2.1 Bilayer thickness and liposome sphericity

The outer diameter and sphericity of the HIV-1 lipid vesicle was measured over the first 1.5 μs of equilibration. Convergence is observed for both parameters, with an average of 145 nm and 0.9975 for the outer diameter and the sphericity, respectively (S3 Fig). During production, an increase of the outer diameter from 145 nm to 147 nm is observed. Sphericity is maintained with an average of 0.9984 throughout 5.2 μs production sampling (S4 Fig).

The first step in computing the hydrophobic thickness was to delineate interior and exterior regions of the vesicle system, such that ‘C2B’ beads (corresponding to carbons C08:0-C12:0) of lipids in the membrane could be classified based on their leaflet of residence (Fig 2A). Calculation of hydrophobic thickness was obtained from N = 1024 uniformly distributed regions of the vesicle (Fig 2B), the positions determined with a Poisson disk sampling technique [32]. About each point in the sample distribution, C2B beads were selected within a search radius of 46.25 Å (Fig 2C), and the center of mass distance between beads in the inner and outer leaflets was computed.

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Fig 2. Hydrophobic thickness analysis.

A Clipped view of the carbon bead selection used for thickness calculation. The selection is superimposed with the volume grid employed to determine the leaflet in which each ‘C2B’ bead resides; blue represents the outer monolayer and green the inner monolayer. The inset shows a zoomed in view of the leaflets delineated by the volume grid, the latter yielded by measure volinterior. B The uniform point distribution (N = 1024) used to sample thickness, yielded via Poisson disk sampling. C Uniform distribution with the volume grid. The inset demonstrates the carbon beads isolated about each test point, in a search radius r_search of 46 Å. Hydrophobic thickness is considered as the center of mass distance between groups of C2B beads in each leaflet. D Resulting analysis over the 5.2 μs trajectory. The dark line shows the mean hydrophobic thickness per frame, while the transparent region shows the standard deviation at each frame for the 1024 values calculated. The mean thickness over the time series, dotted line, is 26 Å with a standard deviation of 1 Å between frames.

https://doi.org/10.1371/journal.pcbi.1009781.g002

Utilizing a high-performance analysis framework outlined previously [29, 32], built on VMD with MPI support, we analyzed the 5.2 μs trajectory (Fig 2D). The average hydrophobic thickness for the time series is 26 ± 1 Å. As shown in the plot, fluctuations of thickness computed in this manner, where the computed value for each frame is a mean of 1,024 samples distributed evenly across the vesicle surface, are relatively small at less than 1 Å. The volume grid used to classify space around the vesicle was computed at intervals of 125 ns throughout the trajectory. The analysis utilized 42 MPI ranks, each of which computed the volume grid with its first frame before analyzing its 125 ns component of the complete time series. Frames utilized for measure volinterior space classification were discarded from analysis to remove an artifact causing thickness to be underestimated.

An additional analysis of overall membrane thickness was carried out in a similar manner. Center of mass distances between head groups in each leaflet were calculated across uniformly distributed regions of the vesicle surface. The values were found to fluctuate within 34 to 36 Å. The observed overall thickness and subsequently small variations is in agreement with observations made by cryo-electron tomography for vesicles with a 42% molar ratio of cholesterol [33]. No relationship between local thickness values and composition was found in our analyses.

2.2 Transmembrane asymmetry

Significant diffusion of lipids between the bilayer leaflets (“transverse” diffusion) is observed throughout the full-scale vesicle simulation (Fig 3, S5 Fig; S2 Movie). To characterize the transverse diffusion of lipids, flip (outer-to-inner) and flop (inner-to-outer) rates were calculated separately during the 5.2 μs of MD production for each lipid species. Previous MD simulation on flat-patch asymmetric membranes suggest the flip and flop rates are slow processes in the second timescale, supported by experimental small-angle neutron scattering (SANS) results [34]. The rate of flip and flop are influenced by the chain length, temperature and chemical character of the lipid headgroup.

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Fig 3. Diffusion of lipids on the complex vesicle model.

A Trans-bilayer rates of lipids present in the vesicle after 5.2 μs of MD production. The average outer to inner rate (blue) and outer to inner (red) rates were estimated by calculating the cumulative number of flipping events per lipid species from three different starting points during the simulation: 0, 200 and 4,000 ns. The values reported are normalized per number of events per molecule. B Lipid lateral diffusion coefficient and C scaling factor. The average is reported at windows sizes of 25, 50, 100, 250, 500 and 1,000 ns.

https://doi.org/10.1371/journal.pcbi.1009781.g003

Average flip-flop rates were calculated for each lipid species over the entire production simulation of the HIV-1 liposome (Fig 3A); transbilayer flip-flop rates over different portions of the simulation are shown in S5 Fig). There are clearly two classes of lipids in Fig 3A: lipids with rates less than 100(10⁻⁵) events/ns × molecule, and lipids with rates higher than 200(10⁻⁵) events/ns × molecule. The first category corresponds exclusively to lipid types that are enriched in the outer leaflet (sphingolipids and saturated chain lipids), while the second is exclusively lipids enriched on the inner leaflet (highly unsaturated lipids with PE and PS headgroups). Although the flip-flop rates are slow (as expected for lipid transbilayer rates), they do represent a substantial lipid translocation in the aggregate for many lipid types. For example, the total number of PAPS inner→ outer events is 40, while the total number of outer → inner events is 15. In spite of this, the initial and final numbers of PAPS in each leaflet are extremely asymmetric, and maintained within ± 2 lipids. Indeed, the total number of flipping events is larger than the number of PAPS in the outer leaflet. This is true for many of the lipid types, and indicates (i) that the difference in flip flop rates observed between inner and outer leaflets is not due to directional transport as the composition equilibrates by flip flop, and (ii) that compositional asymmetry would be maintained over longer timescales. Given that the composition of the two leaflets has not been experimentally determined, it is remarkable that the initial asymmetry is maintained during the t = 5.2 μs of MD production, despite significant rates of lipid flip flop.

Given the observed stability of lipidomic asymmetry, the leaflet compositions reported in S8 Fig yield a good model for an HIV-1 lipid vesicle. These results are not only in agreement with bulk lipidomics results for the HIV-1 virion [21], but are also supported by lipidomics experiments that suggest the formation of lipid domains on the host-cell, where budding and release of the viral particle takes place [35, 36].

Interestingly, transbilayer diffusion of phospholipids in the flat HIV-1 membrane patch was not observed, and the lipid compositions of each leaflet are maintained throughout the entirety of our simulations. This result further suggests a relationship between curvature and lipid flip flop.

2.3 Lateral diffusion of lipids is heterogeneous within and between the leaflets

Characterization of the lateral diffusion of lipids was performed using methods previously developed by the authors for the analysis of full-scale virions [27]. Analysis of time- and ensemble-averaged lipid mean squared displacements (MSD) show the diffusion to be Fickian (not subdiffusive). The diffusion constant (D) for different lipids in the inner and outer leaflets was obtained from fits of the MSD (Fig 3B), with all diffusion constants on the order of 10^-6 cm²/s. Lateral diffusion of lipids in the inner and outer leaflets of the flat HIV-1 system shows the same trend (S11 Fig), where MSD of the inner leaflet is substantially higher than that of the outer leaflet.

Upon visual inspection of the trajectories it is clear that there are lipid domains on the vesicle that displace laterally much more slowly than the surrounding lipid matrix (S3 Movie). To characterize these lipid regions based on their lateral mobility, the root-mean-squared fluctuations were calculated for each lipid molecule over different windows of the final 500 nanoseconds of the production simulation (Fig 4). In Fig 4A, several localized domains of low mobility lipids (dark patches) are observed, with diameters of roughly 10 nm. No such domains are observed on the inner leaflet. A further characterization of some of the most dramatic low-mobility domains on the outer monolayer reveals that these domains are enriched in cholesterol, sphingomyelin and phosphatidylcholine (Fig 4B).

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Fig 4. Mobility analysis of lipids and lipid regions.

A Mobility of lipid headgroups after 1 μs of production MD, in the outer leaflet. Each column shows lipids with decreasing mobility cutoffs, down to 15 Å. B Visualization of the low-mobility domains, circled in panel A, below 15 Å mobility. Chemical species are colored according to the legend provided.

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The low mobility domains remain intact for a few nanoseconds and subsequently diffuse over the surface of the vesicle—they are transient, fluctuating domains which appear to be intrinsic to the composition of the outer leaflet of the lipid vesicle. During the simulation these low-mobility regions appear and disappear, highlighting their dynamic nature (S3 Movie). Importantly, these low mobility regions are observed only in the outer leaflet and completely absent in the inner leaflet (S10 Fig).

2.4 Elastic properties

The bending rigidity k_c [37, 38] of a flat bilayer can be obtained from spectral analysis of the fluctuations of the height of the membrane above a reference plane. However, the HIV-1 lipid vesicle is a quasi-spherical membrane that remains intact during the simulation, and therefore the instantaneous shape of the vesicle is decomposed into spherical harmonics [38] (Fig 5).

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Fig 5. Bending rigidity of the HIV-1 lipid vesicle.

A Undulating surface of the radial fluctuations as obseverd after 5 μs of MD production. Units of fluctuations are given as percent of the average radius. B Undulation spectra from the expansion in spherical harmonic of the undulating surface for a single simulation snapshot of the liposome; the fit is shown for wave-number q cutoffs [38] of 0.75 nm^-1, 0.85 nm^-1 and 1 nm^-1. A linear fit is shown for the initial l-degrees for the three different cutoffs. C Ensemble average undulation spectra of the HIV-1 liposome. The bending rigidity is estimated from the Helfrich continuum model [38] for bilayer undulations yielding a value of 109 k_bT at 298 K.

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Following Braun and Sachs [38], the bending rigidity of the viral liposome was obtained from the power spectrum of shape fluctuations in the spherical harmonic basis. The coefficients for the spherical harmonic expansion were obtained from a nonlinear fit of degree 74 and order 149. The undulation power spectrum in Fig 5B and 5C was then computed by fitting a_lm to the power spectrum model in Eq 5, yielding k_c = 109 k_bT at 298 K. We believe this relatively high bending energy is a result of how we employed the method [38], which required reducing the 5.2 μs timeseries to only 10 frames, with each frame composed of only a subset of headgroups. These measures were taken due to the vesicle’s immense size and lipidomic complexity, which otherwise prevent use of this analysis framework as designed. A framework optimized for large scale, complex lipid systems, founded on the work of Braun and Sachs [38], is in development.

For our asymmetric flat membrane control system (S2 Fig), we employed a method to compute compressibility moduli based on local thickness fluctuations [39, 40], which allows characterization of each leaflet individually. Considering the absence of experimentally-derived reference values gleaned from similar, representative membranes, proper validation of resulting moduli remains a challenge. Nevertheless, the framework [39] is utilized to identify the differences and trends in the compressibility of each leaflet (see Methods for implementation details). For the inner leaflet, we obtained a compressibility modulus of 103 mN/m. For the outer leaflet, we obtained a compressibility modulus of 155 mN/m (S3 Table). Both values were computed at 298 K. Interestingly, our analysis reveals that the outer leaflet, even in the flat patch system where neither leaflet exhibits any sustained curvature, is substantially more rigid than the inner leaflet. Corresponding to our findings related to lateral mobilities, with displacement of lipids in the inner leaflet being markedly higher than the outer leaflet (S10 and S11 Figs), it seems that the asymmetric lipid composition of HIV-1’s membrane leads to significant disparaties in the physical properties of each leaflet.

Flexible envelopes are characteristic of mature HIV-1 virions. Flexibility facilitates entry of mature virions, whereas immature virions exhibit a stiffer viral envelope which cannot enter host cells efficiently [17]. Despite the presence of the low-mobility ordered domains described above, the viral envelope is still clearly in a fluid phase, as the nanoscale ordered domains are transient, and the bending rigidity is still significantly below values reported in the literature for a membrane below the main phase transition temperature [41].

The composition of the outer leaflet of the HIV-1 liposome (rich in sphingolipids and cholesterol) is consistent with raft-like regions of the plasma membrane, from which HIV-1 is believed to escape the cell. In simpler model membrane mixtures, the liquid-ordered phase has several features in common with rafts–it is enriched in high melting temperature lipids (like SM) and cholesterol, the hydrocarbon chains are ordered, and therefore the bending modulus is likely higher than in single component fluid membranes [42, 43]. Recently, Weiner, et al. demonstrated liquid-ordered domain formation in all-atom simulations of more complex mixtures, designed to mimic the asymmetry of the plasma membrane [44].

The transient ordered regions observed in the outer leaflet of the HIV-1 liposome shown in Fig 4 are also observed in bilayer simulations of the liquid-ordered phase [45]. Taken together, the analysis of the HIV-1 liposome simulation indicates that the outer leaflet of the liposome is in an ordered or raft-like phase. The fact that the composition is heterogeneous across the surface of the vesicle suggests that viral assembly might exploit fluctuations in lipid composition to organize surface proteins for critical functions like viral fusion and entry, as suggested previously for influenza [46]. Indeed, Tamm and coworkers have shown that gp41 mediated fusion occurs in heterogeneous membranes at the edge of cholesterol-rich domains [47].

While the absence of gp41 in our simulations precludes any conclusions that may be drawn regarding its effect on the membrane, we have shown that domain formation, potentially requisite for gp41-mediated fusion [47], can occur in protein-free lipid systems. This result suggests that gp41’s hemifusion and fusion activity in vivo is contingent upon, rather than causal to, the presence of these cholesterol-rich domains. Interestingly, several studies have shown that removal of cholesterol, or blocking synthesis thereof in virus-producing cells, significantly diminishes HIV-1 infectivity [48, 49]. Because such domains are observed in both the full-scale vesicle as well as the asymmetric flat patch, it is likely that these domains are emergent from sphingolipid and cholesterol-rich lipid mixtures, representative of the sites from where HIV-1 is known to preferentially bud, yet distinct from typical host membrane compositions. Preference toward a specific lipid composition may additionally relate to localization of MA during assembly, further implicating the lipidome in numerous viral processes.

What role is played by proteins in regulating membrane dynamics and behavior is an intriguing question that is made more complicated by the fact that retroviruses are known to freely and unselectively incorporate host membrane proteins into their envelopes [50–53]. The latter fact may be a clue that the physical characteristics of the envelope, those necessary to successful completion of the viral cycle such as stability, fluidity or elasticity, are robust and independent of the action of proteins. Experimental studies of model membranes have shown the presence of gp41’s N-terminal fusion peptide leads to reductions in stiffness [54, 55]. To our knowledge, a similar study with a lipid composition representative of HIV-1, i.e., rich in cholesterol and sphingomyelin, has not been conducted.

4.1 Vesicle construction

The approximately 300,000 lipid molecule positions were initially seeded in two spheres, representing leaflets, using the packmol library [61]. The relative abundances of the lipid species were based on the average per-virion values obtained in previous lipidomics experiments for HIV-1 [21, 22] (Table 1). Molecular placement with packmol did not fully converge, so an alchemical phasing procedure was used to progressively expand the effective CG particle radii to relax steric conflicts gradually [62]. A 1,000 frame alchemical growth trajectory spanning λ = 0 to λ = 1 was visually inspected at every 10th frame to determine the point at which lipids had deviated too far from the HIV-1 vesicle because of steric conflicts during lambda-expansion. The acceptable movements were capped at λ = 0.2 (frame 20) and all twenty coordinate sets in that set of frames were energy minimized to assess viability (F_max < 10⁴). The least disruptive (lowest) λ value at which coordinates were viable for energy minimization was frame 7 (λ = 0.08), and these coordinates were selected for preparation of a production simulation.

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Table 1. Summary of HIV-1 vesicle lipid composition.

Lipid names match those used in the MARTINI 2.1 forcefield. There are 24 lipid species in total.

https://doi.org/10.1371/journal.pcbi.1009781.t001

The selected lipid vesicle starting configuration was placed in a rhombic dodecahedron container using GROMACS 4.6.5 with a 3.5 nm distance buffer between the vesicle and the simulation container boundary. The dodecahedral system was hydrated with MARTINI water, using a random seed and a van der Waals radius of 0.24 nm. In total, 20,541,842 non-polarizable water particles were added by GROMACS, and the hydrated system was successfully energy-minimized using the steepest descent algorithm in GROMACS. The simulation system was neutralized by replacing 25,000 MARTINI water molecules with Na⁺ ions, followed by another successful steepest descent energy minimization. The final solvent preparation step was to convert to 5% antifreeze particle composition, as described previously [26]. After confirming that the energy minimized solvated coordinates were sensible based on visual inspection, the system was prepared for long-term (production) simulations with GROMACS 2016.

After approximately 1.5 μs of equilibration, we noticed two issues with the HIV-1 vesicle system: there were a few free-floating lipids inside and outside of the ultrastructure, and double bilayer anomalies were present, i.e., regions with more than two lipid leaflets had formed. The bilayer anomalies were excised using a combination of the DBSCAN algorithm [63] in scikit-learn [64] and in-house code to reintegrate false-positive selections.

Following the surgical procedure to remove bilayer anomalies, the vesicular system was rehydrated using GROMACS 4.6.5, with MARTINI water using a van der Waals radius of 0.24 nm. 20,700,856 water particles were added and the hydrated system was energy minimized using the steepest descent algorithm. The hydrated system was neutralized with 22,465 MARTINI sodium ions and again energy minimized with steepest descent. The solvent was converted to 5% antifreeze particles as described above, leaving 19,644,472 conventional waters in the system, and again successfully energy minimized with steepest descent. Following visual inspection of the vesicular system, the extended production simulation was prepared as before using GROMACS 2016.1.

After an additional 1.5 μs of post-surgery vesicle simulation, there was a gap in computational resource availability, and when additional resources were finally secured, we repeated the simulation preparation procedure a third time, this time rehydrating from the final (dehydrated) 1.5 μs post-surgery equilibration snapshot that was still available. 21,666,258 MARTINI waters and 22,465 Na⁺ ions were added, and then solvent was converted to 5% antifreeze particles (1,082,189 added in place of water). Intervening energy minimizations were as described above. To maximize performance, we prepared our long-term production simulation using GROMACS 2018.1.

4.2 Simulation parameters

In addition to the lipid components, the system was solvated with 5% antifreeze particles (1,082,189 MARTINI WF residues), 95% water particles (20,561,604 MARTINI W residues), and 22,465 Na⁺ ions, for a total of 24,585,206 beads.

All simulations were performed using the MARTINI 2.1 coarse-grain forcefieldi [30]. After the 1.5 μs initial equilibration using GROMACS [65] version 2016.4, 5.2 μs production simulations were performed using GROMACS 2018.1 with 10 fs timesteps, the Verlet cutoff scheme, and reaction field electrostatics. Isotropic pressure coupling was employed using the Berendsen barostat at a time constant of 20 ps, compressibility of 1 × 10⁻⁶ bar⁻¹, and reference pressure of 1.0 bar. Lipids and solvent were separately temperature coupled with a 323 K reference temperature using the Berendsen thermostat, and a 1 ps time constant.

4.3 Asymmetric flat membrane

To construct the 46 × 46 nm, asymmetric flat membrane patch, we first used CHARMM-GUI’s Martini Maker tool [66] to create two, symmetric bilayers representing the compositions of the inner and outer leaflets of the HIV-1 liposome. Employing the same CG MARTINI lipid, water and ion models as the vesicle system, each symmetric bilayer was minimized, thermalized then equilibrated for 500 ns using GROMACS 2021.6. With the equilibrated bilayers, we then divided and merged the two systems to create a new asymmetric bilayer, preserving water and ions, and thus the hydrophilic interactions, associated with each equilibrated leaflet. Following the merging procedure, VMD’s atomselect feature was employed to trim overhanging lipids in the X and Y dimensions from the slightly-larger inner leaflet.

The composite system of merged leaflets was then minimized and thermalized. Headgroup restraints were employed with a force constant of 20 kJ/mol, and these were gradually relaxed over the course of 1 μs to allow tail melting. Once restraints were released completely and the unrestrained system was allowed to equilibrate for 1 μs, we simulated the asymmetric flat patch for a total of 7 μs of production sampling. Simulation parameters were chosen to match those described in the previous section for the HIV-1 vesicle system.

4.4 Analysis of simulations

Trajectory data files were read and exposed to the Python interpreter using the MDAnalysis library [67, 68]. Trajectories were visualized using VMD [69], and analysis plots were produced using matplotlib [70]. Array-based calculations of simulation properties leveraged the NumPy library [71]. The SciPy library [72] was used for a number of scientific algorithms. Average mean and Gaussian curvature analyses of the asymmetric flat patch were accomplished using the MDAnalysis library [67, 68].

4.5 Hydrophobic thickness

Hydrophobic thickness was considered as the center of mass distance between uniformly distributed groups of the first acyl carbon bead (‘C2B’) in each leaflet. Leaflets were delineated via VMD measure volinterior [32], and groups of beads were considered in a radius of 46.25 Å from N = 1024 test points, the latter uniformly distributed via a Poisson disk sampling procedure written by the authors [32].

4.6 Lipid translational and trans-bilayer diffusion

The translational diffusion coefficients of the lipids in each leaflet were calculated using the approach previously reported for viral simulations [27] using, (1)

Where MSD represents the mean square displacement (MSD) of the centroid of every lipid, D is the lateral diffusion coefficient and α is an arbitrary scaling factor. D and α were estimated using linear least-square fitting of MSD for simulation windows of size: 5, 25, 50, 100, 250, 500, 1000 ns. The standard deviations for the diffusion coefficient and the scaling factor were derived from the square root of the covariance matrix of the linear least-square fitting as previously described [27].

Analysis of trans-bilayer diffusion measured the number of flip-flop events per unit of time, for each lipid species, using a 3D space classifier developed by the authors [32]. Using lipid tail groups, the volume of the vesicle system was classified such that molecular density corresponding to the tail group selection served as a barrier separating interior and exterior regions of the system, representing the inner and outer leaflets, respectively. For each frame of the trajectory, headgroups were characterized according to their positions within the classified volume, i.e., interior or exterior. The latter was made possible through a massively parallel analysis framework [29]. To mitigate error resulting from undulations of the vesicle, volume classification was repeated every 20 ns throughout the time series analysis. Data resulting from headgroup tracking were used to quantify inner-to-outer and outer-to-inner translocation events and determine effective rates thereof for each species.

4.7 Mobility analysis

Lateral mobility of lipids was measured by estimating the root mean square fluctuation (RMSF) as ; where . RMSF values were calculated for lipid headgroups over a simulation window of size of 1 μs. Results are reported as the mean RMSF for headgroups of each lipid in the vesicle.

4.8 Bending rigidity

The bending rigidity of the full-scale vesicle was calculated from a well-established spherical harmonic analysis for spherical liposomes [38]. First, a single reference frame is defined by estimating the undulating radial surface (URS) [38]. The initial URS is estimated by recasting a ψ,θ-grid from the coordinate system of the vesicle, where θ ∈ [0, ψ] and ψ ∈ [0, 2π], for the colatitude and longitude, respectively. A total of two inital grids were generated, each one corresponding to one monolayer of the vesicle. The angular resolution for the two grids was dθ = dψ = 0.042 rad. based on a cutoff wavenumber of 0.5 nm^-1 and a cutoff filter of 2.5 nm^-1 to mitigate discontinuities at the poles of the vesicle [38]. After defining the surface of the inner (r_in(ϕ, ψ)) and outer monolayer (r_out(ϕ, ψ)), the undulating surface r_und was calculated for the vesicle as shown in Eq 2. (2)

The average radius of the undulating surface was then used to define the normalized radial fluctuation as (3)

Subsequently, spherical harmonic analysis was employed to decompose the normalized radial fluctuations from Eq 3. Liposome fluctuations were expanded in spherical harmonics of degree l and order m as (4)

The linear combination of spherical harmonics from Eq 4 consists of harmonic coefficients a_l,m and basis functions ; where are Legendre polynomials. The order and degree of Y_l,m are dependent on the number of points describing the initial undulating surface. In the case of the HIV-1 vesicle, the spherical harmonics were expanded as a linear combination of degree 74 and order 149.

Finally, the pseudo-inverse of the matrix Y composed by the basis functions is used to estimate the harmonic coefficients a_l,m. The a_lm can be used to obtain the power spectra of undulations by fitting the harmonic coefficients to the Helfrich continuum model for undulations on a sphere with vanishing spontaneous curvature [74], shown in Eq 5. The fitting yields an estimation of the bending rigidity k_c at temperature T as (5) where k_b is the Boltzmann constant.

4.9 Compressibility analysis

We analyzed compressibility using a technique outlined by Doktorova et al. [39], which enables the calculation of individual moduli for each leaflet in the asymmetric system. In particular, we followed the approach based on fluctuations in local thickness. To render the coarse, x-y interpolated grids from which local fluctuations are measured, we used ‘PO4’, ‘C2B’ and ‘C4B’ beads within each leaflet. Thoughtful consideration toward selection of atoms or beads used in defining these surfaces is given by the authors in the method’s paper [39].

Following guidance outlined by the authors, we chose an interpolation radius of 4.6 nm in the x-y plane, which is slightly larger than the bilayer’s overall thickness. This radius was used to average positions of the three selected beads within their respective grid cells. The analysis was accomplished with in-house Tcl procedures, invoked within VMD. Kernel density estimation, for determinations of equilibrium area and thickness used in computing compressibility, was accomplished using the Tcl8.5 ‘::math::statistics’ package. It should be noted that moduli obtained from fluctuations in lateral area, another approach outlined by Doktorova et al., is unsuitable for our flat membrane systems because their large areas lead to underestimations of mechanical stiffness [39].