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Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations
Accepted Manuscript Title: Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations Author: Hwankyu Lee PII: DOI: Reference:
S1093-3263(16)30229-7 http://dx.doi.org/doi:10.1016/j.jmgm.2016.09.014 JMG 6758
To appear in:
Journal of Molecular Graphics and Modelling
Received date: Revised date: Accepted date:
11-6-2016 21-9-2016 22-9-2016
Please cite this article as: Hwankyu Lee, Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations, Journal of Molecular Graphics and Modelling http://dx.doi.org/10.1016/j.jmgm.2016.09.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations
Hwankyu Lee*
1
Department of Chemical Engineering, Dankook University, Yongin, 448-701, South Korea
*Corresponding author Email: [email protected]
1
Graphical abstract
PLL/HA bilayer Higher diffusivity More dense Thinner bilayer
vs. Lower diffusivity Less dense Less salt effect for larger PLL
Thicker bilayer
Highlights We performed MD simulations of PLL/HA bilayers with lipid membranes. Larger PLLs have lower diffusivities than do smaller ones. Larger PLLs are less densely stacked on membrane, leading to the thicker bilayer.
Abstract Polyelectrolyte bilayers, which consist of poly-L-lysine (PLL) and hyaluronic acid (HA) were simulated with lipid membranes at different temperatures and ion concentrations. Starting with the sequential deposition of PLL and HA above the membrane surface, PLL and HA become completely mixed, leading to the formation of stable bilayers. PLL/HA bilayers are thicker at higher salt concentration because of weakened electrostatic interactions between PLLs and membrane lipids, in agreement with experiments. This salt effect decreases as PLL size increases. Also, bilayers become thinner at higher temperature because of the increased surface area of membrane. In particular, regardless of temperature and salt concentration, larger PLLs induce thicker bilayers, although larger PLLs have lower diffusivities than do smaller ones. Bilayers with larger PLLs show larger vacancy (more water) inside the bilayer, indicating that larger PLLs are less densely stacked on membrane 2
surface than do smaller ones and thus form the thicker bilayer. These findings show the lower diffusivity of larger polyelectrolytes, which supports the experimental observation regarding the restricted diffusion of large polymers, and also imply the dependence of bilayer thickness on the polymer size. Keywords: MD simulation layer-by-layer film polyelectrolyte multilayer lipid membrane
Introduction Layer-by-layer (LBL) assembly of polyelectrolytes has shown promise as functional thin films for drug delivery applications because the deposition of polymer layers is controllable, reproducible, robust, and versatile.[1-4] Polyelectrolyte multilayers, whose conformation and stability can be modulated by the properties and interactions of anionic and cationic polymers, can encapsulate drug or ligand molecules and deliver those to the desired site.[5] Also, polyelectrolyte multilayers have been applied to control cellular behaviors such as adhesion, differentiation, and toxicity, since cellular behaviors can be controlled by adjusting thickness and mechanical strength of multilayers coated on the cell surface.[6] To increase the efficiency for these applications, formation and growth mechanism of polyelectrolyte multilayers and their interactions with cell membranes need to be understood, which has motivated many experimental and theoretical studies. In particular, the multilayer composed of poly-L-lysine (PLL) and hyaluronic acid (HA) has been widely studied.[7-9] 3
Experiments have revealed the dependence of the structure, growth, and stability of the PLL/HA multilayer on the solution pH, temperature, ionic strength, charge density and molecular weight of polymers. Picart, Schaaf, Lavalle, and coworkers observed the exponentially growing multilayers during the first few depositions of each layer because of diffusion of polyelectrolytes through the LBL film, while multilayers linearly grow when layers become too thick and hence do not allow diffusion of polyelectrolytes through the entire film.[10-14] Also, polyelectrolytes with higher charge densities yield denser multilayers because of strong electrostatic interactions,[15] while higher temperature and salt concentration make multilayers thicker.[16, 17] In particular, Porcel et al. found that PLL of low molecular weight can diffuse through the PLL/HA multilayer, while diffusion of large ones is limited to the film surface.[18] To confirm this, multilayer diffusivity and its effect on the multilayer conformation need to be understood at nearly the atomic scale, as can be done using molecular dynamics (MD) simulations. To understand the growth mechanism of LBL multilayers, simulations and theoretical studies have been performed. A scaling model for the multilayer formation of semiflexible polymers was developed,[19] and the influence of electrostatic and non-electrostatic interactions on multilayer formation was investigated.[20, 21] Dobrynin et al. performed coarse-grained (CG) MD simulations of polyelectrolytes intermixed through layers and showed that the structure and stability of multilayers can be modulated by charge density and the degree of polymerization.[22-28] Hoda and Larson developed a simple one-dimensional model and found that films exponentially grow when there is an energetic barrier at the film surface.[29] Using all-atom models with explicit water, our group recently simulated three PLL/HA bilayers deposited on lipid membranes, showing that less protonation of PLL-amine 4
groups, higher temperature, and lower salt concentration induce an increase in diffusivity of PLL and HA because of the weakened PLL-HA interaction with many fewer hydrogen bonds.[30] Although these simulations have successfully complemented experimental observations regarding the multilayer swelling and growth mechanism, the effect of PLL size on multilayer conformation and diffusivity at different temperatures and salt concentrations has not yet been systematically quantified through computation. In this work, we therefore perform all-atom MD simulations of a PLL/HA bilayer on the lipid membrane with explicit water at different temperatures and salt concentrations, showing that PLLs of different molecular weights and HAs are well intermixed and form stable bilayers, but their conformations and dynamics differ. Effects of temperature and salt concentration on the PLL/HA-bilayer conformation and dynamics are analyzed by calculating the bilayer thickness, diffusivity, and the interaction strength. In particular, we will show that these effects depend on the polymer size, which supports experimental results regarding the restricted diffusion of large polymers and suggests the dependence of PLL/HA-bilayer thickness on the polymer size.
Methods All simulations and analyses were performed using the GROMACS5.0.4 simulation package [31-33] with the OPLS all-atom force field (FF).[34, 35] Atomic coordinates of 5, 10, and 20-resiude PLLs (respectively, called PLL5, PLL10, and PLL20) were generated in an initially α-helical structure using Swiss-Pdb viewer [36] and equilibrated in TIP4P water at 310 K, leading to the equilibrated configuration of random coils. For HA, we previously downloaded the coordinates of a short 4-monomer oligomer of HA from the Protein Data 5
Bank (PDB code: 3HYA) [37] and generated their potential parameters using the MKTOP tool [38] and the ATB2.2 (Automated Topology Builder) web server [39, 40], which successfully captured the dependence of the multilayer dynamics and stability on temperature, salt concentration, and the protonation state, favorably compared with the experimental observations of the multilayer swelling.[30] Potentials for palmitoyloleoylglycerophosphocholine (POPC) lipids were taken directly from the Berger lipid FF,[41] which was further modified to be compatible with the OPLS FF by Tieleman et al.[42] We previously showed that this modified lipid FF reproduces the area per lipid of 64.6 ± 0.2 Å2 at 298 K for the POPC membrane,[43] in good agreement with the experimental value of 64.3 Å2 at 303 K.[44, 45] A polyelectrolyte bilayer, which consists of PLLs and HAs, was initially placed above the membrane surface, as shown in Figure 1. To include the same amount of lysines and achieve neutrality, 25 HAs (4 e- per HA) were simulated with 20 PLL5, 10 PLL10, or 5 PLL20 molecules (respectively, 5, 10, and 20 e+ per PLL). Note that our previous simulations showed that more than five PLL20 molecules do not form a stable layer [30], and thus here five PLL20 were used for the PLL leaflet of the bilayer. The final simulated system consists of a PLL/HA bilayer, 128 POPC lipids, and ~10700 water molecules in a periodic box of size 6.4 × 6.4 × 13 nm3. For the systems with the salt concentration of 0.5 M, 111 NaCl ions were also added. A pressure of 1 bar and a temperature of either 310 or 323 K were maintained by using the velocity-rescale thermostat [46] and the Parrinello-Rahman barostat [47] in an NPxyPzT ensemble with semi-isotropic pressure coupling. A real space cutoff of 12 Å was applied for Lennard-Jones and Coulomb potentials with the inclusion of particle mesh Ewald summation for long-range electrostatics.[48] The LINCS algorithm was used to constrain the 6
bond lengths.[49, 50] To obtain more samples, three simulations were performed for each system without restraints for 250 ns with a time step of 2 fs on computer facilities supported by the National Institute of Supercomputing and Networking/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC2015-C3-057). The last 50 ns-trajectories were used for analyses. The values were averaged from three replicate simulations, with standard errors signifying 95% confidence intervals.
Results and discussion Polyelectrolyte layers, which consist of PLL of different molecular weights and HA, were simulated with lipid membranes at different temperatures and salt concentrations. Simulated systems are listed in Table 1, where the first initial “P” and number indicate the number of lysine residues per PLL. The second initial and number “i500” describes the ionic concentration of 500 mM NaCl, while “t323” describes the temperature of 323 K. System names without “i” and “t”, respectively, indicate no salt addition and a temperature of 310 K. For example, “P5-i500” designates the system composed of 25 HA and 20 PLL5 (5 lysine residues per PLL) polymers with 500 mM NaCl at 310 K.
Conformation of a PLL/HA bilayer on lipid membrane Figure 1 shows snapshots from the beginning and end of simulations with PLL20. PLL and HA polymers, which were initially separately deposited above the lipid membrane, become mixed while still interacting with the membrane surface even at the high temperature and salt concentration, showing the formation of stable bilayers. This trend is similarly 7
observed for systems with PLL5 and PLL10. To quantify this bilayer formation, the thickness of the PLL/HA bilayer was calculated as a function of time. Here, the bilayer thickness is defined to be twice the distance between the average center of mass (COM) of the polymers and of the P atoms of the membrane leaflet adjacent to the PLL/HA bilayer in the membrane normal direction. Figure 2 shows that these values reach steady states within 200 ns, indicating PLL/HA bilayers are equilibrated within the simulated timescale. In Figure 2 (bottom), average bilayer thickness increases at lower temperature and higher salt concentration. Regardless of temperature and salt concentration, bilayer thickness is higher for P20 than for P5 and P10, showing that larger PLLs form the thicker bilayer. At 0.5 M NaCl, bilayer thicknesses do not significantly differ in the systems with P5, P10, and P20, indicating little effect of PLL size at high salt concentration. Note that different experimental methods have yielded different thicknesses of the PLL/HA bilayer. For instance, Burke and Barrett observed 0.5~1 nm per bilayer [15], while Porcel et al. observed 5~10 nm [18], indicating the effect of experimental conditions on the bilayer thickness. In our simulations, bilayer thicknesses are closer to those measured by Porcel et al. [18], although there are still methodological differences, which limits the quantitative comparison with experiments. These configurations and the extent of bilayer thickness are also confirmed by calculating mass and charge densities. In Figure 3, mass densities of PLL and HA are evenly distributed above membrane surfaces without alternate peaks, indicating that PLL and HA are completely intermixed. P20 shows the thicker PLL/HA bilayer than do P5 and P10, consistent with Figure 2. Also, the distributed extent of PLL and HA densities is in the order of P20-i500 > P20 > P20-t323, again confirming that lower temperature and higher salt concentration makes the PLL/HA layer thicker. This is presumably because the lipid membrane becomes 8
disordered and thinner at high temperature, and thus membrane surface area increases (areas per lipid of 65.1 and 68.4 Å2, respectively, for P5 and P5-t323), leading to the thinner PLL/HA bilayer to interact with the larger membrane surface. To understand the electrostatic distribution of polyelectrolyte layers, charge densities were also calculated. Figure 4 shows that charge densities are evenly distributed without alternate peaks, and their distributed extents are in the order of P20-i500 > P20 > P20-t323, similar to mass densities in Figure 3. Note that the deposition of polyelectrolyte layers is known to be achieved by overcharging the previous layer, which allows the next layer to be stably adsorbed. Since our work focuses on the layer thickness and dynamics rather than on the deposition mechanism, we simulated only one bilayer for each system, which is well equilibrated and thus completely intermixed. This implies that further growth of the multilayer is highly improbable because of the loss of the electrostatic force driving the LBL deposition, which is beyond the scope of this paper. These results indicate that the thickness of PLL/HA bilayers increases as the size of PLL increases, but this effect of PLL size becomes weakened at high salt concentration.
Interactions between PLL and lipid membrane As discussed above, PLL size influences the thickness of the PLL/HA bilayer at 0 M NaCl, but not at 0.5 M NaCl, indicating that the effect of PLL size depends on the salt concentration. To understand this, we calculated radial distribution functions (RDFs) between anionic lipid phosphates and cationic amines of PLL lysines. Figure 5 shows that, regardless of temperature and salt concentration, heights of RDF peaks are in the order of P5≈P10>P20, indicating that larger PLLs have weaker electrostatic interactions with lipid phosphates than do smaller PLLs. In particular, RDFs are much lower for the systems with 0.5 M NaCl than 9
for those without salt, indicating that the presence of salt ions significantly weakens the electrostatic interactions between PLL lysines and lipid phosphates, which can allow the swollen (thicker) PLL/HA bilayer. Since the PLL/HA layers become swollen at 0.5 M NaCl, the effect of larger PLL becomes relatively less dominant, as observed in Figures 2 and 3. To confirm this, we also calculated the number of water molecules within a distance of 2 nm from the membrane surface. Figure 6 shows that for P5 and P10 there are much more water molecules inside the PLL/HA bilayer at 0.5 M NaCl than at 0 M, indicating a larger inner vacancy at high salt concentration. However, for P20, the numbers of water molecules inside the bilayer do not differ at 0 M and 0.5 M NaCl, again indicating no effect of PLL size at high salt concentration. These indicate that salt ions weaken the polyelectrolyte-membrane interaction and thus make the film thicker, although this effect decreases as polyelectrolyte size increases.
Effect of PLL size on conformation and diffusivity of PLL/HA layers Since PLL size influences the thickness of PLL/HA bilayers, this PLL-size effect may be relevant to the polymer diffusivity. Also, note that experiments have shown that small PLL can diffuse through the entire PLL/HA layer, while diffusion of large PLL is restricted to the multilayer surface, indicating the effect of PLL size on diffusivity. To resolve this, diffusion coefficients of PLLs were calculated from the slope of the mean-square displacement of the COM of PLLs. Note that the finite size effect is not corrected here, since simulation boxes have almost the same geometry and hence should not affect the comparison of diffusivities from different systems. Table 2 shows diffusion coefficients obtained from three simulations for each system and their average values, which are plotted in Figure 7. 10
Larger PLLs show lower diffusivities, as expected. For all PLL sizes, diffusion coefficients are higher at higher temperature, apparently because of the reduced solvent viscosity. In particular, the effects of temperature and salt concentration on diffusivity are much more significant for PLL5 and PLL10 than for PLL20, indicating that larger PLLs induce less dependence of diffusivity on temperature and salt concentration, consistent with Figure 2 that shows no significant effect of PLL size on the PLL/HA-layer thickness at 0.5 M NaCl. Note that PLL5 and PLL10 are smaller and thus have higher diffusivity than does PLL20, but PLL20 forms the thicker PLL/HA bilayer, which seems to indicate that polymers with lower diffusivity form the thicker bilayer. Figure 8 visualizes PLL backbones for the systems with PLL5 and PLL20, clearly showing that PLL5 are densely stacked on membrane surface, while PLL20 are sparsely distributed, apparently because of the larger size with linear shape. Also, Figure 6 shows that PLL/HA bilayers with PLL20 include much more water and hence larger vacancy than do those with PLL5 and PLL10, indicating that larger PLLs are stacked with larger vacancy and thus form the thicker bilayer. Note that the simulation and experimental environments and mass transport conditions differ, which precludes any quantitative comparison between simulations and experiments. For example, in experiments PLL and HA respectively consist of ~220 and ~1000-mers, which are much larger than the simulated PLL (5~20-mers) and HA (4-mers) because of the limited simulation size and time scale. Also, in the experiments each layer is deposited and then washed individually, which differs from the assembly process of a single PLL/HA bilayer in simulations. Thus, it cannot be ruled out that larger PLLs might interact more strongly with lipid membranes, leading to different conformations of PLL/HA bilayers. However, we have clearly shown that larger polymers have the lower diffusivity in multilayers, which supports 11
experiments that showed the restricted diffusion of large polymers [18], as well as imply that the effect of polymer size on the bilayer thickness may be due to the stacking conformation of polymers.
Conclusions We performed all-atom MD simulations of PLL/HA bilayers on lipid membranes with explicit water. PLLs of different sizes (5, 10, and 20 lysine residues per PLL) were simulated with and without NaCl at the temperatures of 310 and 323 K. PLL and HA molecules, which were initially sequentially deposited above the membrane surface, become completely mixed, showing the equilibrated conformation of stable bilayers. Thicker bilayers were observed at higher salt concentration because salt ions weaken charge interactions between polymers and lipid head groups, in agreement with experiments showing the swelling and even hole formation in the presence of salt. This salt effect decreases as PLL size increases. Bilayers are thicker at 310 K than at 323K, which conflicts with experiments performed with flat substrates, since lipid membranes are more disordered at higher temperature and thus have larger membrane surface, which makes PLL/HA bilayer thinner. In particular, we find that larger PLLs have lower diffusivities, but they form thicker bilayers regardless of temperature and salt concentration. This is because large PLLs may not be stacked on the membrane surface as densely as small PLLs do, and thus bilayers with large PLLs should include larger vacancy with more water, leading to the thicker bilayer. These simulation findings indicate that larger PLLs have lower diffusivity, which supports the experimental observation on the limited diffusion of large polymers, as well as imply that the dependence of bilayer thickness on polymer size is probably due to different stacking 12
conformations of differently-sized polymers.
Acknowledgments The present research was conducted by the research fund of Dankook University in 2015.
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Figure 1. Snapshots at the beginning (0 ns; left) and end (200 ns; columns 2-4) of simulations of PLL20. Initial configuration is shown only for P20, but this PLL/HA deposition on the lipid membrane is applied for all other systems. Orange and green colors respectively represent PLL and HA, while red and blue colors represent lipid heads (phosphates) and tails in the membrane. Water, Na+ and Cl- ions are shown as light blue, red, and blue dots, respectively. The images were created using Visual Molecular Dynamics.[51]
PLL20 (20 e+)
HA (4 e-)
19
Initial (P20)
P20
P20-i500
P20-t323
Figure 2. Thickness of the PLL/HA bilayer as a function of time (top), and average thickness
Thickness of the PLL/HA bilayer (nm)
of the PLL/HA-bilayer (bottom).
Average bilayer thickness (nm)
Time (ns)
310K, 0.5M NaCl
310K, 0M NaCl
323K, 0M NaCl
No. of lysine residues in PLL
20
Figure 3. Mass density profiles of POPC lipid heads (P atoms of phosphates), PLL, HA, and water.
Mass density (kg/m3)
P5
P10
P20
P20-i500
P20-t323
Simulation box (nm)
21
Figure 4. Charge density profiles of POPC lipid heads (lipid phosphates), PLL, HA, and water.
P5
Charge density (e/nm3)
P10
P20
P20-i500
P20-t323
Simulation box (nm)
22
Figure 5. Radial distribution functions (RDFs) between anionic lipid phosphates and cationic amines of PLL lysines.
310K, 0M NaCl
g (r)
310K, 0.5M NaCl
323K, 0M NaCl
r (nm)
23
Figure 6. Number of water molecules within a distance of 2 nm from the membrane surface (lipid phosphates) at 310 K, as a function of PLL size.
Number of water molecules close to the membrane surface
No. of waters within 2nm from membrane
0.5M NaCl
0M NaCl
No. of lysine residues in PLL
24
D (10-7 cm2 s-1)
Figure 7. Diffusion coefficients (D) of COMs of PLLs.
323K, 0M NaCl 310K, 0M NaCl 310K, 0.5M NaCl
No. of lysine residues in PLL
25
Figure 8. Snapshots of PLL backbones (orange ribbons) for PLL5 and PLL20.
PLL5
PLL20
26
Table 1. List of simulations.
No. of lysines Name per PLL (Mw) 5 (663) P5 P5-i500 P5-t323 10 (1308) P10 P10-i500 P10-t323 20 (2598) P20 P20-i500 P20-t323
No. of molecules PLL HA 20 25 20 25 20 25 10 25 10 25 10 25 5 25 5 25 5 25
27
Conc. of NaCl (mM) 0 500 0 0 500 0 0 500 0
Temp. (K) 310 310 323 310 310 323 310 310 323
No. of simulations 3 3 3 3 3 3 3 3 3
Table 2. Diffusion coefficients (D) of centers of mass (COM) of PLLs. Three values are presented from three simulations for each system.
P5 P5-i500 P5-t323 P10 P10-i500 P10-t323 P20 P20-i500 P20-t323
D (10-7 cm2 s-1) 1 2 2.10 ± 0.39 1.19 ± 0.34 0.74 ± 0.23 1.12 ± 0.28 1.78 ± 0.10 1.98 ± 0.29 1.52 ± 0.05 1.35 ± 0.24 0.98 ± 0.10 1.11 ± 0.44 1.63 ± 0.74 1.57 ± 0.10 0.90 ± 0.02 0.77 ± 0.13 0.52 ± 0.04 0.53 ± 0.27 0.99 ± 0.46 0.78 ± 0.17
28
3 0.97 ± 0.34 1.13 ± 0.39 1.73 ± 0.06 1.21 ± 0.30 0.76 ± 0.06 2.04 ± 0.42 0.47 ± 0.20 0.58 ± 0.02 0.93 ± 0.12
Average D 1.42 1.00 1.83 1.36 0.95 1.75 0.71 0.54 0.90
S1093-3263(16)30229-7 http://dx.doi.org/doi:10.1016/j.jmgm.2016.09.014 JMG 6758
To appear in:
Journal of Molecular Graphics and Modelling
Received date: Revised date: Accepted date:
11-6-2016 21-9-2016 22-9-2016
Please cite this article as: Hwankyu Lee, Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations, Journal of Molecular Graphics and Modelling http://dx.doi.org/10.1016/j.jmgm.2016.09.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of polyelectrolyte size on multilayer conformation and dynamics at different temperatures and salt concentrations
Hwankyu Lee*
1
Department of Chemical Engineering, Dankook University, Yongin, 448-701, South Korea
*Corresponding author Email: [email protected]
1
Graphical abstract
PLL/HA bilayer Higher diffusivity More dense Thinner bilayer
vs. Lower diffusivity Less dense Less salt effect for larger PLL
Thicker bilayer
Highlights We performed MD simulations of PLL/HA bilayers with lipid membranes. Larger PLLs have lower diffusivities than do smaller ones. Larger PLLs are less densely stacked on membrane, leading to the thicker bilayer.
Abstract Polyelectrolyte bilayers, which consist of poly-L-lysine (PLL) and hyaluronic acid (HA) were simulated with lipid membranes at different temperatures and ion concentrations. Starting with the sequential deposition of PLL and HA above the membrane surface, PLL and HA become completely mixed, leading to the formation of stable bilayers. PLL/HA bilayers are thicker at higher salt concentration because of weakened electrostatic interactions between PLLs and membrane lipids, in agreement with experiments. This salt effect decreases as PLL size increases. Also, bilayers become thinner at higher temperature because of the increased surface area of membrane. In particular, regardless of temperature and salt concentration, larger PLLs induce thicker bilayers, although larger PLLs have lower diffusivities than do smaller ones. Bilayers with larger PLLs show larger vacancy (more water) inside the bilayer, indicating that larger PLLs are less densely stacked on membrane 2
surface than do smaller ones and thus form the thicker bilayer. These findings show the lower diffusivity of larger polyelectrolytes, which supports the experimental observation regarding the restricted diffusion of large polymers, and also imply the dependence of bilayer thickness on the polymer size. Keywords: MD simulation layer-by-layer film polyelectrolyte multilayer lipid membrane
Introduction Layer-by-layer (LBL) assembly of polyelectrolytes has shown promise as functional thin films for drug delivery applications because the deposition of polymer layers is controllable, reproducible, robust, and versatile.[1-4] Polyelectrolyte multilayers, whose conformation and stability can be modulated by the properties and interactions of anionic and cationic polymers, can encapsulate drug or ligand molecules and deliver those to the desired site.[5] Also, polyelectrolyte multilayers have been applied to control cellular behaviors such as adhesion, differentiation, and toxicity, since cellular behaviors can be controlled by adjusting thickness and mechanical strength of multilayers coated on the cell surface.[6] To increase the efficiency for these applications, formation and growth mechanism of polyelectrolyte multilayers and their interactions with cell membranes need to be understood, which has motivated many experimental and theoretical studies. In particular, the multilayer composed of poly-L-lysine (PLL) and hyaluronic acid (HA) has been widely studied.[7-9] 3
Experiments have revealed the dependence of the structure, growth, and stability of the PLL/HA multilayer on the solution pH, temperature, ionic strength, charge density and molecular weight of polymers. Picart, Schaaf, Lavalle, and coworkers observed the exponentially growing multilayers during the first few depositions of each layer because of diffusion of polyelectrolytes through the LBL film, while multilayers linearly grow when layers become too thick and hence do not allow diffusion of polyelectrolytes through the entire film.[10-14] Also, polyelectrolytes with higher charge densities yield denser multilayers because of strong electrostatic interactions,[15] while higher temperature and salt concentration make multilayers thicker.[16, 17] In particular, Porcel et al. found that PLL of low molecular weight can diffuse through the PLL/HA multilayer, while diffusion of large ones is limited to the film surface.[18] To confirm this, multilayer diffusivity and its effect on the multilayer conformation need to be understood at nearly the atomic scale, as can be done using molecular dynamics (MD) simulations. To understand the growth mechanism of LBL multilayers, simulations and theoretical studies have been performed. A scaling model for the multilayer formation of semiflexible polymers was developed,[19] and the influence of electrostatic and non-electrostatic interactions on multilayer formation was investigated.[20, 21] Dobrynin et al. performed coarse-grained (CG) MD simulations of polyelectrolytes intermixed through layers and showed that the structure and stability of multilayers can be modulated by charge density and the degree of polymerization.[22-28] Hoda and Larson developed a simple one-dimensional model and found that films exponentially grow when there is an energetic barrier at the film surface.[29] Using all-atom models with explicit water, our group recently simulated three PLL/HA bilayers deposited on lipid membranes, showing that less protonation of PLL-amine 4
groups, higher temperature, and lower salt concentration induce an increase in diffusivity of PLL and HA because of the weakened PLL-HA interaction with many fewer hydrogen bonds.[30] Although these simulations have successfully complemented experimental observations regarding the multilayer swelling and growth mechanism, the effect of PLL size on multilayer conformation and diffusivity at different temperatures and salt concentrations has not yet been systematically quantified through computation. In this work, we therefore perform all-atom MD simulations of a PLL/HA bilayer on the lipid membrane with explicit water at different temperatures and salt concentrations, showing that PLLs of different molecular weights and HAs are well intermixed and form stable bilayers, but their conformations and dynamics differ. Effects of temperature and salt concentration on the PLL/HA-bilayer conformation and dynamics are analyzed by calculating the bilayer thickness, diffusivity, and the interaction strength. In particular, we will show that these effects depend on the polymer size, which supports experimental results regarding the restricted diffusion of large polymers and suggests the dependence of PLL/HA-bilayer thickness on the polymer size.
Methods All simulations and analyses were performed using the GROMACS5.0.4 simulation package [31-33] with the OPLS all-atom force field (FF).[34, 35] Atomic coordinates of 5, 10, and 20-resiude PLLs (respectively, called PLL5, PLL10, and PLL20) were generated in an initially α-helical structure using Swiss-Pdb viewer [36] and equilibrated in TIP4P water at 310 K, leading to the equilibrated configuration of random coils. For HA, we previously downloaded the coordinates of a short 4-monomer oligomer of HA from the Protein Data 5
Bank (PDB code: 3HYA) [37] and generated their potential parameters using the MKTOP tool [38] and the ATB2.2 (Automated Topology Builder) web server [39, 40], which successfully captured the dependence of the multilayer dynamics and stability on temperature, salt concentration, and the protonation state, favorably compared with the experimental observations of the multilayer swelling.[30] Potentials for palmitoyloleoylglycerophosphocholine (POPC) lipids were taken directly from the Berger lipid FF,[41] which was further modified to be compatible with the OPLS FF by Tieleman et al.[42] We previously showed that this modified lipid FF reproduces the area per lipid of 64.6 ± 0.2 Å2 at 298 K for the POPC membrane,[43] in good agreement with the experimental value of 64.3 Å2 at 303 K.[44, 45] A polyelectrolyte bilayer, which consists of PLLs and HAs, was initially placed above the membrane surface, as shown in Figure 1. To include the same amount of lysines and achieve neutrality, 25 HAs (4 e- per HA) were simulated with 20 PLL5, 10 PLL10, or 5 PLL20 molecules (respectively, 5, 10, and 20 e+ per PLL). Note that our previous simulations showed that more than five PLL20 molecules do not form a stable layer [30], and thus here five PLL20 were used for the PLL leaflet of the bilayer. The final simulated system consists of a PLL/HA bilayer, 128 POPC lipids, and ~10700 water molecules in a periodic box of size 6.4 × 6.4 × 13 nm3. For the systems with the salt concentration of 0.5 M, 111 NaCl ions were also added. A pressure of 1 bar and a temperature of either 310 or 323 K were maintained by using the velocity-rescale thermostat [46] and the Parrinello-Rahman barostat [47] in an NPxyPzT ensemble with semi-isotropic pressure coupling. A real space cutoff of 12 Å was applied for Lennard-Jones and Coulomb potentials with the inclusion of particle mesh Ewald summation for long-range electrostatics.[48] The LINCS algorithm was used to constrain the 6
bond lengths.[49, 50] To obtain more samples, three simulations were performed for each system without restraints for 250 ns with a time step of 2 fs on computer facilities supported by the National Institute of Supercomputing and Networking/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC2015-C3-057). The last 50 ns-trajectories were used for analyses. The values were averaged from three replicate simulations, with standard errors signifying 95% confidence intervals.
Results and discussion Polyelectrolyte layers, which consist of PLL of different molecular weights and HA, were simulated with lipid membranes at different temperatures and salt concentrations. Simulated systems are listed in Table 1, where the first initial “P” and number indicate the number of lysine residues per PLL. The second initial and number “i500” describes the ionic concentration of 500 mM NaCl, while “t323” describes the temperature of 323 K. System names without “i” and “t”, respectively, indicate no salt addition and a temperature of 310 K. For example, “P5-i500” designates the system composed of 25 HA and 20 PLL5 (5 lysine residues per PLL) polymers with 500 mM NaCl at 310 K.
Conformation of a PLL/HA bilayer on lipid membrane Figure 1 shows snapshots from the beginning and end of simulations with PLL20. PLL and HA polymers, which were initially separately deposited above the lipid membrane, become mixed while still interacting with the membrane surface even at the high temperature and salt concentration, showing the formation of stable bilayers. This trend is similarly 7
observed for systems with PLL5 and PLL10. To quantify this bilayer formation, the thickness of the PLL/HA bilayer was calculated as a function of time. Here, the bilayer thickness is defined to be twice the distance between the average center of mass (COM) of the polymers and of the P atoms of the membrane leaflet adjacent to the PLL/HA bilayer in the membrane normal direction. Figure 2 shows that these values reach steady states within 200 ns, indicating PLL/HA bilayers are equilibrated within the simulated timescale. In Figure 2 (bottom), average bilayer thickness increases at lower temperature and higher salt concentration. Regardless of temperature and salt concentration, bilayer thickness is higher for P20 than for P5 and P10, showing that larger PLLs form the thicker bilayer. At 0.5 M NaCl, bilayer thicknesses do not significantly differ in the systems with P5, P10, and P20, indicating little effect of PLL size at high salt concentration. Note that different experimental methods have yielded different thicknesses of the PLL/HA bilayer. For instance, Burke and Barrett observed 0.5~1 nm per bilayer [15], while Porcel et al. observed 5~10 nm [18], indicating the effect of experimental conditions on the bilayer thickness. In our simulations, bilayer thicknesses are closer to those measured by Porcel et al. [18], although there are still methodological differences, which limits the quantitative comparison with experiments. These configurations and the extent of bilayer thickness are also confirmed by calculating mass and charge densities. In Figure 3, mass densities of PLL and HA are evenly distributed above membrane surfaces without alternate peaks, indicating that PLL and HA are completely intermixed. P20 shows the thicker PLL/HA bilayer than do P5 and P10, consistent with Figure 2. Also, the distributed extent of PLL and HA densities is in the order of P20-i500 > P20 > P20-t323, again confirming that lower temperature and higher salt concentration makes the PLL/HA layer thicker. This is presumably because the lipid membrane becomes 8
disordered and thinner at high temperature, and thus membrane surface area increases (areas per lipid of 65.1 and 68.4 Å2, respectively, for P5 and P5-t323), leading to the thinner PLL/HA bilayer to interact with the larger membrane surface. To understand the electrostatic distribution of polyelectrolyte layers, charge densities were also calculated. Figure 4 shows that charge densities are evenly distributed without alternate peaks, and their distributed extents are in the order of P20-i500 > P20 > P20-t323, similar to mass densities in Figure 3. Note that the deposition of polyelectrolyte layers is known to be achieved by overcharging the previous layer, which allows the next layer to be stably adsorbed. Since our work focuses on the layer thickness and dynamics rather than on the deposition mechanism, we simulated only one bilayer for each system, which is well equilibrated and thus completely intermixed. This implies that further growth of the multilayer is highly improbable because of the loss of the electrostatic force driving the LBL deposition, which is beyond the scope of this paper. These results indicate that the thickness of PLL/HA bilayers increases as the size of PLL increases, but this effect of PLL size becomes weakened at high salt concentration.
Interactions between PLL and lipid membrane As discussed above, PLL size influences the thickness of the PLL/HA bilayer at 0 M NaCl, but not at 0.5 M NaCl, indicating that the effect of PLL size depends on the salt concentration. To understand this, we calculated radial distribution functions (RDFs) between anionic lipid phosphates and cationic amines of PLL lysines. Figure 5 shows that, regardless of temperature and salt concentration, heights of RDF peaks are in the order of P5≈P10>P20, indicating that larger PLLs have weaker electrostatic interactions with lipid phosphates than do smaller PLLs. In particular, RDFs are much lower for the systems with 0.5 M NaCl than 9
for those without salt, indicating that the presence of salt ions significantly weakens the electrostatic interactions between PLL lysines and lipid phosphates, which can allow the swollen (thicker) PLL/HA bilayer. Since the PLL/HA layers become swollen at 0.5 M NaCl, the effect of larger PLL becomes relatively less dominant, as observed in Figures 2 and 3. To confirm this, we also calculated the number of water molecules within a distance of 2 nm from the membrane surface. Figure 6 shows that for P5 and P10 there are much more water molecules inside the PLL/HA bilayer at 0.5 M NaCl than at 0 M, indicating a larger inner vacancy at high salt concentration. However, for P20, the numbers of water molecules inside the bilayer do not differ at 0 M and 0.5 M NaCl, again indicating no effect of PLL size at high salt concentration. These indicate that salt ions weaken the polyelectrolyte-membrane interaction and thus make the film thicker, although this effect decreases as polyelectrolyte size increases.
Effect of PLL size on conformation and diffusivity of PLL/HA layers Since PLL size influences the thickness of PLL/HA bilayers, this PLL-size effect may be relevant to the polymer diffusivity. Also, note that experiments have shown that small PLL can diffuse through the entire PLL/HA layer, while diffusion of large PLL is restricted to the multilayer surface, indicating the effect of PLL size on diffusivity. To resolve this, diffusion coefficients of PLLs were calculated from the slope of the mean-square displacement of the COM of PLLs. Note that the finite size effect is not corrected here, since simulation boxes have almost the same geometry and hence should not affect the comparison of diffusivities from different systems. Table 2 shows diffusion coefficients obtained from three simulations for each system and their average values, which are plotted in Figure 7. 10
Larger PLLs show lower diffusivities, as expected. For all PLL sizes, diffusion coefficients are higher at higher temperature, apparently because of the reduced solvent viscosity. In particular, the effects of temperature and salt concentration on diffusivity are much more significant for PLL5 and PLL10 than for PLL20, indicating that larger PLLs induce less dependence of diffusivity on temperature and salt concentration, consistent with Figure 2 that shows no significant effect of PLL size on the PLL/HA-layer thickness at 0.5 M NaCl. Note that PLL5 and PLL10 are smaller and thus have higher diffusivity than does PLL20, but PLL20 forms the thicker PLL/HA bilayer, which seems to indicate that polymers with lower diffusivity form the thicker bilayer. Figure 8 visualizes PLL backbones for the systems with PLL5 and PLL20, clearly showing that PLL5 are densely stacked on membrane surface, while PLL20 are sparsely distributed, apparently because of the larger size with linear shape. Also, Figure 6 shows that PLL/HA bilayers with PLL20 include much more water and hence larger vacancy than do those with PLL5 and PLL10, indicating that larger PLLs are stacked with larger vacancy and thus form the thicker bilayer. Note that the simulation and experimental environments and mass transport conditions differ, which precludes any quantitative comparison between simulations and experiments. For example, in experiments PLL and HA respectively consist of ~220 and ~1000-mers, which are much larger than the simulated PLL (5~20-mers) and HA (4-mers) because of the limited simulation size and time scale. Also, in the experiments each layer is deposited and then washed individually, which differs from the assembly process of a single PLL/HA bilayer in simulations. Thus, it cannot be ruled out that larger PLLs might interact more strongly with lipid membranes, leading to different conformations of PLL/HA bilayers. However, we have clearly shown that larger polymers have the lower diffusivity in multilayers, which supports 11
experiments that showed the restricted diffusion of large polymers [18], as well as imply that the effect of polymer size on the bilayer thickness may be due to the stacking conformation of polymers.
Conclusions We performed all-atom MD simulations of PLL/HA bilayers on lipid membranes with explicit water. PLLs of different sizes (5, 10, and 20 lysine residues per PLL) were simulated with and without NaCl at the temperatures of 310 and 323 K. PLL and HA molecules, which were initially sequentially deposited above the membrane surface, become completely mixed, showing the equilibrated conformation of stable bilayers. Thicker bilayers were observed at higher salt concentration because salt ions weaken charge interactions between polymers and lipid head groups, in agreement with experiments showing the swelling and even hole formation in the presence of salt. This salt effect decreases as PLL size increases. Bilayers are thicker at 310 K than at 323K, which conflicts with experiments performed with flat substrates, since lipid membranes are more disordered at higher temperature and thus have larger membrane surface, which makes PLL/HA bilayer thinner. In particular, we find that larger PLLs have lower diffusivities, but they form thicker bilayers regardless of temperature and salt concentration. This is because large PLLs may not be stacked on the membrane surface as densely as small PLLs do, and thus bilayers with large PLLs should include larger vacancy with more water, leading to the thicker bilayer. These simulation findings indicate that larger PLLs have lower diffusivity, which supports the experimental observation on the limited diffusion of large polymers, as well as imply that the dependence of bilayer thickness on polymer size is probably due to different stacking 12
conformations of differently-sized polymers.
Acknowledgments The present research was conducted by the research fund of Dankook University in 2015.
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Figure 1. Snapshots at the beginning (0 ns; left) and end (200 ns; columns 2-4) of simulations of PLL20. Initial configuration is shown only for P20, but this PLL/HA deposition on the lipid membrane is applied for all other systems. Orange and green colors respectively represent PLL and HA, while red and blue colors represent lipid heads (phosphates) and tails in the membrane. Water, Na+ and Cl- ions are shown as light blue, red, and blue dots, respectively. The images were created using Visual Molecular Dynamics.[51]
PLL20 (20 e+)
HA (4 e-)
19
Initial (P20)
P20
P20-i500
P20-t323
Figure 2. Thickness of the PLL/HA bilayer as a function of time (top), and average thickness
Thickness of the PLL/HA bilayer (nm)
of the PLL/HA-bilayer (bottom).
Average bilayer thickness (nm)
Time (ns)
310K, 0.5M NaCl
310K, 0M NaCl
323K, 0M NaCl
No. of lysine residues in PLL
20
Figure 3. Mass density profiles of POPC lipid heads (P atoms of phosphates), PLL, HA, and water.
Mass density (kg/m3)
P5
P10
P20
P20-i500
P20-t323
Simulation box (nm)
21
Figure 4. Charge density profiles of POPC lipid heads (lipid phosphates), PLL, HA, and water.
P5
Charge density (e/nm3)
P10
P20
P20-i500
P20-t323
Simulation box (nm)
22
Figure 5. Radial distribution functions (RDFs) between anionic lipid phosphates and cationic amines of PLL lysines.
310K, 0M NaCl
g (r)
310K, 0.5M NaCl
323K, 0M NaCl
r (nm)
23
Figure 6. Number of water molecules within a distance of 2 nm from the membrane surface (lipid phosphates) at 310 K, as a function of PLL size.
Number of water molecules close to the membrane surface
No. of waters within 2nm from membrane
0.5M NaCl
0M NaCl
No. of lysine residues in PLL
24
D (10-7 cm2 s-1)
Figure 7. Diffusion coefficients (D) of COMs of PLLs.
323K, 0M NaCl 310K, 0M NaCl 310K, 0.5M NaCl
No. of lysine residues in PLL
25
Figure 8. Snapshots of PLL backbones (orange ribbons) for PLL5 and PLL20.
PLL5
PLL20
26
Table 1. List of simulations.
No. of lysines Name per PLL (Mw) 5 (663) P5 P5-i500 P5-t323 10 (1308) P10 P10-i500 P10-t323 20 (2598) P20 P20-i500 P20-t323
No. of molecules PLL HA 20 25 20 25 20 25 10 25 10 25 10 25 5 25 5 25 5 25
27
Conc. of NaCl (mM) 0 500 0 0 500 0 0 500 0
Temp. (K) 310 310 323 310 310 323 310 310 323
No. of simulations 3 3 3 3 3 3 3 3 3
Table 2. Diffusion coefficients (D) of centers of mass (COM) of PLLs. Three values are presented from three simulations for each system.
P5 P5-i500 P5-t323 P10 P10-i500 P10-t323 P20 P20-i500 P20-t323
D (10-7 cm2 s-1) 1 2 2.10 ± 0.39 1.19 ± 0.34 0.74 ± 0.23 1.12 ± 0.28 1.78 ± 0.10 1.98 ± 0.29 1.52 ± 0.05 1.35 ± 0.24 0.98 ± 0.10 1.11 ± 0.44 1.63 ± 0.74 1.57 ± 0.10 0.90 ± 0.02 0.77 ± 0.13 0.52 ± 0.04 0.53 ± 0.27 0.99 ± 0.46 0.78 ± 0.17
28
3 0.97 ± 0.34 1.13 ± 0.39 1.73 ± 0.06 1.21 ± 0.30 0.76 ± 0.06 2.04 ± 0.42 0.47 ± 0.20 0.58 ± 0.02 0.93 ± 0.12
Average D 1.42 1.00 1.83 1.36 0.95 1.75 0.71 0.54 0.90