On the dynamics of molecular self-assembly and the structural analysis of bilayer membranes using coarse-grained molecular dynamics simulations

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Finite-Size Effects in Simulations of Peptide/Lipid Assembly

Abstract

Molecular dynamics simulations are an attractive tool for understanding lipid/peptide self-assembly but can be plagued by inaccuracies when the system sizes are too small. The general guidance from self-assembly simulations of homogeneous micelles is that the total number of surfactants should be three to five times greater than the equilibrium aggregate number of surfactants per micelle. Herein, the heuristic is tested on the more complicated self-assembly of lipids and amphipathic peptides using the Cooke and Martini 3 coarse-grained models. Cooke model simulations with 50 to 1000 lipids and no peptide are dominated by finite-size effects, with usually one aggregate (micelle or nanodisc) containing most of the lipids forming at each system size. Approximately 200 systems of different peptide/lipid (P/L) ratios and sizes of up to 1000 lipids yield a “finite-size phase diagram” for peptide driven self-assembly, including a coexistence region of micelles and discs. Insights from the Cooke model are applied to the assembly of dimyristoylphosphatidylcholine and the ELK-neutral peptide using the Martini 3 model. Systems of 150, 450, and 900 lipids with P/L = 1/6.25 form mixtures of lipid-rich discs that agree in size with experiment and peptide-rich micelles. Only the 150-lipid system shows finite-size effects, which arise from the long-tailed distribution of aggregate sizes. The general rule of three to five times the equilibrium aggregate size remains a practical heuristic for the Cooke and Martini 3 systems investigated here.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1007/s00232-022-00255-9.

Impact of Surface Polarity on Lipid Assembly under Spatial Confinement

Molecular dynamics (MD) simulations in the MARTINI model are used to study the assembly of 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) molecules under spatial confinement, such as during solvent evaporation from ultrasmall (femtoliter quantity) droplets. The impact of surface polarity on molecular assembly is discussed in detail. To the best of our knowledge, this work represents the first of its kind. Our results reveal that solvent evaporation gives rise to the formation of well-defined stacks of lipid bilayers in a smectic alignment. These smectic mesophases form on both polar and nonpolar surfaces but with a notable distinction. On polar surfaces, the director of the stack is oriented perpendicular to the support surface. By contrast, the stacks orient at an angle on the nonpolar surfaces. The packing of head groups on surfaces and lipid molecular mobility exhibits significant differences as surface polarity changes. The role of glycerol in the assembly and stability is also revealed. The insights revealed from the simulation have a significant impact on additive manufacturing, biomaterials, model membranes, and engineering protocells. For example, POPC assemblies via evaporation of ultrasmall droplets were produced and characterized. The trends compare well with the bilayer stack models. The surface polarity influences the local morphology and structures at the interfaces, which could be rationalized via the molecule-surface interactions observed from simulations.

Effect of magnesium sulfate in oxidized lipid bilayers properties by using molecular dynamics

Magnesium sulfate (MgSO₄) has been used as a protector agent for many diseases related to oxidative stress. The effect of MgSO₄ on the oxidized lipid bilayer has not yet been studied using molecular dynamics calculations. In this work, the effects of oxidation were evaluated by using a POPC membrane model at different concentrations of its aldehyde (-CHO) and hydroperoxide (-OOH) derivatives with and without MgSO₄. Several quantitative and qualitative properties were evaluated, such as membrane thickness, area per lipid, area compressibility modulus, snapshots after simulation finish, density distributions, time evolutions of oxidized group positions, and radial distributions of oxidized group concerning Mg. Results indicate that in the absence of MgSO₄ the mobility of oxidized groups, particularly –CHO, toward the surface interface is high. At a low oxidation level of the bilayer there is an increase in the compressibility modulus as compared to the unoxidized bilayer. MgSO₄, at a low oxidation level, tends to lessen the oxidation effects by lowering the dispersion in the distribution of oxidized species toward the membrane surface and the water region. However, MgSO₄ does not change the trends of decreasing membrane thickness and area compressibility modulus and increasing area per lipid upon oxidation. In this regard, MgSO₄ diminishes the electrostatic long-distance attractive interactions between the oxidized groups and the charged headgroups of the interface, owing to the Mg⁺² and SO₄^-2 screening effects and an electrostatic stabilization of the headgroups, preventing the pore formation, which is well-known to occur in oxidized membranes.

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MgSO₄ in vitro restores oxidized membranes but its molecular mechanism is unclear.

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MD simulations of oxidized lipid bilayers were performed with and without of MgSO₄.

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A restriction in the mobility of oxidized groups is produced by MgSO₄.

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Mg⁺² and SO₄⁼ produce screening effects on the oxidized membranes.

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MgSO₄ produce a diminution of electrostatic long-distance attractive interactions.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

We present Swarm-CG, a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

Formation and Properties of a Self-Assembled Nanoparticle-Supported Lipid Bilayer Probed through Molecular Dynamics Simulations

We have carried out coarse-grained molecular dynamics (MD) simulations to study the self-assembly procedure of a system of randomly placed lipid molecules, water beads, and a nanoparticle (NP). The self-assembly results in the formation of the nanoparticle-supported lipid bilayer (NPSLBL), with the self-assembly mechanism being driven by events such as the formation of small lipid clusters, merging of the lipid clusters in the vicinity of the NP to form NP-embedded vesicle with a pore, and collapsing of that pore to eventually form the equilibrated NPSLBL system overcoming a large free-energy barrier. Subsequently, we quantify the properties and the configurations of this NPSLBL system. We reveal that unlike our proposition of an equal number of lipid molecules occupying the inner and outer leaflets in a recent report studying the properties of a preassembled lipid bilayer, the equilibrated self-assembled NPSLBL system demonstrates a much larger number of lipid molecules occupying the outer leaflet as compared to the inner leaflet. Second, the thickness of the water layer entrapped between the NP and the inner leaflet shows similar values as predicted by experiments and our previous study. Finally, we reveal that, similar to our previous study, the diffusivity of the lipid molecules in the outer leaflet is larger than that in the inner leaflet but, due to higher temperature employed during our simulations, are even larger than that predicted by our previous study.

Lipid Packing in Lipid-Wrapped Nanoparticles

Equilibrium simulations of lipid-wrapped nanoparticles (LNP) were performed using a hybrid molecular dynamics/Monte Carlo (MD/MC) approach. The radius, R, of a spherical nanoparticle (NP) core was adjusted with MC moves while a surrounding lipid bilayer was treated with MD. A wide range of LNP sizes, with the largest R ∼ 40 nm, were studied to determine the average NP radius for a given total number of lipids, N, the number of lipids in each layer, and configurational information. A three-bead lipid model was used to allow large N. A nonequilibrium Jarzynski free energy calculation of the optimal R for a given N, was also demonstrated validating the MD/MC method. An order/disorder transition was described, unique to LNP and distinct from lamellar bilayers, that is weak and continuous with small N, but sharpens to a first order transition with N > 10000 at T ≈ 1.1, shifting to higher T with increasing N. The radius and the overlap of the inner and outer layers were used as order parameters charactering the whole system, and the density vs distance from the origin served to describe the transition in individual layers. The ordering effect of the core on the inner layer, and the disordering effect of curvature, are evident. Excellent fits for the number of lipids in the inner and outer layers vs R are presented, based on the idea that the inner layer is described as usual by an area and area/lipid but that the outer layer is slaved to the inner. The most ordered states exhibit interdigitation of the inner head groups with themselves.