Curvature-based sorting of eight lipid types in asymmetric buckled plasma membrane models

Curvature Footprints of Transmembrane Proteins in Simulations with the Martini Force Field

Membranes play essential roles in biological systems and are tremendously diverse in the topologies and chemical and elastic properties that define their functions. In many cases, a given membrane may display considerable heterogeneity, with localized clusters of lipids and proteins exhibiting distinct characteristics compared to adjoining regions. These lipid-protein assemblies can span nanometers to micrometers and are associated with cellular processes such as transport and signaling. While lipid-protein assemblages are dynamic, they can be stabilized by coupling between local membrane composition and shape. Due to the inherent difficulty in resolving atomistic details of membrane proteins in their native lipid environments, these complexes are notoriously challenging to study experimentally; however, molecular dynamics (MD) simulations might be a viable alternative. Here, we aim to assess the utility of coarse-grained (CG) MD simulations with the Martini force field for studying membrane curvature induced by transmembrane (TM) proteins that are reported to generate local curvature. The direction and magnitude of curvature induced by five different TM proteins, as well as certain lipid-protein and protein-protein interactions, were found to be in good agreement with available reference data.

Computing the influence of lipids and lipid complexes on membrane mechanics

Methodology for extracting the spontaneous curvature, bending modulus, and neutral surface of a lipid bilayer is described. The "SPEX" method is a robust technique for computing the bilayer bending modulus while allowing for resolution of the spontaneous curvature of specific interacting lipids and complexes, and the dependence of spontaneous curvature on wavelength. The method is described referring to the publicly available MembraneAnalysis.jl software package.

Predicting lipid sorting in curved membranes

Most biological membranes are curved, and both lipids and proteins play a role in generating curvature. For any given membrane shape and composition, it is not trivial to determine whether lipids are laterally distributed in a homogeneous or inhomogeneous way, and whether the inter-leaflet distribution is symmetric or not. Here we present a simple computational tool that allows to predict the preference of any lipid type for membranes with positive vs. negative curvature, for any given value of curvature. The tool is based on molecular dynamics simulations of tubular membranes with hydrophilic pores. The pores allow spontaneous, barrierless flip-flop of most lipids, while also preventing differences in pressure between the inner and outer water compartments and minimizing membrane asymmetric stresses. Specifically, we provide scripts to build and analyze the simulations. We test the tool by performing simulations on simple binary lipid mixtures, and we show that, as expected, lipids with negative intrinsic curvature distribute to the tubule inner leaflet, the more so when the radius of the tubular membrane is small. Compared to other existing computational methods, relying on membrane buckles and tethers, our method is based on spontaneous inter-leaflet transport of lipids, and therefore allows to explore lipid distribution in asymmetric membranes. The method can easily be adapted to work with any molecular dynamics code and any force field.

Analyzing lipid distributions and curvature in molecular dynamics simulations of complex membranes

We describe methods to analyze lipid distributions and curvature in membranes with complex lipid mixtures and embedded membrane proteins. We discuss issues involved in these analyses, available tools to calculate curvature preferences of lipids and proteins, and focus on tools developed in our group for visual analysis of lipid-protein interactions and the analysis of membrane curvature.

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.

Membranes get in shape: Biophysics of curving bilayers

Membrane curvature is ubiquitous and essential in cell biology. Curved membranes have several distinct features, including specific protein and lipid sorting, distinct lipid ordering, and changes in transbilayer stress. Curvature also interplays with membrane tension to generate forces that change membrane shape. This research highlight summarizes recent contributions to this topic published in Biophysical Journal.

Curvature sensing lipid dynamics in a mitochondrial inner membrane model

Membrane curvature is essential for many cellular structures and processes, and factors such as leaflet asymmetry, lipid composition, and proteins all play important roles. Cardiolipin is the signature lipid of mitochondrial membranes and is essential for maintaining the highly curved shapes of the inner mitochondrial membrane (IMM) and the spatial arrangement of membrane proteins. In this study, we investigate the partitioning behavior of various lipids present in the IMM using coarse-grained molecular dynamics simulations. This study explores curved bilayer systems containing phosphatidylcholine (PC), phosphatidylethanolamine (PE), and cardiolipin (CDL) in binary and ternary component mixtures. Curvature properties such as mean and Gaussian curvatures, as well as the distribution of lipids into the various curved regions of the cristae models, are quantified. Overall, this work represents an advance beyond previous studies on lipid curvature sensing by simulating these systems in a geometry that has the morphological features and scales of curvature consistent with regions of the IMM. We find that CDL has a stronger preference for accumulating in regions of negative curvature than PE lipids, in agreement with previous results. Furthermore, we find lipid partitioning propensity is dominated by sensitivity to mean curvature, while there is a weaker correlation with Gaussian curvature.

Origin of the nonlinear structural and mechanical properties in oppositely curved lipid mixtures

Structural and mechanical properties of membranes such as thickness, tail order, bending modulus and curvature energetics play crucial role in controlling various cellular functions that depend on the local lipid organization and membrane reshaping. While behavior of these biophysical properties are well understood in single component membranes, very little is known about how do they change in the mixed lipid membranes. Often various properties of the mixed lipid bilayers are assumed to change linearly with the mole fractions of the constituent lipids which, however, is true for "ideal" mixing only. In this study, using molecular dynamics simulations, we show that structural and mechanical properties of binary lipid mixture change nonlinearly with the lipid mole fractions, and the strength of the nonlinearity depends on two factors - spontaneous curvature difference and locally inhomogeneous interactions between the lipid components.

Simulation study of membrane bending by protein crowding: a case study with the epsin N-terminal homology domain

The mechanisms by which peripheral membrane proteins generate curvature is currently an active area of research. One of the proposed mechanisms is amphipathic insertion or the 'wedge' mechanism in which the protein shallowly inserts an amphipathic helix inside the membrane to drive the curvature. However, recent experimental studies have challenged the efficiency of the 'wedge' mechanism as it requires unusual protein densities. These studies proposed an alternative mechanism, namely 'protein-crowding', in which the lateral pressure generated by the random collisions among the membrane bound proteins drives the bending. In this study, we employ atomistic and coarse-grained molecular dynamics simulations to investigate the effects of amphipathic insertion and protein crowding on the membrane surface. Considering epsin N-terminal homology (ENTH) domain as a model protein, we show that amphipathic insertion is not essential for membrane bending. Our results suggest that ENTH domains can aggregate on the membrane surface by employing another structured region (H₃ helix). And this protein crowding decreases the cohesive energy of the lipid tails which causes a significant decrease in the membrane bending rigidity. The ENTH domain can generate a similar degree of membrane curvature irrespective of the activity of its H₀ helix. Our results are consistent with the recent experimental results.

Nanoscale membrane curvature sorts lipid phases and alters lipid diffusion

The precise spatiotemporal control of nanoscale membrane shape and composition is the result of a complex interplay of individual and collective molecular behaviors. Here, we employed single-molecule localization microscopy and computational simulations to observe single-lipid diffusion and sorting in model membranes with varying compositions, phases, temperatures, and curvatures. Supported lipid bilayers were created over 50-nm-radius nanoparticles to mimic the size of naturally occurring membrane buds, such as endocytic pits and the formation of viral envelopes. The curved membranes recruited liquid-disordered lipid phases while altering the diffusion and sorting of tracer lipids. Disorder-preferring fluorescent lipids sorted to and experienced faster diffusion on the nanoscale curvature only when embedded in a membrane capable of sustaining lipid phase separation at low temperatures. The curvature-induced sorting and faster diffusion even occurred when the sample temperature was above the miscibility temperature of the planar membrane, implying that the nanoscale curvature could induce phase separation in otherwise homogeneous membranes. Further confirmation and understanding of these results are provided by continuum and coarse-grained molecular dynamics simulations with explicit and spontaneous curvature-phase coupling, respectively. The curvature-induced membrane compositional heterogeneity and altered dynamics were achieved only with a coupling of the curvature with a lipid phase separation. These cross-validating results demonstrate the complex interplay of lipid phases, molecular diffusion, and nanoscale membrane curvature that are critical for membrane functionality.

Molecular Dynamics Simulations of Curved Lipid Membranes

Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.