Multiscale modeling of four-component lipid mixtures: domain composition, size, alignment, and properties of the phase interface

Atomistic Insight into the Lipid Nanodomains of Synaptic Vesicles

Membrane curvature, once regarded as a passive consequence of membrane composition and cellular architecture, has been shown to actively modulate various properties of the cellular membrane. These changes could also lead to segregation of the constituents of the membrane, generating nanodomains with precise biological properties. Proteins often linked with neurodegeneration (e.g., tau, alpha-synuclein) exhibit an unintuitive affinity for synaptic vesicles in neurons, which are reported to lack distinct, ordered nanodomains based on their composition. In this study, all-atom molecular dynamics simulations are used to study a full-scale synaptic vesicle of realistic Gaussian curvature and its effect on the membrane dynamics and lipid nanodomain organization. Compelling indicators of nanodomain formation, from the perspective of composition, surface areas per lipid, order parameter, and domain lifetime, are identified in the vesicle membrane, which are absent in a flat bilayer of the same lipid composition. Therefore, our study supports the idea that curvature may induce phase separation in an otherwise fluid, disordered membrane.

Martini 3 Coarse-Grained Force Field for Cholesterol

Cholesterol plays a crucial role in biomembranes by regulating various properties, such as fluidity, rigidity, permeability, and organization of lipid bilayers. The latest version of the Martini model, Martini 3, offers significant improvements in interaction balance, molecular packing, and inclusion of new bead types and sizes. However, the release of the new model resulted in the need to reparameterize many core molecules, including cholesterol. Here, we describe the development and validation of a Martini 3 cholesterol model, addressing issues related to its bonded setup, shape, volume, and hydrophobicity. The proposed model mitigates some limitations of its Martini 2 predecessor while maintaining or improving the overall behavior.

Membrane Domain Anti-Registration Induces an Intrinsic Transmembrane Potential

Plasma membrane segregation into various nanoscale membrane domains is driven by distinct interactions between diverse lipids and proteins. Among them, liquid-ordered (Lo) membrane domains are defined as "lipid rafts" and liquid-disordered (Ld) ones as "lipid non-rafts". Using model membrane systems, both intra-leaflet and inter-leaflet dynamics of these membrane domains are widely studied. Nevertheless, the biological impact of the latter, which is accompanied by membrane domain registration/anti-registration, is far from clear. Hence, in this work, we studied the biological relevance of the membrane domain anti-registration using both all-atom molecular dynamics (MD) simulations and confocal fluorescence microscopy. All-atom MD simulations suggested an intrinsic transmembrane potential for the case of the membrane anti-registration (Lo/Ld). Meanwhile, confocal fluorescence microscopy experiments of HeLa and 293T cell lines indicated that membrane cholesterol depletion could significantly alter the transmembrane potential of cells. Considering differences in the cholesterol content between Lo and Ld membrane domains, our confocal fluorescence microscopy experiments are consistent with our all-atom MD simulations. In short, membrane domain anti-registration induces local membrane asymmetry and, thus, an intrinsic transmembrane potential.

Efficient calculation of the free energy for protein partitioning using restraining potentials

An approach for the efficient simulation of phase-separated lipid bilayers, for use in the calculation of equilibrium free energies of partitioning between lipid domains, is proposed. The methodology exploits restraint potentials and rectangular aspect ratios that enforce lipid phase separation, allowing for the simulation of smaller systems that approximately reproduce bulk behavior. The utility of this approach is demonstrated through the calculation of potentials of mean force for the translation of a transmembrane protein between lipid domains. The impact of the imposed restraints on lipid tail ordering and lipid packing are explored, providing insight into how restraints can best be employed to compute accurate free-energy surfaces. This approach should be useful in the accurate calculation of equilibrium partition coefficients for transmembrane protein partitioning in heterogeneous membranes, providing insight into the thermodynamic driving forces that control this fundamental biophysical phenomenon.

Phase separation in a ternary DPPC/DOPC/POPC system with reducing hydration

The maintenance of plasma membrane structure is vital for the viability of cells. Disruption of this structure can lead to cell death. One important example is the macroscopic phase separation observed during dehydration associated with desiccation and freezing, often leading to loss of permeability and cell death. It has previously been shown that the hybrid lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) can act as a line-active component in ternary lipid systems, inhibiting macroscopic phase separation and stabilising membrane microdomains in lipid vesicles [1]. The domain size is found to decrease with increasing POPC concentration until complete mixing is observed. However, no such studies have been carried out at reduced hydration. To examine if this phase separation is unique to vesicles in excess water, we have conducted studies on several binary and ternary model membrane systems at both reduced hydration ("powder" type samples and oriented membrane stacks) and in excess water (supported lipid bilayers) at 0.2 mol fraction POPC, in the range where microdomain stabilisation is reported. Differential scanning calorimetry (DSC) and Fourier transform infrared spectroscopy (FTIR) are used to map phase transition temperatures, with X-ray and neutron scattering providing details of the changes in lipid packing and phase information within these boundaries. Atomic force microscopy (AFM) is used to image bilayers on a substrate in excess water. In all cases, macroscopic phase separation was observed rather than microdomain formation at this molar ratio. Thus POPC does not stabilise microdomains under these conditions, regardless of the type of model membrane, hydration or temperature. Thus we conclude that the driving force for separation under these conditions overcomes any linactant effects of the hybrid lipid.

CHARMM-GUI Membrane Builder: Past, Current, and Future Developments and Applications

Molecular dynamics simulations of membranes and membrane proteins serve as computational microscopes, revealing coordinated events at the membrane interface. As G protein-coupled receptors, ion channels, transporters, and membrane-bound enzymes are important drug targets, understanding their drug binding and action mechanisms in a realistic membrane becomes critical. Advances in materials science and physical chemistry further demand an atomistic understanding of lipid domains and interactions between materials and membranes. Despite a wide range of membrane simulation studies, generating a complex membrane assembly remains challenging. Here, we review the capability of CHARMM-GUI Membrane Builder in the context of emerging research demands, as well as the application examples from the CHARMM-GUI user community, including membrane biophysics, membrane protein drug-binding and dynamics, protein-lipid interactions, and nano-bio interface. We also provide our perspective on future Membrane Builder development.

Membrane domain formation induced by binding/unbinding of curvature-inducing molecules on both membrane surfaces

The domain formation of curvature-inducing molecules, such as peripheral or transmembrane proteins and conical surfactants, is studied in thermal equilibrium and nonequilibrium steady states using meshless membrane simulations. These molecules can bind to both surfaces of a bilayer membrane and also move to the opposite leaflet by a flip-flop. Under symmetric conditions for the two leaflets, the membrane domains form checkerboard patterns in addition to striped and spot patterns. The unbound membrane stabilizes the vertices of the checkerboard. Under asymmetric conditions, the domains form kagome-lattice and thread-like patterns. In the nonequilibrium steady states, a flow of the binding molecules between the upper and lower solutions can occur via flip-flop.

Molecular View on the Impact of DHA Molecules on the Physical Properties of a Model Cell Membrane

Docosahexaenoic acid (DHA) is a ω-3 polyunsaturated fatty acid, which can be uptaken by cells and is essential for proper neuronal and retinal function. However, the detailed physical impact of DHA molecules on the plasma membrane is still unclear. Hence, in this work, we carried out μs-scale coarse-grained molecular dynamics (MD) simulations to reveal the interactions between DHA molecules and a model cell membrane. As is known, the cell membrane can segregate into liquid-ordered (L_o) and liquid-disordered (L_d) membrane domains due to the differential interactions between lipids and proteins. In order to capture this feature, we adopted the three-component phase-separated lipid membranes and considered both anionic and neutral DHA molecules in the current work. Our results showed that DHA molecules can spontaneously self-assemble into nanoclusters, fuse with lipid membranes, and localize preferably in L_d membrane domains. During the membrane fusion process, DHA molecules can change the intrinsic transmembrane potential of the lipid membrane, and the effects of anionic DHA molecules are much more significant. Besides, the presence of DHA molecules mainly in the L_d membrane domains could regulate the differences in the lipid chain order, membrane thickness, cholesterol preference, and cholesterol flip-flop basically in a concentration-dependent manner, which further promote the stability of the intraleaflet dynamics and inhibit the interleaflet dynamics (or promote membrane domain registration) of the membrane domains. In short, the impact of DHA molecules on the physical properties of a model cell membrane on the molecular level revealed in our work will provide useful insights for understanding the biological functions of DHA molecules.

Molecular Organization of a Raft-like Domain in a Polyunsaturated Phospholipid Bilayer: A Supervised Machine Learning Analysis of Molecular Dynamics Simulations

Numerous health benefits are associated with omega-3 polyunsaturated fatty acids (n-3 PUFA) consumed in fish oils. An understanding of the mechanism remains elusive. The plasma membrane as a site of action is the focus in this study. With large-scale all-atom MD simulations run on a model membrane (1050 lipid molecules), we observed the evolution over time (6 μs) of a circular (raft-like) domain composed of N-palmitoylsphingomyelin (PSM) and cholesterol embedded into a surrounding (non-raft) patch composed of polyunsaturated 1-palmitoyl-2-docosahexaenoylphosphatylcholine (PDPC) (1:1:1 mol). A supervised machine learning algorithm was developed to characterize the migration of each lipid based on molecular conformation and the local environment. PDPC molecules were seen to infiltrate the ordered raft-like domain in a small amount, while a small concentration of PSM and cholesterol molecules was seen to migrate into the disordered non-raft region. Enclosing the raft-like domain, a narrow (∼2 nm in width) interfacial zone composed of PDPC, PSM, and cholesterol that buffers the substantial difference in order (ΔS_CD ≈ 0.12) between raft-like and non-raft environments was seen to form. Our results suggest that n-3 PUFA regulate the architecture of lipid rafts enriched in sphingolipids and cholesterol with a minimal effect on order within their interior in membranes.

LiPyphilic: A Python Toolkit for the Analysis of Lipid Membrane Simulations

Molecular dynamics simulations are now widely used to study emergent phenomena in lipid membranes with complex compositions. Here, we present LiPyphilic-a fast, fully tested, and easy-to-install Python package for analyzing such simulations. Analysis tools in LiPyphilic include the identification of cholesterol flip-flop events, the classification of local lipid environments, and the degree of interleaflet registration. LiPyphilic is both force field- and resolution-agnostic, and by using the powerful atom selection language of MDAnalysis, it can handle membranes with highly complex compositions. LiPyphilic also offers two on-the-fly trajectory transformations to (i) fix membranes split across periodic boundaries and (ii) perform nojump coordinate unwrapping. Our implementation of nojump unwrapping accounts for fluctuations in the box volume under the NPT ensemble-an issue that most current implementations have overlooked. The full documentation of LiPyphilic, including installation instructions and links to interactive online tutorials, is available at https://lipyphilic.readthedocs.io/en/latest.

Impact of the Protonation State of Phosphatidylinositol 4,5-Bisphosphate (PIP2) on the Binding Kinetics and Thermodynamics to Transient Receptor Potential Vanilloid (TRPV5): A Milestoning Study

The binding of phosphatidylinositol 4,5-bisphosphate (PIP2) to the ion channel transient receptor potential vanilloid 5 (TRPV5) is critical for its function. We use atomically detailed simulations and the milestoning theory to compute the free energy profile and the kinetics of PIP2 binding to TRPV5. We estimate the rate of binding and the impact of the protonation state on the process. Several channel residues are identified as influential in the association event and will be interesting targets for mutation analysis. Our simulations reveal that PIP2 binds to TRPV5 in an unprotonated state and is protonated in the membrane. The switch between the protonation state of PIP2 is modeled as a diabatic transition and occurs about halfway through the reaction.

Nonconverged Constraints Cause Artificial Temperature Gradients in Lipid Bilayer Simulations

Molecular dynamics (MD) simulations have become an indispensable tool to investigate phase separation in model membrane systems. In particular, simulations based on coarse-grained (CG) models have found widespread use due to their increased computational efficiency, allowing for simulations of multicomponent lipid bilayers undergoing phase separation into liquid-ordered and liquid-disordered domains. Here, we show that a significant temperature difference between molecule types can artificially arise in CG MD membrane simulations with the standard Martini simulation parameters in GROMACS. In particular, the linear constraint solver (LINCS) algorithm does not converge with its default settings, resulting in serious temperature differences between molecules in a time step-dependent manner. We demonstrate that the underlying reason for this behavior is the presence of highly constrained moieties, such as cholesterol. Their presence can critically impact numerous structural and dynamic membrane properties obtained from such simulations. Furthermore, any preference of these molecules toward a certain membrane phase can lead to spatial temperature gradients, which can amplify the degree of phase separation or even induce it in compositions that would otherwise mix well. We systematically investigated the effect of the integration time step and LINCS settings on membrane properties. Our data show that for cholesterol-containing membranes, a time step of 20 fs should be combined with at least lincs_iter = 2 and lincs_order = 12, while using a time step of 30 fs requires at least lincs_iter = 3 and lincs_order = 12 to bring the temperature differences to a level where they do not perturb central membrane properties. Moreover, we show that in cases where stricter LINCS settings are computationally too demanding, coupling the lipids in multiple groups to the temperature bath offers a practical workaround to the problem, although the validity of this approach should be further verified. Finally, we show that similar temperature gradients can also emerge in atomistic simulations using the CHARMM force field in combination with settings that allow for a 5 fs integration step.

The fine-tuning of cell membrane lipid bilayers accentuates their compositional complexity

Cell membranes are now emerging as finely tuned molecular systems, signifying that re-evaluation of our understanding of their structure is essential. Although the idea that cell membrane lipid bilayers do little more than give shape and form to cells and limit diffusion between cells and their environment is totally passé, the structural, compositional, and functional complexity of lipid bilayers often catches cell and molecular biologists by surprise. Models of lipid bilayer structure have developed considerably since the heyday of the fluid mosaic model, principally by the discovery of the restricted diffusion of membrane proteins and lipids within the plane of the bilayer. In reviewing this field, we now suggest that further refinement of current models is necessary and propose that describing lipid bilayers as "finely-tuned molecular assemblies" best portrays their complexity and function. Also see the video abstract here: https://www.youtube.com/watch?v=ddkP-QRZTl8.

Role of polyunsaturated phospholipids in liquid-ordered and liquid-disordered phases

Polyunsaturated phospholipids play a strong repulsive role in the liquid-disordered phase but a weak role in the liquid-ordered phase.

Effect of alcohol on the phase separation in model membranes

The discovery of coexisting liquid-ordered and liquid-disordered phases in multicomponent lipid bilayers has received widespread attention due to its potential relevance for biological systems. One of the many open questions is how the presence of additional components affects the nature of the coexisting phases. Of particular interest is the addition of alcohols because their anesthetic properties may arise from modulating bilayer behavior. We use coarse-grained Molecular Dynamics simulations to gain insight into the partitioning preferences of linear n-alcohols into ordered and disordered bilayers alongside their effects on local membrane structure. We find that alcohols cause only small changes to membrane composition alongside a lack of significant effects on membrane thickness and lipid tail order. Cholesterol and n-alcohol trans-bilayer motion is measured and found to be near or within the range of previous atomistic results. The cholesterol flip-flop rates increase with both n-alcohol length and concentration for octanol, dodecanol, and hexadecanol, indicating a decrease in lipid order. Umbrella sampling simulations of removing cholesterol from tertiary membranes find no significant difference with or without n-alcohols at various concentrations. Simulations of a phase-separated bilayer show that octanol preferentially partitions into the liquid-disordered phase in a ratio of approximately 3:1 over the liquid-ordered phase. Furthermore, partition coefficients of alcohol in single-phase membranes show a preference for longer alcohols (dodecanol and hexadecanol) to partition preferentially into the liquid-ordered phase, while decreasing the length of the alcohol reverses this trend. Our work tests experimental results while also investigating the ability for coarse-grained MARTINI simulations to capture minute differences in model membrane spatial arrangements on the nanoscale level.

Modulated and spiral surface patterns on deformable lipid vesicles

We investigate the behavior of two-dimensional systems that exhibit a transition between homogeneous and spatially inhomogeneous phases, which have spherical topology, and whose mechanical properties depend on the local value of the order parameter. One example of such a system is multicomponent lipid bilayer vesicles, which serve as a model to study cellular membranes. Under certain conditions, such bilayers separate into coexisting liquid-ordered and liquid-disordered regions. When arranged into the shape of small vesicles, this phase coexistence can result in spatial patterns that are more complex than the basic two-domain configuration encountered in typical bulk systems. The difference in bending rigidity between the liquid-ordered and liquid-disordered regions couples the shape of the vesicle to the local composition. We show that this interplay gives rise to a rich phase diagram that includes homogeneous, separated, and axisymmetric modulated phases that are divided by regions of spiral patterns in the surface morphology.

Bilayer compositional asymmetry influences the nanoscopic to macroscopic phase domain size transition

The eukaryotic plasma membrane (PM) exhibits lipid mixing heterogeneities known as lipid rafts. These lipid rafts, the result of liquid-liquid phase separation, can be modeled by coexisting liquid ordered (Lo) and liquid disordered (Ld) domains. Four-lipid component systems with a high-melting lipid, a nanodomain-inducing low-melting lipid, a macrodomain-inducing low-melting lipid, and cholesterol (chol) can give rise to domains of different sizes. These four-component systems have been characterized in experiments, yet there are few studies that model the asymmetric distribution of lipids actually found in the PM. We used molecular dynamics (MD) simulations to analyze the transition from nanoscopic to macroscopic domains in symmetric and in asymmetric model membranes. Using coarse-grained MD simulations, we found that asymmetry promotes macroscopic domain growth in a case where symmetric systems exhibit nanoscopic domains. Also, macroscopic domain formation in symmetric systems is highly dependent on registration of like phases in the cytoplasmic and exoplasmic leaflets. Using united-atom MD simulations, we found that symmetric Lo domains are only slightly more ordered than asymmetric Lo domains. We also found that large Lo domains in our asymmetric systems induce a slight chain ordering in the apposed cytoplasmic regions. The chol fractions of phase-separated Lo and Ld domains of the exoplasmic leaflet were unchanged whether the system was symmetric or asymmetric.

Carotenoids promote lateral packing and condensation of lipid membranes

Carotenoids are pigment molecules that protect biomembranes against degradation and may be involved in the formation of functional bacterial membrane microdomains. Little is known on whether different types of carotenoids have different effects on the membrane or if there is any concentration dependence of these effects. In this work, we present results from molecular dynamics simulations of phospholipid bilayers containing different amounts of either β-carotene or zeaxanthin. Both β-carotene and zeaxanthin show the ability to laterally condense the membrane lipids and reduce their inter-leaflet interactions. With increasing concentrations, both carotenoids increase the bilayer thickness and rigidity. The results reveal that carotenoids have similar effects to cholesterol on regulating the behavior of fluid-phase membranes, suggesting that they could function as sterol substitutes and confirming their potential role in the formation of functional membrane domains.

Inserting Small Molecules across Membrane Mixtures: Insight from the Potential of Mean Force

Small solutes have been shown to alter the lateral organization of cell membranes and reconstituted phospholipid bilayers; however, the mechanisms by which these changes happen are still largely unknown. Traditionally, both experiment and simulation studies have been restricted to testing only a few compounds at a time, failing to identify general molecular descriptors or chemical properties that would allow extrapolating beyond the subset of considered solutes. In this work, we probe the competing energetics of inserting a solute in different membrane environments by means of the potential of mean force. We show that these calculations can be used as a computationally efficient proxy to establish whether a solute will stabilize or destabilize domain phase separation. Combined with umbrella-sampling simulations and coarse-grained molecular dynamics simulations, we are able to screen solutes across a wide range of chemistries and polarities. Our results indicate that for the system under consideration, preferential partitioning and therefore effectiveness in altering membrane phase separation are strictly linked to the location of insertion in the bilayer (i.e., midplane or interface). Our approach represents a fast and simple tool for obtaining structural and thermodynamic insight into the partitioning of small molecules between lipid domains and its relation to phase separation, ultimately providing a platform for identifying the key determinants of this process.

Lipid Rafts: Controversies Resolved, Mysteries Remain

The lipid raft hypothesis postulates that lipid-lipid interactions can laterally organize biological membranes into domains of distinct structures, compositions, and functions. This proposal has in equal measure exhilarated and frustrated membrane research for decades. While the physicochemical principles underlying lipid-driven domains has been explored and is well understood, the existence and relevance of such domains in cells remains elusive, despite decades of research. Here, we review the conceptual underpinnings of the raft hypothesis and critically discuss the supporting and contradicting evidence in cells, focusing on why controversies about the composition, properties, and even the very existence of lipid rafts remain unresolved. Finally, we highlight several recent breakthroughs that may resolve existing controversies and suggest general approaches for moving beyond questions of the existence of rafts and towards understanding their physiological significance.

Nanodomain Clustering of the Plant Protein Remorin by Solid-State NMR

Nanodomains are dynamic membrane subcompartments, enriched in specific lipid, and protein components that act as functional platforms to manage an abundance of cellular processes. The remorin protein of plants is a well-established nanodomain marker and widely serves as a paradigm to study nanodomain clustering. Located at the inner leaflet of the plasma membrane, remorins perform essential functions during signaling. Using deuterium and phosphorus solid-state NMR, we inquire on the molecular determinants of the lipid-protein and protein-protein interactions driving nanodomain clustering. By monitoring thermotropism properties, lipid acyl chain order and membrane thickness, we report the effects of phosphoinositides and sterols on the interaction of various remorin peptides and protein constructs with the membrane. We probed several critical residues involved in this interaction and the involvement of the coiled-coil homo-oligomerisation domain into the formation of remorin nanodomains. We trace the essential role of the pH in nanodomain clustering based on anionic lipids such as phosphoinositides. Our results reveal a complex interplay between specific remorin residues and domains, the environmental pH and their resulting effects on the lipid dynamics for phosphoinositide-enriched membranes.

Gangliosides Destabilize Lipid Phase Separation in Multicomponent Membranes

Gangliosides (GMs) form an important class of lipids found in the outer leaflet of the plasma membrane. Typically, they colocalize with cholesterol and sphingomyelin in ordered membrane domains. However, detailed understanding of the lateral organization of GM-rich membranes is still lacking. To gain molecular insight, we performed molecular dynamics simulations of GMs in model membranes composed of coexisting liquid-ordered and liquid-disordered domains. We found that GMs indeed have a preference to partition into the ordered domains. At higher concentrations (>10 mol %), we observed a destabilizing effect of GMs on the phase coexistence. Further simulations with modified GMs show that the structure of the GM headgroup affects the phase separation, whereas the nature of the tail determines the preferential location. Together, our findings provide a molecular basis to understand the lateral organization of GM-rich membranes.

Role of Transmembrane Proteins for Phase Separation and Domain Registration in Asymmetric Lipid Bilayers

It is well known that the formation and spatial correlation of lipid domains in the two apposed leaflets of a bilayer are influenced by weak lipid–lipid interactions across the bilayer’s midplane. Transmembrane proteins span through both leaflets and thus offer an alternative domain coupling mechanism. Using a mean-field approximation of a simple bilayer-type lattice model, with two two-dimensional lattices stacked one on top of the other, we explore the role of this “structural” inter-leaflet coupling for the ability of a lipid membrane to phase separate and form spatially correlated domains. We present calculated phase diagrams for various effective lipid–lipid and lipid–protein interaction strengths in membranes that contain a binary lipid mixture in each leaflet plus a small amount of added transmembrane proteins. The influence of the transmembrane nature of the proteins is assessed by a comparison with “peripheral” proteins, which result from the separation of one single integral protein into two independent units that are no longer structurally connected across the bilayer. We demonstrate that the ability of membrane-spanning proteins to facilitate domain formation requires sufficiently strong lipid–protein interactions. Weak lipid–protein interactions generally tend to inhibit phase separation in a similar manner for transmembrane as for peripheral proteins.

FRET Detects the Size of Nanodomains for Coexisting Liquid-Disordered and Liquid-Ordered Phases

Biomembranes with as few as three lipid components can form coexisting liquid-disordered (Ld) and liquid-ordered (Lo) phases. In the coexistence region of Ld and Lo phases, the lipid mixtures 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC)/1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/chol or brain sphingomyelin (bSM)/DOPC/chol form micron-scale domains that are easily visualized with light microscopy. Although large domains are not observed in the mixtures DSPC/1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/chol and bSM/POPC/chol, lateral heterogeneity is nevertheless detected using techniques with nanometer-scale spatial resolution. We propose a simple and accessible method to measure domain sizes below optical resolution (∼200 nm). We measured nanodomain size for the latter two mixtures by combining experimental Förster resonance energy transfer data with a Monte-Carlo-based analysis. We found a domain radius of 7.5-10 nm for DSPC/POPC/chol, similar to values obtained previously by neutron scattering, and ∼5 nm for bSM/POPC/chol, slightly smaller than measurable by neutron scattering. These analyses also detect the domain-size transition that is observed by fluorescence microscopy in the four-component lipid mixture bSM/DOPC/POPC/chol. Accurate measurements of fluorescent-probe partition coefficients are especially important for the analysis; therefore, we exploit three different methods to measure the partition coefficient of fluorescent molecules between Ld and Lo phases.

Exploring the impact of proteins on the line tension of a phase-separating ternary lipid mixture

The separation of lipid mixtures into thermodynamically stable phase-separated domains is dependent on lipid composition, temperature, and system size. Using molecular dynamics simulations, the line tension between thermodynamically stable lipid domains formed from ternary mixtures of di-C16:0 PC:di-C18:2 PC:cholesterol at 40:40:20 mol. % ratio was investigated via two theoretical approaches. The line tension was found to be 3.1 ± 0.2 pN by capillary wave theory and 4.7 ± 3.7 pN by pressure tensor anisotropy approaches for coarse-grained models based on the Martini force field. Using an all-atom model of the lipid membrane based on the CHARMM36 force field, the line tension was found to be 3.6 ± 0.9 pN using capillary wave theory and 1.8 ± 2.2 pN using pressure anisotropy approaches. The discrepancy between estimates of the line tension based on capillary wave theory and pressure tensor anisotropy methods is discussed. Inclusion of protein in Martini membrane lipid mixtures was found to reduce the line tension by 25%-35% as calculated by the capillary wave theory approach. To further understand and predict the behavior of proteins in phase-separated membranes, we have formulated an analytical Flory-Huggins model and parameterized it against the simulation results. Taken together these results suggest a general role for proteins in reducing the thermodynamic cost associated with domain formation in lipid mixtures and quantifies the thermodynamic driving force promoting the association of proteins to domain interfaces.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Molecular Dynamics Simulations Reveal Leaflet Coupling in Compositionally Asymmetric Phase-Separated Lipid Membranes

The eukaryotic plasma membrane has an asymmetric distribution of its component lipids. Rafts that result from liquid-liquid phase separation are a feature of its exoplasmic leaflet, but how these exoplasmic leaflet domains are coupled to the cytoplasmic leaflet is not understood. These rafts can be studied in model membranes of three-component mixtures that produce coexisting liquid ordered (Lo) and liquid disordered (Ld) domains. We conducted all-atom molecular dynamics simulations of compositionally asymmetric lipid bilayers that reflect a more realistic model of the plasma membrane. One leaflet contained phase-separated domains with phosphatidylcholine and cholesterol, representing the exoplasmic leaflet, whereas the other contained phosphatidylethanolamine, phosphatidylserine, and cholesterol, which are the predominant components of the cytoplasmic leaflet. Inspired by findings of domain alignment across the two leaflets in compositionally symmetric model membranes, we examined the coupling between the two leaflets to see how the single-phase cytoplasmic leaflet would respond to phase separation in the other leaflet and if information could be communicated across the membrane. We found the region of the single-phase leaflet apposing the Lo domain to be slightly more ordered and thicker than the region apposing the Ld domain. The region across from the Lo domain is somewhat enriched in cholesterol and significantly depleted of polyunsaturated lipids.

Structure of lateral heterogeneities in a coarse-grained model for multicomponent membranes

We study the lateral domain structure in a coarse-grained molecular model for multicomponent lipid bilayers by semi-grandcanonical Monte Carlo simulations. The membranes are filled with liquid ordered (lo) domains surrounded by a liquid disordered (ld) matrix. Depending on the membrane composition and temperature, we identify different morphological regimes: one regime (I) where the lo domains are small and relatively compact, and two regimes (II, II') where they are larger and often interconnected. In the latter two regimes, the ld matrix forms a network of disordered trenches separating the lo domains, with a relatively high content of interdigitated line defects. Since such defects are also a structural element of the modulated ripple phase in one component membranes, we argue that the regimes II, II' may be amorphous equivalents of the ripple phase in multicomponent membranes. We also analyze the local structure and provide evidence that the domains in regime I are stabilized by a monolayer curvature mechanism postulated in earlier work [S. Meinhardt et al., PNAS, 2013, 110, 4476].

How to Determine Lipid Interactions in Membranes from Experiment Through the Ising Model

The determination and the meaning of interactions in lipid bilayers are discussed and interpreted through the Ising model. Originally developed to understand phase transitions in ferromagnetic systems, the Ising model applies equally well to lipid bilayers. In the case of a membrane, the essence of the Ising model is that each lipid is represented by a site on a lattice and that the interaction of each site with its nearest neighbors is represented by an energy parameter ω. To calculate the thermodynamic properties of the system, such as the enthalpy, the Gibbs energy, and the heat capacity, the partition function is derived. The calculation of the configurational entropy factor in the partition function, however, requires approximations or the use of Monte Carlo (MC) simulations. Those approximations are described. Ultimately, MC simulations are used in combination with experiment to determine the interaction parameters ω in lipid bilayers. Several experimental approaches are described, which can be used to obtain interaction parameters. They include nearest-neighbor recognition, differential scanning calorimetry, and Förster resonance energy transfer. Those approaches are most powerful when used in combination of MC simulations of Ising models. Lipid membranes of different compositions are discussed, which have been studied with these approaches. They include mixtures of cholesterol, saturated (ordered) phospholipids, and unsaturated (disordered) phospholipids. The interactions between those lipid species are examined as a function of molecular properties such as the degree of unsaturation and the acyl chain length. The general rule that emerges is that interactions between different lipids are usually unfavorable. The exception is that cholesterol interacts favorably with saturated (ordered) phospholipids. However, the interaction of cholesterol with unsaturated phospholipids becomes extremely unfavorable as the degree of unsaturation increases.

Cholesterol Effects on the Physical Properties of Lipid Membranes Viewed by Solid-state NMR Spectroscopy

In this chapter, we review the physical properties of lipid/cholesterol mixtures involving studies of model membranes using solid-state NMR spectroscopy. The approach allows one to quantify the average membrane structure, fluctuations, and elastic deformation upon cholesterol interaction. Emphasis is placed on understanding the membrane structural deformation and emergent fluctuations at an atomistic level. Lineshape measurements using solid-state NMR spectroscopy give equilibrium structural properties, while relaxation time measurements study the molecular dynamics over a wide timescale range. The equilibrium properties of glycerophospholipids, sphingolipids, and their binary and tertiary mixtures with cholesterol are accessible. Nonideal mixing of cholesterol with other lipids explains the occurrence of liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids, and may drive formation of lipid rafts. The functional dependence of ²H NMR spin-lattice relaxation (R _1Z) rates on segmental order parameters (S _CD) for lipid membranes is indicative of emergent viscoelastic properties. Addition of cholesterol shows stiffening of the bilayer relative to the pure lipids and this effect is diminished for lanosterol. Opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale can potentially affect lipid raft formation in cellular membranes.

Regimes of Complex Lipid Bilayer Phases Induced by Cholesterol Concentration in MD Simulation

Cholesterol is essential to the formation of phase-separated lipid domains in membranes. Lipid domains can exist in different thermodynamic phases depending on the molecular composition and play significant roles in determining structure and function of membrane proteins. We investigate the role of cholesterol in the structure and dynamics of ternary lipid mixtures displaying phase separation using molecular dynamics simulations, employing a physiologically relevant span of cholesterol concentration. We find that cholesterol can induce formation of three regimes of phase behavior: 1) miscible liquid-disordered bulk, 2) phase-separated, domain-registered coexistence of liquid-disordered and liquid-ordered domains, and 3) phase-separated, domain-antiregistered coexistence of liquid-disordered and newly identified nanoscopic gel domains composed of cholesterol threads we name "cholesterolic gel" domains. These findings are validated and discussed in the context of current experimental knowledge, models of cholesterol spatial distributions, and models of ternary lipid-mixture phase separation.

Effects of Passive Phospholipid Flip-Flop and Asymmetric External Fields on Bilayer Phase Equilibria

Compositional asymmetry between the leaflets of bilayer membranes modifies their phase behavior and is thought to influence other important features such as mechanical properties and protein activity. We address here how phase behavior is affected by passive phospholipid flip-flop, such that the compositional asymmetry is not fixed. We predict transitions from "pre-flip-flop" behavior to a restricted set of phase equilibria that can persist in the presence of passive flip-flop. Surprisingly, such states are not necessarily symmetric. We further account for external symmetry breaking, such as a preferential substrate interaction, and show how this can stabilize strongly asymmetric equilibrium states. Our theory explains several experimental observations of flip-flop-mediated changes in phase behavior and shows how domain formation and compositional asymmetry can be controlled in concert, by manipulating passive flip-flop rates and applying external fields.

A mixed alchemical and equilibrium dynamics to simulate heterogeneous dense fluids: Illustrations for Lennard-Jones mixtures and phospholipid membranes

An algorithm to efficiently simulate multi-component fluids is proposed and illustrated. The focus is on biological membranes that are heterogeneous and challenging to investigate quantitatively. To achieve rapid equilibration of spatially inhomogeneous fluids, we mix conventional molecular dynamics simulations with alchemical trajectories. The alchemical trajectory switches the positions of randomly selected pairs of molecules and plays the role of an efficient Monte Carlo move. It assists in accomplishing rapid spatial de-correlations. Examples of phase separation and mixing are given in two-dimensional binary Lennard-Jones fluid and a DOPC-POPC membrane. The performance of the algorithm is analyzed, and tools to maximize its efficiency are provided. It is concluded that the algorithm is vastly superior to conventional molecular dynamics for the equilibrium study of biological membranes.

Relating the structure factors of two-dimensional materials in planar and spherical geometries

Scattering structure factors provide essential insight into material properties and are routinely obtained in experiments, computer simulations, and theoretical analyses. Different approaches favor different geometries of the material. In case of lipid bilayers, scattering experiments can be performed on spherical vesicles, while simulations and theory often consider planar membrane patches. We derive an approximate relationship between the structure functions of such a material in planar and spherical geometries. We illustrate the usefulness of this relationship in a case study of a Gaussian material that supports both homogeneous and microemulsion phases. Within its range of applicability, this relationship enables a model-free comparison of structure factors of the same material in different geometries.

Lipid-Protein Interactions Are Unique Fingerprints for Membrane Proteins

Cell membranes contain hundreds of different proteins and lipids in an asymmetric arrangement. Our current understanding of the detailed organization of cell membranes remains rather elusive, because of the challenge to study fluctuating nanoscale assemblies of lipids and proteins with the required spatiotemporal resolution. Here, we use molecular dynamics simulations to characterize the lipid environment of 10 different membrane proteins. To provide a realistic lipid environment, the proteins are embedded in a model plasma membrane, where more than 60 lipid species are represented, asymmetrically distributed between the leaflets. The simulations detail how each protein modulates its local lipid environment in a unique way, through enrichment or depletion of specific lipid components, resulting in thickness and curvature gradients. Our results provide a molecular glimpse of the complexity of lipid-protein interactions, with potentially far-reaching implications for our understanding of the overall organization of real cell membranes.

Phospholipid Chain Interactions with Cholesterol Drive Domain Formation in Lipid Membranes

Cholesterol is a key component of eukaryotic membranes, but its role in cellular biology in general and in lipid rafts in particular remains controversial. Model membranes are used extensively to determine the phase behavior of ternary mixtures of cholesterol, a saturated lipid, and an unsaturated lipid with liquid-ordered and liquid-disordered phase coexistence. Despite many different experiments that determine lipid-phase diagrams, we lack an understanding of the molecular-level driving forces for liquid phase coexistence in bilayers with cholesterol. Here, we use atomistic molecular dynamics computer simulations to address the driving forces for phase coexistence in ternary lipid mixtures. Domain formation is directly observed in a long-timescale simulation of a mixture of 1,2-distearoyl-sn-glycero-3-phosphocholine, unsaturated 1,2-dilinoleoyl-sn-glycero-3-phosphocholine, and cholesterol. Free-energy calculations for the exchange of the saturated and unsaturated lipids between the ordered and disordered phases give insight into the mixing behavior. We show that a large energetic contribution to domain formation is favorable enthalpic interactions of the saturated lipid in the ordered phase. This favorable energy for forming an ordered, cholesterol-rich phase is opposed by a large unfavorable entropy. Martini coarse-grained simulations capture the unfavorable free energy of mixing but do not reproduce the entropic contribution because of the reduced representation of the phospholipid tails. Phospholipid tails and their degree of unsaturation are key energetic contributors to lipid phase separation.

Stable micelles based on a mixture of coiled-coils: the role of different oligomeric states

Homomeric micelles with tunable size, shape and stability have been extensively studied for biomedical applications such as drug carriers. However, designing the local valency and self-assembled morphology of nanophase-separated multicomponent micelles with varied ligand binding possibilities remains challenging. Here, we present micelles self-assembled from amphiphilic peptide-PEG-lipid hybrid conjugates, where the peptides can be either a 3-helix or 4-helix coiled-coil. We demonstrate that the micelle size and sphericity can be controlled based on the coiled-coil oligomeric state. Using theory and coarse-grained dissipative particle dynamics (DPD) simulations in an explicit solvent simulation, we studied the distribution of 3-helix and 4-helix conjugates within the mixed micelles and observed self-organization into nanodomains within the mixed micelle. We discovered that the phase separation behavior is dictated by the geometry mismatch in the alkyl chain length from different coiled-coil oligomeric states. Our analyses of the self-assembly tendency and drug delivery potency of mixed micelles with controlled multivalency provide important insights into the assembly and formation of nanophase-separated micelles.

Composition Fluctuations in Lipid Bilayers

Cell membranes contain multiple lipid and protein components having heterogeneous in-plane (lateral) distribution. Nanoscale rafts are believed to play an important functional role, but their phase state—domains of coexisting phases or composition fluctuations—is unknown. As a step toward understanding lateral organization of cell membranes, we investigate the difference between nanoscale domains of coexisting phases and composition fluctuations in lipid bilayers. We simulate model lipid bilayers with the MARTINI coarse-grained force field on length scales of tens of nanometers and timescales of tens of microseconds. We use a binary and a ternary mixture: a saturated and an unsaturated lipid, or a saturated lipid, an unsaturated lipid, and cholesterol, respectively. In these mixtures, the phase behavior can be tuned from a mixed state to a coexistence of a liquid-crystalline and a gel, or a liquid-ordered and a liquid-disordered phase. Transition from a two-phase to a one-phase state is achieved by raising the temperature and adding a hybrid lipid (with a saturated and an unsaturated chain). We analyze the evolution of bilayer properties along this transition: domains of two phases transform to fluctuations with local ordering and compositional demixing. Nanoscale domains and fluctuations differ in several properties, including interleaflet overlap and boundary length. Hybrid lipids show no enrichment at the boundary, but decrease the difference between the coexisting phases by ordering the disordered phase, which could explain their role in cell membranes.

Partitioning of nanoscale particles on a heterogeneous multicomponent lipid bilayer

Partitioning of nanoparticles into different lipid phases of a cell membrane is regulated by the physical properties of both the membrane and nanoparticles.

Critical size dependence of domain formation observed in coarse-grained simulations of bilayers composed of ternary lipid mixtures

Model cellular membranes are known to form micro- and macroscale lipid domains dependent on molecular composition. The formation of macroscopic lipid domains by lipid mixtures has been the subject of many simulation investigations. We present a critical study of system size impact on lipid domain phase separation into liquid-ordered and liquid-disordered macroscale domains in ternary lipid mixtures. In the popular di-C16:0 PC:di-C18:2 PC:cholesterol at 35:35:30 ratio mixture, we find systems with a minimum of 1480 lipids to be necessary for the formation of macroscopic phase separated domains and systems of 10 000 lipids to achieve structurally converged conformations similar to the thermodynamic limit. To understand these results and predict the behavior of any mixture forming two phases, we develop and investigate an analytical Flory-Huggins model which is recursively validated using simulation and experimental data. We find that micro- and macroscale domains can coexist in ternary mixtures. Additionally, we analyze the distributions of specific lipid-lipid interactions in each phase, characterizing domain structures proposed based on past experimental studies. These findings offer guidance in selecting appropriate system sizes for the study of phase separations and provide new insights into the nature of domain structure for a popular ternary lipid mixture.