Mechanical properties of Ester- and Ether-DPhPC bilayers: a molecular dynamics study

Abstract

In addition to its biological importance, DPhPC lipid bilayers are widely used in droplet bilayers, study of integral membrane proteins, drug delivery systems as well as patch-clamp electrophysiology of ion channels, yet their mechanical properties are not fully measured. Herein, we examined the effect of the ether linkage on the mechanical properties of ester- and ether-DPhPC lipid bilayers using all-atom molecular dynamics simulation. The values of area per lipid, thickness, intrinsic lateral pressure profile, order parameter, and elasticity moduli were estimated using various computational frameworks and were compared with available experimental values. Overall, a good agreement was observed between the two. The global properties of the two lipid bilayers are vastly different, with ether bilayer being stiffer, less ordered, and thicker than ester bilayer. Moreover, ether linkage decreased the area per lipid in the ether lipid bilayer. Our computational framework and output demonstrate how ether modification changes the mechano-chemical properties of DPhPC bilayers.

1. Introduction

Biological membranes are an indispensable part of living cell. They separate the cells and the sub-cellular compartments from the extracellular environment, while enabling them to transport and communicate with their exterior. The main constituent of the cell membrane is the amphipathic lipid molecules, making it worthwhile to study the model membranes that are merely comprised of lipids. Composition of the lipid membrane, in most cases a bilayer made up of phospholipids, varies from cell to cell; making it possible for cells to perform different functions and survive under different environmental conditions [1–5].

Many of microorganisms that thrive under harsh conditions are grouped as a separate domain of life called Archaea which are evolutionarily distinct from Eukarya and Bacteria [6]. Archaeal lipids have a different chemical composition from that of Bacteria, allowing a better adaptation to various extreme conditions such as very high or low temperatures, extreme pH, and high pressure or salt concentrations. In contrast to lipids of other cells, most Archaeal lipids have regularly branched tails that are linked to the head groups via ether linkage. As a result of their unique lipid structure, Archaeal membranes are more stable and have a lower permeability to ions and water [7], higher viscosity [8], and higher density of packing [9].

Branched lipid tails are not limited to Archaea and can be found in Bacteria as well [10]. Chain branching has been investigated in experimental studies with a special interest in DPhPC (diphytanoyl-phosphatidylcholine) model membranes [11–13]. Molecular dynamics simulations have also been used as a valuable tool, providing an atomic resolution insight into the study of the branching effects. It has been shown in the previous studies that branching decreases permeability and increases area per lipid [14, 15]. Shinoda et al. compared structure, permeability, and dynamics of the straight-chained DPPC (dipalmitoyl-phosphatidylcholine) with the branched DPhPC in a series of molecular dynamics studies [16–18]. The results of their simulations indicate that branching in lipid tails slows down the conformational motion of the hydrophobic chain, which consequently decreases the permeability. Similar topics have been investigated in several other computational studies as well [19–22].

Another area of interest is the effect of the linkage connecting the head group to the fatty acid chains. In conventional lipids, this linkage is through an ester bond, whereas in ether lipids, the bridge is formed through an ether bond. Although ether linkage is a characteristic of Archaeal lipids, it is not just limited to this domain. For instance, a considerable number of phospholipids in human red and white blood cells are ether lipids [23]. Given the implications of lipid bilayer properties in modulation of mechanosensitive ion channels, it is imperative to characterize the properties of such lipids [24].

It is known that ester bond is more prone to chemical reaction than its ether counterpart, which is chemically more robust [25]. Unlike ester lipids, ether lipids lack polar carbonyl oxygen. Besides, ether oxygen is less polar; altogether changing the interfacial region and overall membrane properties [25].

Due to their chemical composition, Archaeal lipids are an excellent choice for liposome formation. Archaeal lipids are thermally stable and their tight packing prohibits solute leakage [26]. In addition, they can be stored at 4°C without aggregation or fusion for a long period of time and are not susceptible to enzymatic degradation by phospholipases [27]. Also, studies indicate that Archaeal lipids are safe to use and their tissue distribution, thermal and pH stability may provide a preferable alternative in various biotechnological applications such as drug and gene delivery or imaging agents [28].

Area compressibility modulus (K_A), as well as the area per lipid (APL) and membrane thickness are among critical properties of biological membranes. Although there have been studies investigating pure ester- and ether-DPhPC bilayers [25, 29, 30], there is still a need for more careful examination of the aforementioned properties. The area compressibility modulus for ester- and ether-DPhPC is expected to be around 220–250 $\raisebox{1ex}{$\mathit{mN}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ based on the monolayer experiments carried out by Yasmann and Sukharev [25]. However, previous computational studies report a higher value for area compressibility modulus of ester-DPhPC, than expected from the aforementioned monolayer study [20, 31].

In this study, the area compressibility modulus of ester- and ether-DPhPC have been estimated using two different approaches. Moreover, the equilibrium area per lipid for the two lipids are compared over a 400 ns simulation (Figure 1, representative snapshots of ester- and ether-DPhPC bilayers). Furthermore, bilayer thinning is examined while different surface tensions are applied to the bilayer. Finally, to directly compare our results with the available experimental data on ester- and ether-DPhPC monolayers [25], we have performed a series of monolayer simulations and compared their surface pressure with the experimental value.

Figure 1.

Snapshots of ester-DPhPC (left) and ether-DPhPC (right) systems, comprised of 76 lipids with the chemical structure of each lipid shown on the sides.

Recently it has been proposed that certain cell membrane proteins such as mechanosensitive channels of large conductance (MscL) can potentially be used as a clever nanovalve in liposomal drug delivery systems by attaching superparamagnetic particles to their N-terminus [32–34]. One of the challenges of this method could be the increase of the temperature as a result of the application of a static magnetic field for modulation of the channel gating.

Moreover, tremendous progress has been made in use of lipid bilayers in desalination platforms. It has been indicated that mechanical properties of the bilayers under various mechanical loading (e.g. tension or compression) greatly affect the desalination efficiency and endurance of these systems depends on the thermal stability, bending and stretching stiffness of their lipid bilayers [35]. Hence the importance of precise calculations of the mechanical properties and behavior of ether lipids are more emphasized as they exhibit a higher thermal and structural stability.

2. Materials and Methods

The bilayers of pure ester-DPhPC and ether-DPhPC are comprised of 76 lipid molecules and 3759 water molecules. The ester-DPhPC system was built using Membrane Builder [36–38] in CHARMM-GUI [39, 40], while the ether-DPhPC was built by manipulating its ester linkage. For both systems, all-atom CHARMM36 (Chemistry at HARvard Macromolecular Mechanics) force field was employed. In addition, since ether bond parameters has not yet been incorporated in the CHARMM36, parameters provided by Shinoda et al. was used for the ether linkage [29].

All simulations were carried out with GPU-accelerated NAMD [41–44]. Periodic boundary condition is used with NPT ensemble to maintain P = 1 bar and T = 323 K by employing Langevin piston and Langevin dynamics, respectively. Considering all hydrogen-heavy atom bonds constrained to their equilibrium length (using SETTLE algorithm for waters and SHAKE for the rest), a 2.0 fs time step was used for the numerical integration of the Newtonian equations of motion. For the short-range electrostatics, Lennard Jones interactions with a 8 to 12 Å switching function was used, and long-range electrostatics were taken into account using particle mesh Ewald (PME) [45].

In the first step toward the equilibration of the membranes, all atoms were fixed, except for the lipid tails, and lipid tails were allowed to melt for a few nanoseconds after energy minimization. Subsequently, the system was minimized one more time and then equilibration started without any restraints imposed on the systems for 20 nanoseconds. Simulations of both ester- and ether-DPhPC are further continued for 400 ns. In order to get better statistics, two replicas have been simulated for each system with different initial velocities.

For the calculation of the area per lipid, simulation cell area is divided by the number of lipids in each leaflet. In order to find the area compressibility modulus (K_A), two approaches were adopted. In addition to area fluctuations of a tensionless membrane, tension variations with respect to the area of the membrane can be used as follows [46]:

$$K_A=\frac{k_{B}T\langle A\rangle }{\langle \delta A^2\rangle }=A{\left(\frac{\partial \gamma }{\partial A}\right)}_T$$ (1)

where K_B is Boltzmann’s constant, T is temperature, 〈A〉 is the average area and 〈δA²〉 is the mean square fluctuation of the area. In the course of the simulation, area of the system is saved every 1 ps. In order to calculate area per lipid and area compressibility modulus and their standard errors, block averaging is used with block sizes of 20 ns. Moreover, the final coordinates of the 400 ns simulations without surface tension is used as a starting point for applying tension to the membranes and finding the equilibrium area of the systems under different lateral tensions. In this regard, both ester- and ether-DPhPC are simulated under 4 different surface tensions including 5, 10, 15 and 20 $\raisebox{1ex}{$\mathit{mN}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$, each for 150 ns (each system two replicas).

Finally, for validation of the simulation parameters used in this study, monolayer simulations of ester- and ether-DPhPC have been performed and compared with the available experimental data [25]. Initial configuration of the monolayers are prepared form the equilibrated bilayer systems. Each monolayer system is comprised of two leaflets with 53 lipids, separated by a water slab, with the lipid headgroups oriented towards the water. In consistence with the experimental set up, monolayers are simulated at 295 K. Monolayers are simulated in NVT ensemble at 4 different lateral areas corresponding to 85, 90, 95, and 100 Ų/lipid. Each system is simulated for 140 ns and the last 120 ns is used for analysis. Surface tensions are computed using [47]:

$$\gamma =\frac{1}{2}\langle L_z\left(P_{zz}-\frac{1}{2}\left(P_{xx}+P_{yy}\right)\right)\rangle$$ (2)

where L_z denotes the length of the simulation box perpendicular to the monolayer surface, P_zz is the pressure normal to the monolayer, P_xx and P_yy are the tangential components. Having the surface tension, surface pressure of the monolayer (π) is evaluated using:

$$\pi ={\gamma }_w-\gamma$$ (3)

in which γ_w is the experimental value for the surface tension of pure water, 72.4 mN/m at 295 K [48].

3. Results

Area per lipid, being a common indicator of the accuracy of lipid bilayer simulations, is calculated for both ester- and ether-DPhPC. Following 20 ns of equilibration, the time evolution of area per lipid is shown in Figure 2 over 400 ns of production simulations for the first replica (second replica shown in Figure S.1). Using blocks of size 20 ns, aggregating both replicas, area per lipid is 80.8 ± 0.1 and 77.3 ± 0.1 (Ų) corresponding to the ester- and ether-DPhPC, respectively. To make sure system size is not affecting our results, one system comprised of 304 lipids (152 per leaflet) for ether-DPhPC bilayer is simulated for 230 ns. Area per lipid for this large system is computed from the last 200 ns to be 77.2 ± 0.1 (Ų) which matches that of the smaller system (see Figure S.2).

Figure 2.

Time evolution of area per lipid shown for the first replica, alongside aggregate averages, including both replicas, of 80.8 and 77.3 (Ų) for ester- and ether-DPhPC, respectively.

Using the area fluctuation approach, the area compressibility modulus is calculated (Equation 1) for both systems. The ester- and ether-DPhPC bilayers were determined to have an area compressibility modulus of 347 ± 22 and 379 ± 24 (mN/m), respectively.

In another set of simulations both systems were studied under 4 different surface tensions. The final states of each system in the previous tension-free simulations were used as the starting point for applying tension. In these simulations, pressure in z direction (normal to the bilayer) is set to 1 bar and surface tension is set to be 5, 10, 15, and 20 (mN/m). Systems were simulated under each tension for 150 ns, where the first 50 ns is not considered in the analysis to ensure that the bilayers have reached equilibrium first (Figure S.3, S.4). Upon application of different surface tensions, the change in area per lipid and thickness of the bilayers were investigated (Figure 3 and 4). Besides, from the changes in area per lipid with respect to the applied tension, area compressibility modulus is obtained (Equation 1). K_A values obtained using this approach were higher for ether-DPhPC compared to ester-DPhPC, 340 ± 38 and 292 ± 37(mN/m), respectively. The area compressibility moduli obtained from both approaches have been summarized in Figure 5A.

Figure 3.

Variation of the area per lipid under different surface tensions in ester- and ether-DPhPC at 323 (K).

Figure 4.

Variation of the distance between the headgroup phosphates (D_HH) under different surface tensions in ester- and ether-DPhPC bilayers at 323 (K).

Figure 5.

Values of area compressibility (A) and bending elastic modulus (B) of the bilayers obtained at 323 (K) using area fluctuation and applied tension approaches.

Bending Elastic modulus of the bilayer, K_C, can be estimated through K_C = Et³/24, where t is the bilayer thickness and E is the Young’s modulus of the bilayer [24, 49, 50]. Given the bilayers are almost incompressible, E = K_A/t [24, 50]. Therefore, the apparent bending modulus can be calculated as:

$$K_C=\frac{K_A{t}^2}{24}$$ (4)

The bending modulus for ether- and ester- DPhPC bilayers are presented in Figure 5B. There are also other molecular approaches that has been proposed for calculating the bending modulus of lipid bilayers [51].

Two of the most important bilayer properties are lateral pressure profile as well as the order parameter. The lateral pressure profile of lipid bilayer describes the membrane mechanical stability via the direct effect on the area compressibility modulus (K_A), local membrane curvature, bending modulus (K_C), and Young’s modulus (E) of the bilayer [52–54]. Here we measured these parameters for both ether- and ester-DPhPC bilayers. As shown in Figure 6, the overall pressure profile for both lipids are similar, except small deviations at the lipid-water interface. This is expected since the ester linkage is slightly bulkier than that of ether, hence occupies more area at the interface. However, the order parameters of the two lipids (see Figure 7) are quite different especially for carbons near the headgroups. This could be due to the difference between the lipid-water interface and the induced local curvature in the bilayer caused by asymmetry of the pressure profile [55].

Figure 6.

The effect of ether/ester linkage on the distribution of pressure profile along the DPhPC bilayer membrane thickness at 323 (K).

Figure 7.

Order parameter -SCD for the Sn-1 and Sn-2 chains of ester- and ether-DPhPC bilayers at 323 (K) as a function of the carbon atom index.

Monolayer simulations of ester- and ether-DPhPC performed at 4 different constant areas corresponding to area per lipids of 85, 90, 95, and 100 Ų (total of 8 systems) are performed for 140 ns and values of pressure are extracted from the last 120 ns. Using equations 2 and 3, surface tension and surface pressure are calculated. Figure 8 shows surface pressure for ester- and ether-DPhPC monolayers which have a good agreement with the experimental values.

Figure 8.

Monolayer surface pressure-area (π-A) of ester- and ether-DPhPC at 295 (K). Experimental values from Yasmann and Sukharev [25].

4. Discussion

In this study, the ester- and ether-DPhPC lipid bilayers were investigated using a series of molecular dynamics simulations. First, area per lipid and area compressibility modulus of both bilayers were calculated from 400 ns of tensionless simulations. Furthermore, to estimate the area compressibility modulus and the thinning of the bilayers, another series of simulations under different tensions were carried out.

Since in the force field used in this study, CHARMM36, area per lipid is a specific target, agreement with the experiment data is anticipated for this parameter. The experimental value of the area per lipid for ester-DPhPC at 323 (K) is determined to be 83.6 ± 1.7 (Ų) by Kučerka et al. [56] which is in a good agreement with our simulation results (80.8 ± 0.1 (Ų)). Moreover, comparing ester and ether phospholipids, it has been shown that ether linkage reduces the average area per lipid [15]. This has been reflected in our results with ether-DPhPC showing a lower area per lipid compared to ester-DPhPC.

Once we ensure the accuracy of the area per lipid, we can estimate the mechanical properties and check if these results are also in an acceptable range with the experiments. With regard to the area compressibility modulus of these systems, although there are no experimental data for bilayers, in monolayer systems of ester- and ether-DPhPC this modulus has been measured to be 122 ± 7 and 114 ± 8 $(\raisebox{1ex}{$\mathit{mN}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.)$ at 303 (K), respectively [25]. Therefore, the value for area compressibility in these bilayer systems is anticipated to be about twice the corresponding value in monolayer systems. Our result for area compressibility of ester-DPhPC is lower than earlier simulations, for example 522 ± 49 $(\raisebox{1ex}{$\mathit{mN}$}\!\left/ \!\raisebox{-1ex}{$m$}\right.)$ at 323 (K) [19], and is closer to the predicted value from the monolayer experiment. However, regardless of the difference between the monolayer and the bilayer, the modulus obtained for ester-DPhPC is lower than that of ether-DPhPC in the monolayer experiment which is in contradiction with our results.

Therefore, we estimated the area compressibility modulus using a different approach and through monitoring the behavior of the bilayer under different surface tensions. In these simulations, the results also indicated a higher modulus for the ether-DPhPC compared to the ester-DPhPC. Further experiments are therefore required to validate this point. The discrepancy observed between the computational and experimental values can well stem from the limitations of CHARMM36 and/or the choice of force field parameters used by Shinoda et al. [29]. Also, there is a size-dependent difference between the true and apparent area compressibility due to undulations. However, as the size of the system decreases this difference becomes smaller. For instance, in Waheed, Q., & Edholm, O. (2009) has been shown that in a system comprised of 256 lipids, the undulation corrections are ~5–10% which is of the same order of magnitude or smaller than the statistical errors presented in the simulations [57]. As in the present study, all the systems are consisting of 76 lipids, the undulation corrections will be smaller than the statistical errors. Moreover, our system size is larger than the convergence limit demonstrated by de Veris et al. [58] to ensure artificial periodicity and finite-size effects do not compromise the results. One possibility to check the size-dependency of mechanical properties of membranes and other bio-assemblies is adopting new approaches such as the machine-learning interatomic potentials (MLIPs) trained over ab-initio molecular dynamics trajectories. This technique can be used for evaluating the properties and responses of structurally complex microstructures with ideal precision and at a minimal computational cost [59, 60].

The ether-DPhPC shows a lower area per lipid without applying tension which indicates that these lipids are more densely packed (Figure 3). When the tension is applied, the slope of the fitted line for the ether lipid is steeper thus demonstrates a higher resistance to change in the area and subsequently a higher area compressibility modulus.

The ether linkage also had an impact on the bilayer thickness (distance between headgroup phosphates, D_HH) and ether-DPhPC demonstrates a higher thickness than the ester-DPhPC (Figure 4). Moreover, D_HH changes more rapidly in ester-DPhPC than its ether counterpart upon application of surface tensions. This was anticipated as the K_A in ester-DPhPC is lower.

Finally, the area per lipid results for ester- and ether-DPhPC bilayers indicated more densely packed lipids in ether-DPhPC. In spite of the predicted values from a monolayer experiment, our results for area compressibility modulus of the more densely packed bilayer (ether-DPhPC) were higher than that of the ester-DPhPC. Also the discrepancies in the bilayer thickness of the studied bilayers is likely to have a role in modulation of integral membrane proteins (such as mechanosensitive ion channels) due to the change in hydrophobic mismatch between the bilayer and the protein [53, 61].

While values such as bending and stretch moduli provide a global value for the entire lipid bilayer, bilayer pressure profile describes the stress values along the thickness of the bilayer from the head groups to the last carbon in the acyl chain. Also, all before mentioned parameters can be derived independently from bilayer pressure profile. Here, we showed that the pressure profile of ester versus ether lipids are dissimilar at the lipid-water interface and overall ester bilayers have larger peak values, perhaps due to their higher packing order. This, in addition to their difference in the order parameter, could explain why they have higher bending modulus compared to ester lipid bilayers.

Conclusion

In this study, we used plethora of computational approaches based on molecular dynamics simulations to examine the consequences of alteration in the linkage connecting the head group to the fatty acid chains of DPhPC bilayers. Specifically, we studied the mechanical properties of ester- and ether-DPhPC, both widely used in many biophysical assays to study membrane proteins such as ion channels. We found that the overall properties of both bilayers, despite the small change in the head-to-tail linker, are vastly different. Ester-DPhPC is less stiff, more ordered, bulkier and thinner than the ether-DPhPC. Our computations provide a valuable quantitative input to researchers in various disciplines who are interested in using those lipid bilayers in various applications.