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The molecular mechanism of lipid monolayer collapse

Edited by Stuart A. Rice, University of Chicago, Chicago, IL, and approved May 8, 2008 (received for review December 7, 2007)
Abstract
Lipid monolayers at an air–water interface can be compressed laterally and reach high surface density. Beyond a certain threshold, they become unstable and collapse. Lipid monolayer collapse plays an important role in the regulation of surface tension at the air–liquid interface in the lungs. Although the structures of lipid aggregates formed upon collapse can be characterized experimentally, the mechanism leading to these structures is not fully understood. We investigate the molecular mechanism of monolayer collapse using molecular dynamics simulations. Upon lateral compression, the collapse begins with buckling of the monolayer, followed by folding of the buckle into a bilayer in the water phase. Folding leads to an increase in the monolayer surface tension, which reaches the equilibrium spreading value. Immediately after their formation, the bilayer folds have a flat semielliptical shape, in agreement with theoretical predictions. The folds undergo further transformation and form either flat circular bilayers or vesicles. The transformation pathway depends on macroscopic parameters of the system: the bending modulus, the line tension at the monolayer–bilayer connection, and the line tension at the bilayer perimeter. These parameters are determined by the system composition and temperature. Coexistence of the monolayer with lipid aggregates is favorable at lower tensions of the monolayer–bilayer connection. Transformation into a vesicle reduces the energy of the fold perimeter and is facilitated for softer bilayers, e.g., those with a higher content of unsaturated lipids, or at higher temperatures.
Lipid molecules are insoluble in both polar and apolar media because of their amphipathic nature. At polar–apolar interfaces, they form monomolecular films that reduce the surface tension. Lipid monolayers form the main structural component (≈97% by weight) of lung surfactant at the gasexchange interface in the lung alveoli (1) and constitute the outer layer of tear film in the eyes (2). The properties of lipid monolayers vary with their surface density (3). For example, the higher the density, the lower is the resulting surface tension at the interface. At a certain very high surface density, however, a further reduction of the surface tension is not possible: the monolayers become unstable at the interface and collapse (4) (see scheme in Fig. 1). Besides being of fundamental interest for surface science, lipid monolayer collapse is crucial for maintaining low surface tension at the gasexchange interface in the lungs during breathing (5).
Collapse is characterized by loss of material from the interface and can proceed through different pathways. The modes of collapse and the surface tension at which collapse occurs depend on the molecular composition of the monolayer and on temperature (6–13), which determine the morphology and material properties of the monolayer. Although lipid monolayers in the liquid state do not usually sustain low surface tensions, the monolayers in a condensed state [e.g., pure dipalmitoylphosphatidylcholine (DPPC) below its mainphase transition temperature, 314K] can achieve high surface densities and low surface tensions (9, 14) (nearzero values). Depending on the monolayer material properties, collapse of a 2D monolayer may lead to the formation of different 3D lipid aggregates in the subphase, e.g., bilayer folds (Fig. 1 c), vesicles (Fig. 1 f), tubes, micelles, etc. If these aggregates can readily respread at the interface upon decrease of the monolayer surface density, then the collapse is reversible; otherwise, it leads to irreversible loss of material from the interface. Interestingly, the mechanism of monolayer collapse and the collapse surface tension also depend on the rate of increase of the monolayer surface density (15), which reflects the speed of lateral compression. At high rates, a monolayer in a liquid state can be supercompressed (14) into a metastable state and thus achieve a low surface tension.
These monolayer phenomena have been studied extensively by using experimental techniques (see refs. 7, 9, 12, 16, and 17 and references therein) and theoretical models (18–21). From theoretical models, it follows that the monolayer is destabilized at the interface and buckles at vanishing surface tension. The buckling is facilitated for a monolayer with nonzero spontaneous curvature and at domain boundaries. The final structures of lipid aggregates formed upon monolayer collapse have been characterized experimentally. The pathway from a 2D monolayer to a certain 3D structure, however, remains unclear. It is also not clear which properties of the constituting lipid molecules determine the structure of 3D aggregates and the reversibility of monolayer collapse. Experimentally, it is difficult to characterize the monolayer transformations at the molecular level, whereas theoretical models usually consider a monolayer as an elastic continuum and disregard molecular structure.
In this study, we use molecular dynamics simulations to investigate the mechanism of lipid monolayer collapse. Previous simulations of monolayer collapse (22, 23) considered relatively small systems (with box lateral size ≈10 nm), which limited both the modes of monolayer collapse and the variety of possible lipid aggregates that could be observed. Although these simulations allowed displacements of individual molecules from the interface, a collective molecular response to collapse was energetically unfavorable. The simulation time scales investigated were also relatively short (up to 30 ns) for following a possible evolution of the collapsed structures. We employ a coarsegrained lipid force field (24) to access larger length scales (≈50 nm) of lipid monolayer collapse as a collective phenomenon and characterize monolayer transformations upon collapse on the microsecond time scale. To investigate the dependence of monolayer transformations on its material properties, we use binary lipid mixtures of DPPC and palmitoyloleoylphosphatidylglycerol (POPG) at two concentrations, 4:1 and 1:1, at 310 K. We simulate the collapse of lipid monolayers on lateral compression, which proceeds by buckling of the monolayer surface and folding of the monolayer into a bilayer in water. The simulations show that bilayer folds initially adopt semielliptical shape, in agreement with predictions of the theory of cracks in elastic medium (20). Then the folds undergo further transformations and form either flat circular bilayers or vesicles. The structures of lipid aggregates formed upon monolayer collapse depend on macroscopic properties of the system: the line tensions of the bilayer perimeter and the monolayerbilayer connection, and the bilayer bending modulus.
Results
Collapse of Lipid Monolayers Induced by Lateral Compression.
To increase the monolayer surface density and induce its collapse, we performed monolayer lateral compression with different methods (see Simulation Details in Methods) and rates (c ≈ 0.01–0.0006 ns^{−1}) for two compositions (DPPC and POPG in ratios 4:1 and 1:1) at 310 K. Compression rates that can be obtained in the simulations are much faster than the experimental compression rates (c ≈ 0.5–0.0005 s^{−1}). To allow monolayer equilibration, compression was stopped at selected surface densities and followed by simulations at constant monolayer area.
The calculated surface tensionarea isotherms of the monolayers near collapse are shown in Fig. 2 a. At low tensions, monolayers of both compositions adopted the homogeneous liquidexpanded phase, with high molecular mobility, low orientational order, and no longrange translational order [see supporting information (SI) Text and Fig. S1]. At positive surface tensions, the monolayers remained in a flat geometry at the interface, with thermal undulations growing upon reduction of the surface tension (Fig. 3 a). Upon compression to negative surface tensions, steady buckling developed from undulations (Fig. 3 b), which was nearly axisymmetric around the monolayer normal. Upon continuing compression, the buckling deformations grew in amplitude (Fig. 3 c and d) and then folded to form a bilayer in water (Fig. 3 e and f). Once started, folding completed within 100 ns. Folding resulted in an increase of the monolayer tension to a positive value, corresponding to an equilibrium spreading tension. In all simulations, one fold per monolayer per simulation box was formed. At faster compression rates, the monolayers developed larger buckling amplitudes and achieved lower surface tensions before folding. The pathway of monolayer collapse was independent of monolayer composition, compression method, and rate.
Structure of Lipid Aggregates Formed upon Monolayer Collapse.
To investigate the transformations of lipid aggregates formed upon monolayer collapse, the precompressed monolayers were equilibrated at fixed interfacial areas. For each concentration (DPPC and POPG in ratios of 4:1 and 1:1) we simulated two copies with two monolayers each, for 4 μs per simulation. The transformation of a collapsed monolayer is shown in Fig. 4. The initial pathway of monolayer collapse (shown in Fig. 3) was the same for both compositions and resulted in bilayer folds of a flat semielliptical shape oriented approximately perpendicular to the monolayers (Fig. 4 a). The flat semielliptical folds underwent further transformations, which differed depending on the composition.
The folds readily became more circular, reducing their connection to the monolayer in the 4:1 mixture (Fig. 4 b). The surface tension in the monolayer, γ _{m} , in coexistence with folds (or equilibrium tension) equaled 20.7 ± 0.2 mN/m. In the 1:1 mixture, the folds retained their flat semielliptical shape on a time scale of 400 ns. Then the flat bilayer folds bent (Fig. 4 c) and reconnected on their perimeter to the monolayer, resulting in semivesicles attached to the monolayers (Fig. 4 d). For all four folds, the transformation took <500 ns. The semivesicles were stable and did not detach from the monolayers on a microsecond time scale. The surface tension in the monolayers in coexistence with vesicles was 22.8 ± 0.2 mN/m, slightly higher than the tension of 21.0 ± 0.3 mN/m for the same monolayer coexisting with folds due to partial incorporation of lipids from the interface into vesicles. In the 4:1 mixture, three of the four folds maintained their circular shape and remained connected to the monolayer for 4 μs. One fold transformed into a semivesicle (between 2.4 and 3.2 μs) and remained connected to the monolayer. Different transformations of folds in the two mixtures originate from differences in their properties.
To analyze the observed foldtovesicle transformations, we calculated several macroscopic properties, shown in Table 1 and Fig. 2 b, from simulations of auxiliary systems (see SI Text ). The monolayer area compression moduli, K_{A} , found from the slope of the tensionarea isotherm, are in good agreement with previously calculated values, but somewhat larger then reported experimental values (for review, see ref. 25). The larger values in simulations likely originate from suppressed thermal undulations and enhanced symmetry due to periodic boundary conditions (26). The bilayer bending moduli, K_{b} , were calculated from simulations of bilayer cylinders in water (27). The obtained values are somewhat larger than the experimental values of (0.6–1.4)·10^{−19} J (28, 29). The discrepancy with previously calculated values of 0.4·10^{−19} J and 2.1·10^{−19} J (30, 31) can originate from the differences in composition, temperature, the version of the forcefield, and calculation procedures (using the bilayer undulation spectrum) based on approximations that include decoupling of deformation modes (27, 32). The line tensions at the perimeter of the bilayer fold, λ_{p}, were calculated from simulation of a semiperiodic bilayer slab in water. The obtained values are in agreement with previous simulations (50 pN) (33) and somewhat larger than experimental values (5–30 pN) (34, 35). The line tension at the bilayer connection to the monolayer, λ _{c,} was obtained from simulations of monolayers connected by a bilayer. To our knowledge, no data on this parameter is available. The monolayer (inplane) shear moduli, G(s), as a function of shear rate, s, near collapse (γ _{m} ≈ 1 mN/m) were calculated by introducing dynamic shear deformation of the simulation box. The monolayer response to shear depends strongly on its phase state. In the considered liquidexpanded phase, the shear moduli are negligible at low rates (vanishing in the limit of a static shear) and increase with increasing rates. The monolayer apparent surface shear viscosity η ^{a} = G(s)/s ≈ 10^{−10} Pa·m·s (for both mixtures) is comparable with previous simulations results for lipid bilayers (36), and is much smaller than the reported experimental values for lipid monolayers in the LE phase ≈10^{−6} to 10^{−7} Pa·m·s (37, 38). Therefore, the monolayer transformations in simulations proceed faster than in experimental systems. The calculated values of shear moduli are one to two orders of magnitude larger than the experimental values for Langmuir monolayers in a liquid phase (39, 40). At the same time, the simulation shear rates (s ≈ 0.2–0.001 ns^{−1}) are also much faster than the typical shear rates used for experimental measurements (s ≈ 10–0.001 s^{−1}). The actual shear rates during monolayer collapse in real systems are probably higher, leading to larger shear moduli (20). Finite shear moduli allow buckling and folding to develop on monolayer lateral compression.
Discussion
Lipid Monolayer Collapse Is Initiated by Buckling.
The simulations show that monolayer collapse is initiated by buckling. For the considered compositions and temperature, the monolayers near collapse form a homogeneous liquidexpanded phase, in which (inplane) shear modulus is vanishing for static deformations and develops upon increasing strain rate. Buckling of the liquidlike monolayers is thus of dynamic nature as a response to lateral compression. Buckling is similar to wrinkling of thin films (41, 42), which occurs in both solid (elastic) and liquid (viscous) (43) films at finite deformation rates. Monolayers in a condensed (solid) phase (with more saturated lipids and/or at lower temperatures) can withstand shear, and buckling can be static. Its topology depends on the monolayer phase state: in rigid monolayers, it becomes asymmetric/elongated to reduce the energetic cost of bending and shearing (11). For example, stable ridges have been observed experimentally (12) in condensed Langmuir monolayers. Although the details of buckling deformations are defined by monolayer composition and temperature, the monolayer's ability to buckle at finite compression rates is a general property.
The amplitudes and wavelengths of the buckling deformations depend on the elastic (viscous) properties of monolayer and the subphases (41, 42). In simulations, the buckling deformations are limited to one wavelength per simulation box (because of the imposed periodicity of the system). Monolayer bending at shorter wavelengths is associated with higher energies. The smaller the monolayer, the higher is the energy barrier to bend it, and the more it is stable against collapse. Absence of defects or domain boundaries, which facilitate buckling (18), additionally stabilizes flat monolayers in simulations. As a result, microscopic monolayers in simulations buckle at lower surface tensions than real macroscopic monolayers.
“Nucleation” of Folds.
Buckling of monolayers is followed by their folding into bilayers to release the stress of bending deformations. The subphase for folding is determined by the balance of surface energies, which depend on the surfactant constituting the monolayer and on the polar–apolar interface. For lipid monolayers at the air–water interface, the folding proceeds into the water subphase, reducing the surface energy of the hydrocarbon chains exposed to air (44).
Immediately after collapse, the bilayer folds are connected to the monolayer and have a semielliptical shape. Nucleation of folds on monolayer collapse has been described theoretically (20) in analogy to formation of cracks in elastic plates (see SI Text ). The theory predicts a semielliptical fold shape: , where x is the coordinate along the fold, D is fold depth, and L_{c} is fold length at the fold connection to the monolayer (see Fig. S2). The surface energy of fold formation, ε, is approximated (20) as the surface tension of the hydrocarbon chain–air interface ε = 22 mN/m (45). By using the calculated values for both mixtures (G(s) = 7 mN/m at s = 0.1 ns^{−1}) near collapse (γ _{m} = 0 mN/m), the theory predicts D(0)/L_{c} , ≈0.8, in agreement with the fold depthtolength ratio observed in simulations. According to the theory, the critical fold length (above which the fold will grow) is L _{c} ^{cr} = 2/π·(4K_{A}Gλ _{c} )/((K_{A} + G)(ε − γ _{m} )^{2}), and the energy barrier for fold nucleation is ΔE = 1/2·λ _{c} ·L _{c} ^{cr}. Using the calculated values, we obtain L _{c} ^{cr} < 2 nm for both compositions, ΔE < 2k_{B}T for the 1:1 mixture and ≈7k_{B}T for the 4:1 mixture. The energy barriers decrease for lower shear rates and can be overcome by thermal energy, which indicates that on buckling (at γ _{m} < 0 mN/m) folding proceeds rapidly. Compression at fast rates in simulations, however, reduces the time available for fold nucleation. As a result, monolayers develop large buckling amplitudes before folding. At low surface tensions, the fold nucleation barrier is small and favors folding. At higher surface tensions, the fold nucleation barrier would increase (diverging at γ _{m} → ε) and folding would not proceed spontaneously (20). In simulations, monolayers buckle only at low tensions because of their small size. Buckling is thus a limiting step for monolayer collapse in simulations.
The above equations describe instantaneous fold shape on monolayer collapse. The transfer of lipids from the monolayer to the folds leads to an increase of monolayer surface tension. Once it reaches the equilibrium value, the flow of lipids into the folds stops. The monolayers coexist with the folds; at fixed interfacial area the number of lipids in them remains constant to maintain the equilibrium tension. The folds, however, can change their shape with time and detach from the monolayer.
Folds Can Transform into Vesicles.
Further collapse transformations are controlled by several macroscopic properties. In particular, these properties determine whether the transformation of a bilayer fold into a vesicle is energetically favorable. First, the energetic cost of bending a flat bilayer fold to form a vesicle is characterized by the bilayer bending modulus. Second, lipid molecules at the open edges (along the perimeter) of the bilayer fold are highly deformed (high positive curvature). The energetic penalty for this can be expressed as a line tension at the fold perimeter. Third, lipid molecules are also highly deformed at the connection of the bilayer fold or vesicle to the monolayer. The deformation here is characterized by high negative curvature, the opposite compared with bilayer edges. The associated energetic cost can be characterized by the line tension at the monolayer–bilayer connection. These properties enter the energy balance for a given structure of a lipid aggregate, and their magnitude determines the equilibrium structure.
To illustrate the effect of these macroscopic properties on the transformations of lipid aggregates, we consider the following idealized shapes: a semicircular bilayer fold connected to a monolayer; a separate flat circular bilayer in water; a semivesicle connected to a monolayer; and a separate vesicle in water. Simple estimates (see SI Text ) show that a flat bilayer fold will remain connected to the monolayer if λ _{c} /λ _{p} < 2/3, independent of its size. Then, a flat semicircular bilayer fold of radius R will form a semivesicle connected to the monolayer if R > 4K_{b} /(λ _{p} − 1/3λ _{c} ). Fold bending reflects its tendency to reduce the open edges. Next, a semivesicle of radius R/2 will detach from the monolayer to form a vesicle if R > 4K_{b} /λ _{c} . Finally, a separate flat circular bilayer of radius R will transform into a vesicle if R > 4K_{b} /λ _{p} . The outlined arguments show the following trends: (i) fold to vesicle transformation is favorable for larger and softer (with lower bending modulus) aggregates and (ii) is driven by the line tension at the bilayer edges; (iii) the connectivity of the aggregates depends on the monolayer–bilayer line tension.
The calculated values of the macroscopic properties can explain the observed foldtovesicle transformations. The bending modulus decreases with increasing concentration of POPG lipid, because the unsaturated hydrocarbon chain makes the bilayer softer. Fold bending and vesicle formation are thus facilitated in the 1:1 mixture as compared with the 4:1 mixture. Line tensions at the bilayer fold perimeter indicate that it is almost equally unfavorable to maintain open bilayer edges for both systems. The line tension at the monolayer–bilayer connection decreases with increasing concentration of POPG lipid, because its negative spontaneous curvature facilitates the monolayer–bilayer connection. The molecule has a smaller head group than a DPPC lipid and an unsaturated chain, which makes the hydrocarbon tail region wider. Lower line tension at the monolayer–bilayer connection in the 1:1 mixture leads to a longer connecting line of the bilayer folds and a wider vesicle connecting radius (see Fig. 4 and Fig. S2). In the 4:1 mixture, higher line tension results in a shorter monolayer–bilayer connection line, and flat folds become more circular to minimize the energy of the total perimeter (bilayer edges and the connection line) at a fixed amount of lipids in the fold. Combining the calculated values with the above formulas, we expect both the flat folds and the semivesicles to remain connected to the monolayer in the simulations, the latter because of their small radius (≈8 nm).
Lipid monolayer collapse with formation of both folds and vesicles has been observed experimentally. In particular, in a system of similar composition (DPPC and POPG in ratio 7:3), monolayer collapse produced folds at lower temperatures (<301 K) and vesicles at higher temperatures (>307 K) (7).
We showed that several macroscopic properties control the structure of lipid aggregates formed upon monolayer collapse. The calculated values of these properties are, of course, affected by the molecular representations chosen for the simulations. The conclusions describing potential transformation pathways are independent of the lipid composition and, we believe, are generally valid. These conclusions can be summarized as follows:

Line tension at the bilayer fold perimeter favors the formation of vesicles or other closed shapes (e.g., bilayer tubes). Lipids with positive spontaneous curvature (having a larger head group or only one hydrocarbon chain) will reduce the energy of the fold perimeter and stabilize flat folds.

Higher values of the bending modulus will favor flat folds over curved shapes, e.g., vesicles or tubes. Saturated lipids will generally increase the bilayer bending modulus.

Low line tension at the monolayer–bilayer connection regulates the connectivity of lipid aggregates to the monolayer. The connectivity facilitates the transfer of lipids back at the interface on monolayer expansion and thus provides reversibility of monolayer collapse. Lipids with negative spontaneous curvature (having smaller head groups or unsaturated hydrocarbon chains) and cholesterol (46) will yield low line tension at the monolayer–bilayer connection.

The larger the size of the flat fold, the more advantageous is its transformation into a vesicle or other closed shapes (e.g., bilayer tubes). For lipids with positive spontaneous curvature, the flat folds are likely to detach from the monolayer first and then form vesicles. For lipids with negative spontaneous curvature, the vesicle formation proceeds attached to the monolayer independent of their size. Smaller semivesicles connected to the monolayer are thermodynamically stable. Separation from the monolayer is favorable for larger vesicles, but can be kinetically hindered. This process is similar to vesicle fission (47), which involves complex intermediates and implies high activation barriers.
Biologically important systems (e.g., lung surfactant) usually contain a complex mixture of various lipids and proteins. The above conclusions can explain the role of individual lipids in transformations of lipid aggregates formed upon collapse of multicomponent monolayers.
Conclusions
Our simulations provide information on collapse of lipid monolayers at the air–water interface induced by lateral compression, at Angstrom level with picosecond resolution, which cannot be achieved experimentally. Upon lateral compression, the monolayer collapse proceeds by buckling and folding into a bilayer in water. Immediately after collapse, the bilayer folds have a semielliptical shape, in accord with theoretical predictions. Furthermore, the folds can transform into flat circular bilayers or vesicles and disconnect from the monolayer. We showed that the transformations during collapse and its reversibility depend on several macroscopic parameters. These parameters are determined by lipid composition and temperature and can explain the role of individual lipids in collapse of multicomponent monolayers.
Methods
We performed molecular dynamics simulations of a number of lipid aggregates containing DPPC and POPG lipids in ratios of 4:1 and 1:1 at 310 K. To study the mechanism of monolayer collapse, we simulated symmetric systems containing two lipid monolayers (Fig. S3a and SI Text ) and increased gradually the monolayer surface density by compressing in a lateral direction without changing the box size in the normal direction. To investigate the transformations of lipid aggregates formed on monolayer collapse, we performed simulations at constant volume of the box, with constant areas of the two interfaces and a fixed box size in the direction normal to the interfaces. In a number of auxiliary simulations, we calculated the macroscopic properties determining the final structure of collapsed monolayers and the reversibility of monolayer collapse (see SI Text and Fig. S3 b–d ). In particular, we simulated a cylindrical bilayer in water to calculate the bilayerbending modulus, a system with two smaller monolayers under shear deformation to calculate the shear modulus as a function of strain rate, a (periodic) bilayer in water to calculate the bilayer area compression modulus, a semiperiodic bilayer in water to calculate the line tension of the bilayer edge, and two monolayers connected by a bilayer in water slab bounded by vacuum to calculate the line tension of the monolayer–bilayer connection.
Monolayer Lateral Compression.
The simulation setup included a water slab bounded by vacuum on both sides with two symmetric monolayers at the two water–vacuum interfaces (Fig. 2 a). We simulated monolayer compression in the lateral direction to increase the lipid surface density. To investigate the influence of the method of compression on the mechanism of monolayer collapse, we used two different approaches. In method 1, positive lateral pressure was applied to the system. For a system containing two symmetric monolayers, the applied lateral pressure, P_{L} (P_{L} = P_{xx} = P_{yy} ), corresponds to imposing equal surface tensions in each monolayer, γ _{m} , given by the formula: γ _{m} = (P_{N} − P_{L} )·L_{z} /2, where L_{z} is the box normal size, and P_{N} is the normal pressure in the box. This method allows setting a required value of the surface tension in monolayers (as an outcome of compression). For each of the two compositions, four simulations were performed with this method, by using lateral pressures of 5, 10, 20, and 50 bar and semiisotropic pressure coupling. The system compressibility was set to 5 × 10^{−5} bar ^{−1} in the lateral direction and to zero in the normal direction. The latter ensures constant size of the box normal to the membrane. In method 2, the box dimensions were varied during the simulation. To change the interfacial area available to each monolayer, the box x and y dimensions, L_{x} and L_{y} , were changed at equal rates (ΔL_{x} /Δt = ΔL_{y} /Δt, nm/ns) while the box z size was kept constant. For each of the two compositions, we used compression speeds of −0.154, −0.0308, and −0.0154 nm/ns. Considering both compression methods, a total of 14 simulations of monolayer compression were carried out. The monolayer compression rates (c ≈ 1/A_{xy} ·ΔA_{xy} /Δt, where A_{xy} is the monolayer area) varied in the range c ≈ 0.01–0.0006 ns^{−1}. After lateral compression, the evolution of the bilayer folds was simulated starting from different frames of the compression runs.
The system setup with two monolayers included 8,192 lipids in total. For the mixture of DPPC and POPG in a ratio of 4:1, it contained 3,072 DPPC and 1,024 POPG lipids in each monolayer, and 317,277 water particles and 2,048 Na^{+} ions in the box. For the mixture of DPPC and POPG in a ratio of 1:1, it contained 2,048 DPPC and 2,048 POPG in each monolayer and 313,708 water particles and 4,096 Na^{+} ions in the box. For all compression runs, the size of the starting structure was 52 × 52 × 50 nm^{3}. This corresponds to an average area per lipid of 0.67 nm^{2} and a surface tension of ≈42 mN/m. To follow the transformations of the compressed monolayers after collapse, the starting structure (40 × 40 × 50 nm^{3}) was obtained by applying a lateral pressure of 50 bar for 64 ns.
Simulation Details.
For all of the simulations, we used a prerelease version of the MARTINI force field, a coarsegrained (CG) model for biomolecular simulations (24). In this model, the molecules are represented by grouping four heavy atoms into a particle, which reduces the number of degrees of freedom. The force field is systematically parameterized on the partitioning free energies of many chemical compounds between polar and apolar phases. Combined with shortrange interaction potentials, computational efficiency is increased by three orders of magnitude relative to atomistic simulations. Particles of a different chemical nature are distinguished by different particle types, with an interaction strength between two particles that depends on their types. The model reproduces well the properties of various lipid phases and phase transitions in lipid bilayers (48) and monolayers (45). DPPC is a standard component of the force field and contains 12 particles. For POPG lipids, the head group consists of two hydrophilic particles: the charged phosphate group is represented by a charged particle (Qa), the glycerol group is represented by a polar particle (P4). For nonbonded interactions, the standard cutoffs for the CG force field were used: the Lennard–Jones interactions were shifted to zero between 0.9 and 1.2 nm, whereas the Coulomb potential was shifted to zero between 0 and 1.2 nm. The relative dielectric constant was 15. A formal time step of 20 fs was used in all of the simulations; the neighbor list for nonbonded interactions was updated every 10 steps.
The Berendsen algorithm was used in all of the simulations with pressure coupling, with a coupling constant τ_{P} = 4.0 ps. Temperature coupling was used in all simulations, with the lipids and water with ions coupled separately to Berendsen heat baths (49) at T = 310 K, with a coupling constant τ_{T} = 1 ps.
Lateral compression runs of the large monolayers were 80 to 800ns long, depending on the compression rate or the magnitude of the applied lateral pressure; the monolayers were simulated at constant areas for 400 ns to calculate the surface tension minus area isotherms. To follow the transformation of the collapsed monolayers, we performed two independent simulations of the compressed monolayers for 4 μs for each composition. The times reported here are effective times sampled by the CG model, rescaled by a factor of four to compensate for the accelerated sampling of the phase space in the model (30). All of the simulations were performed by using the GROMACS (v.3.3.1) simulation package (50).
Acknowledgments
S.B. is an Alberta Ingenuity postdoctoral fellow, L.M. is an Alberta Heritage Foundation for Medical Research (AHFMR) postdoctoral fellow, D.P.T. is an AHFMR Senior Scholar and Canadian Institutes of Health Research New Investigator. This work was supported by the Natural Science and Engineering Research Council (Canada). Simulations were performed in part on WestGrid (Canada) facilities.
Footnotes
 ^{§}To whom correspondence should be addressed. Email: tieleman{at}ucalgary.ca

Author contributions: S.B. and D.P.T. designed research; S.B., L.M., and H.J.R. performed research; S.B. and L.M. analyzed data; and S.B., L.M., S.J.M., and D.P.T. wrote the paper.

↵ ^{†}Present address: Laboratory of Physics, Helsinki University of Technology, Espoo, 02015, Finland.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0711563105/DCSupplemental.

Freely available online through the PNAS open access option.
 © 2008 by The National Academy of Sciences of the USA
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