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

The Importance of Bilayer Asymmetry in Biological Membranes: Insights from Model Membranes

This mini-review intends to highlight the importance of bilayer asymmetry. Biological membranes are complex structures that are a physical barrier separating the external environment from the cellular content. This complex bilayer comprises an extensive lipid repertory, suggesting that the different lipid structures might play a role in the membrane. Interestingly, this vast repertory of lipids is asymmetrically distributed between leaflets that form the lipid bilayer. Here, we discuss the properties of the plasma membrane from the perspective of experimental model membranes, consisting of simplified and controlled in vitro systems. We summarize some crucial features of the exoplasmic (outer) and cytoplasmic (inner) leaflets observed through investigations using symmetric and asymmetric membranes. Symmetric model membranes for the exoplasmic leaflet have a unique lipid composition that might form a coexistence of phases, namely the liquid disordered and liquid order phases. These phase domains may appear in different sizes and shapes depending on lipid composition and lipid-lipid interactions. In contrast, symmetric model membranes for the cytoplasmic leaflet form a fluid phase. We discuss the outcomes reported in the literature for asymmetric bilayers, which vary according to lipid compositions and, consequently, reflect different intra- and inter-leaflet interactions. Interestingly, the asymmetric bilayer could show induced domains in the inner leaflet, or it could decrease the tendency of the outer leaflet to phase separation. If cells regulate the lipid composition of the plasma membrane, they can adjust the existence and sizes of the domains by tuning the lipid composition.

Budding of Asymmetric Lipid Bilayers: Effects of Cholesterol, Anionic Lipid, and Electric Field

Membrane budding is vital for various cellular processes such as synaptic activity regulation, vesicle transport and release, and endocytosis/exocytosis. Although protein-mediated membrane budding has been extensively investigated, the effects of the lipid asymmetry of the two leaflets and the asymmetrically electrical environments of the cellular membrane on membrane budding remain elusive. In this work, using coarse-grained molecular dynamics simulations, we systematically investigate the impacts of lipid bilayer asymmetry and external electric fields mimicking the asymmetric membrane potential on the membrane budding. The results show that the differential stress induced by the asymmetric distribution of lipids in the two leaflets is a crucial factor for the membrane budding. The unidirectional flip of cholesterol induced by the membrane curvature and the asymmetric ion adsorption induced by the anionic lipids promote the budding process. Furthermore, the external electric field applied perpendicularly to the bilayer plane increases the transmembrane potential and produces an additional differential stress across the leaflets by imposing an asymmetric torque on the lipid headgroups in the two leaflets, facilitating the membrane budding. These findings offer insights into how the structural and the environmental asymmetry in natural cellular membranes influence membrane budding in cellular processes.

Enhancing the Assembly Properties of Bottom-Up Coarse-Grained Phospholipids

A plethora of key biological events occur at the cellular membrane where the large spatiotemporal scales necessitate dimensionality reduction or coarse-graining approaches over conventional all-atom molecular dynamics simulation. Constructing coarse-grained descriptions of membranes systematically from statistical mechanical principles has largely remained challenging due to the necessity of capturing amphipathic self-assembling behavior in coarse-grained models. We show that bottom-up coarse-grained lipid models can possess metastable morphological behavior and that this potential metastability has ramifications for accurate development and training. We in turn develop a training algorithm which evades metastability issues by linking model training to self-assembling behavior, and demonstrate its robustness via construction of solvent-free coarse-grained models of various phospholipid membranes, including lipid species such as phosphatidylcholines, phosphatidylserines, sphingolipids, and cholesterol. The resulting coarse-grained lipid models are orders of magnitude faster than their atomistic counterparts while retaining structural fidelity and constitute a promising direction for the development of coarse-grained models of realistic cell membranes.

Effect of leaflet asymmetry on the stretching elasticity of lipid bilayers with phosphatidic acid

The asymmetry of membranes has a significant impact on their biophysical characteristics and behavior. This study investigates the composition and mechanical properties of symmetric and asymmetric membranes in giant unilamellar vesicles (GUVs) made of palmitoyloleoyl phosphatidylcholine (POPC) and palmitoyloleoyl phosphatidic acid (POPA). A combination of fluorescence quantification, zeta potential measurements, micropipette aspiration, and bilayer molecular dynamics simulations are used to characterize these membranes. The outer leaflet composition in vesicles is found consistent across the two preparation methods we employed, namely electroformation and inverted emulsion transfer. However, characterizing the inner leaflet poses challenges. Micropipette aspiration of GUVs show that oil residues do not substantially alter membrane elasticity, but simulations reveal increased membrane thickness and decreased interleaflet coupling in the presence of oil. Asymmetric membranes with a POPC:POPA mixture in the outer leaflet and POPC in the inner leaflet display similar stretching elasticity values to symmetric POPC:POPA membranes, suggesting potential POPA insertion into the inner leaflet during vesicle formation and suppressed asymmetry. The inverse compositional asymmetry, with POPC in the outer leaflet and POPC:POPA in the inner one yield less stretchable membranes with higher compressibility modulus compared with their symmetric counterparts. Challenges in achieving and predicting compositional correspondence highlight the limitations of phase-transfer-based methods. In addition, caution is advised when using fluorescently labeled lipids (even at low fractions of 0.5 mol %), as unexpected gel-like domains in symmetric POPC:POPA membranes were observed only with a specific type of labeled DOPE (dioleoylphosphatidylethanolamine) and the same fraction of unlabeled DOPE. The latter suggest that such domain formation may result from interactions between lipids and membrane fluorescent probes. Overall, this study underscores the complexity of factors influencing GUV membrane asymmetry, emphasizing the need for further research and improvement of characterization techniques.

Non-affine deformation analysis and 3D packing defects: A new way to probe membrane heterogeneity in molecular simulations

Here, we discuss a new framework developed over the last 5 years in our group to probe nanoscale membrane heterogeneity. The framework is based on the idea of characterizing lateral heterogeneity through non-affine deformation (NAD) measurements, transverse heterogeneity through three dimensional (3D) lipid packing defects, and using these approaches to formalize the seemingly trivial correlation between lateral organization and lipid packing in biological membranes. We find that measurements from NAD analysis, a prescription which is borrowed from Physics of glasses and granular material, can faithfully distinguish between liquid-ordered and disordered phases in membranes at molecular length scales and, can also be used to identify phase boundaries with high precision. Concomitantly, 3D-packing defects can not only distinguish between the two co-existing fluid phases based on their molecular scale packing (or membrane free volume), but also provide a route to connect the membrane domains to their functionality, such as exploring the molecular origins of inter-leaflet domain registration and peptide partitioning. The correlation between lateral membrane order and transverse packing presents novel molecular design-level features that can explain functions such as protein/peptide partitioning and small-molecule permeation dynamics in complex and heterogeneous membranes with high-fidelity. The framework allows us to explore the nature of lateral organization and molecular packing as a manifestation of intricate molecular interactions among a chemically rich variety of lipids and other molecules in a membrane with complex membrane composition and asymmetry across leaflets.

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.

Building complex membranes with Martini 3

The Martini model is a popular force field for coarse-grained simulations. Membranes have always been at the center of its development, with the latest version, Martini 3, showing great promise in capturing more and more realistic behavior. In this chapter we provide a step-by-step tutorial on how to construct starting configurations, run initial simulations and perform dedicated analysis for membrane-based systems of increasing complexity, including leaflet asymmetry, curvature gradients and embedding of membrane proteins.

Spontaneous curvature generation by peptides in asymmetric bilayers

Peptides and proteins play crucial roles in membrane remodeling by inducing spontaneous curvature. However, extracting spontaneous curvatures from simulations of asymmetric bilayers is challenging because differential stress (i.e., the difference of the leaflet surface tensions) arising from leaflet area strains can vary substantially among initial conditions. This study investigates peptide-induced spontaneous curvatureδc 0 p in asymmetric bilayers consisting of a single lipid type and a peptide confined to one leaflet;δc 0 p is calculated from the Helfrich equation using the first moment of the lateral pressure tensor and an alternative expression using the differential stress. It is shown that differential stress introduced during initial system generation is effectively relaxed by equilibrating using P21 periodic boundary conditions, which allows lipids to switch leaflets across cell boundaries and equalize their chemical potentials across leaflets. This procedure leads to robust estimates ofδc 0 p for the systems simulated, and is recommended when equality of chemical potentials between the leaflets is a primary consideration.

Modeling asymmetric cell membranes at all-atom resolution

Molecular dynamics (MD) simulations are a useful tool when studying the properties of membranes as they allow for a molecular view of lipid interactions with proteins, nucleic acids, or small molecules. While model membranes are usually symmetric in their lipid composition between leaflets and include a small number of lipid components, physiological membranes are highly complex and vary in the level of asymmetry. Simulation studies have shown that changes in leaflet asymmetry can alter the properties of a membrane. It is therefore necessary to carefully build asymmetric membranes to accurately simulate membranes. This chapter carefully describes the different methods for building asymmetric membranes and the advantages/disadvantages of each method. The simplest methods involve building a membrane with either an equal number of lipids per leaflet or an equal initial surface area (SA) estimated by the area per lipid. More detailed methods include combining two symmetric membranes of equal SA or altering an asymmetric membrane and adjusting the number of lipids after equilibration to minimize an observable such as differential stress (0-DS). More complex methods that require specific simulation software are also briefly described. The challenges and assumptions are listed for each method which should help guide the researcher to choose the best method for their unique MD simulation of an asymmetric membrane.

Efficient Simulations of Solvent Asymmetry Across Lipid Membranes Using Flat-Bottom Restraints

The routinely employed periodic boundary conditions complicate molecular simulations of physiologically relevant asymmetric lipid membranes together with their distinct solvent environments. Therefore, separating the extracellular fluid from its cytosolic counterpart has often been performed using a costly double-bilayer setup. Here, we demonstrate that the lipid membrane and solvent asymmetry can be efficiently modeled with a single lipid bilayer by applying an inverted flat-bottom potential to ions and other solute molecules, thereby restraining them to only interact with the relevant leaflet. We carefully optimized the parameters of the suggested method so that the results obtained using the flat-bottom and double-bilayer approaches become mutually indistinguishable. Then, we apply the flat-bottom approach to lipid bilayers with various compositions and solvent environments, covering ions and cationic peptides to validate the approach in a realistic use case. We also discuss the possible limitations of the method as well as its computational efficiency and provide a step-by-step guide on how to set up such simulations in a straightforward manner.

Unraveling the Phase Behavior, Mechanical Stability, and Protein Reconstitution Properties of Polymer-Lipid Hybrid Vesicles

Hybrid vesicles consisting of natural phospholipids and synthetic amphiphilic copolymers have shown remarkable material properties and potential for biotechnology, combining the robustness of polymers with the biocompatibility of phospholipid membranes. To predict and optimize the mixing behavior of lipids and copolymers, as well as understand the interaction between the hybrid membrane and macromolecules like membrane proteins, a comprehensive understanding at the molecular level is essential. This can be achieved by a combination of molecular dynamics simulations and experiments. Here, simulations of POPC and PBD22-b-PEO14 hybrid membranes are shown, uncovering different copolymer configurations depending on the polymer-to-lipid ratio. High polymer concentrations created thicker membranes with an extended polymer conformation, while high lipid content led to the collapse of the polymer chain. High concentrations of polymer were further correlated with a decreased area compression modulus and altered lateral pressure profiles, hypothesized to result in the experimentally observed improvement in membrane protein reconstitution and resistance toward destabilization by detergents. Finally, simulations of a WALP peptide embedded in the bilayer showed that only membranes with up to 50% polymer content favored a transmembrane configuration. These simulations correlate with previous and new experimental results and provide a deeper understanding of the properties of lipid-copolymer hybrid membranes.