Membrane heterogeneity: manifestation of a curvature-induced microemulsion

Curvature-induced clustering of cell adhesion proteins

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such a curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670).

A Survey of Models of Cell Membranes: Toward a New Understanding of Membrane Organization

The cell membrane, the boundary that separates living cells from their environment, has been the subject of study for over a century. The fluid-mosaic model of Singer and Nicolson in 1972 proposed the plasma membrane as a two-dimensional fluid composed of lipids and proteins. Fifty years hence, advances in biophysical and biochemical tools, particularly optical imaging techniques, have allowed for a better understanding of the physical nature, organization, and composition of cell membranes. This has been made possible by visualizing membrane heterogeneities and their dynamics and appreciating the asymmetrical arrangement of lipids in living cell membranes. Despite these advances, mechanisms underlying the local spatiotemporal organization of membrane components remain unclear. This review surveys various models of membrane organization, culminating in a new model that incorporates nonequilibrium processes and forces exerted by interactions with extramembrane elements such as the actin cytoskeleton. The proposed model provides a comprehensive understanding of membrane organization, taking into account the dynamic nature of the cell membrane and its interactions with its immediate environment.

A lattice model of ternary mixtures of lipids and cholesterol with tunable domain sizes

Much of our understanding of the physical properties of raft domains in biological membranes, and some insight into the mechanisms underlying their formation stem from atomistic simulations of simple model systems, especially ternary mixtures consisting of saturated and unsaturated lipids, and cholesterol (Chol). To explore the properties of such systems at large spatial scales, we here present a simple ternary mixture lattice model, involving a small number of nearest neighbor interaction terms. Monte Carlo simulations of mixtures with different compositions show excellent agreement with experimental and atomistic simulation observations across multiple scales, ranging from the local distributions of lipids to the phase diagram of the system. The simplicity of the model allows us to identify the roles played by the different interactions between components, and the interplay between them. Importantly, by changing the value of one of the model parameters, we can tune the size of the liquid-ordered domains, thereby simulating both Type II mixtures exhibiting macroscopic phase separation and Type I mixtures with nanoscopic domains. The Type II mixture simulation results fit well to the experimentally determined phase diagram of mixtures containing saturated DPPC/unsaturated DOPC/Chol. When the tunable parameter is changed, we obtain the Type I version of DPPC/DOPC/Chol, i.e., a mixture not showing thermodynamic phase transitions but one that may be fitted to the same phase diagram if local measures are used to distinguish between the different states. Our model results suggest that short range packing is likely to be a key regulator of the stability and size distribution of biological rafts.

Extent of raft composition in a model plasma membrane

"Rafts" are nanometer-size inhomogeneities in the plasma membrane that, in the outer leaflet, are enriched in sphingomyelin and cholesterol. They are thought to provide a platform for proteins to carry out biological processes (1-4). Here we employ a model asymmetric plasma membrane to address the question of the range of sphingomyelin and cholesterol compositions in which one would expect the formation of rafts. We define a weight for the likelihood of raft formation, and evaluate it as a function of the sphingomyelin mole fraction in the outer leaflet for three bilayers with total cholesterol mole fractions of 0.30, 0.40, and 0.50. Not surprisingly, the weight decreases when there is little sphingomyelin. Less expected, we find that the weight also decreases when there is a large mole fraction of sphingomyelin. The weight is largest in the bilayer with a total cholesterol mole fraction of 0.30, and decreases rapidly with increasing total cholesterol. We explicate the reasons for these behaviors. In the 0.30 cholesterol bilayer, the largest weight occurrs at a sphingomyelin mole fraction in the outer leaflet of approximately 0.23. The weight falls to one half its maximum value at sphingomylin mole fractions of 0.15 and 0.33. In terms of the sphingomyelin mole fraction of the asymmetric bilayer, the maximum weight occurs at 0.12 and falls to half maximum at 0.08 and 0.17.

Active emulsions in living cell membranes driven by contractile stresses and transbilayer coupling

The spatiotemporal organization of proteins and lipids on the cell surface has direct functional consequences for signaling, sorting, and endocytosis. Earlier studies have shown that multiple types of membrane proteins, including transmembrane proteins that have cytoplasmic actin binding capacity and lipid-tethered glycosylphosphatidylinositol-anchored proteins (GPI-APs), form nanoscale clusters driven by active contractile flows generated by the actin cortex. To gain insight into the role of lipids in organizing membrane domains in living cells, we study the molecular interactions that promote the actively generated nanoclusters of GPI-APs and transmembrane proteins. This motivates a theoretical description, wherein a combination of active contractile stresses and transbilayer coupling drives the creation of active emulsions, mesoscale liquid order (lo) domains of the GPI-APs and lipids, at temperatures greater than equilibrium lipid phase segregation. To test these ideas, we use spatial imaging of molecular clustering combined with local membrane order, and we demonstrate that mesoscopic domains enriched in nanoclusters of GPI-APs are maintained by cortical actin activity and transbilayer interactions and exhibit significant lipid order, consistent with predictions of the active composite model.

A Theoretical Basis for Nanodomains

We review the current theories of nanodomain, or "raft," formation. We emphasize that the idea that they are co-exisiting Lo and Ld phases is fraught with difficulties, as is the closely related idea that they are due to critical fluctuations. We then review an alternate theory that the plasma membrane is a two-dimensional microemulsion, and that the mechanism that drives to zero the line tension between Lo and Ld phases is the coupling of height and composition fluctuations. The theory yields rafts of SM and cholesterol in the outer leaf and POPS and POPC in the inner leaf. The "sea" between rafts consists of POPC in the outer leaf and POPE and cholesterol in the inner leaf. The characteristic size of the domain structures is tens of nanometers.

Spatial extent of a single lipid's influence on bilayer mechanics

To what spatial extent does a single lipid affect the mechanical properties of the membrane that surrounds it? The lipid composition of a membrane determines its mechanical properties. The shapes available to the membrane depend on its compositional material properties, and therefore, the lipid environment. Because each individual lipid species' chemistry is different, it is important to know its range of influence on membrane mechanical properties. This is defined herein as the lipid's mechanical extent. Here, a lipid's mechanical extent is determined by quantifying lipid redistribution and the average curvature that lipid species experience on fluctuating membrane surfaces. A surprising finding is that, unlike unsaturated lipids, saturated lipids have a complicated, nonlocal effect on the surrounding surface, with the interaction strength maximal at a finite length-scale. The methodology provides the means to substantially enrich curvature-energy models of membrane structures, quantifying what was previously only conjecture.

Domain formation in bicomponent vesicles induced by composition-curvature coupling

Lipid vesicles composed of a mixture of two types of lipids are studied by intensive Monte Carlo numerical simulations. The coupling between the local composition and the membrane shape is induced by two different spontaneous curvatures of the components. We explore the various morphologies of these biphasic vesicles coupled to the observed patterns such as nano-domains or labyrinthine mesophases. The effect of the difference in curvatures, the surface tension, and the interaction parameter between components is thoroughly explored. Our numerical results quantitatively agree with the previous analytical results obtained by Gueguen et al. [Eur. Phys. J. E 37, 76 (2014)] in the disordered (high temperature) phase. Numerical simulations allow us to explore the full parameter space, especially close to and below the critical temperature, where analytical results are not accessible. Phase diagrams are constructed and domain morphologies are quantitatively studied by computing the structure factor and the domain size distribution. This mechanism likely explains the existence of nano-domains in cell membranes as observed by super-resolution fluorescence microscopy.

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.

Double membrane formation in heterogeneous vesicles

Lipids are capable of forming a variety of structures, including multi-lamellar vesicles. Layered lipid membranes are found in cell organelles, such as autophagosomes and mitochondria. Here, we present a mechanism for the formation of a double-walled vesicle (i.e., two lipid bilayers) from a unilamellar vesicle through the partitioning and phase separation of a small molecule. Using molecular dynamics simulations, we show that double membrane formation proceeds via a nucleation and growth process - i.e., after a critical concentration of the small molecules, a patch of double membrane nucleates and grows to cover the entire vesicle. We discuss the implications of this mechanism and theoretical approaches for understanding the evolution and formation of double membranes.

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.

Microscopic Picture of Calcium-Assisted Lipid Demixing and Membrane Remodeling Using Multiscale Simulations

The specificity of anionic phospholipids-calcium ion interaction and lipid demixing has been established as a key regulatory mechanism in several cellular signaling processes. The mechanism and implications of this calcium-assisted demixing have not been elucidated from a microscopic point of view. Here, we present an overview of atomic interactions between calcium and phospholipids that can drive nonideal mixing of lipid molecules in a model lipid bilayer composed of zwitterionic (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)) and anionic (1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (POPS)) lipids with computer simulations at multiple resolutions. Lipid nanodomain formation and growth were driven by calcium-enabled lipid bridging of the charged phosphatidylserine (PS) headgroups, which were favored against inter-POPS dipole interactions. Consistent with several experimental studies of calcium-associated membrane sculpting, our analyses also suggest modifications in local membrane curvature and cross-leaflet couplings as a response to such induced lateral heterogeneity. In addition, reverse mapping to a complementary atomistic description revealed structural insights in the presence of anionic nanodomains, at timescales not accessed by previous computational studies. This work bridges information across multiple scales to reveal a mechanistic picture of calcium ion's impact on membrane biophysics.

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.

Recent Experiments Support a Microemulsion Origin of Plasma Membrane Domains: Dependence of Domain Size on Physical Parameters

It is widely, but not universally, believed that the lipids of the plasma membrane are not uniformly distributed, but that “rafts” of sphingolipids and cholesterol float in a “sea” of unsaturated lipids. The physical origin of such heterogeneities is often attributed to a phase coexistence between the two different domains. We argue that this explanation is untenable for several reasons. Further, we note that the results of recent experiments are inconsistent with this picture. However, they are quite consistent with an alternate explanation, namely, that the plasma membrane is a microemulsion of the two kinds of regions. To show this, we briefly review a simplified version of this theory and its phase diagram. We also explicate the dependence of the predicted domain size on four physical parameters. They are the energy cost of gradients in the composition, the spontaneous curvature of the membrane, its bending modulus and its surface tension. Taking values of the latter two from experiment, we obtain domain sizes for several different cell types that vary from 58 to 88 nm.

Lattice Models for Protein Organization throughout Thylakoid Membrane Stacks

Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by microscopy and fluorescence spectroscopy and demonstrated by computer simulations of a coarse-grained model. The architecture of thylakoid membranes, however, also provides opportunities for interlayer interactions that instead disfavor the high protein densities of ordered arrangements. Here, we explore the interplay between these opposing driving forces and, in particular, the phase transitions that emerge in the periodic geometry of stacked thylakoid membrane disks. We propose a lattice model that roughly accounts for proteins' attraction within a layer and across the stromal gap, steric repulsion across the lumenal gap, and regulation of protein density by exchange with the stroma lamellae. Mean-field analysis and computer simulation reveal rich phase behavior for this simple model, featuring a broken-symmetry striped phase that is disrupted at both high and low extremes of chemical potential. The resulting sensitivity of microscopic protein arrangement to the thylakoid's mesoscale vertical structure raises intriguing possibilities for regulation of photosynthetic function.

Model Plasma Membrane Exhibits a Microemulsion in Both Leaves Providing a Foundation for "Rafts"

We consider a model lipid plasma membrane, one that describes the outer leaf as consisting of sphingomyelin, phosphatidylcholine, and cholesterol and the inner leaf of phosphatidylethanolamine, phosphatidylserine, phosphatidylcholine, and cholesterol. Their relative compositions are taken from experiment; the cholesterol freely interchanges between leaves. Fluctuations in local composition are coupled to fluctuations in the local membrane curvature, as in the Leibler-Andelman mechanism. Structure factors of components in both leaves display a peak at nonzero wavevector. This indicates that the disordered fluid membrane is characterized by structure of the corresponding wavelength. The scale is given by membrane properties: its bending modulus and its surface tension, which arises from the membrane's connections to the cytoskeleton. From measurements on the plasma membrane, this scale is on the order of 100 nm. We find that the membrane can be divided into two different kinds of domains that differ not only in their composition but also in their curvature. The first domain in the outer, exoplasmic leaf is rich in cholesterol and sphingomyelin, whereas the inner, cytoplasmic leaf is rich in phosphatidylserine and phosphatidylcholine. The second kind of domain is rich in phosphatidylcholine in the outer leaf and in cholesterol and phosphatidylethanolamine in the inner leaf. The theory provides a tenable basis for the origin of structure in the plasma membrane and an illuminating picture of the organization of lipids therein.

Deciphering Melatonin-Stabilized Phase Separation in Phospholipid Bilayers

Lipid bilayers are fundamental building blocks of cell membranes, which contain the machinery needed to perform a range of biological functions, including cell-cell recognition, signal transduction, receptor trafficking, viral budding, and cell fusion. Importantly, many of these functions are thought to take place in the laterally phase-separated regions of the membrane, commonly known as lipid rafts. Here, we provide experimental evidence for the "stabilizing" effect of melatonin, a naturally occurring hormone produced by the brain's pineal gland, on phase-separated model membranes mimicking the outer leaflet of plasma membranes. Specifically, we show that melatonin stabilizes the liquid-ordered/liquid-disordered phase coexistence over an extended range of temperatures. The melatonin-mediated stabilization effect is observed in both nanometer- and micrometer-sized liposomes using small angle neutron scattering (SANS), confocal fluorescence microscopy, and differential scanning calorimetry. To experimentally detect nanoscopic domains in 50 nm diameter phospholipid vesicles, we developed a model using the Landau-Brazovskii approach that may serve as a platform for detecting the existence of nanoscopic lateral heterogeneities in soft matter and biological materials with spherical and planar geometries.

Thermodynamic equilibrium of binary mixtures on curved surfaces

We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on nontrivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical subdiagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semianalytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multicomponent lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.

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].

Membrane Lipid Nanodomains

Lipid membranes can spontaneously organize their components into domains of different sizes and properties. The organization of membrane lipids into nanodomains might potentially play a role in vital functions of cells and organisms. Model membranes represent attractive systems to study lipid nanodomains, which cannot be directly addressed in living cells with the currently available methods. This review summarizes the knowledge on lipid nanodomains in model membranes and exposes how their specific character contrasts with large-scale phase separation. The overview on lipid nanodomains in membranes composed of diverse lipids (e.g., zwitterionic and anionic glycerophospholipids, ceramides, glycosphingolipids) and cholesterol aims to evidence the impact of chemical, electrostatic, and geometric properties of lipids on nanodomain formation. Furthermore, the effects of curvature, asymmetry, and ions on membrane nanodomains are shown to be highly relevant aspects that may also modulate lipid nanodomains in cellular membranes. Potential mechanisms responsible for the formation and dynamics of nanodomains are discussed with support from available theories and computational studies. A brief description of current fluorescence techniques and analytical tools that enabled progress in lipid nanodomain studies is also included. Further directions are proposed to successfully extend this research to cells.

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.

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.

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.

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.

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.

Generalization of the swelling method to measure the intrinsic curvature of lipids

Via computer simulation of a coarse-grained model of two-component lipid bilayers, we compare two methods of measuring the intrinsic curvatures of the constituting monolayers. The first one is a generalization of the swelling method that, in addition to the assumption that the spontaneous curvature linearly depends on the composition of the lipid mixture, incorporates contributions from its elastic energy. The second method measures the effective curvature-composition coupling between the apposing leaflets of bilayer structures (planar bilayers or cylindrical tethers) to extract the spontaneous curvature. Our findings demonstrate that both methods yield consistent results. However, we highlight that the two-leaflet structure inherent to the latter method has the advantage of allowing measurements for mixed lipid systems up to their critical point of demixing as well as in the regime of high concentration (of either species).

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 dynamics at the nanoscale in simple biomembranes

Nature is known to engineer complex compositional and dynamical platforms in biological membranes. Understanding this complex landscape requires techniques to simultaneously detect membrane re-organization and dynamics at the nanoscale. Using super-resolution stimulated emission depletion (STED) microscopy coupled with fluorescence correlation spectroscopy (FCS), we reveal direct experimental evidence of dynamic heterogeneity at the nanoscale in binary phospholipid-cholesterol bilayers. Domain formation on the length scale of ~200–600 nm due to local cholesterol compositional heterogeneity is found to be more prominent at high cholesterol content giving rise to distinct intra-domain lipid dynamics. STED-FCS reveals unique dynamical crossover phenomena at length scales of ~100–150 nm within each of these macroscopic regions. The extent of dynamic heterogeneity due to intra-domain hindered lipid diffusion as reflected from the crossover length scale, is driven by cholesterol packing and organization, uniquely influenced by phospholipid type. These results on simple binary model bilayer systems provide novel insights into pathways leading to the emergence of complex nanodomain substructures with implications for a wide variety of membrane mediated cellular events.

Size and mobility of lipid domains tuned by geometrical constraints

In the plasma membrane of eukaryotic cells, proteins and lipids are organized in clusters, the latter ones often called lipid domains or "lipid rafts." Recent findings highlight the dynamic nature of such domains and the key role of membrane geometry and spatial boundaries. In this study, we used porous substrates with different pore radii to address precisely the extent of the geometric constraint, permitting us to modulate and investigate the size and mobility of lipid domains in phase-separated continuous pore-spanning membranes (PSMs). Fluorescence video microscopy revealed two types of liquid-ordered (l_o) domains in the freestanding parts of the PSMs: (i) immobile domains that were attached to the pore rims and (ii) mobile, round-shaped l_o domains within the center of the PSMs. Analysis of the diffusion of the mobile l_o domains by video microscopy and particle tracking showed that the domains' mobility is slowed down by orders of magnitude compared with the unrestricted case. We attribute the reduced mobility to the geometric confinement of the PSM, because the drag force is increased substantially due to hydrodynamic effects generated by the presence of these boundaries. Our system can serve as an experimental test bed for diffusion of 2D objects in confined geometry. The impact of hydrodynamics on the mobility of enclosed lipid domains can have great implications for the formation and lateral transport of signaling platforms.

High-resolution structure of coexisting nanoscopic and microscopic lipid domains

We studied coexisting micro- and nanoscopic liquid-ordered/liquid-disordered domains in fully hydrated multilamellar vesicles using small-angle X-ray scattering. Large domains exhibited long-range out-of-plane positional correlations of like domains, consistent with previous reports. In contrast, such correlations were absent in nanoscopic domains. Advancing a global analysis of the in situ data allowed us to gain a deep insight into the structural and elastic properties of the coexisting domains, including the partitioning of cholesterol in each domain. In agreement with a previous report, we found that the thickness mismatch between ordered and disordered domains decreased for nanoscopic domains. At the same time, we found also the lipid packing mismatch to be decreased for nano-domains, mainly due to the liquid-disordered domains becoming more densely packed when decreasing their size.

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.

Hydrodynamic collective effects of active proteins in biological membranes

Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown [A. S. Mikhailov and R. Kapral, Proc. Natl. Acad. Sci. USA 112, E3639 (2015)PNASA60027-842410.1073/pnas.1506825112] that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

First-order patterning transitions on a sphere as a route to cell morphology

We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an individual pattern is robustly reproducible by a single species and a similar set of developmental stages produces a variety of patterns. We argue that the pattern diversity and reproducibility may be explained by interpreting the pattern development as a first-order phase transition to a spatially modulated phase. Brazovskii showed that for such transitions on a flat, infinite sheet, the patterns are uniform striped or hexagonal. Biological objects, however, have finite extent and offer different topologies, such as the spherical surfaces of pollen grains. We consider Brazovskii transitions on spheres and show that the patterns have a richer phenomenology than simple stripes or hexagons. We calculate the free energy difference between the unpatterned state and the many possible patterned phases, taking into account fluctuations and the system's finite size. The proliferation of variety on a sphere may be understood as a consequence of topology, which forces defects into perfectly ordered phases. The defects are then accommodated in different ways. We also argue that the first-order character of the transition is responsible for the reproducibility and robustness of the pattern formation.

Equilibrium microphase separation in the two-leaflet model of lipid membranes

Because of the coupling between local lipid composition and the thickness of the membrane, microphase separation in two-component lipid membranes can take place; such effects may underlie the formation of equilibrium nanoscale rafts. Using a kinetic description, this phenomenon is analytically and numerically investigated. The phase diagram is constructed through the stability analysis for linearized kinetic equations, and conditions for microphase separation are discussed. Simulations of the full kinetic model reveal the development of equilibrium membrane nanostructures with various morphologies from the initial uniform state.

Sub-ten-nanometer heterogeneity of solid supported lipid membranes determined by solution atomic force microscopy

Visually detecting nanoscopic structures in lipid membranes is important for elucidating lipid-lipid interactions, which are suggested to play a role in mediating membrane rafts. We use solution atomic force microscopy (AFM) to study lateral and normal organization in multicomponent lipid membranes supported by mica substrate. Nanoscopic heterogeneity is observed in a three-component system composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/brain-sphingomyelin (bSM)/cholesterol (Chol). We find sub-ten-nanometer correlation lengths that are used to describe membrane lateral organization. In addition, we find that the correlation length is independent on cholesterol concentration, while the height fluctuation (variation) is not. To explore the mechanism that controls the size of membrane heterogeneity, we extend our study to a four-component system composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/POPC/bSM/Chol. By systematically adjusting the relative amount of DOPC and POPC, we obtain macroscopic-to-nanoscopic size transition of membrane heterogeneity. In contrast to the results from vesicle based fluorescence microscopy, we find that the structural transition is continuous both in the lateral and normal directions. We compare our nanoscopic structures to two theoretical models, and find that both the critical fluctuations and the nanodomain models are not sufficient to account for our solution AFM data. Finally, we propose a nanoheterogeneity model that could serve as the organization principle of the observed nanoscopic structures in multicomponent lipid membranes.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

Membrane composition variation and underdamped mechanics near transmembrane proteins and coats

We study the effect of transmembrane proteins on the shape, composition, and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough, the nearby membrane composition and shape both undergo a transition from overdamped to underdamped spatial variation, well before the membrane becomes unstable in the bulk. This transition is associated with a change in the sign of the thermodynamic energy and, hence, favors the early stages of coat assembly necessary for vesiculation (budding) and may suppress the activity of mechanosensitive membrane channels and transporters. Our results suggest an approach to obtain physical parameters of the membrane that are otherwise difficult to measure.

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.

Seeing the Forest in Lieu of the Trees: Continuum Simulations of Cell Membranes at Large Length Scales

Biological membranes exhibit long-range spatial structure in both chemical composition and geometric shape, which gives rise to remarkable physical phenomena and important biological functions. Continuum models that describe these effects play an important role in our understanding of membrane biophysics at large length scales. We review the mathematical framework used to describe both composition and shape degrees of freedom, and present best practices to implement such models in a computer simulation. We discuss in detail two applications of continuum models of cell membranes: the formation of microemulsion and modulated phases, and the effect of membrane-mediated interactions on the assembly of membrane proteins.

Membrane sorting via the extracellular matrix

We consider the coupling between a membrane and the extracellular matrix. Computer simulations demonstrate that the latter coupling is able to sort lipids. It is assumed that membranes are elastic manifolds, and that this manifold is disrupted by the extracellular matrix. For a solid-supported membrane with an actin network on top, regions of positive curvature are induced below the actin fibers. A similar mechanism is conceivable by assuming that the proteins which connect the cytoskeleton to the membrane induce local membrane curvature. The regions of non-zero curvature exist irrespective of any phase transition the lipids themselves may undergo. For lipids that prefer certain curvature, the extracellular matrix thus provides a spatial template for the resulting lateral domain structure of the membrane.