Interfacial behavior of phospholipid monolayers revealed by mesoscopic simulation

Abstract

A mesoscopic model with molecular resolution is presented for dipalmitoyl phosphatidylcholine (DPPC) and palmitoyl oleoyl phosphatidylcholine (POPC) monolayer simulations at the air-water interface using many-body dissipative particle dynamics (MDPD). The parameterization scheme is rigorously based on reproducing the physical properties of water and alkane and the interfacial property of the phospholipid monolayer by comparison with experimental results. Using much less computing cost, these MDPD simulations yield a similar surface pressure-area isotherm as well as similar pressure-related morphologies as all-atom simulations and experiments. Moreover, the compressibility modulus, order parameter of lipid tails, and thickness of the phospholipid monolayer are quantitatively in line with the all-atom simulations and experiments. This model also captures the sensitive changes in the pressure-area isotherms of mixed DPPC/POPC monolayers with altered mixing ratios, indicating that the model is promising for applications with complex natural phospholipid monolayers. These results demonstrate a significant improvement of quantitative phospholipid monolayer simulations over previous coarse-grained models.

Significance

Quantitative study on phospholipid monolayers at the air-water interface is crucial to understand the biophysics of cell membranes and lung surfactants. However, it remains challenging to quantitatively model the phospholipid monolayers at the mesoscopic scale limited by the scale of all-atom molecular dynamics (AAMD) simulations and the defect in the surface tensions of coarse-grained (CG) MD simulations. Herein, we proposed a mesoscopic model for dipalmitoyl phosphatidylcholine and palmitoyl oleoyl phosphatidylcholine monolayers at the air-water interface using many-body dissipative particle dynamics (MDPD). The interfacial and mechanical properties and the molecular structure derived by MDPD phospholipid monolayers are quantitatively in line with the AAMD simulations and experiments, which demonstrates a significant improvement over previous CGMD simulations.

Introduction

Lipid monolayers at the air-water interface are of interest in a variety of disciplines. Through the correspondence between the lipid monolayer and bilayer, the interpretation of the lipid bilayer properties can be obtained from lipid monolayer experiments, which are more easily performed than bilayer experiments (1, 2, 3, 4). An exemplary case of monolayer is the lung surfactant monolayer. Lung surfactant is composed of hundreds of lipids (∼90% by weight), mainly dipalmitoyl phosphatidylcholine (DPPC) and unsaturated phosphatidylcholines (PCs), and four types of surfactant proteins (∼10% by weight) (5, 6, 7). It can adsorb on the surface of the alveolar fluid that reduces the surface tension of the alveoli to maintain tidal respiration (8,9).

Studying the structure and mechanical properties of the lipid monolayer during compression and expansion is central to elucidating the biophysics of lung surfactant (10, 11, 12). Experimental studies can measure the phase coexistence, compressibility, and surface tension of the lipid monolayer through atomic force microscopy, Langmuir-Blodgett balance, the captive bubble method, and other techniques (13, 14, 15, 16, 17). However, although it is still difficult to directly study and observe the mesoscopic details through these experiments, these can be obtained from molecular dynamics (MD) simulations (18, 19, 20, 21).

At present, the commonly used MD methods for biomembrane include all-atom (AA) MD and coarse-grained (CG) MD (22). Although AAMD methods such as the CHARMM force fields (23) have high simulation accuracy, they require tremendous computing resources and time to simulate biological systems with a spatial scale of more than tens of nanometers and thus are not suitable for simulating the mesoscopic phenomena of the lipid monolayer. In CGMD simulations, clusters of atoms are considered beads that interact with each other, therefore decreasing the freedom of the total atoms and saving lots of computing costs. Nowadays, Martini force field CGMD (24,25) and dissipative particle dynamics (DPD) (26) are the two most popular CGMD methods for biological systems. The famous Martini force field provides systematic force field parameters for commonly used lipids and other biological molecules and thus is suitable for modeling the complex lipid monolayers at the air-water interface. However, the Martini water model underestimates the air-water surface tension because of the narrow well of the Lennard-Jones potential, which is flawed for modeling interfacial adsorption, pore formation, and the pressure-area isotherm of the monolayers (27). The Shinoda model (28,29) and the Chiu-Scott-Jakobosson water model combined with the Martini force field (9,30) have achieved good results on presenting the pressure-area isotherms of DPPC. These pioneering works have encouraged us to improve the numerical models for better simulation of the phospholipid monolayers at relatively large scale. DPD was initially proposed for simulating complex fluids at the mesoscopic scale and has also been widely used for biomembrane simulations (31). Compared to the Martini force field, DPD has a soft potential that allows a larger timestep in simulations and is more suitable for modeling mesoscopic thermodynamics because of the included dissipative forces and random forces (32). However, the accuracy and universality of DPD are normally inferior to the Martini force field model. Most importantly, DPD cannot handle the problems of the air-water interface because of the absence of attractions in its interaction potential.

Many-body (or multibody) DPD (MDPD) modifies the original DPD by replacing the purely repulsive conservative forces with forces deriving from a many-body potential (33). In this way, the equation of state has a higher-order pressure-density curve to accommodate vapor-liquid coexistence than DPD models. Thus, the conservative force of MDPD was modified to be related to density (34). The conservative force of MDPD was further developed by adding a pair of soft attractive interactions with a larger cutoff radius than the repulsive interactions (35). Recently, MDPD has been used for studying the adsorption behavior of surfactants with simple chemical structure such as sodium dodecyl sulfate (36,37). However, it is still difficult to use the MDPD model for quantitative lipid simulations.

Herein, we propose an MDPD model for two commonly used phospholipids, namely DPPC and palmitoyl oleoyl phosphatidylcholine (POPC), for lipid monolayer simulations. The parameterization for the lipid models is rigorously based on reproducing the experimental density and surface tension of reference systems (water and alkane) and the surface pressure-area isotherm of the lipid monolayer. Then, we examine the mechanical property (compressibility modulus) and the molecular structures, including pore formation, collapse, thickness, and order parameter, of the modeled lipid monolayers by comparison with experiments and other simulations. Finally, we extend the model to simulate the mixed DPPC/POPC monolayer at different ratios and obtain the pressure isotherm in good agreement with the experimental results, showing the versatility of this scheme.

Materials and methods

MDPD simulations

Theory and algorithm

The motion of the MDPD particles is described according to Newton’s second law, and the total force F_i on the bead i over all beads j within certain cutoffs consists of conservative force ${\mathbf{F}}_{ij}^C$, dissipative force ${\mathbf{F}}_{ij}^D$, and random force ${\mathbf{F}}_{ij}^R$:

$$\frac{d{\mathbf{v}}_i}{dt}={\mathbf{F}}_i=\sum _{i\ne j}\left({\mathbf{F}}_{ij}^C+{\mathbf{F}}_{ij}^D+{\mathbf{F}}_{ij}^R\right).$$ (1)

The conservative force of this expression is represented as (35)

$${\mathbf{F}}_{ij}^C=A_{ij}{\omega }_c\left(r_{ij}\right){\mathbf{e}}_{ij}+B_{ij}({\overline{\rho }}_i+{\overline{\rho }}_j){\omega }_d\left(r_{ij}\right){\mathbf{e}}_{ij},$$ (2)

where the first term with a matrix of attraction amplitudes A_ij stands for an attractive interaction within a range r_c = 1, and the second many-body term with a matrix of repulsion amplitudes B_ij is the density-dependent repulsive interaction within a short range r_d = 0.75. There is a no-go theorem that constraints the condition for the parameters of the multicomponent system, which means the force law is not conservative unless B_ij is a constant matrix (38). Therefore, a single repulsion parameter B can be used to replace B_ij. The weight function is ω_c= 1 − r_ij/r_c for r_ij ≤ r_c and ω_c = 0 for r_ij > r_c and ω_d = 1 − r_ij/r_d for r_ij ≤ r_d and ω_d = 0 for r_ij > r_d. The local density of the repulsive term is defined as ρ_i = $\sum _{i\ne j}{\omega }_{\rho }$(r_ij) for each particle, and the generalized weight function is expressed as (35)

$${\omega }_{\rho }\left(r\right)=\frac{15}{2\pi r_d^3}{\left(1-r/r_d\right)}^2.$$ (3)

The dissipative and random forces are defined, respectively, as

$${\mathbf{F}}_{ij}^D=-\gamma {\omega }_D\left(r_{ij}\right)({\mathbf{e}}_{ij}\cdot {\mathbf{v}}_{ij}){\mathbf{e}}_{ij}$$ (4)

and

$${\mathbf{F}}_{ij}^R=\delta {\omega }_R\left(r_{ij}\right){\xi }_{ij}\Delta t^{-1/2}{\mathbf{e}}_{ij},$$ (5)

where γ is the dissipative parameter, ξ_ij is a random variable conforming to a Gaussian distribution, e_ij = r_ij/r_ij, and v_ij = v_i − v_j. The system satisfies the Gibbsian equilibrium and the fluctuation-dissipation theorem (39) if the dissipative parameter γ and the amplitudes of random force δ satisfy δ² = 2γk_BT and the weight function follows ω_D(r) = [ω_R(r)]². The combined effect of dissipative force and random force acts as a thermostat.

CG models of phospholipids

In the classic DPD CG strategy developed by Groot (31), one water bead (W) corresponds to three water molecules. Thus, the number N_m = 3 can be considered the CG degree of the model. At this CG degree, the value of the repulsive parameter B in these MDPD simulations was fixed at 25 (35,38). Inspired by the CG schemes in the Martini force field (24), the CG model of DPPC has two hydrophilic head beads (H) representing the phosphate moiety and the choline moiety, two backbone beads (G) representing the glycerol linkage, and five hydrophobic tail beads (T/C1) at each tail with each bead corresponding to three carbon atoms. Note that the CG degree of lipid tails is the same as that of the MDPD water, which is different from the Martini CG degree (Fig. 1 A) (24,40). The only difference between the CG models of POPC and DPPC is the bead type of the second bead near the glycerol linkage on the main tail chain because of the presence of an unsaturated bond in POPC. Therefore, this carbon bead containing a double bond was redefined as type T/C2.

Figure 1.

(A) CG MDPD models for DPPC and POPC molecules. Orange, yellow, and green beads represent head (H), glycerol (G), and tail (T) beads, respectively. (B) Setups for calculations of water-air, water-oil, and phospholipid monolayer surface tensions. To see this figure in color, go online.

Bonded interactions between connected beads are represented by a weak harmonic potential. Following Groot and Gao (31,41), bonds are described by V_bond(r) = $\left(1/2\right)$K_bond(r − r₀)² with an equilibrium bond distance r₀ = 0.45r_c, and a force constant of K_bond = 400 k_BT/$r_c^2$ is applied on all neighboring beads except for the glycerol linkage bead (r₀ = 0.40r_c). Angles are described by V_angle(θ) = $\frac{1}{2}$K_angle(θ − θ₀)² for three adjacent beads. A force constant of K_angle = 4 k_BT/rad² and an equilibrium value of the angle θ₀ = 180° are applied to two head beads connected to one glycerol bead, the second head bead connected to the first glycerol bead and tail bead, a glycerol bead connected to two tail beads, and three consecutive tail beads; for two glycerol beads connected to a head bead or tail bead, K_angle = 4 k_BT/rad² and θ₀ = 120°; for the angles involving the cis double bond, K_angle = 6 k_BT/rad² and θ₀ = 120°. For two glycerol beads connected to the first bead of the sn-1 tail chain, the angle was set to K_angle = 4 k_BT/rad² and θ₀ = 100° in the DPPC model, but K_angle = 1 k_BT/rad² in the POPC model.

System setup

For calculations of the surface tension at the air-water interface, the simulation setup (Fig. 1 B) included a small water cube of 8 × 8 × 10 r_c containing 4352 water beads in an 8 × 8 × 20 r_c simulation box and a large water cube of 30 × 30 × 10 r_c containing 61,200 water beads in a 30 × 30 × 30 r_c simulation box. To determine the interaction parameters of the tail beads and water, 774 hexadecane (C5) molecules or 968 dodecane (C4) were placed in an 8 × 8 × 20 r_c box with an ensemble. In the simulation of coexistence of oil and water phase (Fig. 1 B), a water slab containing 4352 water beads and two boundary oil slabs containing 840 hexadecane (C5) molecules were placed in a box of the same size.

For monolayer simulations, we simulated DPPC, POPC, and mixed DPPC/POPC monolayers. The simulation setup of the monolayer included a water slab with two air-water interfaces that were covered by two symmetrical monolayers (Fig. 1 B). For mixed DPPC/POPC monolayers, DPPC and POPC were mixed at three molar ratios of 1:3, 1:1, and 3:1. For all the above phospholipid monolayers, the small system contained 444 molecules per monolayer and 21,792 water beads; the large system contained 4000 molecules per monolayer and 196,128 water beads. To obtain the surface pressure-area isotherms, a series of initial structures of lipid monolayers with different values of area per lipid (APL) were generated by controlling the lateral box size using the PACKMOL package (42). The lateral size of the small box is in the range of 15–25 r_c, and the large box is in the range of 45–75 r_c.

Surface pressure-area isotherm calculation

The surface pressure-area isotherm is given by a series of surface pressure points corresponding to the relation π(a) = γ₀ − γ(a), where γ₀ denotes the surface tension of the air-water interface. The surface tension in the monolayer, γ, is calculated from the differences in the normal pressure P_N and lateral pressure P_L in the box according to the Irving-Kirkwood approach (43), expressed as γ = (P_N − P_L) × L_z/2 = (P_zz − (P_xx + P_yy)/2) × L_z/2, where L_z is the size of the box in the normal direction and P_xx, P_yy, and P_zz are the ensemble-time average of pressure components in the x, y, and z directions, respectively. Each point of the surface pressure-area isotherm was obtained from one independent simulation at the constant area. The points of the surface pressure-area isotherm were obtained once the calculated ensemble-time averaged surface tension stabilized, i.e., the simulated phospholipid monolayer reached a metastable or quasiequilibrium state.

Simulation details

All simulations were performed using the Meso-DPD module in the LAMMPS package (44,45). Note that the original Lucy kernel function in the MDPD package was replaced by Eq. 3 to calculate the local density. All simulations were performed in a three-dimensional box with periodic boundary conditions in all directions. The time step was set to δt = 0.01 with the MDPD time unit and the equilibration simulation was sustained by 1,000,000 time steps for small systems and 10,000,000 time steps for large systems to ensure simulation convergence. The criterion for convergence is that the calculated surface tension remains constant over a long period of time. All simulations were carried out at 300 K using the NVT ensemble. The visualization of molecular configurations and simulation results was performed using the VMD software (46).

Constrained drop surfactometry experiments

Monolayer formation

DPPC (purity >99%) and chloroform (CHCl₃, purity >99%) were purchased from Avanti Polar Lipids (Alabaster, AL). POPC (purity >99%) was purchased from Sigma-Aldrich (St. Louis, MO). Phospholipids for the experiments were used without further purification. Ultrapure water (pH 7.4) from the Millipore Simplicity water purification system was used in all experiments. First, 20 mg DPPC or POPC was dissolved in 20 mL chloroform to form 1 mg/mL DPPC or POPC stock solutions, respectively. DPPC/POPC mixture stock solutions were prepared according to the molecular weights of DPPC (734.04) and POPC (760.08). The molar ratios of DPPC/POPC were 1:3, 1:1, and 3:1. Subsequently, an ultrasonic water bath was used to sonicate all prepared stock solutions at 25°C and 40 kHz for 5 min to obtain a series of uniformly mixed stock solutions. The droplet (∼15 μL volume) was constrained on a hydrophilic pedestal (∼3 mm in diameter) that uses its knife-sharp edge to prevent film leakage and to maintain the droplet integrity. A small amount of stock solution (1 mg/mL) was spread onto the droplet using a microsyringe. Then, the droplet could completely evaporate chloroform in 1 min without interference.

Surface pressure-area isotherm measurement

The droplet was slowly expanded to increase the surface tension (γ) of the monolayer until it was close to the surface tension (γ₀) of pure water. The spread lipid monolayer was subsequently compressed at a rate of 0.005 cm²/s and the real-time profile images of the droplet were directly displayed in the Axisymmetric Drop Shape Analysis graphical user interface, processed, and analyzed to generate a series of real-time surface tension measurement values to obtain the complete compression pressure-area isotherm (47, 48, 49). Each measurement was repeated three times to ensure the accuracy and repeatability of the experimental results. All measurements were carried out at 300 ± 0.1 K.

Results and discussion

Parameterization of water and oil and lipid tail

We first calibrate the MDPD parameters for the water model by mapping the liquid phase properties of water to its actual physical properties and correlating the MDPD dimensionless units to the actual units. The interaction parameter A_WW of water beads is set to −50, following the previous MDPD water model that can consistently reproduce the interface properties of water (50). In the simulation results, the equilibrium number density of water beads in both the large and small boxes is 6.8 $r_c^{-3}$. One water bead represents three water molecules and the volume of one water molecule is 30 Å³, which means that one water bead in a box occupies a real volume of 90 Å³. According to the number density of the water beads in the box, the simulated characteristic length r_c = 8.49 Å is obtained, which determines the length scale of the system. In addition, the surface tension of water in the MDPD unit is 12.4 k_BT/$r_{\text{c}}^2$. From the simple scaling relations, the calculated density and surface tension of water are 997 kg ⋅ m⁻³ and 71.2 mN/m at a room temperature of 300 K, which is consistent with the experimental results. The calculated surface tensions of water at different temperatures are validated against the constrained drop surfactometry (CDS) measurements in Table S2. After the characteristic length of the simulation is determined, the timescale of the simulation is obtained through mapping the calculated diffusion coefficient D_bead of water to the experimental value D_water = 2.43 × 10⁻⁹ m² ⋅ s⁻¹. Note that this calculated diffusion coefficient is corrected using the protocol of Yeh and Hummer (51). The correspondence between the MDPD parameters in dimensionless units and the actual physical values is shown in Table 1.

Table 1.

Correspondence between the MDPD parameters in dimensionless units and physical values

MDPD		MDPD → real units	Physical units
Parameter	Value		Value
Bead	1	Nm	3 H2O
rc	1	(ρNmV)1/3	8.49 Å
ρ	6.8	ρNmM/Na$r_c^3$	997 kg ⋅ m3
γ	12.4	γkBT/$r_c^2$	71.2 mN ⋅ m−1
p	0.1	pkBT/$r_c^3$	6.75 MPa
δt	0.01	NmDbead$r_c^2$/Dwater	0.46 ps

Note: physical properties r_c, ρ, γ, p, and δt correspond to the cutoff radius, density, surface tension, pressure, and time step, respectively. V is the volume of one water molecule, M is the molar weight of a water molecule, N_a is Avogadro’s number, k_B is Boltzmann’s constant, and T is 300 K.

Given that the monolayer surface tension is mainly dominated by the interactions tail-air and headgroup-water, we calibrate the parameters of the tail and head beads individually. The carbon atom in the saturated tail is similar to the one in the alkane compounds, such as hexadecane and dodecane. Thus, we compare the calculated bulk and surface properties of the alkanes with the experimental values to calibrate the parameters of the tail beads. The other beads of the lipid, including group beads, linkage beads, and unsaturated beads, are calibrated by directly comparing the calculated and experimental pressure-area isotherms of the lipid monolayer, which is shown in the next section.

The hexadecane molecule model is divided into five CG beads, and the dodecane is divided into four beads. The bond length between two adjacent carbon beads is set to 0.45r_c, bonding stiffness is 400 k_BT/$r_c^2$, and angular stiffness is 4 k_BT/rad² based on a previous model (41). The attraction interaction parameter A_ij is appropriately adjusted by fitting the density of the oil and the surface tensions of the oil-air and oil-water well with the experimental values. When A_CC is tuned to −23, the hexadecane-air surface tension is 26.6 mN/m and the density is 767 kg ⋅ m⁻³; the dodecane-air surface tension is 25.6 mN/m, and the density is 756 kg ⋅ m⁻³. When A_WC is set to −26, the hexadecane-water surface tension is 52.8 mN/m. These results are in good agreement with experimental values (52). Surface tensions between different phases are shown in Table 2.

Table 2.

Interfacial tension between different phases

System	MDPD	Martini	Experimental
Water-air	71.2	32.0	72.0
Dodecane-air	25.6	25.3	24.0
Hexadecane-air	26.6	27.2	27.3
Hexadecane-water	52.8	55.2	53.0

Interfacial tension measured in mN/m.

Surface pressure-area isotherms of the DPPC and POPC monolayers

After determining the interaction parameters between carbon beads (T/C1) and water beads (W), we screen the parameters of other beads within a reasonable interval to determine the interaction parameters. The DPPC monolayer in the small system is simulated to obtain a group of pressure-area isotherms with a series of parameter sets that are compared to the experimental results (Fig. S1 A). In this way, we can determine a set of parameters that fits the calculated isotherm well with the experimental one. After parameters of the head beads and the linkage beads are calibrated, the parameterization of the T/C2 beads of the POPC molecule can be obtained through the same methods (Fig. S1 B). The nonbonded interaction parameters for all pairs of beads are shown in Table 3.

Table 3.

MDPD bead-pair nonbonded interaction parameters

Aij	W	H	G	T/C1	T/C2
W	−50	−51	−48	−26	−30
H	−51	−37	−34	−30	−32
G	−48	−34	−34	−27	−27
T/C1	−26	−30	−27	−23	−21
T/C2	−30	−32	−27	−21	−23

The calculated surface pressure-area isotherm of the DPPC monolayer is shown in Fig. 2 A with the isotherms determined by other techniques. There are four main phase regions in the calculated isotherm. When the APL is larger than 0.9 nm², the monolayer in the liquid-expanded (LE) phase coexists with pores (the corresponding snapshot is shown in Fig. 2 B). At this stage, the surface pressure is reduced to near 0 mN/m and the APL is 0.9 nm², which is much more coincident with the experimental and AAMD results than the Martini force field. When the APL ranges from 0.9 to 0.65 nm², the DPPC monolayer is in the LE phase with no pores and the lipid tails are mainly disordered (Fig. 2 C). As the APL continues decreasing (0.65–0.5 nm²), the isotherm reaches a plateau and the slope of the isotherm fluctuates around zero, indicating a coexistence of LE and liquid-condensed (LC) phases (Fig. 2 D). The plateaus obtained by these MDPD simulations fit the experiments (15,53) and the AAMD simulations (54) more closely than the Martini simulations (12). For the APL range of 0.55–0.45 nm², the monolayer is in the LC phase and the tails are ordered (Fig. 2 E). However, the slope of the isotherm in the LC phase is much larger than that of the experiments, probably because of some inaccuracy of the force field and the NVT ensemble that leads to the large forces between the overlapped CG particles (55,56). As the surface pressure reaches 70 mN/m, that is, the surface tension is 0 mN/m, the monolayer is unstable and collapses with the lipids extruded to the water phase to form a micelle structure (Fig. 2 F). In general, the pressure-area isotherm with the corresponding monolayer morphology determined by the MDPD simulations is more coincident with the experimental results than the Martini force field (12). In addition, the calculated pressure-area isotherms of different sizes of monolayers using these MDPD simulations are consistent, which is somehow advantageous over the traditional AAMD and CGMD methods in simulating the lipid membranes because of the artificial rigidity and suppressed undulations in small systems (57, 58, 59).

Figure 2.

For a Figure360 author presentation of this figure, see https://doi.org/10.1016/j.bpj.2021.09.031. (A) Surface pressure-area isotherms of pure DPPC monolayers from MDPD simulations and CDS experiments compared to the literature data, including AAMD (54), Martini simulations (12), and experiments (15,53). Note that the isotherm in Martini simulations is corrected by shifting along the y axis. (B) Top view of the pore formation in the DPPC monolayer in the small system. (C) Side view of DPPC monolayers in nonporous LE phase with the enlarged local structure for disordered tail lipid chains at the side and top views. (D) Side view of DPPC monolayers in LE-LC coexistence phase with the enlarged local structure for disordered tail lipid chains (LE phase) and ordered tail lipid chains (LC phase) at the side view. (E) Side view of DPPC monolayer in LC phase with the enlarged local structure for ordered tail lipid chains at the side and top views. (F) Side view of the DPPC monolayer collapsed to form micelles in the water phase. The corresponding APLs are given below the snapshots. To see this figure in color, go online.

Slightly different from the DPPC molecule, the POPC molecule has one unsaturated C=C bond in one of its tails and increases the disorder of the tails. Simulated MDPD and experimental CDS pressure-area isotherms are shown in Fig. 3 A and compared to AAMD (54) and several experimental isotherms (60, 61, 62) at the same temperature. In the APL range of 0.45–1.15 nm², the surface pressure of the POPC monolayer is higher overall than that of the DPPC monolayer at the same APL (Fig. S2). The POPC monolayer is more stable than the DPPC monolayer at low surface pressure, and the pore formation starts at APL = 1.0 nm² (Fig. 3 B). In addition, the POPC monolayer is always in the LE phase at 300 K (Fig. 3, C and D) because of the unsaturated chains in the POPC molecules.

Figure 3.

(A) Comparison of surface pressure-area isotherms of pure POPC monolayers from these MDPD simulations, CDS experiments, AAMD simulations (54), and others’ experiments (60, 61, 62). (B) Top view of the hole formation in the POPC monolayer. (C and D) Side views of POPC monolayers with disordered lipid tail chains at different APLs of the LE phase. To see this figure in color, go online.

The calculated DPPC isotherms at different temperatures are shown in Fig. 4 A to validate against the previous experiment data (63). The temperature clearly affects the calculated isotherms near the LE-LC coexistence phase but only slightly affects the high and low surface pressure region in the isotherms, which is similar to the existing experimental measurements (15,64,65). In particular, an increase in temperature leads to an upward shift and a shortened plateau related to the LE-LC coexistence. When the temperature is higher than the main phase transition temperature of DPPC (314 K), the LE-LC coexistence phase disappears and only the LE phase is left, as confirmed by the molecular structures (Fig. 4, B–D). Similarly, the shapes of POPC isotherms at the temperatures above the main phase transition temperature (273 K) are almost identical (Fig. S3). In addition, our model can also capture the temperature effects on the phase behavior of phospholipid bilayers. For example, the increase of the temperature results in the melting of the DPPC bilayer (53), as shown by the comparison of the lipid diffusion at 300 and 330 K (Fig. S4).

Figure 4.

(A) Comparison of surface pressure-area isotherms of pure DPPC monolayers at different temperatures (300, 310, 320, and 330 K) from these MDPD simulations and the existing experiment (63). Top view of DPPC monolayers at APL = 0.57 nm² at 300 K (B), 310 K (C), 320 K (D), and 330 K (E) is shown. The LE phase coexistence is surrounded by red lines for clarity in (B) and (C). To see this figure in color, go online.

Mechanical properties of the DPPC and POPC monolayers

From the slopes of the pressure-area isotherms, we can obtain the area compressibility modulus Cs⁻¹, which is the reciprocal of the compressibility Cs and equivalent to elasticity. The compressibility can be expressed as

$$Cs=-\frac{1}{A}{\left(\frac{\partial A}{\partial \pi }\right)}_{\text{T}},$$ (6)

where A and π are the APL and surface pressure, respectively. A typical area compressibility modulus of DPPC monolayers measured via experiments and simulations is in the range of 10–50 mN/m in the LE phase and 100–250 mN/m in the LC phase (12,15,53,54). We summarize our simulated and experimental data as well as the data in the existing literature in Table 4. The area compressibility moduli of the LC and LE phases of the monolayer are approximated by linear regression from the pressure-area isotherm. The calculated compressibility modulus of the MDPD DPPC monolayer in the LC phase is close to the Martini simulations (12) and is much larger than the experimental results (15,53) and AAMD simulations (54), whereas that in the LE phase is more closed to experimental results and the AAMD simulations than Martini simulations. Because of the high rigidity of the LC phase, the lipid diffusion in the LC phase is orders of magnitude lower than that in the LE phase, which is consistent with the previous experimental data (66) (Fig. S5). The POPC monolayer is mainly at the LE phase in the APL range of 0.55–1.0 nm², and the slope of the isotherm obviously changes at such a range. Thus, the calculated compressibility modulus of the POPC ranges from 30 to 85 mN/m in relation to the APL and the calculated values are similar to the CDS experiments as well as previous experiments (62, 63, 64) and AAMD simulations (54). At the same APL, the modulus of the POPC monolayer is much smaller than that of the DPPC monolayer, which is in accordance with the experimental results.

Table 4.

Experimental and simulated area compressibility moduli

	Temperature (K)	Phase	Cs−1 (mN/m)	Area (Å2)
DPPC monolayers	Varies			Varies
MDPD large	300	LC	∼894	∼48.5
MDPD small	300	LC	∼835	∼48.5
CDS	300	LC	∼378	∼43.6
Tieleman et al. (12) (Martini)	300	LC	∼786	∼47.6
Javanainen et al. (54) (AAMD)	298	LC	∼315	∼50.2
Crane et al. (15) (Exp)	298	LC	∼272	∼45.0
Mansour et al. (53) (Exp)	298	LC	∼215	∼46.2
MDPD large	300	LE	∼50	∼70
MDPD small	300	LE	∼51	∼70
CDS	300	LE	∼36	∼75
Tieleman et al. (12) (Martini)	300	LE	∼243	∼58.9
Javanainen et al. (54) (AAMD)	298	LE	∼58	∼78.2
Crane et al. (15) (Exp)	298	LE	∼32	∼79.7
Mansour et al. (53) (Exp)	298	LE	∼34	∼74.5
POPC monolayers	Varies			Varies
MDPD large	300	LE	∼164	∼62.9
	300	LE	∼53	∼80
MDPD small	300	LE	∼164	∼62.9
	300	LE	∼53	∼80
CDS	300	LE	∼110	∼52
	300	LE	∼58	∼70
Javanainen et al. (54) (AAMD)	298	LE	∼153	∼67.2
	298	LE	∼58	∼86.2
Olżyńska et al. (60) (Exp)	298	LE	∼86	∼60
	298	LE	∼38	∼90
Brown et al. (61) (Exp)	297	LE	∼114	∼58
	297	LE	∼45	∼90
Prenner et al. (62) (Exp)	298	LE	∼119	∼55
	298	LE	∼47	∼80

Molecular structures of the DPPC and POPC monolayers

During expression and expansion, the lipid monolayer at the air-water interface exhibits different molecular structures. In this section, we examine the molecular structures of the DPPC and POPC monolayers at different stages. First, we show the molecular structure transformation of the DPPC and POPC monolayers at the rupture and collapse stages under the extremely high and low surface tension in Fig. 5.

Figure 5.

Snapshots for the simulations of DPPC monolayers in the large system at the collapse and rupture stages. (A and B) Pore formation of DPPC and POPC monolayers at APL = 0.9 and 1.0 nm², respectively, in the top view. (C) Structure transformation of the DPPC monolayer at the collapse stage: forming small undulations (top left), buckling grows (top right), and the monolayers collapse, forming extruded bilayers in the water phase (bottom right and bottom left). To see this figure in color, go online.

For the DPPC monolayer, the pore formation of the monolayer starts at APL = 0.9 nm² with stable pores, and these pores grow with an increase in the APL to 1.0 nm². Formation of pores was also confirmed by the AAMD simulation at APL = 1.1 nm² (54) and the existing experiment at APL = 1.1 nm² (67). Considering the possible deviation of the operating conditions in experiments and the intrinsic uncertainty involved in molecular simulations, we feel that the difference of the pore formation between our study and the other results is acceptable. Compared to the DPPC monolayer, the POPC monolayer is more stable at high surface tension and starts to form pores at APL = 1.0 nm². This is because the work of formation of a round pore of radius r equals 2πrΓ − πr²σ (Γ is the line tension at the edge of the pore and σ is the surface tension) (68), and the POPC molecule has a larger line tension because of the unsaturated bead. At the collapse stage, the DPPC monolayer collapses from the small undulations, and DPPC molecules are extruded to form the bilayer structure in the water phase, which is similar to the previous CGMD simulations (69). In addition, the structure transformation between the DPPC molecules in the water phase and at the air-water interface is governed by the surface pressure of the DPPC monolayer as revealed by the previous experiment (53). This model also demonstrated that the DPPC molecules in the water phase could adsorb to the DPPC monolayer at the air-water interface if the surface pressure is below the equilibrium surface pressure of the monolayer (∼45 mN/m), whereas such adsorption was inhibited under the surface pressure larger than the equilibrium surface pressure, as shown in Fig. S6. However, the desorption of the lipids was not observed in our simulations when the surface tension was above 45 mN/m, which was possibly caused by the high compressibility of the DPPC monolayer.

Except for the rupture and collapse stages, although the lipid monolayer is always flat under expression and expansion, it exhibits different molecular structures at the different surface tensions. The order parameter of the lipid tails is an important property to quantitatively describe the orientation of the lipids and the phase separation. It is defined as (20)

$$S_z=\frac{3}{2}⟨\mathrm{co}{s}^2{\theta }_n⟩-\frac{1}{2},$$ (7)

where θ_n is the angle between the calculated molecular axis connecting the n − 1 and n + 1 sites of the hydrocarbon chain and the normal z axis of the monolayer. At a low surface tension (APL = 0.45, 0.47 nm²), the DPPC monolayer is in the LC phase and the corresponding order parameter is much larger than in the LE phase (APL ≥ 0.63 nm²) as shown in Fig. 6 A. These calculated average values of the order parameter are quantitatively in line with the Martini CGMD simulations (12). Besides, the DPPC tails in the LC phase exhibit an averaged tilt of ∼26.34° (Fig. S7) that agrees well with the previous experimental measurement of 25° (70). It should be noted that the collective tilt of the DPPC chains in the LC phase is still hardly observed. This is similar to the previous Martini simulations (12,71) but different from other DPD simulations (72). The POPC monolayer has a bond angle of 120° in the unsaturated tail chain, thus leading to an obvious decrease in the order parameter in the sn-1 tail (Fig. 6 B). Generally, the order parameters of the POPC monolayer are much smaller than those of the DPPC monolayer at the same APL. The bead density distributions of the monolayer at the z axis (Fig. S8) shows that the DPPC monolayer is little thinner than the POPC monolayer at the same APL. This indicates that the POPC molecules are more likely to be arranged in parallel at the air-water interface, which is in accordance with the order parameters. We also notice that there is an obvious hydration layer near the headgroups by examining the water distribution along the headgroups of the monolayer (Fig. S9).

Figure 6.

Order parameters of tail beads in the DPPC (A) and POPC (B) monolayers at various APLs and the typical snapshots for the molecular structure at different APLs. The bead numbers stand for the bead series in the tails, in which 1, 2, and 3 are the second, third, and fourth bead in each tail, respectively. The first bead and the last bead in each tail were not included in the calculation of order parameter. To see this figure in color, go online.

Pressure-area isotherms of mixed DPPC/POPC monolayers

The natural lung surfactant monolayer has complex and unique biophysical properties because of its complex lipid composition. Therefore, modeling toward the real multicomponent lipid monolayer is crucial for understanding the biophysics of the lung surfactant monolayer. Next, we study the experimental and simulated isotherms of three mixed DPPC/POPC monolayers of different ratios, as shown in Fig. 7. The isotherms of the simulated and experimental mixed DPPC/POPC monolayers are between the isotherms of the pure DPPC and POPC monolayers. With the increase in the ratio of POPC, the LE-LC coexistence phase plateau of isotherms of the mixed monolayer gradually disappeared, and the slope at the low APLs decreased as well. When the mixed ratio is larger than 50%, the shape of the simulated isotherms of the mixed monolayers is essentially similar to the that of the pure POPC monolayer without an obvious plateau, which manifests the same trend as our CDS experiment and the existing experiment (73). Therefore, these MDPD models are promising in capturing the important feature of the mixed monolayers, for example, a shift from an isotherm with a plateau to that without a plateau depending on the ratio of DPPC/POPC molecules. However, it should be noted that at an APL <0.5 nm², the calculated isotherms of mixed monolayer have a larger slope with a steep increase in the pressure, whereas the pressure in the experimental isotherms slowly increases, leading to a slight deviation in the compressibility between the simulations and experiments. Generally, our model is capable of capturing the features of the mixed lipid monolayer, and the parameterization scheme could be applied to more types of phospholipids, which can be used to mimic the mesoscopic behavior of natural lipid monolayers.

Figure 7.

Surface pressure-area isotherms of three mixed DPPC/POPC monolayers and pure (DPPC or POPC) monolayers obtained by the MDPD simulations (A) and the CDS experiments (B). The mixing ratio of DPPC molecules in the mixed monolayers was set to 25, 50, and 75%. To see this figure in color, go online.

It should be noted that although our MDPD model can quantitatively simulate the phospholipid monolayers at the mesoscale, there are still some limitations. First, for simulating a large system of DPPC monolayers with a horizontal size of 60 × 60 nm and a total bead number of 366,000, it takes ∼1.05 h to run 1,000,000 steps on 720 CPU cores in 30 nodes (320 ns). Although this MDPD took only quarter of the computing time for the Martini CGMD with a similar simulation system (Table S1), our simulation scale is limited to hundreds of nanometers and microseconds. Second, our MDPD model does not include any electrostatic interactions. Third, the bond and angle parameters refer to previous DPD lipid models and are worth optimizing for more accurate monolayer simulations.

Conclusions

Although phospholipid monolayers at the air-water interface have been widely studied using experimental and computational methods, it is still difficult to quantitatively model the physical properties of the phospholipid monolayers at the mesoscopic scale. Here, we present an MDPD model for two commonly used phospholipids, DPPC and POPC. Using a parameterization scheme based on mapping the calculated physical properties to the experimental values, we reproduced the pressure-area isotherms of the phospholipid monolayers in MDPD simulations with a good fitting to our CDS experiments. In addition, the mechanical properties and molecular structures of phospholipid monolayers were quantitatively and qualitatively in line with the experiments and AAMD simulations. This model can also capture the sensitive changes in the pressure isotherms of the mixed DPPC/POPC monolayers by altering the mixing ratios of the components. These results demonstrated that our model can be applied for mesoscale phospholipid simulations at the air-water interface with molecular resolution but less computing cost.

Author contributions

G.H. and X.B. designed the research. Y.Z. performed the simulations and experiments. Y.Z. and X.B. analyzed and interpreted the data. X.B., Y.Z., and G.H. wrote the manuscript.

Editor: Siewert Jan Marrink.

Supporting citations

Reference (74) appears in the Supporting material.

Supporting material

Data S1

Input files for the MDPD simulations