaction with the lipid bilayer, we evaluate the shape gyration tensor of the dendrimer. The principle moments of inertia of the dendrimer are calculated by diagonalizing the gyration matrix Gmn, whose elements are defined as80

where rmi and Rm are the coordinates of atoms and the m coordinate of the center of mass of the dendrimer respectively, mi is the mass of the ith atom, and M is the total mass of the dendrimer. The three eigenvalues of Gmn are Iz, Iy, and Ix (descending order). The aspect ratios of the principle moments I I ( z and z ) of inertia yield information about the shape of the

Surface and Bound Water. To get a measure of the hydration of the dendrimer, we also evaluate the number of bound water molecules that hydrate the interior as well as the surface of the dendrimer. The calculation of bound water using a simple distance cutoff criterion overestimates the water density due to the asphericity of the dendrimer structure as well as the roughness of the dendrimer surface. To resolve this issue, we have used a criterion developed in our previous work50 and briefly outline the procedure here. The solvent accessible surface area (SASA) of each atom of the dendrimer was calculated using a probe of radius 6 Å. Those atoms with nonzero SASA were identified as dendrimer surface atoms. We next calculated the surface bound water (nsurf) which are water molecules that lie within 4 Å from the dendrimer surface atoms. The buried domain is defined as the internal regime of dendrimer, 3 Å away from the surface atoms. We calculated the water molecules (ninner) which are in the buried domain of the dendrimer by excluding the surface bound water. Bulk water molecules (nbulk) are water molecules that lie between 4 and 7 Å from the surface of the dendrimer atoms, excluding the surface and inner bound water.50

dendrimer. The asphericity gives more quantitative information about the shape of the dendrimer in addition to the information we get from the aspect ratios. The asphericity (δ) is defined as81

RESULTS AND DISCUSSION Dendrimer Interactions with Lipid Membrane in Explicit Water Solvent. The interactions of the protonated

Gmn =

N ⎤ 1 ⎡⎢ ∑ mi(rmi − R m)(rni − R n)⎥, ⎥⎦ M ⎢⎣ i

m, n = x , y , z (2)

Iy

■

Ix

D


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Figure 2. (a) Dendrimer (PAMAM) distance from the center of mass of the lipid membrane (DMPC) and (b) number of close contacts between the dendrimer and lipid membrane in different sets of simulations using various force field parameter sets. In the case of the GROMOS dendrimer, the dendrimer-lipid membrane distance settles around 23 Å and the number of contacts between the dendrimer and lipid reaches a maximum after 150 ns simulation, confirming the binding of the GROMOS dendrimer with the lipid membrane. In contrast, the CHARMM and GAFF dendrimers move away from the surface of the membrane, and the dendrimer-lipid distance settles at ∼60 Å. As a consequence, the number of contacts between dendrimer and lipid reduces to zero after 150 ns simulation.

Table 2. Radius of Gyration (Rg), Inner (ninner), Surface (nsurf), Bulk (nbulk) Bound Water, and Asphericity (δ) of Dendrimer CHARMM property Rg (Å) ninner nsurf nbulk δ

PAMAM 14.08 58.10 558.51 880.84 0.08

± ± ± ± ±

0.2 7.80 13.72 18.54 0.007

GAFF

PAMAM+DMPC 14.52 64.36 596.94 962.8 0.22

± ± ± ± ±

0.3 7.06 12.86 19.21 0.03

PAMAM 15.52 67.12 610.85 963.58 0.04

± ± ± ± ±

0.3 10.3 17.56 31.06 0.03

GROMOS PAMAM+DMPC 15.0 67.78 595.64 925.64 0.124

± ± ± ± ±

0.3 6.85 11.28 23.95 0.06

PAMAM 16.19 48.24 583.059 1077.14 0.062

± ± ± ± ±

0.77 10.09 43.61 94.04 0.068

PAMAM+DMPC 16.14 43.96 373.50 650.20 0.065

± ± ± ± ±

0.27 6.60 13.69 20.19 0.022

computed and tabulated in Table 2 to understand the structural changes upon binding to the lipid membrane. It is observed that there is no significant change in Rg of the dendrimer in the vicinity of the lipid membrane when compared with the dendrimer only present in solvent. In the presence of the lipid membrane, the asphericity (δ) of CHARMM and GAFF dendrimers increases, whereas there is no change in δ of the GROMOS dendrimer. The bound water calculations reveal that the hydration of CHARMM and GAFF dendrimers is not affected by the presence of the lipid membrane due to their weak interaction with the membrane and behave essentially like dendrimers in bulk water. Due to the stronger binding with the lipid membrane, the number of surface (nsurf) and bulk (nbulk) bound water molecules of GROMOS dendrimer is reduced by 36% and 40%, respectively, when compared with the dendrimer in bulk solvent. However, the number of inner (ninner) bound water molecules is only marginally reduced by 9%. This reduction in dendrimer hydration can be understood as a consequence of induced anisotropy in the hydration of GROMOS dendrimer, which is bound to the membrane at the lipid−water interface. We also point out that there are differences in the hydration levels between the different force fields used. In bulk water, GAFF has a higher tendency to hydrate the dendrimer when compared with CHARMM and GROMOS, with the exception of the bulk water (nbulk) which is marginally higher for the GROMOS force field when compared with GAFF. Hydration of the dendrimer interior is the smallest for GROMOS when compared with either CHARMM or GAFF indicating a relatively stronger hydrophobicity of the dendrimer interior with the GROMOS force field. We have performed three independent simulations in each case of CHARMM, GAFF, and GROMOS dendrimers to demonstrate the reproducibility of simulation results as shown

G3 PAMAM dendrimer with DMPC lipid membrane are studied using three different force field parameters in explicit water. Figures 1a, 1b, and 1c show the instantaneous snapshots of the lipid-dendrimer system at different time points during the 200 ns simulation for the three different cases. Initially, the dendrimer is placed on the surface of the lipid membrane in all cases. For the CHARMM and GAFF dendrimers, the dendrimer moves away from the membrane surface during the course of the simulation as shown in Figures 1a and 1b. However, in the case of GROMOS, the dendrimer remains bound to the surface of the lipid membrane as shown in Figure 1c. The distance between the center of mass of dendrimer and center of mass of lipid membrane evaluated over the course of the simulation is shown in Figure 2a. CHARMM and GAFF dendrimers behave very similarly on the surface of lipid membrane, and in each case, the dendrimer moves away from the surface of lipid membrane settling at a distance of ∼60 Å after 150 ns. In contrast, the GROMOS dendrimer interacts with the lipid head groups and binds with the lipid membrane. As a consequence, the dendrimer distance decreases settling at a constant value of ∼23 Å. The number of close contacts between the dendrimer and lipid atoms as a function of simulation time using a distance cutoff of 3 Å is evaluated to assess dendrimer-lipid binding (Figure 2). The number of close contacts decreases to zero after 150 ns for both CHARMM and GAFF dendrimers due to the unbinding of dendrimer with the lipid membrane. However, for the GROMOS dendrimer, the number of close contacts increases and saturates after 150 ns as shown in Figure 2b. The large number of dendrimer-lipid close contacts confirms that the GROMOS dendrimer is strongly bound to the lipid membrane. The structural properties of the dendrimer such as reflected in the radius of gyration (Rg), asphericity (δ), and hydration are E


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Figure 3. Distance of the center of mass of the dendrimer (G3 PAMAM) from the center of the lipid membrane (DMPC) and number of close contacts between the dendrimer and lipid membrane as a function of simulation time are shown for (a) CHARMM, (b) GAFF, and (c) GROMOS dendrimers in the presence of explicit water (TIP3P/SPC) solvent, respectively. For each case, three independent simulations were performed. In all force field cases, the nature of dendrimer-lipid interactions is invariant with the explicit water solvent model (TIP3P/SPC) used in the simulation.

repulsive having a barrier of ∼20 kcal/mol at the lipid headgroup water interface. The PMF profile of the CHARMM dendrimer along the bilayer normal in the presence of explicit (TIP3P) solvent is in sharp contrast to the attractive binding observed by Kelly et al.44 where the PMF for the G3 dendrimer was obtained using implicit (distance dependent dielectric constant) solvent simulations with the CHARMM22 force field. This casts a doubt on the validity of using implicit solvent simulations while simulating dendrimer-membrane interactions. We believe that solvation of the dendrimer plays a major role and modulates the dendrimer-lipid interaction. This is due to the strong dependency of the interaction between dendrimer and lipid membranes on solvent models, which is discussed later in this study. The situation is dramatically different in the case of the GROMOS dendrimer. In contrast to the CHARMM and GAFF dendrimers, the PMF profile of the GROMOS dendrimer shows that the dendrimer-lipid interaction is attractive as shown in Figure 4 with a binding energy of ∼40 kcal/mol. This is in a similar range as the binding energy of 50 kcal/mol

in Figure 3. The binding behavior of the G3 PAMAM dendrimer in the presence of the DMPC lipid membrane is preserved in all cases. In order to understand the dependency of the explicit water models (TIP3P/SPC) on the observed dendrimer-lipid interactions, we also performed simulations using GAFF and GROMOS FFs with TIP3P water (Figure 3). The results of the GAFF/GROMOS force fields with TIP3P water (Figure 3) were quantitatively similar to the results obtained with the GAFF/GROMOS force fields with SPC water (Figure 2). These results indicate that the nature of dendrimer-lipid interactions is not influenced by the choice of the explicit (TIP3P/SPC) water models used in our simulations. Potential of the Mean Force Calculations along the Bilayer Normal. Potential of the mean force (PMF) of the dendrimer along the bilayer normal is obtained in order to understand the influence of different force fields on the binding free energy of the dendrimer with the lipid membrane in the presence of explicit water. The PMF profiles of CHARMM and GAFF dendrimers show that the dendrimer-lipid interaction is F


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and lipid are favorable in dendrimer binding (Figures 5a and 5d), whereas the dendrimer-water and dendrimer-ions nonbonded energy contributions are unfavorable in dendrimer binding (Figures 5b, 5e, 5c, and 5f). The asymmetry in hydration of dendrimer near the lipid−water interface causes a positive enthalpy change in the dendrimer-water energy contributions which is unfavorable for dendrimer-lipid binding. We also find that both LJ and electrostatic contributions to the dendrimer-lipid interaction energy are higher for the GROMOS dendrimer when compared to the CHARMM and GAFF dendrimers (Figures 5a and 5d). For the GROMOS dendrimer, the higher dendrimer-lipid attractive interaction energy overcomes the repulsive interaction energy between dendrimer and solvent, to facilitate strong dendrimer-membrane binding. Thus, the PMF profile for the GROMOS dendrimer is distinctly attractive, contrasting the repulsive nature of the PMF for the CHARMM and GAFF dendrimers. Dendrimer Hydration and Its Structure. Hydration energy of the dendrimer is one of the key parameters which govern dendrimer interactions with the lipid membrane. Dendrimer hydration can be quantified using bound water analysis as described in the Methods section. Here, we have calculated inner, surface, and bulk bound water (ninner, nsurf, and nbulk) of dendrimer along the bilayer normal to understand the changes in hydration, while the dendrimer binds to the lipid membrane as shown in Figures 6a, 6b, and 6c. The number of inner bound water molecules (ninner) which are bound in the interior parts of dendrimer is constant and independent of the dendrimer-membrane distance (Figure 6a). In contrast to the number of inner bound water (ninner), the surface and bulk bound water (nsurf and nbulk) decrease as the dendrimers approach the lipid−water interface (Figures 6b and 6c). The number of inner and bulk water (ninner and nbulk) is the same for all three different FF (CHARMM, GAFF, and GROMOS), but the number of surface bound water of the GROMOS dendrimer is lower when compared to the number of surface

Figure 4. Potential of the mean force (PMF) of the G3-PAMAM dendrimer along the bilayer normal using different available dendrimer and lipid force fields. PMF profiles conclude that the dendrimermembrane interaction is attractive (−41 kcal/mol) in the case of GROMOS, whereas the interaction is repulsive (+20 kcal/mol) in the case of both the CHARMM and GAFF force fields.

reported by Kim et al.,54 for a neutral amine terminated G3 PAMAM dendrimer (GROMOS86) with a DPPC bilayer. Equilibrium simulations as well as free energy calculations conclude that the GROMOS dendrimer binds strongly to the lipid membrane, whereas the CHARMM and GAFF dendrimers do not bind to the lipid bilayer in the presence of explicit water. These contrasting results are surprising and disconcerting, as these are widely used FFs to study dendrimer solution properties as well as various lipid properties. In fact both these FFs accurately predict properties of dendrimer solutions and lipid bilayers in good agreement with experimental data.24,49,63,82 In order to understand the FF dependence of the PMF profiles of dendrimer, we have computed different components of the nonbonded energy contributions for all the cases as shown in Figure 5 during the PMF calculation. We find that both the LJ and electrostatic interactions between dendrimer

Figure 5. Partitioning of potential energy contributions between dendrimer and other components obtained during the PMF computation. LennardJones energy of (a) dendrimer-lipid, (b) dendrimer-water, and (c) dendrimer-ions and electrostatic energy of (d) dendrimer-lipid, (e) dendrimerwater, and (f) dendrimer-ions. Parts (a) and (d) clearly show that strong nonbonding (both Lennard-Jones and electrostatic) interactions between the GROMOS dendrimer and lipid results in favorable binding of the GROMOS dendrimer with the DMPC lipid membrane. G


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Figure 6. Number of bound water molecules quantifies the extent of dendrimer hydration. Here ninner, nsurf, and nbulk are the (a) inner, (b) surface, and (c) bulk bound water molecules respectively of the dendrimer obtained during the PMF computation along the membrane normal. (d) Number of hydrogen bonds (nh) between dendrimer and water as a function of the dendrimer-membrane distance. Surface bound water molecules of the GROMOS dendrimer are lower when compared to those of CHARMM and GAFF dendrimers. This results in a reduction in the number of hydrogen bonds for the GROMOS dendrimer.

Figure 7. (a) Radius of gyration (Rg), (b) asphericity (δ), aspect ratios (c) Iz/Iy, and (d) Iz/Ix are quantification of size and shape of dendrimer as a function of the dendrimer-membrane distance during the PMF computation. The Rg, asphericity, and aspect ratios of dendrimer fluctuate along the bilayer normal.

with those of CHARMM and GAFF dendrimers due to its lower surface hydration. The difference in nh between the other dendrimers and the GROMOS dendrimers, Δnh = 20, when the dendrimer is away from the lipid membrane increases to Δnh = 35 when the dendrimer reaches the surface of membrane. This increase in Δnh is consistent with the different trends in the

water of CHARMM and GAFF dendrimers (Figure 6b). The number of hydrogen bonds (nh) between dendrimer and water is also a measure of dendrimer hydration. The number of hydrogen bonds (nh) between dendrimer and water as a function of dendrimer-membrane distance is shown in Figure 6d. The nh of the GROMOS dendrimer is lower in comparison H


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Figure 8. a) Potential and (b) electrostatic field profiles along the lipid membrane normal for all three force fields. The dashed lines correspond to the “FREE” case where the dendrimer is not present in the simulation, and the solid lines correspond to the “ADS” case where the dendrimer is also present along with the DMPC membrane, water, and ions. The lipid headgroup region is colored in brown, and the region where water is present is shown in gray. The large gradient of the GROMOS potential at the lipid−water interface in both FREE and ADS cases is the key difference when compared with GAFF and CHARMM potentials. This implies that the GROMOS DMPC lipid prefers adsorption of positively charged dendrimer terminal groups, due to the negative electric field in this region (b).

(∼±20 Å), which is the major difference when compared with GAFF and CHARMM. In the electric field profile, we see the formation of a distinct negative region located beneath the lipid−water interface (Figure 8(b)) for the GROMOS FF, absent in the CHARMM and GAFF. The electric fields in the case of CHARMM and GAFF are always positive, as expected from the potential profiles. We believe that these differences in the electrostatic potential profiles, which are the properties of the underlying force field parameters, dictate the adsorption behaviors observed in this study. Dendrimer Interactions with Lipid Membrane in Implicit Solvent. Our PMF calculations in explicit solvent using both CHARMM and GAFF FFs showed that the dendrimer does not bind to the DMPC bilayer, and the positive free energy implies a repulsive interaction with the bilayer. This is in contrast to the earlier report by Kelly et al.,44,84 where they report an attractive PMF using a distance dependent dielectric implicit solvent model in combination with CHARMM FF. To compare the effect of solvent models (explicit vs implicit) on the nature of dendrimer-membrane interaction, we perform MD simulations of the G3 PAMAM-DMPC system using CHARMM FF with the Generalized Born (GB)62 implicit solvent. The nature of dendrimer-membrane interactions in implicit solvent simulations is in sharp contrast to the trends obtained from the explicit solvent simulations. We find that the dendrimer is flattened and remains strongly bound to the lipid head groups in the case of the implicit solvent as shown in Figure 9a. This is in contrast to the simulation using explicit solvent, where the dendrimer moves away from the membrane surface as shown in Figure 9b. The time evolution of the distance of the dendrimer from bilayer center as well as the time evolution of the number of close contacts between the dendrimer and bilayer as shown in Figures 10a and 10b also confirms that the dendrimer is strongly bound to the lipid membrane in implicit solvent simulations. We speculate that the absence of a hydration layer or explicit bound water molecules in the vicinity of dendrimer could result in the attractive interaction between dendrimer and lipid membrane in the presence of implicit solvent. Hence the barrier for desolvating the dendrimer is expected to be lower for the case of the implicit solvent. Next, we compute the PMF of the dendrimer using CHARMM and GAFF FFs with both an implicit solvent and explicit solvent representation to compare the dendrimer binding strength with the lipid bilayer. The PMF profiles of

PMF profiles for different cases. The lower number of surface water and corresponding reduction in the number of hydrogen bonds along with a higher dendrimer-lipid interaction energy results in a stronger affinity for the GROMOS dendrimer which preferentially binds to the DMPC lipid membrane. We have also calculated several structural properties of the dendrimer such as radius of gyration, aspect ratios, and asphericity as a function of distance from the bilayer and have plotted them in Figures 7a, 7b, 7c, and 7d. The dendrimer undergoes large size and shape fluctuations while coming toward the lipid membrane, and these fluctuations are minimum at a distance of ∼35 Å from lipid center. We find that there is a rise in the value of Rg, and aspect ratios as the dendrimer move closer to the surface of the membrane. This rise in Rg and the aspect ratios of the dendrimer are due to the deformation of the dendrimer on the surface of the membrane. Microscopic Origin of Dendrimer Binding to GROMOS Lipid. To understand the microscopic origin of why the dendrimer binds to GROMOS lipid but not to the CHARMM and GAFF lipids, we have calculated the mean electrostatic potential (Figure 8a) and fields (Figure 8b) along the lipid bilayer normal. The electrostatic potential V(z) is obtained by carrying out a double integration of the charge density, ρ(z) using the following expression V (z ) = −

1 εo

∫0

z

dz′

∫0

z

′

ρ(z ′′)dz ′′

(4)

where ε0 is the free space permittivity. Here z = 0 represents the center of the lipid bilayer where the electrostatic potential and field are set to zero.83 The electric field can be obtained using E (z ) =

1 εo

∫0

z

ρ(z′)dz′

(5)

We have calculated the potentials and fields for two different sets of simulations, one where the dendrimer is absent which we refer to as the FREE case and one where the dendrimer is present which we denote as the ADS case. Both of these sets of simulations are performed at the same salt concentration level (0.15 M NaCl). The averaged potential and field profiles (over last 10 ns of the simulation time) shown in Figure 8(a) and (b) are not very different in both the simulations, suggesting that the charges redistribute among themselves to maintain the same potential in both the cases. The potential in the case of GROMOS is slightly positive near the lipid−water interface I


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distance 25 to 50 Å compared to those seen in explicit solvent simulations. The dendrimer stretches its branches and elongates in implicit solvent due to the increased dendrimerlipid attraction. Our calculation shows that the dendrimer interaction with the lipid membrane strongly depends on the solvent models, and hydration effects play an important role in capturing dendrimer-membrane interactions.

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SUMMARY AND CONCLUSIONS We have carried out all-atom MD simulations to study the interaction of PAMAM dendrimers with a DMPC lipid bilayer using various available force fields (CHARMM, GAFF, and GROMOS) in explicit water solvent to assess the differences between these widely used force fields on dendrimer-lipid interactions. We observe that with the CHARMM and GAFF FFs, the dendrimers prefer to remain solvated in the bulk aqueous regions away from the bilayer during the course of the simulation. In sharp contrast, the dendrimer remains adsorbed on the surface of lipid bilayer bound to the lipid head groups in the case of the GROMOS FF. Potential of the mean force (PMF) computations of the dendrimer along the bilayer normal reveal a repulsive barrier (∼20 kcal/mol) between dendrimer and lipid bilayer in the case of CHARMM and GAFF FFs but in the case of the GROMOS FF; the nature of interaction is strongly attractive (∼40 kcal/mol). The different behavior of the GROMOS dendrimer is due to higher electrostatic and van der Waals interaction between the dendrimer and lipid as well as the lower surface hydration of the dendrimer when compared to CHARMM and GAFF dendrimers. Additionally, there is a reduction in dendrimer hydration as well as number of dendrimer-water hydrogen bonds when the dendrimer binds to the membrane. In all cases the dendrimer undergoes large size/shape fluctuations, while the dendrimer is moved toward the surface of the lipid membrane. To understand the microscopic origin of the dendrimer binding to the GROMOS lipid, we have also calculated the mean electrostatic potential and field on the bilayer surface and show a clear correlation between the membrane potential and dendrimer binding; GROMOS lipid gives rise to a large gradient in the field on the bilayer surface which appears to drive the bind of the positively charge dendrimer. We have also studied the effect of solvent models on dendrimer-membrane interactions. It has been observed that the CHARMM dendrimer is strongly bound to the lipid bilayer in the presence

Figure 9. Initial and final simulation snapshots of the protonated G3PAMAM CHARMM dendrimer on the DMPC lipid membrane using different solvent models: a) GBIS and b) TIP3P. The CHARMM dendrimer strongly binds to the lipid membrane in the presence of implicit solvent, whereas the same dendrimer moves away from the surface of the lipid membrane without binding in the presence of explicit water solvent. This indicates that the dendrimer-lipid interactions are strongly dependent on the solvent model.

the G3 PAMAM dendrimer as a function of distance along the bilayer normal are shown in Figures 11a and 11b. The PMF profile of the CHARMM dendrimer in the presence of implicit solvent (Figure 11a) shows that the dendrimer-membrane interaction is attractive, and the binding strength is ∼80 kcal/ mol while there exists a repulsive barrier of ∼20 kcal/mol in the presence of explicit water solvent (Figure 11b). The attractive interaction between dendrimer and lipid membrane in the presence of the GB implicit solvent model is consistent with the earlier reports by Kelly et al.;44 a distant dependent dielectric (ε=4rε0) implicit solvent model was used. Structural properties of dendrimer such as Rg, asphericity, and aspect ratios along the bilayer normal are also calculated in the presence of implicit solvent (GB) model and compared with those obtained in explicit water (Figures 12a, 12b, 12c, and 12d). The Rg of dendrimer in GB solvent model is smaller compared to that obtained in explicit water simulations due to the continuum treatment solvent effects nearer to the dendrimer surface. A high deformation in size and shape of dendrimer is observed in the presence of implicit solvent at the

Figure 10. (a) Distance between the center of mass of the dendrimer and the center of mass of the lipid membrane and (b) number of contacts between the dendrimer and lipid membrane using different solvent models. The distance and number of contacts profiles show that the dendrimer is adsorbed on the surface of the lipid membrane in the presence of implicit solvent (Generalized Born; GB), whereas the dendrimer moves away from the lipid membrane in the presence of explicit TIP3P water model for the solvent. J


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Figure 11. Potential of the mean force (PMF) of the G3-PAMAM dendrimer along the bilayer normal using different solvent models: a) GB and b) TIP3P. The nature of the dendrimer-membrane interaction is attractive in the presence of implicit solvent, whereas the same dendrimer-lipid interactions become repulsive in the presence of explicit water solvent for both CHARMM and GAFF dendrimers. These PMF profiles confirm that the nature of dendrimer-lipid interaction strongly depends on the solvent model.

Figure 12. (a) Radius of gyration (Rg) (b) asphericity (δ), and aspect ratios (c) Iz/Iy and (d) Iz/Ix of the G3 PAMAM dendrimer as a function of dendrimer-lipid distance along the bilayer normal in the presence of different solvent models (GB and TIP3P). High deviation in size and shape of dendrimer is observed in the presence of the implicit solvent model compared to those of explicit solvent simulations at a distance of 25−50 Å.

dendrimer-membrane system. Only in the case of the united atom GROMOS force field, we observe an attractive interaction with the membrane in explicit solvent. Our observation is consistent with recent MD simulation results of Kim et al.,54 where a GROMOS FF with explicit solvent resulted in an attractive interaction with both DPPC and DOPG membranes. Binding of the G3 dendrimer with zwitterionic membranes is consistent with several experimental observations where smaller generation PAMAM dendrimers (G2-G4) have been shown to bind to the membrane without causing membrane disruption.28,40,41,46 Hence, the experimentally26,45,46 observed behavior of the G3 PAMAM dendrimer is reproduced by GROMOS FF, whereas the GAFF and CHARMM FFs do not capture the experimental observations in the presence of explicit water solvent. However, in the implicit solvent simulation, we observe G3 PAMAM dendrimer binding to DMPC in both the GAFF and CHARMM simulation. Specific studies with G3 dendrimers show binding and partial membrane penetration as observed in our study (with the

of an implicit solvent (GB), whereas binding is not observed in the presence of an explicit water solvent. The contrasting dendrimer-membrane interactions with explicit and implicit solvents lead us to conclude that hydration effects and desolvation barriers play an important role in accurately capturing dendrimer-lipid interactions. This is reflected in part, by the binding observed with the united atom GROMOS FF with explicit water (TIP3P/SPC) where reduced hydration and hydrogen bonding is observed, when compared with the all-atom CHARMM and GAFF force fields. In order to reconcile the different dendrimer binding scenarios for the different force fields used in this study as well as in the published literature, we have summarized the binding energies reported for PAMAM dendrimer-membrane systems in Table 3. An attractive binding energy is obtained for G3 dendrimers by Kelly et al.,44,46 with different surface charges on the dendrimers using the CHARMM force field with an implicit solvent model. In contrast, our results with an explicit solvent model result in a repulsive interaction for the similar K


L

negative

positive

positive

positive

positive

neutral

positive

positive

G344

G3 (this study) G3 (this study) G3 (this study) G3 (this study) G3 (this study) G354

G354

G439

G439

G333

G442/G540

G538

G538

G4 /G5

40

neutral

G344

42

positive

G344

positive

PEGylation (partially charged) /neutral positive

positive

positive

positive

positive

charge

generation

force field

DPD

all-atom CHARMM22 with implicit solvent all-atom CHARMM22 with implicit solvent all-atom CHARMM22 with implicit solvent all-atom CHARMM22 with explicit solvent all-atom CHARMM22 with implicit solvent all-atom GAFF with explicit solvent all-atom GAFF with implicit solvent united-atom GROMOS with explicit solvent united-atom GROMOS with explicit solvent united-atom GROMOS with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent DPD

PAMAM dendrimer

DPPC

DMPC/ DPPC DMPC/ DPPC DPPC

DPPC/ DPPG DPPC/ DPPG POPC

POPG

DPPC

DMPC

DMPC

DMPC

DMPC

DMPC

DMPC

DMPC

DMPC

name

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

anionic

anionic

anionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

zwitterionic

charge

force field

DPD

all-atom CHARMM27 with implicit solvent all-atom CHARMM27 with implicit solvent all-atom CHARMM27 with implicit solvent all-atom CHARMM36 with explicit solvent all-atom CHARMM36 with implicit solvent all-atom Lipid14 with explicit solvent all-atom Lipid14 with implicit solvent united-atom GROMOS with explicit solvent united-atom GROMOS with explicit solvent united-atom GROMOS with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent coarse-grained MARTINI with explicit solvent DPD

lipid membrane

Table 3. Nature of Dendrimer Interactions with Lipid Membrane with Different Studies

interaction strength of G5 terminals-lipid heads is strong interaction strength of G5 inner-lipid tails is strong

attractive

attractive

attractive

repulsive

attractive

attractive

attractive

attractive

attractive

repulsive

attractive

repulsive

attractive

attractive

attractive

interaction

penetrated inside the membrane penetrated inside the membrane adsorbed on the surface of membrane adsorbed on the surface of membrane penetrated inside the membrane

−83 (pH = ∼7) −60 (pH = ∼5) +41 (pH = ∼10)

−88

−50

−41

−33

+20

−81

+23

−47

−26

−36

free energy of binding (kcal/mol)

Journal of Chemical Theory and Computation Article


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Journal of Chemical Theory and Computation GROMOS FF) as well as in the study by Kim et al.54 Interestingly coarse-grained models such as MARTINI and DPD are also in agreement with experimental findings for larger G5 dendrimers, indicating that solvent effects are implicitly captured despite different levels of coarse graining. We finally mention that the choice of force field as well as the treatment of the solvent (explicit vs implicit) can influence the binding energies for dendrimer-membrane systems, and a judicious choice of the force field is required to connect molecular dynamics simulations with experimental observations. Accurate force fields with improved predictability will enhance our molecular level understanding of dendrimermembrane interactions which can potentially lead to the development of using dendrimers as suitable drug and gene delivery vehicles.

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AUTHOR INFORMATION

Corresponding Authors

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

Subbarao Kanchi: 0000-0001-9147-0101 K. G. Ayappa: 0000-0001-7599-794X Prabal K. Maiti: 0000-0002-9956-1136 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank DST, India for financial support and Supercomputer Education and Research Center, (SERC) IISc Bangalore for providing access to the high-performance supercomputer SahasratT. We also thank Christopher Kelly and Yongbin Kim for providing the CHARMM and GROMOS parameters for PAMAM dendrimer respectively. S.K. thanks UGC (University Grants Commission, India) and M.G. thanks CSIR (Council of Scientific and Industrial Research) for the research fellowships.

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