Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: a simulation study

Pattern formation of lipid domains in bilayer membranes

Phase separation plays an important role in spatial organization and material distribution of biological membranes, which are essential for crucial biological functions ranging from signaling and stress response to vesicle trafficking. Domains arising from demixing of molecules coarsen indefinitely unless growth is arrested at a finite size by additional mechanisms (e.g., membrane elasticity). The resulting finite-size domains self-organize into regular patterns such as stripes and dots, which are called modulated phases. Here, we examine the size and morphology of lipid domains with a minimal theoretical model that considers both the elastic deformation of the membrane and the chemical interactions between lipids, which are coupled by a preferred membrane curvature that depends on the local lipid composition. Microscopically, the coupling is caused by an asymmetry between leaflets which emerges after extra lipids (e.g., DPPC) are introduced to the outer leaflet. The additional lipid partitions preferentially to domains where it is enriched, creating a preferred curvature that depends on local composition. We use an amplitude expansion to determine the domain size and morphology of patterns that minimize the total free energy, which is validated by numerical simulations and compared against experiments in synthetic model membranes and cell-derived membranes. The morphology of patterns varies with membrane lipid composition following a complex morphological diagram, which is in good agreement with experiments. The domain size decreases monotonically with a membrane bending modulus but can be non-monotonic with surface tension. Our results offer testable predictions, such as pattern hysteresis upon cycling external stimuli, diverse pattern morphology near critical points, and non-monotonic dependence of the domain size on osmotic pressure, which motivate future experiments. The presented theoretical framework is generally applicable to pattern formation on deformable surfaces.

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.

Adsorption on a Spherical Colloidal Particle from a Mixture of Nanoparticles with Competing Interactions

Adsorption of nanoparticles on a spherical colloidal particle is studied by molecular dynamics simulations. We consider a generic model for a mixture of nanoparticles with energetically favored self-assembly into alternating layers of the two components. When both components are attracted to the colloidal particle, the adsorbed nanoparticles self-assemble either into alternating parallel tori and clusters at the two poles of the colloidal particle, or into alternating spirals wrapped around the spherical surface. The long-lived metastable states obtained in simulations follow from the spherical shape of the adsorbing surface and the requirement that the neighboring chains of the nanoparticles are composed of different components. A geometrical construction leading to all such patterns is presented. When the second component particles are repelled from the colloidal particle and the attraction of the first component is strong, the attracted particles form a monolayer at the surface of the colloidal particle that screens the repulsion of the second component. The subsequent adsorbed alternating spherical layers of the two components form together a thick shell. This structure leads to the adsorption that is larger than in the case of the same attraction of the two components to the colloidal particle.

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.

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.

A combined molecular/continuum-modeling approach to predict the small-angle neutron scattering of curved membranes

This paper develops a framework to compute the small-angle neutron scattering (SANS) from highly curved, dynamically fluctuating, and potentially inhomogeneous membranes. This method is needed to compute the scattering from nanometer-scale membrane domains that couple to curvature, as predicted by molecular modeling. The detailed neutron scattering length density of a small planar bilayer patch is readily available via molecular dynamics simulation. A mathematical, mechanical transformation of the planar scattering length density is developed to predict the scattering from curved bilayers. By simulating a fluctuating, curved, surface-continuum model, long time- and length-scales can be reached while, with the aid of the planar-to-curved transformation, the molecular features of the scattering length density can be retained. A test case for the method is developed by constructing a coarse-grained lipid vesicle following a protocol designed to relieve both the osmotic stress inside the vesicle and the lipid-number stress between the leaflets. A question was whether the hybrid model would be able to replicate the scattering from the highly deformed inner and outer leaflets of the small vesicle. Matching the scattering of the full (molecular vesicle) and hybrid (continuum vesicle) models indicated that the inner and outer leaflets of the full vesicle were expanded laterally, consistent with previous simulations of the Martini forcefield that showed thinning in small vesicles. The vesicle structure is inconsistent with a zero-tension leaflet deformed by a single set of elastic parameters, and the results show that this is evident in the scattering. The method can be applied to translate observations of any molecular model's neutron scattering length densities from small patches to large length and timescales.

Lateral heterogeneity and domain formation in cellular membranes

As early as the development of the fluid mosaic model for cellular membranes, researchers began observing the telltale signs of lateral heterogeneity. Over the decades this has led to the development of the lipid raft hypothesis and the ensuing controversy that has unfolded, as a result. Here, we review the physical concepts behind domain formation in lipid membranes, both of their structural and dynamic origins. This, then leads into a discussion of coarse-grained, phenomenological approaches that describe the wide range of phases associated with lipid lateral heterogeneity. We use these physical concepts to describe the interaction between raft-lipid species, such as long-chain saturated lipids, sphingomyelin, and cholesterol, and non-raft forming lipids, such as those with short acyl chains or unsaturated fatty acids. While debate has persisted on the biological relevance of lipid domains, recent research, described here, continues to identify biological roles for rafts and new experimental approaches have revealed the existence of lipid domains in living systems. Given the recent progress on both the biological and structural aspects of raft formation, the research area of membrane lateral heterogeneity will not only expand, but will continue to produce exciting results.

The antioxidant vitamin E as a membrane raft modulator: Tocopherols do not abolish lipid domains

The antioxidant vitamin E is a commonly used vitamin supplement. Although the multi-billion dollar vitamin and nutritional supplement industry encourages the use of vitamin E, there is very little evidence supporting its actual health benefits. Moreover, vitamin E is now marketed as a lipid raft destabilizing anti-cancer agent, in addition to its antioxidant behaviour. Here, we studied the influence of vitamin E and some of its vitamers on membrane raft stability using phase separating unilamellar lipid vesicles in conjunction with small-angle scattering techniques and fluorescence microscopy. We find that lipid phase behaviour remains unperturbed well beyond physiological concentrations of vitamin E (up to a mole fraction of 0.10). Our results are consistent with a proposed line active role of vitamin E at the domain boundary. We discuss the implications of these findings as they pertain to lipid raft modification in native membranes, and propose a new hypothesis for the antioxidant mechanism of vitamin E.

Self-assembly of spiral patterns in confined systems with competing interactions

Colloidal particles in polymer solutions and functionalized nanoparticles often exhibit short-range attraction coupled with long-range repulsion (SALR) leading to the spontaneous formation of symmetric patterns. Chiral nanostructures formed by thin films of SALR particles have not been reported yet. In this study, we observe striking topological transitions from a symmetric pattern of concentric rings to a chiral structure of a spiral shape, when the system is in hexagonal confinement. We find that the spiral formation can be induced either by breaking the system symmetry with a wedge, or by melting of the rings. In the former case, the chirality of the spiral is determined by the orientation of the wedge and thus can be controlled. In the latter, the spiral arises due to thermally induced defects and is absent in the average particle distribution, which forms highly regular hexagonal patterns in the central part of the system. These hexagonal patterns can be explained by interference of planar density waves. Thermodynamic considerations indicate that equilibrium spirals can appear spontaneously in any stripe-forming system confined in a hexagon with a small wedge, provided that certain conditions are satisfied by a set of phenomenological parameters.

Encapsulation of hydrophobic components in dendrimersomes and decoration of their surface with proteins and nucleic acids

Reconstructing the functions of living cells using nonnatural components is one of the great challenges of natural sciences. Compartmentalization, encapsulation, and surface decoration of globular assemblies, known as vesicles, represent key early steps in the reconstitution of synthetic cells. Here we report that vesicles self-assembled from amphiphilic Janus dendrimers, called dendrimersomes, encapsulate high concentrations of hydrophobic components and do so more efficiently than commercially available stealth liposomes assembled from phospholipid components. Multilayer onion-like dendrimersomes demonstrate a particularly high capacity for loading low-molecular weight compounds and even folded proteins. Coassembly of amphiphilic Janus dendrimers with metal-chelating ligands conjugated to amphiphilic Janus dendrimers generates dendrimersomes that selectively display folded proteins on their periphery in an oriented manner. A modular strategy for tethering nucleic acids to the surface of dendrimersomes is also demonstrated. These findings augment the functional capabilities of dendrimersomes to serve as versatile biological membrane mimics.

Lipid Raft Phase Modulation by Membrane-Anchored Proteins with Inherent Phase Separation Properties

Cell plasma membranes are a heterogeneous mixture of lipids and membrane proteins. The importance of heterogeneous lipid domains (also called lipid rafts) as a molecular sorting platform has been implicated in many physiological processes. Cell plasma membranes that are detached from the cytoskeletal structure spontaneously phase separate into distinct domains at equilibrium, which show their inherent demixing properties. Recently, researchers have discovered that proteins with strong interprotein interactions also spontaneously phase separate into distinct protein domains, thus enabling the maintenance of many membraneless organelles. Protein phase separation may also take place on the lipid membranes via lipid-anchored proteins, which suggests another potential molecular sorting platform for physiological processes on the cell membrane. When two-phase separation properties coexist physiologically, they may change the resulting phase behavior or serve as independent sorting platforms. In this paper, we used in vitro reconstitution and fluorescence imaging to systematically quantify the phase behavior that arises when proteins with inherent phase separation properties interact with raft mixture lipid membranes. Our observations and simulations show both that the proteins may enhance lipid phase separation and that this is a general property of phase-separating protein systems with a diverse number of components involved. This suggests that we should consider the overall effect of the properties of both membrane-anchored proteins and lipids when interpreting molecular sorting phenomena on the membranes.

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].

Lowering line tension with high cholesterol content induces a transition from macroscopic to nanoscopic phase domains in model biomembranes

Chemically simplified lipid mixtures are used here as models of the cell plasma membrane exoplasmic leaflet. In such models, phase separation and morphology transitions controlled by line tension in the liquid-disordered (Ld) + liquid-ordered (Lo) coexistence regime have been described [1]. Here, we study two four-component lipid mixtures at different cholesterol fractions: brain sphingomyelin (BSM) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC)/1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/cholesterol (Chol). On giant unilamellar vesicles (GUVs) display a nanoscopic-to-macroscopic transition of Ld + Lo phase domains as POPC is replaced by DOPC, and this transition also depends on the cholesterol fraction. Line tension decreases with increasing cholesterol mole fractions in both lipid mixtures. For the ternary BSM/DOPC/Chol mixture, the published phase diagram [19] requires a modification to show that when cholesterol mole fraction is >~0.33, coexisting phase domains become nanoscopic.

A Rationale for Mesoscopic Domain Formation in Biomembranes

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also be observed in vitro on model systems such as supported membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and liquid-disordered phases below a demixing temperature play a pivotal role in this context. Protein-protein and protein-lipid interactions also contribute to membrane shaping by promoting small domains or clusters. Such phase separations displaying characteristic length-scales falling in-between the nanoscopic, molecular scale on the one hand and the macroscopic scale on the other hand, are named mesophases in soft condensed matter physics. In this review, we propose a classification of the diverse mechanisms leading to mesophase separation in biomembranes. We distinguish between mechanisms relying upon equilibrium thermodynamics and those involving out-of-equilibrium mechanisms, notably active membrane recycling. In equilibrium, we especially focus on the many mechanisms that dwell on an up-down symmetry breaking between the upper and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in condensed matter physics at the heart of several important phenomena. In the present case, it can be either spontaneous (domain buckling) or explicit, i.e., due to an external cause (global or local vesicle bending properties). Whenever possible, theoretical predictions and simulation results are confronted to experiments on model systems or living cells, which enables us to identify the most realistic mechanisms from a biological perspective.

Tuning Length Scales of Small Domains in Cell-Derived Membranes and Synthetic Model Membranes

Micron-scale, coexisting liquid-ordered (L_o) and liquid-disordered (L_d) phases are straightforward to observe in giant unilamellar vesicles (GUVs) composed of ternary lipid mixtures. Experimentally, uniform membranes undergo demixing when temperature is decreased: domains subsequently nucleate, diffuse, collide, and coalesce until only one domain of each phase remains. The sizes of these two domains are limited only by the size of the system. Under different conditions, vesicles exhibit smaller-scale domains of fixed sizes, leading to the question of what sets the length scale. In membranes with excess area, small domains are expected when coarsening is hindered or when a microemulsion or modulated phase arises. Here, we test predictions of how the size, morphology, and fluorescence levels of small domains vary with the membrane's temperature, tension, and composition. Using GUVs and cell-derived giant plasma membrane vesicles, we find that 1) the characteristic size of domains decreases when temperature is increased or membrane tension is decreased, 2) stripes are favored over circular domains for lipid compositions with low energy per unit interface, 3) fluorescence levels are consistent with domain registration across both monolayer leaflets of the bilayer, and 4) small domains form in GUVs composed of lipids both with and without ester-linked lipids. Our experimental results are consistent with several elements of current theories for microemulsions and modulated phases and inconsistent with others, suggesting a motivation to modify or enhance current theories.

Orientational ordering of lamellar structures on closed surfaces

Self-assembly of particles with short-range attraction and long-range repulsion interactions on a flat and on a spherical surface is compared. Molecular dynamics simulations are performed for the two systems having the same area and the density optimal for formation of stripes of particles. Structural characteristics, e.g., a cluster size distribution, a number of defects, and an orientational order parameter (OP), as well as the specific heat, are obtained for a range of temperatures. In both cases, the cluster size distribution becomes bimodal and elongated clusters appear at the temperature corresponding to the maximum of the specific heat. When the temperature decreases, orientational ordering of the stripes takes place and the number of particles per cluster or stripe increases in both cases. However, only on the flat surface, the specific heat has another maximum at the temperature corresponding to a rapid change of the OP. On the sphere, the crossover between the isotropic and anisotropic structures occur in a much broader temperature interval; the orientational order is weaker and occurs at significantly lower temperature. At low temperature, the stripes on the sphere form spirals and the defects resemble defects in the nematic phase of rods adsorbed at a sphere.

Regulation of phase boundaries and phase-segregated patterns in model membranes

Demixing of components has long been described in model membranes. It is a consequence of non-ideal lateral interactions between membrane components, and it causes the presence of segregated phases, forming patches (domains) of different properties, thus introducing heterogeneity into the membrane. In the present review we first describe the processes through which domains are generated, how they grow, and why they are rounded, striped or fractal-like, as well as why they get distributed forming defined patterns. Next, we focus on the effect of an additive on a lipid mixture, which usually induces shifts in demixing points, thus stabilizing or destabilizing the phase-segregated state. Results found for different model membranes are summarized, detailing the ways in which phase segregation and the generated patterns may be modulated. We focus on which are, from our viewpoint, the most relevant regulating factors affecting the surface texture observed in model membranes. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Computation of a Theoretical Membrane Phase Diagram and the Role of Phase in Lipid-Raft-Mediated Protein Organization

Lipid phase heterogeneity in the plasma membrane is thought to be crucial for many aspects of cell signaling, but the physical basis of participating membrane domains such as "lipid rafts" remains controversial. Here we consider a lattice model yielding a phase diagram that includes several states proposed to be relevant for the cell membrane, including microemulsion-which can be related to membrane curvature-and Ising critical behavior. Using a neural-network-based machine learning approach, we compute the full phase diagram of this lattice model. We analyze selected regions of this phase diagram in the context of a signaling initiation event in mast cells: recruitment of the membrane-anchored tyrosine kinase Lyn to a cluster of transmembrane IgE-FcεRI receptors. We find that model membrane systems in microemulsion and Ising critical states can mediate roughly equal levels of kinase recruitment (binding energy ∼ -0.6 k_B T), whereas a membrane near a tricritical point can mediate a much stronger kinase recruitment (-1.7 k_B T). By comparing several models for lipid heterogeneity within a single theoretical framework, this work points to testable differences between existing models. We also suggest the tricritical point as a new possibility for the basis of membrane domains that facilitate preferential partitioning of signaling components.

Fluctuation tension and shape transition of vesicles: renormalisation calculations and Monte Carlo simulations

It has been known for long that the fluctuation surface tension of membranes r, computed from the height fluctuation spectrum, is not equal to the bare surface tension σ, which is introduced in the theory either as a Lagrange multiplier to conserve the total membrane area or as an external constraint. In this work we relate these two surface tensions both analytically and numerically. They are also compared to the Laplace tension γ, and the mechanical frame tension τ. Using the Helfrich model and one-loop renormalisation calculations, we obtain, in addition to the effective bending modulus κ_eff, a new expression for the effective surface tension σ_eff = σ - εk_BT/(2a_p) where k_BT is the thermal energy, a_p the projected cut-off area, and ε = 3 or 1 according to the allowed configurations that keep either the projected area or the total area constant. Moreover we show that the crumpling transition for an infinite planar membrane occurs for σ_eff = 0, and also that it coincides with vanishing Laplace and frame tensions. Using extensive Monte Carlo (MC) simulations, triangulated membranes of vesicles made of N = 100-2500 vertices are simulated within the Helfrich theory. As compared to alternative numerical models, no local constraint is applied and the shape is only controlled by the constant volume, the spontaneous curvature and σ. It is shown that the numerical fluctuation surface tension r is equal to σ_eff both with radial MC moves (ε = 3) and with corrected MC moves locally normal to the fluctuating membrane (ε = 1). For finite vesicles of typical size R, two different regimes are defined: a tension regime for [small sigma, Greek, circumflex]_eff = σ_effR²/κ_eff > 0 and a bending one for -1 < [small sigma, Greek, circumflex]_eff < 0. A shape transition from a quasi-spherical shape imposed by the large surface energy, to more deformed shapes only controlled by the bending energy, is observed numerically at [small sigma, Greek, circumflex]_eff ≃ 0. We propose that the buckling transition, observed for planar supported membranes in the literature, occurs for [small sigma, Greek, circumflex]_eff ≃ -1, the associated negative frame tension playing the role of a compressive force. Hence, a precise control of the value of σ_eff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.

Complex biomembrane mimetics on the sub-nanometer scale

Biomimetic lipid vesicles are indispensable tools for gaining insight into the biophysics of cell physiology on the molecular level. The level of complexity of these model systems has steadily increased, and now spans from domain-forming lipid mixtures to asymmetric lipid bilayers. Here, we review recent progress in the development and application of elastic neutron and X-ray scattering techniques for studying these systems in situ and under physiologically relevant conditions on the nanometer to sub-nanometer length scales. In particular, we focus on: (1) structural details of coexisting liquid-ordered and liquid-disordered domains, including their thickness and lipid packing mismatch as a function of a size transition from nanoscopic to macroscopic domains; (2) membrane-mediated protein partitioning into lipid domains; (3) the role of the aqueous medium in tuning interactions between membranes and domains; and (4) leaflet-specific structure in asymmetric bilayers and passive lipid flip-flop.

Line Tension Controls Liquid-Disordered + Liquid-Ordered Domain Size Transition in Lipid Bilayers

To better understand animal cell plasma membranes, we studied simplified models, namely four-component lipid bilayer mixtures. Here we describe the domain size transition in the region of coexisting liquid-disordered (Ld) + liquid-ordered (Lo) phases. This transition occurs abruptly in composition space with domains increasing in size by two orders of magnitude, from tens of nanometers to microns. We measured the line tension between coexisting Ld and Lo domains close to the domain size transition for a variety of lipid mixtures, finding that in every case the transition occurs at a line tension of ∼0.3 pN. A computational model incorporating line tension and dipole repulsion indicated that even small changes in line tension can result in domains growing in size by several orders of magnitude, consistent with experimental observations. We find that other properties of the coexisting Ld and Lo phases do not change significantly in the vicinity of the abrupt domain size transition.

Molecular Insight into the Line Tension of Bilayer Membranes Containing Hybrid Polyunsaturated Lipids

Line tension (γ) is a key parameter for the structure and dynamics of membrane domains. It was proposed that hybrid lipids, with mixed saturated and unsaturated acyl chains, participate in the relaxation of γ through different mechanisms. In this work, we used molecular dynamics simulations of the coarse-grained MARTINI model to measure γ in liquid-ordered-liquid-disordered (Lo-Ld) membranes, with increasingly larger relative proportion of the hybrid polyunsaturated lipid PAPC (4:0-5:4PC) to DAPC (di5:4PC) (i.e., X_H). We also calculated an elastic contribution to γ by the Lo-Ld thickness mismatch, tilt moduli, and bending moduli, as predicted by theory. We found that an increase in X_H decreased the overall γ value and the elastic contribution to line tension. The effect on the elastic line tension is driven by a reduced hydrophobic mismatch. Changes in the elastic constants of the phases due to an increase in X_H produced a slightly larger elastic γ term. In addition to this elastic energy, other major contributions to γ are found in these model membranes. Increasing X_H decreases both elastic and nonelastic contributions to γ. Finally, PAPC also behaves as a linactant, relaxing γ through an interfacial effect, as predicted by theoretical results. This study gives insight into the actual contribution of distinct energy terms to γ in bilayers containing polyunsaturated hybrid lipids.

Electrostatic interactions at the microscale modulate dynamics and distribution of lipids in bilayers

For decades, it has been assumed that electrostatic long-range (micron distances) repulsions in lipid bilayers are negligible due to screening from the aqueous milieu. This concept, mostly derived from theoretical calculations, is broadly accepted in the biophysical community. Here we present experimental evidence showing that domain-domain electrostatic repulsions in charged and also in neutral lipid bilayers regulate the diffusion, in-plane structuring and merging of lipid domains in the micron range. All the experiments were performed on both, lipid monolayers and bilayers, and the remarkable similarity in the results found in bilayers compared to monolayers led us to propose that inter-domain repulsions occur mainly within the plane of the membrane. Finally, our results indicate that electrostatic interactions between the species inserted in a cell membrane are not negligible, not only at nanometric but also at larger distances, suggesting another manner for regulating the membrane properties.

Thermal-driven domain and cargo transport in lipid membranes

Domain migration is observed on the surface of ternary giant unilamellar vesicles held in a temperature gradient in conditions where they exhibit coexistence of two liquid phases. The migration localizes domains to the hot side of the vesicle, regardless of whether the domain is composed of the more ordered or disordered phase and regardless of the proximity to chamber boundaries. The distribution of domains is explored for domains that coarsen and for those held apart due to long-range repulsions. After considering several potential mechanisms for the migration, including the temperature preferences for each lipid, the favored curvature for each phase, and the thermophoretic flow around the vesicle, we show that observations are consistent with the general process of minimizing the system's line tension energy, because of the lowering of line interface energy closer to mixing. DNA strands, attached to the lipid bilayer with cholesterol anchors, act as an exemplar "cargo," demonstrating that the directed motion of domains toward higher temperatures provides a route to relocate species that preferentially reside in the domains.

Physical mechanisms of micro- and nanodomain formation in multicomponent lipid membranes

This article summarizes a variety of physical mechanisms proposed in the literature, which can generate micro- and nanodomains in multicomponent lipid bilayers and biomembranes. It mainly focusses on lipid-driven mechanisms that do not involve direct protein-protein interactions. Specifically, it considers (i) equilibrium mechanisms based on lipid-lipid phase separation such as critical cluster formation close to critical points, and multiple domain formation in curved geometries, (ii) equilibrium mechanisms that stabilize two-dimensional microemulsions, such as the effect of linactants and the effect of curvature-composition coupling in bilayers and monolayers, and (iii) non-equilibrium mechanisms induced by the interaction of a biomembrane with the cellular environment, such as membrane recycling and the pinning effects of the cytoplasm. Theoretical predictions are discussed together with simulations and experiments. The presentation is guided by the theory of phase transitions and critical phenomena, and the appendix summarizes the mathematical background in a concise way within the framework of the Ginzburg-Landau theory. This article is part of a Special Issue entitled: Lipid order/lipid defects and lipid-control of protein activity edited by Dirk Schneider.

Millimeter-area, free standing, phospholipid bilayers

Minimal model biomembrane studies have the potential to unlock the fundamental mechanisms of cellular function that govern the processes upon which life relies. However, existing methods to fabricate free-standing model membranes currently have significant limitations. Bilayer sizes are often tens of micrometers, decoupling curvature or substrate effects, orthogonal control over tension, and solvent exchange combined with microscopy techniques is not possible, which restricts the studies that can be performed. Here, we describe a versatile platform to generate free standing, planar, phospholipid bilayers with millimeter scale areas. The technique relies on an adapted thin-film balance apparatus allowing for the dynamic control of the nucleation and growth of a planar black lipid membrane in the center of an orifice surrounded by microfluidic channels. Success is demonstrated using several different lipid types, including mixtures that show the same temperature dependent phase separation as existing protocols, moreover, membranes are highly stable. Two advantages unique to the proposed method are the dynamic control of the membrane tension and the possibility to make extremely large area membranes. We demonstrate this by showing how a block polymer, F68, used in drug delivery increases the membrane compliance. Together, the results demonstrate a new paradigm for studying the mechanics, structure, and function of model membranes.

Curvature-driven positioning of Turing patterns in phase-separating curved membranes

We introduce a new finite difference scheme to study the dynamics of Turing patterns of a two-species activator-inhibitor system embedded on a phase-separating curved membrane, modelling for instance a lipid bilayer. We show that the underlying binary fluid can strongly affect both the dynamical and the steady state properties of the ensuing Turing patterns. Furthermore, geometry plays a key role, as a large enough local membrane curvature can both arrest the coarsening of the lipid domains and position the patterns selectively at areas of high or small local curvature. The physical phenomena we observe are due to a minimal coupling, between the diffusivity of the Turing components and the local membrane composition. While our study is theoretical in nature, it can provide a framework within which to address intracellular pattern formation in systems of interacting membrane proteins.

Effects of Transmembrane α-Helix Length and Concentration on Phase Behavior in Four-Component Lipid Mixtures: A Molecular Dynamics Study

We used coarse-grained molecular dynamics simulations to examine the effects of transmembrane α-helical WALP peptides on the behavior of four-component lipid mixtures. These mixtures contain a high-melting temperature (high-Tm) lipid, a nanodomain-inducing low-Tm lipid, a macrodomain-inducing low-Tm lipid and cholesterol to model the outer leaflet of cell plasma membranes. In a series of simulations, we incrementally replace the nanodomain-inducing low-Tm lipid by the macrodomain-inducing low-Tm lipid and measure how lipid and phase properties are altered by the addition of WALPs of different length. Regardless of the ratio of the two low-Tm lipids, shorter WALPs increase domain size and all WALPs increase domain alignment between the two leaflets. These effects are smallest for the longest WALP tested, and increase with increasing WALP concentration. Thus, our simulations explain the experimental observation that WALPs induce macroscopic domains in otherwise nanodomain-forming lipid-only mixtures (unpublished). Since the cell plasma membrane contains a large fraction of transmembrane proteins, these findings link the behavior of lipid-only model membranes in vitro to phase behavior in vivo.

Lipid bilayers: clusters, domains and phases

In the present chapter we discuss the complex mixing behaviour of plasma membrane lipids. To do so, we first introduce the plasma membrane and membrane mixtures often used to model its complexity. We then discuss the nature of lipid phase behaviour in bilayers and the distinction between these phases and other manifestations of non-random mixing found in one-phase mixtures, such as clusters, micelles and microemulsions. Finally, we demonstrate the applicability of Gibbs phase diagrams to the study of increasingly complex model membrane systems, with a focus on phase coexistence, morphology and their implications for the cell plasma membrane.

Hybrid copolymer-phospholipid vesicles: phase separation resembling mixed phospholipid lamellae, but with mechanical stability and control

Vesicles whose bilayer membranes contain phospholipids mixed with co-polymers or surfactants comprise new hybrid materials having potential applications in drug delivery, sensors, and biomaterials. Here we describe a model polymer-phospholipid hybrid membrane system exhibiting strong similarities to binary phospholipid mixtures, but with more robust membrane mechanics. A lamella-forming graft copolymer, PDMS-co-PEO (polydimethylsiloxane-co-polyethylene oxide) was blended with a high melting temperature phospholipid, DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine), over a broad compositional range. The resulting giant hybrid unilamellar vesicles were compared qualitatively and quantitatively to analogous mixed phospholipid membranes in which a low melting temperature phospholipid, DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), was blended with DPPC. The mechanical properties of the hybrid vesicles, even when phase separated, were robust with high lysis stresses and strains approaching those of the pure copolymer vesicles. The temperature-composition phase diagram of the hybrid vesicles closely resembled that of the mixed phospholipids; with only slightly greater nonidealities in the hybrid compared with DOPC/DPPC mixed membranes. In both systems, it was demonstrated that tension could be used to manipulate DPPC solidification into domains of patchy or striped morphologies that exhibited different tracer incorporation. The patch and stripe-shaped domains are thought to be different solid DPPC polymorphys: ripple and tilt (or gel). This work demonstrates that in mixed-phospholipid bilayers where a high-melting phospholipid solidifies on cooling, the lower-melting phospholipid may be substituted by an appropriate copolymer to improve mechanical properties while retaining the underlying membrane physics.

Microemulsions, modulated phases and macroscopic phase separation: a unified picture of rafts

We consider two mechanisms that can lead to an inhomogeneous distribution of components in a multicomponent lipid bilayer: macroscopic phase separation and the formation of modulated phases. A simple model that encompasses both mechanisms displays a phase diagram that also includes a structured fluid, a microemulsion. Identifying rafts with the inhomogeneities of this structured fluid, we see how rafts are related to the occurrence of macroscopic phase separation or the formation of modulated phases in other systems, and focus our attention on specific differences between them.

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

Simplified lipid mixtures are often used to model the complex behavior of the cell plasma membrane. Indeed, as few as four components-a high-melting lipid, a nandomain-inducing low-melting lipid, a macrodomain-inducing low-melting lipid, and cholesterol (chol)-can give rise to a wide range of domain sizes and patterns that are highly sensitive to lipid compositions. Although these systems are studied extensively with experiments, the molecular-level details governing their phase behavior are not yet known. We address this issue by using molecular dynamics simulations to analyze how phase separation evolves in a four-component system as it transitions from small domains to large domains. To do so, we fix concentrations of the high-melting lipid 16:0,16:0-phosphatidylcholine (DPPC) and chol, and incrementally replace the nanodomain-inducing low-melting lipid 16:0,18:2-PC (PUPC) by the macrodomain-inducing low-melting lipid 18:2,18:2-PC (DUPC). Coarse-grained simulations of this four-component system reveal that lipid demixing increases as the amount of DUPC increases. Additionally, we find that domain size and interleaflet alignment change sharply over a narrow range of replacement of PUPC by DUPC, indicating that intraleaflet and interleaflet behaviors are coupled. Corresponding united atom simulations show that only lipids within ∼2 nm of the phase interface are significantly perturbed regardless of domain composition or size. Thus, whereas the fraction of interface-perturbed lipids is negligible for large domains, it is significant for smaller ones. Together, these results reveal characteristic traits of bilayer thermodynamic behavior in four-component mixtures, and provide a baseline for investigation of the effects of proteins and other lipids on membrane phase properties.

Macroscopic phase separation, modulated phases, and microemulsions: a unified picture of rafts

We simulate a simple phenomenological model describing phase behavior in a multicomponent membrane, a model capable of producing macroscopic phase separation, modulated phases, and microemulsions, all of which have been discussed in terms of raft phenomena. We show that one effect of thermal fluctuations on the mean-field phase diagram is that it permits a direct transition between either one of the coexisting liquid phases to a microemulsion. This implies that one system exhibiting phase separation can be related to a similar system exhibiting the heterogeneities characteristic of a microemulsion. The two systems could differ in their average membrane composition or in the relative compositions of their exoplasmic and cytoplasmic leaves. The model provides a unified description of these raft-associated phenomena.

Prediction of the dependence of the line tension on the composition of linactants and the temperature in phase separated membranes

We calculate the line tension between domains in phase separated, ternary membranes that comprise line active molecules (linactants) that tend to increase the compatibility of the two phase separating species. The predicted line tension, which depends explicitly on the linactant composition and temperature, is shown to decrease significantly as the fraction of linactants in the membrane increases toward a Lifshitz point, above which the membrane phase separates into a modulated phase. We predict regimes of zero line tension at temperatures close to the mixing transition and clarify the two different ways in which the line tension can be reduced: (1) The linactants uniformly distribute in the system and reduce the compositional mismatch between the two bulk domains. (2) The linactants accumulate at the interface with a preferred orientation. Both of these mechanisms have been observed in recent experiments and simulations. The second one is unique to line active molecules, and our work shows that it is increasingly important at large fraction of linactants and is necessary for the emergence of a regime of zero line tension. The methodology is based on the ternary mixture model proposed by Palmieri and Safran [Palmieri, B.; Safran, S. A. Langmuir 2013, 29, 5246], and the line tension is calculated via variationally derived, self-consistent profiles for the local variation of composition and linactant orientation in the interface region.

Mixed lipid bilayers with locally varying spontaneous curvature and bending

A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau Hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields ψ 1 and ψ 2, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as C 0 + C 1(ψ 1 - ψ 2/2), and a bending modulus equal to κ 0 + κ 1(ψ 1 + ψ 2)/2. This model allows us to define curved patches as membrane domains where the asymmetry in composition, ψ 1 - ψ 2, is large, and thick and stiff patches where ψ 1 + ψ 2 is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of saturated lipids forming a liquid-ordered domain and are known to be thick and flat nano-domains. The lipid-lipid structure factors and correlation functions are computed for globally spherical membranes and planar ones and for a whole set of parameters including the surface tension and the coupling in the two leaflet compositions. Phase diagrams are established, within a Gaussian approximation, showing the occurrence of two types of Structure Disordered phases, with correlations between either curved or thick patches, and an Ordered phase, corresponding to the divergence of the structure factor at a finite wave vector. The varying bending modulus plays a central role for curved membranes, where the driving force κ 1 C 0 (2) is balanced by the line tension, to form raft domains of size ranging from 10 to 100 nm. For planar membranes, raft domains emerge via the cross-correlation with curved domains. A global picture emerges from curvature-induced mechanisms, described in the literature for planar membranes, to coupled curvature- and bending-induced mechanisms in curved membranes forming a closed vesicle.

Line active molecules promote inhomogeneous structures in membranes: theory, simulations and experiments

We review recent theoretical efforts that predict how line-active molecules can promote lateral heterogeneities (or domains) in model membranes. This fundamental understanding may be relevant to membrane composition in living cells, where it is thought that small domains, called lipid rafts, are necessary for the cells to be functional. The theoretical work reviewed here ranges in scale from coarse grained continuum models to nearly atomistic models. The effect of line active molecules on domain sizes and shapes in the phase separated regime or on fluctuation length scales and lifetimes in the single phase, mixed regime, of the membrane is discussed. Recent experimental studies on model membranes that include line active molecules are also presented together with some comparisons with the theoretical predictions.

Lattice simulations of phase morphology on lipid bilayers: renormalization, membrane shape, and electrostatic dipole interactions

When liquid phases coexist at equilibrium but are not driven to minimize domain interfacial contact energy, the resulting patterns of phase domains can have important implications for living cells. In this study we explore some of the interactions and conditions that produce the stable patterned phases that are observed in model lipid mixtures. By use of Monte Carlo simulations we find that background curvature is important for the formation of patterned (modulated) phases. The interactions that stabilize nanoscopic phase separation are still not well understood. We show that inclusion of an electrostatic dipole repulsion with decay lengths as short as two to four lipid diameters can break up domains at the nanometer scale and that the location of the miscibility critical point is sensitive to this interaction. The use of a coarse-grained simulation raises questions about comparing parameters in simulations performed at different length scales. Using renormalization group techniques we show how to reconcile this problem, treating line tension as a running coupling constant.

Hybrid and nonhybrid lipids exert common effects on membrane raft size and morphology

Nanometer-scale domains in cholesterol-rich model membranes emulate lipid rafts in cell plasma membranes (PMs). The physicochemical mechanisms that maintain a finite, small domain size are, however, not well understood. A special role has been postulated for chain-asymmetric or hybrid lipids having a saturated sn-1 chain and an unsaturated sn-2 chain. Hybrid lipids generate nanodomains in some model membranes and are also abundant in the PM. It was proposed that they align in a preferred orientation at the boundary of ordered and disordered phases, lowering the interfacial energy and thus reducing domain size. We used small-angle neutron scattering and fluorescence techniques to detect nanoscopic and modulated liquid phase domains in a mixture composed entirely of nonhybrid lipids and cholesterol. Our results are indistinguishable from those obtained previously for mixtures containing hybrid lipids, conclusively showing that hybrid lipids are not required for the formation of nanoscopic liquid domains and strongly implying a common mechanism for the overall control of raft size and morphology. We discuss implications of these findings for theoretical descriptions of nanodomains.

Toward a better raft model: modulated phases in the four-component bilayer, DSPC/DOPC/POPC/CHOL

The liquid-liquid (Ld + Lo) coexistence region within a distearoyl-phosphatidylcholine/dioleoyl-phosphatidylcholine/palmitoyl-oleoyl-phosphatidylcholine/cholesterol (DSPC/DOPC/POPC/CHOL) mixture displays a nanoscopic-to-macroscopic transition of phase domains as POPC is replaced by DOPC. Previously, we showed that the transition goes through a modulated phase regime during this replacement, in which patterned liquid phase morphologies are observed on giant unilamellar vesicles (GUVs). Here, we describe a more detailed investigation of the modulated phase regime along two different thermodynamic tielines within the Ld + Lo region of this four-component mixture. Using fluorescence microscopy of GUVs, we found that the modulated phase regime occurs at relatively narrow DOPC/(DOPC+POPC) ratios. This modulated phase window shifts to higher values of DOPC/(DOPC+POPC) when CHOL concentration is increased, and coexisting phases become closer in properties. Monte Carlo simulations reproduced the patterns observed on GUVs, using a competing interactions model of line tension and curvature energies. Sufficiently low line tension and high bending moduli are required to generate stable modulated phases. Altogether, our studies indicate that by tuning the lipid composition, both the domain size and morphology can be altered drastically within a narrow composition space. This lends insight into a possible mechanism whereby cells can reorganize plasma membrane compartmentalization simply by tuning the local membrane composition or line tension.

Phase diagram of a 4-component lipid mixture: DSPC/DOPC/POPC/chol

We report the first 4-component phase diagram for the lipid bilayer mixture, DSPC/DOPC/POPC/chol (distearoylphosphatidylcholine/dioleoylphosphatidylcholine/1-palmitoyl, 2-oleoylphosphatidylcholine/cholesterol). This phase diagram, which has macroscopic Ld+Lo phase domains, clearly shows that all phase boundaries determined for the 3-component mixture containing DOPC transition smoothly into the boundaries for the 3-component mixture containing POPC, which has nanoscopic phase domains of Ld+Lo. Our studies start from two published ternary phase diagrams, and show how these can be combined into a quaternary phase diagram by study of a few hundred samples of intermediate compositions.