ReVesicle: Curation and Equilibration of Lipid Vesicles for Mesoscale Simulations

Abstract

Molecular dynamics simulations provide essential atomistic insights into the organization and dynamics of complex biological membranes. However, the equilibration of large-scale, curved lipid assemblies at the all-atom level remains a significant challenge. Standard construction approaches, such as wrapping planar bilayers onto spherical meshes, frequently reverberate into structural instabilities, including membrane holes, infiltrated water, lipid flipping, and nonequilibrated densities, which hinder stable production simulations. Here, we present ReVesicle, an iterative equilibration protocol designed to restore and stabilize quasi-spherical lipid vesicles with complex compositions and large dimensions. The proposed protocol combines selective identification and removal of infiltrated water molecules and flipped lipids with short nonequilibrium MD cycles and anisotropic pressure equilibration. These steps are organized into a modular, iterative sequence that progressively recovers bilayer continuity while preserving the vesicle geometry and enabling global density relaxation. Local vacuum-induced stress generated during nonequilibrium phases promotes lipid tail melting and hole curation, while anisotropic equilibration allows relaxation of box dimensions and system density. To demonstrate the robustness of ReVesicle, we applied the protocol to six biologically realistic vesicle systems: synaptic vesicles, plasma membranes, late endosomes, exosomes, mitochondria-derived vesicles, and the HIV-1 lipid envelope. These systems span diameters from 40 to 105 nm and reach total sizes of up to ∼150 million atoms with heterogeneous and asymmetric lipid compositions. Across all cases, ReVesicle consistently converges to continuous, tightly packed bilayers. Structural and biophysical analyses, including vesicle diameter, sphericity, area per lipid, and lipid acyl-chain order parameters, indicate preservation of quasi-spherical geometry and structural integrity. Overall, ReVesicle provides a reproducible framework for equilibrating large, heterogeneous lipid vesicles suitable for downstream all-atom simulations of complex biological environments.

1. Introduction

Since the introduction of the fluid mosaic model, membranes have been understood as dynamic, heterogeneous structures that actively shape cellular processes. Membranes are complex systems that play a crucial role in various biological processes and provide the structural foundation for compartmentalization, selective transport, and cellular communication. Their ability to adopt highly diverse geometries, from planar bilayers to tubular shapes and quasi-spherical vesicles, is key to ensure membrane’s biological functions, including organelle organization, vesicle trafficking, and viral assembly. In particular, quasi-spherical membranes have been extensively studied as they are involved in important biological processes such as neurotransmission (synaptic vesicles, SVs), intercellular communication (exosomes), and infection (viral envelopes). , Overall, the functional diversity of membranes is underpinned by their remarkable physical–chemical complexity. Eukaryotic membranes comprise hundreds of lipid species that vary in headgroup chemistry, glycosylation, lipid tail length, and saturation. ,− Major eukaryotic phospholipid categories are phosphatidylcholine (PC), phosphatidylethanolamine (PE), sphingomyelin (SM), phosphatidylserine (PS), phosphatidylinositols (PI), and sphingolipid-based glycolipids. Moreover, sterols (e.g., cholesterol) and organelle-specific lipids (e.g., cardiolipin in mitochondria or bis­(monoacylglycero)­phosphate (BMP) enrichment in late endosomes) play crucial roles in membrane diversification and specificity. − Lipid’s asymmetric distribution between inner and outer leaflets further enriches this complexity. ,, Generally, the outer leaflets are enriched in PC, SM, glycolipids, and cholesterol, while PE, PS, and PI are enriched in the inner leaflet. ,,,

Far from being passive structural elements, lipids act as dynamic players in cellular signaling and in the regulation of protein sorting and activity. , Each organelle exhibits a characteristic lipid fingerprint, reflecting its specialized function. In mitochondria, the unique dimeric phospholipid cardiolipin governs curvature and contributes to respiratory chain activity. , Late endosomes are enriched in BMP, a cone-shaped lipid with unusual fusion-genic properties that support vesicular trafficking and domain heterogeneity. Exosomes, extracellular vesicles critical for intercellular communication, are enriched in sphingolipids and cholesterol, reflecting their role in cargo sorting and stability. , Synaptic vesicles, central to neurotransmission, display high cholesterol levels and specific phosphoinositides (PI) that couple lipid metabolism to the exoendocytic cycle. ,, Together, these compositional fingerprints highlight how membranes integrate structural and functional specialization.

Molecular dynamics (MD) simulations are key to understanding membrane organization and dynamics in atomic detail. Accurate modeling and equilibration of membranes are essential for developing complex biological systems, including those with transmembrane proteins and other embedded components (e.g., ion channels, receptors, or viral proteins). , Advances in force fields and membrane-building platforms have enabled the construction of complex bilayers and more intricate shapes. − At the coarse-grained (CG) level, frameworks that enable the efficient generation of large-scale membranes with complex geometries are available. , In contrast, at the all-atom (AA) level, the commonly adopted tools primarily focus on the construction of planar lipid bilayers, where equilibration can be achieved with established protocols. Despite the success of CG approaches for large membranes, full atomistic resolution remains essential for accurately capturing lipid–lipid interactions, membrane thickness, and curvature-dependent effects in heterogeneous membranes. Recent direct comparisons between CG and AA molecular dynamics simulations and cryo-electron microscopy observables have shown that CG models can exhibit systematic deviations in bilayer thickness and lipid organization in highly curved, compositionally complex membranes, whereas AA simulations show close agreement with experimental data. Hybrid multiscale approaches combining atomistic and reduced representations have also been proposed to bridge the gap between AA detail and CG models, highlighting ongoing efforts to balance accuracy and scalability. ,− These observations motivate the development of a reliable AA protocol capable of equilibrating large, curved lipid assemblies without introducing structural artifacts. Ultimately, curved membranes remain challenging to equilibrate at the atomic level. When planar bilayers are wrapped into spherical vesicles starting from the planar bilayer, numerous interfaces are created and need to be equilibrated. In this framework, simulations frequently suffer from instabilities such as hole formation, curvature relaxation (including flattening and swelling), and lipid escape from the bilayer. To date, common strategies to mitigate these artifacts mostly rely on manual, system-specific interventions, such as modifying local membrane composition or inserting lipid patches, which introduce new interfaces requiring equilibration.

Here we present ReVesicle, an equilibration protocol that enables reliable restoration and equilibration of a quasi-spherical lipid vesicle with complex compositions and large dimensions (Figure ). Protocol implementation combines a defined sequence of MD equilibration steps with tailored coordinate selection and system setup scripts, enabling portability across MD engines, force fields, and trajectory manipulation tools. To demonstrate its robustness, we applied the method to six different large-scale all-atom lipid vesicles: synaptic vesicle (SV), plasma, endosome, exosome, mitochondrial-derived vesicle (MDV), and HIV-1 (Figures and ). These six distinct vesicles have been designed based on experimental lipidomic data, each reflecting a biologically realistic composition of up to 11 different species, considering phospholipids, cholesterol, and glycolipids (Figure ). ,,,,, Vesicle dimensions reflect a realistic 1:1 scale, spanning a wide range of sizes, with diameters from 40 to 105 nm and total atom counts ranging from ∼10 million to ∼150 million atoms, including explicit water molecules (Figure ). By enabling a well-behaved and reproducible equilibration of heterogeneous vesicles at biologically relevant scales, this approach provides a streamlined framework to build stable, quasi-spherical membranes suitable for downstream large-scale all-atom simulations.

1.

(A) Schematic representation of the ReVesicle protocol. STEP-1: Selective water and lipid removal. STEP-2: Lipid tail melting. STEP-3: Restraints release. STEP-4: Selective water and lipid removal. STEP-5: Anisotropic equilibration. (B) Left: Zoomed-in holes in the vesicle (top view). Center: Early-stage vesicle with holes. Right: Zoomed-in flipped lipids (lateral view). (C) Left: Zoomed-in view (top view). Center: Water and lipids removed from the early-stage vesicle (panel B, center). Right: Zoomed-in view of removed flipped lipids (lateral view).

2.

Lipid species used to build the six vesicles. For each lipid species, the left panel shows a 3D CPK representation extracted from simulations, while the right panel shows the corresponding 2D chemical structure. The set comprises all lipid species included in the membrane models, including phospholipids, glycolipids, and cholesterol.

3.

Modeled vesicle systems and compositions. The representative snapshots show a fully equilibrated state of the corresponding system. For each system, the vesicle diameter, total atom count, and lipid composition are reported. Full system details are provided in Tables – (Methods).

2. Methods

2.1. ReVesicle Protocol: Iterative Equilibration via Short Nonequilibrium MD Simulation

The proposed protocol is capable of hole curation and membrane restoration in large-scale quasi-spherical lipid vesicle systems by combining selective removal of infiltrated water, short nonequilibrium MD, and anisotropic pressure equilibration (Figure A). These operations are organized into a modular, iterative sequence of system restoration and simulation steps designed to progressively recover bilayer continuity and system stability. STEP-1: Selective identification and removal of infiltrated water molecules and flipped lipids within the vesicle’s membrane bilayer (Figure B,C). STEP-2: Short restrained nonequilibrium NVT simulation where applied restraints allow lipid tails melting (Figure A). STEP-3: Short NVT simulation with scaling restraints on water (Figure A). STEP-4: Selective identification and removal of infiltrated water molecules and flipped lipids within the vesicle’s membrane bilayer (Figure B,C). STEP-5: NPT simulations with anisotropic pressure coupling and restraints to allow equilibration of box dimensions and system density (Figure A). For reference, a single full ReVesicle iteration (comprising two consecutive executions of STEP-1 to STEP-3, followed by STEP-4 and STEP-5) corresponds to a total simulation time of 6.2 ns. Multiple iterations of the proposed steps are needed to obtain a continuous lipid bilayer. While remaining transferable across MD software and force fields, the proposed protocol is implemented here using VMD embedded scripting and selection languages in combination with the NAMD , simulation engine as a reference platform. Validation of the protocol is based on testing six different lipid compositions and three vesicle dimensions. The membrane’s structural properties are monitored along the entire trajectory, as reported in section . Details of each step and the simulated system are provided below.

2.1.1. STEP-1: Selective Water and Lipid Removal

The first stage of the protocol involves the identification and selective removal of infiltrated water molecules (those entering the hydrophobic membrane interior). Selection is based on the definition of two concentric spheres using a tailored selection function (Figure S1): a smaller and a larger sphere are defined such that their surfaces coincide with the O3 atoms of cholesterol residues in the inner and outer leaflets, respectively. Water molecules located between these two spherical surfaces are identified and selectively removed (Figure A,C). Often, we observe lipids with their polar heads positioned within the hydrophobic lipid tail region (i.e., flipped lipids). Here, we selectively remove the flipped lipids following the same logic used for selective water removal (Figures B,C and S1). To selectively remove flipped lipids, the selection function applies a tighter buffer between the two concentric spheres than the one used for water removal. STEP-1 requires only an input structural file (e.g., .pdb, .gro, .js) containing atomic coordinates, typically corresponding to the final frame of a simulation in which membrane holes are detected. After the selected water and/or lipid is removed, the total system charge is checked and, if necessary, adjusted to preserve overall neutrality, and the resulting system is prepared for the following MD simulation steps described below. Restraint files required for STEP-2 and STEP-3 are then generated.

2.1.2. STEP-2: Lipid Tail Melting

The second stage of the protocol consists of a short (0.7 ns), nonequilibrium NVT simulation in which harmonic positional restraints (10 kcal·mol^–1·Å^–2) are applied to all atoms except lipid tails (Figure A). STEP-2 requires only the output files from STEP-1 as input; velocities are reinitialized at 310 K, and the 0.7 ns simulation is started directly without prior energy minimization, temperature ramping, or heating. This step allows the lipid tails to equilibrate and partially occupy the voids created by water/lipid removal performed in the previous step.

2.1.3. STEP-3: Release Water Constraint

In the third step, the equilibration is continued using the coordinates and velocities from the final frame of STEP-2, and a 1.4 ns NVT simulation is performed with gradually released harmonic positional restraints applied to water molecules (Figure A). The restraints are scaled as follows: the restraint force constant is set to 4 kcal·mol^–1·Å^–2 for the first 0.35 ns, reduced to 2 kcal·mol^–1·Å^–2 for the subsequent 0.35 ns, and then fully released (0 kcal·mol^–1·Å^–2) for the final 0.7 ns. This stage promotes hole curation by allowing lipid molecules to rapidly adjust and occupy the void, although partial water reinfiltration into the membrane might occur.

2.1.4. STEP-4: Selective Water and Lipid Removal

After two consecutive iterations of STEP-1 to STEP-3, the protocol proceeds to STEP-4. STEP-4 follows the same procedure described for STEP-1. To address possible water infiltration from STEP-3, infiltrated water molecules and flipped lipids are identified using the two-concentric-sphere selection function and are selectively removed. As in STEP-1, system neutrality is verified and corrected (if necessary); restraint files required for the subsequent MD steps are generated, and the resulting structure is prepared for the subsequent step.

2.1.5. STEP-5: Anisotropic Equilibration

This stage consists of a short anisotropic run (2 ns, NPT ensemble), allowing equilibration of the simulation box dimensions and system density (Figure A). Here, lipid headgroups are positionally restrained using a force constant of 10 kcal·mol^–1·Å^–2 to maintain the quasi-spherical geometry of the vesicle and ensure continued applicability of the spherical water selection criterion when returning to STEP-1. After STEP-5 is completed, the protocol restarts from STEP-1 and is iterated until holes are no longer detected. Simulation box dimensions are updated as STEP-5 is completed.

In detail, STEP-5 utilizes anisotropic pressure coupling with fixed box angles, allowing the x, y, and z box dimensions to relax independently and the system to achieve global density equilibration. While the nonequilibrium NVT phases in STEP-2 and STEP-3 serve as the “engine” of the protocol, using local vacuum-induced stress to drive the fusion of the bilayer and the curation of holes, they do not allow for the relaxation of the whole simulation box. As a result, the system remains in a high-tension state that is not representative of the equilibrium density. The anisotropic flexibility introduced in STEP-5 is therefore essential, as it enables the simulation cell to accommodate the directional stresses generated during the preceding hole-closure phases, effectively “tightening” the boundaries around the vesicle. By maintaining fixed 90° box angles, we ensure rapid volume relaxation without the risk of triclinic skewing, while the position restraints on lipid headgroups preserve the quasi-spherical integrity of the bilayer during this final phase.

2.1.6. Production Run

After multiple iterations of the five steps, resulting in a continuous quasi-spherical lipid bilayer with no detectable holes, a 50 ns NPT production run is performed without applying any restraints (Figure A). This last step allowed us to verify the membrane’s stability under standard MD production conditions.

2.2. Analysis

2.2.1. Removed Water Partitioning

At STEP-1 and STEP-4 of each ReVesicle iteration, infiltrated water molecules were identified as those lying within the bilayer defined by a two-concentric-sphere selection function (Figure S1). All water molecules located between these two spherical surfaces were flagged and removed, and the number of removed molecules was recorded at each iteration, while the cumulative total was calculated. To distinguish between inner and outer water removal, a third intermediate sphere was defined midway between the two original spheres, with its radius chosen to bisect the distance between the inner and outer spheres. Each water molecule was then assigned to the nearest leaflet. The obtained data were subsequently plotted as (i) the number of water molecules removed per iteration and (ii) cumulative removal curves for the inner and outer regions (Figures and S2–S7). This analysis was performed using in-house Tcl scripts executed in VMD.

4.

Water removal during MDV vesicle equilibration. (A) Number of water molecules removed at each water removal step (either STEP-1 or STEP-4) of the ReVesicle equilibration protocol as iteratively applied during vesicle equilibration. Water removed from the vesicle interior is shown in pink, while water removed from the exterior is shown in light pink. (B) Representative snapshots illustrating removed water molecules. (C) The corresponding evolution of the vesicle structure at selected iterations of the ReVesicle protocol.

2.2.2. Lipid Order Analysis

Calculating the lipid acyl chain order parameter from an all-atom membrane simulation is a relatively straightforward task, as all hydrogen atoms within the lipids are explicitly represented. The order parameter reflects the orientation of each C–H bond vector with respect to the bilayer normal. Lipid tail order parameters were computed using the gorder tool, averaging all lipids of the same type and considering the entire simulation time of each vesicle system (Figure and S9–S26). Importantly, gorder enables this analysis for curved systems, such as quasi-spherical vesicles, by calculating the membrane normal locally for each lipid rather than assuming a global z-axis. This approach ensures accurate estimation of order parameters across membranes with variable dimensions and curvature. The resulting order profiles were compared with the available literature values. ,

5.

Structural and morphological characterization of vesicles. (A) POPC acyl-chain order parameters for all systems. (B) Sphericity distributions. (C) Area per lipid over time. (D) Vesicle diameter evolution during equilibration.

2.2.3. Diameter and Sphericity

The vesicle diameter was calculated over the entire trajectory (equilibration and production run) along the three principal Cartesian axes (x, y, and z) for each frame, accounting for deviations from a perfect spherical shape, using an in-house Tcl script implemented in VMD. This metric was monitored to assess the structural stability of the vesicle and to confirm the preservation of its quasi-spherical geometry. The individual x, y, and z values are reported singularly (Figures S27–S32) and computed as the average of the three (Figure ).

In addition to the diameter, the sphericity (Ψ) of the vesicle was calculated to provide a quantitative measure of the deviation from an ideal sphere (Figure ). Sphericity was obtained following Wadell’s definition:

$$\mathrm{\Psi }=\frac{{\pi }^{1/3}\times {(6V_P)}^{2/3}}{A_P}$$

where V _p and A _p are the volume and surface area of the vesicle, respectively. A perfect sphere yields Ψ = 1, while lower values indicate an increasing deviation from sphericity. The combination of diameter and sphericity analyses allows the assessment of shape stability across the simulation trajectory. This analysis was performed using a Python-based workflow built on MDAnalysis. ,

2.2.4. Area Per Lipid

The area per lipid (APL) was calculated using a Python workflow based on MDAnalysis. , For each frame, the vesicle center was defined as the center of geometry of all lipid atoms. Here, each lipid was represented by the headgroup position (phosphate P for phospholipids, phosphate O3 for cholesterol, and the COM of P–P1 for cardiolipin). The radial distances of these headgroup positions from the vesicle center were computed and separated into inner and outer leaflets using k-means clustering (k = 2). For each leaflet, the mean headgroup radius R _mean was used to estimate the leaflet surface area as a sphere:

$$A_{leaflet}=4\pi R_{mean}^2$$

APL was then calculated as

$$AP{L}_{leaflet}=\frac{A_{leaflet}}{N_{leaflet}}$$

where N _leaflet is the number of lipids in that leaflet. APL values were computed for every frame of the equilibrated trajectories for both the inner and outer leaflets (Figure ).

2.3. Planar Lipid Bilayers Construction and Equilibration

To generate biologically relevant membranes, we defined the lipid compositions based on experimental characterization, such as lipidomic data. The distribution of lipid species across the outer and inner leaflets was informed by lipidomic profiles of the selected membranes. ,,,,,,,,, For each of the six systems (HIV-1, plasma, late endosome, exosome, mitochondria-derived vesicle, synaptic vesicle), an asymmetric bilayer patch was constructed using CHARMM-GUI’s membrane input generator in lipid count mode (see Tables – for detailed compositions). The HIV-1 asymmetric bilayer patch was previously constructed. The obtained patches have been standardized in dimensions to 200 Å × 200 Å. Each system was subsequently solvated using TIP3P water and neutralized to a physiological salt concentration of 0.15 M NaCl, ensuring a 25 Å buffer between the solute and periodic boundaries.

1. Lipid Composition of Synaptic Vesicle (SV) .

Synaptic vesicle (SV) composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
Chl	CHOL	40%	0.64	901	0.36	507
PE	POPE	19.2%	0.30	203	0.70	473
	SAPE	4.8%	0.30	51	0.70	118
PC	POPC	16%	0.75	422	0.25	141
	SAPC	4%	0.80	113	0.20	28
PS	POPS	6.4%	0.00	0	1.00	225
	SAPS	1.6%	0.00	0	1.00	56
SM	PSM	5%	0.75	132	0.25	44
PI	PI(4,5)P2	3%	0.00	0	1.00	106

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

6. Lipid Composition of HIV-1 Membrane .

HIV-1 membrane composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
Chl	CHOL	33%	0.60	416	0.40	260
PE	POPE	21%	0.25	108	0.75	320
SM	PSM	16%	0.75	248	0.25	82
PS	POPS	13%	0.00	0	1.00	260
PC	POPC	10%	0.75	150	0.25	46
	DPPC	7%	0.75	120	0.25	30

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

3. Lipid Composition of Late Endosome Membrane .

Late Endosome membrane composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
PC	POPC	39%	0.70	961	0.30	412
endosomal	BMP/LBPA	15%	0.00	0	1.00	528
Chl	CHOL	14%	0.60	296	0.40	197
PE	POPE	12%	0.30	127	0.70	296
SM	PSM	12%	1.00	422	0.00	0
PI	PI(3,5)P2	5%	0.00	0	1.00	176
PS	POPS	3%	0.00	0	1.00	106

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

4. Lipid Composition of Exosome Membrane .

Exosome membrane composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
Chl	CHOL	46%	0.59	955	0.41	664
PC	POPC	12%	0.65	274	0.35	148
PS	SOPS	11%	0.00	0	1.00	387
PE	SOPE	6%	0.20	42	0.80	169
SM	PSM	6%	0.00	0	1.00	197
	LSM	5%	1.00	183	0.00	0
	NSM	5%	1.00	183	0.00	0
Glycolipid	GM3	3%	1.00	106	0.00	0
	LacCer	2%	1.00	70	0.00	0
	HexCer	2%	1.00	70	0.00	0
PI	POPI	2%	0.00	0	1.00	70

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

All six lipid patch systems were equilibrated as described below. All simulations were performed on the Triton Shared Computing Cluster (TSCC) at the San Diego Supercomputer Center. The planar membrane bilayer was equilibrated using all-atom MD simulations in NAMD3 with the CHARMM36m force field. ,− The equilibration followed a multistep protocol. First, the system was subjected to energy minimization of 5,019 steps using the conjugate gradient method. Next, to allow lipid tail equilibration, the temperature was gradually increased from 10 to 310 K over 0.6 ns in the NVT ensemble (Langevin thermostat), using a 1 fs time step. During this phase, lipid headgroups were restrained by applying positional harmonic restraints to the P atom in phospholipids, to the O3 atom in CHOL, and to the C1S atom for glycosylated ceramides. This was followed by an additional 20,076 steps of energy minimization. Afterward, the system was equilibrated in the NPT ensemble for 50 ns using a 2 fs time step and an anisotropic pressure coupling scheme (useFlexibleCell = yes, useConstantArea = no, Langevin thermostat 310 K, Nosé–Hoover Langevin piston 1.01325 bar), with all restraints removed. − In this context, key membrane and lipid properties were carefully monitored and compared with experimental values. , After 50 ns of anisotropic equilibration, we observed convergence in these parameters, which confirmed that the system was sufficiently relaxed to proceed with the final equilibration stage. Finally, a 70 ns production-like NPT simulation without any restraints was performed to ensure bilayer relaxation. Nonbonded interactions (van der Waals and short-range electrostatic) were calculated at each time step by using a cutoff of 12 Å and a switching distance of 10 Å. All simulations were performed using periodic boundary conditions, employing the particle-mesh Ewald method with a grid spacing of 2.1 Å to evaluate long-range electrostatic interactions every three time steps. The SHAKE algorithm was adopted to keep the atomic bonds involving hydrogens fixed. Frames were saved every 50 000 steps (100 ps).

2.4. From Planar Bilayer to Large-Scale Lipid Vesicles

To build all-atom quasi-spherical lipid vesicle models, we employed a bottom-up approach. First, we generated a simplified model of the lipid vesicle using a triangulated icospherical mesh, which served as a geometrical scaffold. This simplified model matches experimental estimates for each system: a diameter of 105 nm for HIV-1, a diameter of 70 nm for plasma, late endosome, exosome, and MDV, and a diameter of 40 nm for SV. ,,,,, The 3D surface mesh, designed in Blender (http://www.blender.org) and exported in COLLADA (.dae) format, approximates the vesicle’s surface and serves as input geometry for LipidWrapper. The equilibrated planar bilayer patch is wrapped onto the icospherical mesh surface using LipidWrapper, a Python-based program designed for creating large-scale lipid-bilayer models of arbitrary geometry. Input parameters included a 0.9 Å headgroup clash cutoff. This process generated six quasi-spherical lipid vesicles with the corresponding six unique compositions and three different diameters. Each obtained vesicle was solvated both internally and externally with explicit TIP3P water molecules. Then, we added Na⁺ and Cl^– ions as required to first bring the system to electrical neutrality and then to model a counterion concentration of 0.15 M. System dimensions and atom counts are reported in Table .

7. Vesicle Systems Summary .

System	Icosphere diameter	Box dimensions	Atom count
SV	40 nm	49.2 nm × 49.5 nm × 49.7 nm	11,163,105
Plasma	70 nm	79.4 nm × 79.5 nm × 79.5 nm	47,852,098
Endosome	70 nm	79.2 nm × 79.3 nm × 79.2 nm	47,052,643
Exosome	70 nm	80.3 nm × 80.5 nm × 80.4 nm	49,930,332
MDV	70 nm	79.3 nm × 79.3 nm × 79.0 nm	46,502,894
HIV-1	105 nm	114.7 nm × 114.5 nm × 114.9 nm	148,674,927

^aThe icospheric diameter corresponds to the diameter specified in Blender. Box dimensions and atom counts are reported for the fully solvated initial systems ready for MD simulations.

Upon system preparation, all-atom MD simulations were performed on the Frontera supercomputing system at the Texas Advanced Computing Center (TACC). We used a memory-optimized version of NAMD3 and the CHARMM36m force field. ,− The initial equilibration followed a multistep protocol. First, the system was subjected to energy minimization of ∼20,000 steps using the conjugate gradient method. Next, the temperature was gradually increased from 10 to 310 K over 2.4 ns in the NVT ensemble (Langevin thermostat), using a 1 fs time step, allowing lipid tail relaxation. During this phase, lipid headgroups were restrained by applying positional harmonic restraints (force constant = 10 kcal/mol) to the P atom in phospholipids, the O3 atom in CHL, and the C1S atom in glycosylated ceramides. Next, a 2.2 ns anisotropic equilibration (NPT ensemble, useFlexibleCell = yes, useConstantArea = no, Langevin thermostat 310 K, Nosé–Hoover Langevin piston 1.01325 bar, time step 2 fs) was performed, gradually releasing the harmonic restraints on the lipid headgroups (force constant from 10 to 0 kcal/mol). − Here, we observed the creation of several holes in each system. Then, the proposed protocol was applied until hole curation was completed (vide supra, section ). Nonbonded interactions (van der Waals and short-range electrostatic) were calculated at each time step using a cutoff of 12 Å and a switching distance of 10 Å. All simulations were performed using periodic boundary conditions, employing the particle-mesh Ewald method with a grid spacing of 2.1 Å to evaluate long-range electrostatic interactions every three time steps. The SHAKE algorithm was adopted to keep the atomic bonds involving hydrogens fixed. Frames were saved every 50,000 steps (100 ps).

3. Results and Discussion

3.1. Equilibration of Quasi-Spherical Lipid Vesicles: Plasma, Late Endosome, Mitochondria-Derived, Exosome, HIV-1 Lipid Envelope, Synaptic Vesicles

To demonstrate the robustness of the protocol, we tested six quasi-spherical lipid vesicles spanning six different system compositions and three different diameters (Figure ; see the Methods section for details). First, four different compositions (Tables –) were tested at a fixed vesicle diameter of 70 nm (plasma, endosome, exosome, and MDV), enabling assessment of protocol adaptability across diverse membrane chemistries. Then, two additional systems were examined to further probe the fruition of the protocol across distinct vesicle sizes and curvature regimes: an HIV-1 vesicle (Table ) with a diameter of 105 nm to test applicability to larger systems, and SV (Table ) with a diameter of 40 nm to assess performance under higher curvature conditions. Total system sizes ranged from ∼11 million atoms (SV) to ∼150 million atoms (HIV-1) (Table ), while composition complexity spanned from a minimum of 6 different lipid species (plasma, HIV-1) to a maximum of 11 different lipid species (exosome) (Tables –). Following energy minimization, heating, and restraint relaxation, holes systematically appeared in the membranes due to reduced lipid density introduced during the wrapping process. To address these defects, we applied the ReVesicle iterative equilibration protocol, which combines selective removal of infiltrated water, short nonequilibrium MD cycles, and equilibration with anisotropic pressure coupling to progressively restore bilayer continuity (Figure ; see Methods section for details). The protocol proceeds through two consecutive iterations of STEPS-1–3 followed by the execution of STEP-4 and STEP-5. Briefly, STEP-1 involves selective identification and removal of infiltrated water molecules and flipped lipids; STEP-2 consists of 0.7 ns of restrained nonequilibrium NVT simulation that allows lipid tails to relax; STEP-3 comprises 1.4 ns of NVT simulation with progressively released restraints on water molecules; STEP-4 consists of selective identification and removal of infiltrated water molecules and flipped lipids; and STEP-5 consists of 2 ns of anisotropic NPT simulation that enables equilibration of box dimensions and system density. Depending on the vesicle size and composition, full equilibration was typically achieved within 18–37 iterations, corresponding to a total equilibration time of ∼50–90 ns, after which all systems displayed continuous lipid bilayers. Following equilibration, 50 ns of unrestrained NPT production simulations were performed to assess stability. All scripts required to perform a full ReVesicle equilibration cycle, including VMD (Tcl) and NAMD, are publicly available on GitHub at https://github.com/matteo-castelli/ReVesicle.

2. Lipid Composition of Plasma Membrane .

Plasma membrane composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
Chl	CHOL	31.9%	0.56	629	0.44	493
PC	POPC	29.5%	0.69	714	0.31	323
PE	POPE	15.5%	0.20	102	0.80	442
SM	PSM	15.5%	0.69	374	0.31	170
PS	POPS	5.3%	0.00	0	1.00	187
PI	POPI	2.4%	0.00	0	1.00	85

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

5. Lipid Composition of Mitochondria-derived Vesicle (MDV) .

Mitochondria-derived vesicle (MDV) membrane composition
Lipid category	Lipid	Percent abundance	Outer leaflet fraction	Outer leaflet count	Inner leaflet fraction	Inner leaflet count
PC	POPC	40%	0.80	1126	0.20	282
PE	POPE	30%	0.40	422	0.60	633
mitochondrial	TLCL (cardiolipin)	15%	0.80	106	0.20	422
PI	PLPI	7%	0.30	74	0.70	172
Chl	CHOL	5%	0.60	106	0.40	70
PS	SLPS	3%	0.80	84	0.20	21

^aLipid numbers are taken from the planar lipid bilayer generated with the CHARMM-GUI Membrane Builder using lipid count mode and reflect the actual planar lipid patch that was simulated prior to vesicle assembly.

3.2. Water Removal and Membrane Curation

Across all six tested systems, successive ReVesicle iterations reduced both the number and size of membrane holes and were accompanied by a progressive decrease in the amount of water removed per cycle, ultimately yielding an equilibrated, continuous quasi-spherical lipid bilayer. To assess the effectiveness of the ReVesicle protocol, we calculated the number of water molecules removed at each water-removal step (Figure A and S2–S7)corresponding to either STEP-1 or STEP-4 of the ReVesicle cycleas well as the cumulative number removed over the entire vesicle equilibration process (Figures S2–S7), in both cases distinguishing between water originating from the vesicle interior and exterior. As shown in Figure A for MDV vesicle and in Figures S2–S7 for the other systems, this analysis reveals a decreasing trend in the number of water molecules removed at successive water-removal steps (Figure B), with progressively fewer molecules being removed as the number and size of membrane holes decrease and the system approaches full equilibration (Figure C). A perfectly balanced 50/50 distribution between inner and outer water removal is not expected, as the larger volume encompassed by the outer selection sphere inherently leads to a slightly higher number of water molecules being removed from the outer leaflet. Consequently, the cumulative number of water molecules removed from the outer region remains slightly higher across all systems (Figures S2–S7). Ultimately, the total number of removed water molecules varies substantially among systems, ranging from ∼200,000 to ∼1.7 million (Figures S2–S7). This variability appears to be primarily driven by membrane composition, whereas system size plays a comparatively secondary role.

Notably, the endosomal vesicle exhibited particularly large membrane holes during the early equilibration stages, including elongated, canyon-like openings (Figure S4C and D; Movie S3), which required extensive water removal during ReVesicle equilibration, yielding the highest number of removed water molecules (Table ). Nonetheless, the ReVesicle protocol enabled convergence toward a continuous and tightly packed bilayer (Figure , S4C, and Movie S3).

8. Quantitative Summary of the ReVesicle Equilibration Protocol).

System	Vesicle initial diameter	Vesicle final diameter	Initial atom count	Final atom count	Total water molecules removed	Total lipid molecules removed	Total simulation time
SV	45.2 nm	43.1 nm	11.1 M	10.3 M	270,034	54	123 ns
Plasma	75.4 nm	72.2 nm	47.8 M	44.7 M	1,032,653	127	140 ns
Endosome	75.1 nm	72.7 nm	47.1 M	41.9 M	1,714,156	433	121 ns
Exosome	76.5 nm	75.2 nm	49.9 M	46.9 M	1,008,373	262	128 ns
MDV	75.1 nm	72.8 nm	46.5 M	44.3 M	745,643	21	99 ns
HIV-1	110.8 nm	108.0 nm	148.7 M	148.1 M	185,083	192	138 ns

^aReported values include initial and final vesicle diameters, initial and final atom counts, cumulative numbers of removed water and lipid molecules, and the total simulation time (including the 50 ns production run.

3.3. Structural Integrity and Morphological Properties

We next sought to assess whether the ReVesicle preserved membrane structural integrity and vesicle morphology during equilibration. To this end, we evaluated lipid tail order parameters, vesicle sphericity, area per lipid (APL), and vesicle diameter as complementary metrics of local membrane organization, global shape retention, and lipid packing.

Lipid order parameters, which report the average orientation and flexibility of lipid acyl chains relative to the membrane normal and inform local organization, were computed for all lipid species, excluding cholesterol. The resulting order profiles (Figure A and S9–S26) are consistent with values reported in the literature, , indicating that the ReVesicle equilibration protocol does not perturb the lipid tail ordering.

To analyze the vesicle shape retention, the sphericity (Ψ) was measured for each system over the entire trajectory. As a result, all vesicles remain close to an ideal spherical geometry (Figure B), indicating that the ReVesicle equilibration protocol preserves overall structural integrity. Maintaining a quasi-spherical shape is essential for the ReVesicle protocol, as the selective removal of infiltrated water relies on the definition of two concentric spherical surfaces (see Methods and Figure S1). We note that slight deviations from an ideal sphere are expected on longer time scales, as biological lipid vesicles are not perfectly spherical.

Area per lipid (APL) was monitored throughout the whole trajectory to evaluate the lipid packing. Although the absolute APL values vary across systems, as expected from their distinct lipid compositions, all vesicles exhibit a consistent decrease in APL over the course of equilibration (Figure C). The loose lipid packing introduced by the initial vesicle wrapping is progressively resolved during ReVesicle equilibration, as reflected by a gradual decrease in the APL toward a compact, equilibrated membrane state (Figure C). This reduction in APL reflects the gradual shrinkage of the vesicle and tightening of lipid packing, which is consistent with the closure of holes and the removal of infiltrated water from the bilayer during the ReVesicle equilibration protocol (Movies S1–S6).

Finally, the vesicle diameter was monitored throughout the trajectories (Figure D), showing gradual shrinkage during the ReVesicle iterations, followed by low-amplitude fluctuations during the final unrestrained NPT production runs. Consistent with the observed reduction in APL and the calculated system sphericity value, analysis of the diameter along the three principal axes further confirms that all vesicles retain their quasi-spherical geometry (Figures S27–S32).

3.4. Limitations and Caveats

While the proposed ReVesicle equilibration protocol has shown consistent performance across systems with different lipid compositions and sizes, several limitations, caveats, and potential avenues for future improvement remain and are discussed below.

In addition to the canonical membrane holes, other structural defects can occasionally be observed after a few ReVesicle equilibration iterations. Among these, the most recurring artifact involves flipped lipid head-clumping, in which lipid molecules cluster with their polar heads positioned within the hydrophobic lipid tail region (Figure C). This artifact can be addressed at STEP-1 and/or STEP-4 of the protocol, concomitantly with the canonical removal of infiltrated water, by selectively removing flipped lipids using the same geometric criteria applied for water removal (Figure S1B). Although lipid removal can, in principle, be performed at each STEP-1 and STEP-4 of a ReVesicle iteration (Figure ), we recommend applying this correction only once per iteration, specifically during STEP-1 (in the first execution cycle). The ReVesicle protocol then proceeds to the next step, as defined in Figure (either STEP-2 or STEP-5). As a general guideline, we recommend prioritizing hole closure before removing flipped lipids. Removing flipped lipids in early stages (i.e., before all canonical membrane holes have closed) may prolong equilibration and require additional ReVesicle iterations to restore bilayer continuity. While such local structural artifacts can be effectively corrected, the success of the ReVesicle equilibration protocol relies on the accuracy of the selection procedure to detect infiltrated water molecules and/or clumped flipped lipids. Inaccurate selection, either excessive or insufficient removal, can hinder proper equilibration. For example, over-removal of water, dictated by improper definition of the two-concentric-sphere function, may induce local bilayer separation, while excessive removal of lipids can increase the size of membrane holes. Conversely, insufficient removal of either water or lipids can leave residual infiltrated water or flipped lipids within the hydrophobic bilayer, respectively, promoting reopening of membrane holes and/or reemergence of other structural instabilities. Importantly, the water and/or lipids selection routine is the only procedure within ReVesicle that strictly requires careful visual inspection. We therefore recommend reassessing the definition of the two-concentric-sphere selection function (Figure S1) at the end of STEP-5, in preparation for the subsequent ReVesicle iteration.

Occasionally, simulation instabilities were also observed after the removal of infiltrated water molecules (STEP-1), specifically upon restarting the simulation at STEP-2. In rare cases, RATTLE constraint failures were encountered, leading to simulation termination. This behavior arises when STEP-5 is not sufficiently long to allow water molecules to reinfiltrate regions transiently depleted during water removal, resulting in localized low-density regions where atoms experience excessively large forces. In such cases, repeating STEP-5 consistently resolves the issue by allowing adequate water redistribution and equilibration prior to restarting the protocol. Moreover, in AA large-scale systems, it is not uncommon to observe low-density regions at the simulation box edges following system heating. Performing a longer anisotropic NPT equilibration of the solvated system before initiating the ReVesicle protocol mitigates this effect. In all cases tested, repetition of STEP-5 within the ReVesicle workflow was sufficient to relax these density artifacts and restore stable equilibration along the protocol path.

A more practical consideration concerns determining when to terminate the application of the ReVesicle protocol for a given system. In general, multiple ReVesicle iterations are required to obtain a fully equilibrated vesicle, with the exact number depending on system size, composition, and initial conditions. Convergence of the number of water molecules removed per cycle, absence of flipped lipid clumps, and visual inspection confirming the lack of membrane holes together provide reliable indicators that the system has reached a state suitable for unrestrained MD simulations.

Another critical aspect to monitor during large-scale vesicle modeling concerns the equilibration of the planar lipid bilayer used as the initial building block. Poor equilibration of the lipid slab propagates to the tessellated vesicle, resulting in loosely packed lipids. In this context, the NPT equilibration step with anisotropic pressure coupling is particularly important, as it allows lipid density and membrane thickness to equilibrate (see Methods, section ). To quantify the impact of planar bilayer equilibration, we compare vesicles generated using a short anisotropic equilibration (0.4 ns) with those obtained from a longer anisotropic equilibration (50 ns, as described in section ), reporting the resulting differences in total atom counts in the assembled vesicle systems (Table S1). For larger systems, such as the HIV-1 vesicle, which accounts for ∼16 million atoms in the dry state, differences in the equilibration of the initial planar lipid slab can translate into variations in the total atom count exceeding 2 million atoms, as reported in Table S1.

In addition to these methodological caveats, a current limitation concerns the geometric applicability of the ReVesicle approach to more complex membrane shapes. The proposed protocol has been tailored to quasi-spherical vesicles, as the identification of the infiltrated water molecules is based on a two-concentric-sphere selection function (Figure S1). In principle, the same framework could be extended to arbitrary geometries by defining an ensemble of equations that describe the membrane surface, thereby generalizing the selective water-removal logic to nonspherical architectures. However, such an extension becomes increasingly challenging for more complex morphologies (e.g., the inner mitochondrial membrane).

Finally, the ReVesicle protocol combines a defined sequence of MD equilibration steps with geometry-based coordinate selection and system setup scripts, enabling portability across MD engines, force fields, and trajectory manipulation tools. While remaining transferable in principle, the protocol is implemented here using VMD selection language in combination with the NAMD simulation engine as a reference platform for large- and mesoscale molecular dynamics simulations.

4. Conclusions

Accurate modeling and equilibration of biological membranes are critical for constructing complex systems, including those with transmembrane proteins and other embedded components such as viral proteins. ,,,− Large-scale curved membranes remain particularly challenging to equilibrate at the atomic level. When planar bilayers are wrapped into spherical vesicles, numerous interfaces are created that must be relaxed, and simulations frequently encounter structural instabilities and defects, such as hole formation. To tackle this, we developed ReVesicle, an equilibration protocol specifically designed to curate holes in large, quasi-spherical lipid vesicles. In the present study, we demonstrated that ReVesicle enables the generation of continuous lipid vesicles on biologically relevant scales. By combining selective removal of infiltrated water, short nonequilibrium MD runs, and NPT equilibration with anisotropic pressure coupling, the method minimizes the need for manual interventions, such as hole patching with external lipids, and offers an effective route to obtaining stable vesicles with realistic compositions and dimensions. Further, we demonstrated the robustness and transferability of the protocol by applying it to six distinct vesicle systems (HIV-1, plasma, endosome, exosome, MDV, and SV) spanning three diameters (40, 70, and 105 nm), atom counts from ∼10 to ∼150 million, and up to 11 lipid species per system. Across all cases, iterative application of ReVesicle consistently curates membrane holes and structural defects, yielding continuous quasi-spherical bilayers suitable to undergo production-run MD simulations. Analysis of structural and biophysical properties (i.e., vesicle diameter, sphericity, area per lipid, and lipid tail order parameters) consistently indicates that the membranes retain realistic local lipid organization throughout the equilibration process. Consistent with these observations, the analysis of water removal reveals a progressive reduction of vesicle defects over successive ReVesicle iterations. The effectiveness of the protocol depends on precise geometric selection of infiltrated water and flipped lipids, as inaccuracies in this step can compromise defect curation. As the present implementation is optimized for quasi-spherical vesicles due to its reliance on a two-concentric-sphere selection function, future development will focus on expanding and generalizing the selection strategy to support more complex membrane geometries.

Importantly, we introduced glycolipids in an AA, large-scale, curved membrane. Despite their established roles in membrane organization and recognition, ,, glycolipids are frequently omitted from simulations due to their structural complexity and the additional challenges they pose. Moreover, glycosylation has been shown to play critical roles in viral infection and immune evasion, as well as in cancer-related processes, where glycans and the glycocalyx are key determinants of biological function. ,− By explicitly incorporating glycolipids into fully solvated, atomically detailed vesicles, the present work extends the scope of realistic membrane modeling toward systems that more faithfully capture the compositional and structural complexity of biological membranes. In curved membrane environments, such as vesicles, the spatial organization and exposure of glycolipid headgroups may critically influence the formation, thickness, and heterogeneity of the glycocalyx. In particular, the collective conformational ensemble of glycolipid-associated glycans can give rise to a dense surface glycan brush, which modulates molecular accessibility and recognition at the membrane–solvent interface (Figure ) Together with the proposed equilibration protocol, this capability establishes a foundation for future studies aimed at probing glyco-shielding phenomena and glycan-mediated interactions in large, heterogeneous membrane assemblies.

6.

Glycolipid-derived glycan brush in the exosome vesicle. Left: full-vesicle view showing glycolipid-associated glycans rendered as an ensemble overlay (blue), where each trace corresponds to a glycan conformation sampled during the unrestrained NPT simulation. Right: zoomed-in lateral view highlighting the outward orientation and dense surface coverage of the glycans, consistent with the formation of a glycolipid-derived glycan brush (glycocalyx-like layer).

Overall, the successful equilibration of six vesicles demonstrates that the ReVesicle protocol can reliably generate stable all-atom vesicle models across a diverse range of structural and chemical contexts. By turning large-vesicle equilibration into a routine and reproducible step, this approach establishes an effective foundation to tackle the simulation of increasingly realistic membrane systems. This capability is particularly timely, as rapidly growing computational resources continue to push molecular simulations toward systems of unprecedented size and complexity.

All scripts required to perform a complete ReVesicle equilibration cycle, including the VMD Tcl script, NAMD input files, and Python analysis codes, are publicly available on GitHub at https://github.com/matteo-castelli/ReVesicle. All initial and final equilibrated vesicle structures, together with the corresponding stripped equilibration trajectories, are available through the Amaro lab database (https://amarolab.ucsd.edu/data.php). Full simulation data sets will be made available upon reasonable request.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.6c00219.

• Supporting figures (S1–S32) for two-concentric-sphere selection function, water removal procedures, lipid order analysis, and vesicle diameter. Table S1 for planar lipid bilayer equilibration (PDF)

• Movie S1. Equilibration trajectory of the synaptic vesicle (MP4)

• Movie S2. Equilibration trajectory of the plasma membrane vesicle (MP4)

• Movie S3. Equilibration trajectory of the late endosome vesicle (MP4)

• Movie S4. Equilibration trajectory of the exosome vesicle (MP4)

• Movie S5. Equilibration trajectory of the mitochondria-derived vesicle (MP4)

• Movie S6. Equilibration trajectory of the HIV-1 lipid envelope (MP4)

M.C. constructed the synaptic vesicle, plasma, endosome, mitochondrial-derived vesicle, and HIV-1 vesicle models; performed molecular dynamics simulations; designed and carried out simulation analyses; and generated figures and movies. L.C. constructed the exosome vesicle model; performed molecular dynamics simulations; designed and carried out simulation analyses; and generated figures and movies. M.C. and L.C. conceptualized the ReVesicle protocol and developed the associated code. M.C., L.C., and R.E.A. wrote the original draft and contributed to manuscript review and editing. L.C. mentored M.C. and provided critical feedback throughout the project. R.E.A. designed and supervised the research and secured resources for the project.

The authors declare no competing financial interest.