Stabilizing Leaflet Asymmetry under Differential Stress in a Highly Coarse-Grained Lipid Membrane Model

Biomembranes balance many types of leaflet asymmetries

Many biological membranes host different lipid species in their two leaflets. Since their spontaneous curvatures are typically not the same, this compositional asymmetry generally entails bending torques, which can be counteracted by differential stress-the difference between the two leaflet tensions. This stress, in turn, can affect elastic parameters or phase behavior of the membrane or each individual leaflet, or push easily flippable species, especially cholesterol, from the compressed leaflet into the tense leaflet. In short, breaking the symmetry of a single observable (to wit: composition), essentially breaks all other symmetries as well, with many potentially interesting consequences. This brief report examines the elastic aspects of this interplay, focusing on some elementary conditions of mechanical and thermodynamic equilibrium, but also shows how this poses novel questions that we are only beginning to appreciate.

Nanoparticle induced fusion of lipid membranes

Membrane fusion is crucial for infection of enveloped viruses, cellular transport, and drug delivery via liposomes. Nanoparticles can serve as fusogenic agents facilitating such membrane fusion for direct transmembrane transport. However, the underlying mechanisms of nanoparticle-induced fusion and the ideal properties of such nanoparticles remain largely unknown. Here, we used molecular dynamics simulations to investigate the efficacy of spheroidal nanoparticles with different size, prolateness, and ligand interaction strengths to enhance fusion between vesicles. By systematically varying nanoparticle properties, we identified how each parameter affects the fusion process and determined the optimal parameter range that promotes fusion. These findings provide valuable insights for the design and optimization of fusogenic nanoparticles with potential biotechnological and biomedical applications.

Methyl-β-cyclodextrin asymmetrically extracts phospholipid from bilayers, granting tunable control over differential stress in lipid vesicles

Lipid asymmetry - that is, a nonuniform lipid distribution between the leaflets of a bilayer - is a ubiquitous feature of biomembranes and is implicated in several cellular phenomena. Differential tension - that is, unequal lateral monolayer tensions comparing the leaflets of a bilayer- is closely associated with lipid asymmetry underlying these varied roles. Because differential tension is not directly measurable in combination with the fact that common methods to adjust this quantity grant only semi-quantitative control over it, a detailed understanding of lipid asymmetry and differential tension are impeded. To overcome these challenges, we leveraged reversible complexation of phospholipid by methyl-β-cyclodextrin (mbCD) to tune the direction and magnitude of lipid asymmetry in synthetic vesicles. Lipid asymmetry generated in our study induced (i) vesicle shape changes and (ii) gel-liquid phase coexistence in 1-component vesicles. By applying mass-action considerations to interpret our findings, we discuss how this approach provides access to phospholipid thermodynamic potentials in bilayers containing lipid asymmetry (which are coupled to the differential tension of a bilayer). Because lipid asymmetry yielded by our approach is (i) tunable and (ii) maintained over minute to hour timescales, we anticipate that this approach will be a valuable addition to the experimental toolbox for systematic investigation into the biophysical role(s) of lipid asymmetry (and differential tension).

Quantifying uncertainty in trans-membrane stresses and moments in simulation

The lateral stress profile of a lipid bilayer constitutes a valuable link between molecular simulation and mesoscopic elastic theory. Even though it is frequently calculated in simulations, its statistical precision (or that of observables derived from it) is often left unspecified. This omission can be problematic, as uncertainties are prerequisite to assessing statistical significance. In this chapter, we provide a comprehensive yet accessible overview of the statistical error analysis for the lateral stress profile. We detail two relatively simple but powerful techniques for generating error bars: block-averaging and bootstrapping. Combining these methods allows us to reliably estimate uncertainties, even in the presence of both temporal and spatial correlations, which are ubiquitous in simulation data. We illustrate these techniques with simple examples like stress moments, but also more complex observables such as the location of stress profile extrema and the monolayer neutral surface.

Multiscale remodeling of biomembranes and vesicles

Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.

Simulating asymmetric membranes using P21 periodic boundary conditions

Molecular dynamics (MD) simulations of symmetric lipid bilayers are now well established, while those of asymmetric ones are considerably less developed. This disjunction arises in part because the surface tensions of leaflets in asymmetric bilayers can differ (unlike those of symmetric ones), and there is no simple way to determine them without assumptions. This chapter describes the use of P21 periodic boundary conditions (PBC), which allow lipids to switch leaflets, to generate asymmetric bilayers under the assumption of equal chemical potentials of lipids in opposing leaflets. A series of examples, ranging from bilayers with one lipid type to those with peptides and proteins, provides a guide for the use of P21 PBC. Critical properties of asymmetric membranes, such as spontaneous curvature, are highly sensitive to differences in the leaflet surface tensions (or differential stress), and equilibration with P21 PBC substantially reduces differential stress of asymmetric bilayers assembled with surface area-based methods. Limitations of the method are discussed. Technically, the nonstandard unit cell is difficult to parallelize and to incorporate restraints. Inherently, the assumption of equal chemical potentials, and therefore the method itself, is not applicable to all target systems. Despite these limitations, it is argued that P21 simulations should be considered when designing equilibration protocols for MD studies of most asymmetric membranes.

Extension of the iSoLF implicit-solvent coarse-grained model for multicomponent lipid bilayers

iSoLF is a coarse-grained (CG) model for lipid molecules with the implicit-solvent approximation used in molecular dynamics (MD) simulations of biological membranes. Using the original iSoLF (iSoLFv1), MD simulations of lipid bilayers consisting of either POPC or DPPC and these bilayers, including membrane proteins, can be performed. Here, we improve the original model, explicitly treating the electrostatic interactions between different lipid molecules and adding CG particle types. As a result, the available lipid types increase to 30. To parameterize the potential functions of the new model, we performed all-atom MD simulations of each lipid at three different temperatures using the CHARMM36 force field and the modified TIP3P model. Then, we parameterized both the bonded and non-bonded interactions to fit the area per lipid and the membrane thickness of each lipid bilayer by using the multistate Boltzmann Inversion method. The final model reproduces the area per lipid and the membrane thickness of each lipid bilayer at the three temperatures. We also examined the applicability of the new model, iSoLFv2, to simulate the phase behaviors of mixtures of DOPC and DPPC at different concentrations. The simulation results with iSoLFv2 are consistent with those using Dry Martini and Martini 3, although iSoLFv2 requires much fewer computations. iSoLFv2 has been implemented in the GENESIS MD software and is publicly available.

Building Asymmetric Lipid Bilayers for Molecular Dynamics Simulations: What Methods Exist and How to Choose One?

The compositional asymmetry of biological membranes has attracted significant attention over the last decade. Harboring more differences from symmetric membranes than previously appreciated, asymmetric bilayers have proven quite challenging to study with familiar concepts and techniques, leaving many unanswered questions about the reach of the asymmetry effects. One particular area of active research is the computational investigation of composition- and number-asymmetric lipid bilayers with molecular dynamics (MD) simulations. Offering a high level of detail into the organization and properties of the simulated systems, MD has emerged as an indispensable tool in the study of membrane asymmetry. However, the realization that results depend heavily on the protocol used for constructing the asymmetric bilayer models has sparked an ongoing debate about how to choose the most appropriate approach. Here we discuss the underlying source of the discrepant results and review the existing methods for creating asymmetric bilayers for MD simulations. Considering the available data, we argue that each method is well suited for specific applications and hence there is no single best approach. Instead, the choice of a construction protocol-and consequently, its perceived accuracy-must be based primarily on the scientific question that the simulations are designed to address.

Distribution of cholesterol in asymmetric membranes driven by composition and differential stress

Many lipid membranes of eukaryotic cells are asymmetric, which means the two leaflets differ in at least one physical property, such as lipid composition or lateral stress. Maintaining this asymmetry is helped by the fact that ordinary phospholipids rarely transition between leaflets, but cholesterol is an exception: its flip-flop times are in the microsecond range, so that its distribution between leaflets is determined by a chemical equilibrium. In particular, preferential partitioning can draw cholesterol into a more saturated leaflet, and phospholipid number asymmetry can force it out of a compressed leaflet. Combining highly coarse-grained membrane simulations with theoretical modeling, we investigate how these two driving forces play against each other until cholesterol's chemical potential is equilibrated. The theory includes two coupled elastic sheets and a Flory-Huggins mixing free energy with a χ parameter. We obtain a relationship between χ and the interaction strength between cholesterol and lipids in either of the two leaflets, and we find that it depends, albeit weakly, on lipid number asymmetry. The differential stress measurements under various asymmetry conditions agree with our theoretical predictions. Using the two kinds of asymmetries in combination, we find that it is possible to counteract the phospholipid number bias, and the resultant stress in the membrane, via the control of cholesterol mixing in the leaflets.

Fluid-gel coexistence in lipid membranes under differential stress

A widely conserved property of many biological lipid bilayers is their asymmetry. In addition to having distinct compositions on its two sides, a membrane can also exhibit different tensions in its two leaflets, a state known as differential stress. Here, we examine how this stress can influence the phase behavior of the constituent lipid monolayers of a single-component membrane. For temperatures sufficiently close to, but still above, the main transition, molecular dynamics simulations show the emergence of finite gel domains within the compressed leaflet. We describe the thermodynamics of this phenomenon by adding two empirical single-leaflet free energies for the fluid-gel transition, each evaluated at its respective asymmetry-dependent lipid density. Finite size effects arising in simulation are included in the theory through a geometry-dependent interfacial term. Our model reproduces the phase coexistence observed in simulation. It could therefore be used to connect the "hidden variable" of differential stress to experimentally observable properties of the main phase transition. These ideas could be generalized to any first-order bilayer phase transition in the presence of asymmetry, including liquid-ordered/liquid-disordered phase separation.

Membrane thickness, lipid phase and sterol type are determining factors in the permeability of membranes to small solutes

Cell membranes provide a selective semi-permeable barrier to the passive transport of molecules. This property differs greatly between organisms. While the cytoplasmic membrane of bacterial cells is highly permeable for weak acids and glycerol, yeasts can maintain large concentration gradients. Here we show that such differences can arise from the physical state of the plasma membrane. By combining stopped-flow kinetic measurements with molecular dynamics simulations, we performed a systematic analysis of the permeability of a variety of small molecules through synthetic membranes of different lipid composition to obtain detailed molecular insight into the permeation mechanisms. While membrane thickness is an important parameter for the permeability through fluid membranes, the largest differences occur when the membranes transit from the liquid-disordered to liquid-ordered and/or to gel state, which is in agreement with previous work on passive diffusion of water. By comparing our results with in vivo measurements from yeast, we conclude that the yeast membrane exists in a highly ordered and rigid state, which is comparable to synthetic saturated DPPC-sterol membranes.

Membrane permeability of small molecules depends on the composition of the lipid bilayer. Here, authors compare permeability measured on membranes in different physical states and conclude that the yeast membrane exists in a highly ordered phase.

Model Membrane Systems Used to Study Plasma Membrane Lipid Asymmetry

It is well known that the lipid distribution in the bilayer leaflets of mammalian plasma membranes (PMs) is not symmetric. Despite this, model membrane studies have largely relied on chemically symmetric model membranes for the study of lipid–lipid and lipid–protein interactions. This is primarily due to the difficulty in preparing stable, asymmetric model membranes that are amenable to biophysical studies. However, in the last 20 years, efforts have been made in producing more biologically faithful model membranes. Here, we review several recently developed experimental and computational techniques for the robust generation of asymmetric model membranes and highlight a new and particularly promising technique to study membrane asymmetry.