Phase segregation on different length scales in a model cell membrane system

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.

Hybrid Live Cell–Supported Membrane Interfaces for Signaling Studies

A wide range of cell–microenvironmental interactions are mediated by membrane-localized receptors that bind ligands present on another cell or the extracellular matrix. This situation introduces a number of physical effects including spatial organization of receptor–ligand complexes and development of mechanical forces in cells. Unlike traditional experimental approaches, hybrid live cell–supported lipid bilayer (SLB) systems, wherein a live cell interacts with a synthetic substrate supported membrane, allow interrogation of these aspects of receptor signaling. The SLB system directly offers facile control over the identity, density, and mobility of ligands used for engaging cellular receptors. Further, application of various nano- and micropatterning techniques allows for spatial patterning of ligands. In this review, we describe the hybrid live cell–SLB system and its application in uncovering a range of spatial and mechanical aspects of receptor signaling. We highlight the T cell immunological synapse, junctions formed between EphA2- and ephrinA1-expressing cells, and adhesions formed by cadherin and integrin receptors.

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.

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.

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.

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.

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.

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.

Macroscopic lateral heterogeneity observed in a laterally mobile immiscible mixed polyelectrolyte-neutral polymer brush

We studied mixed poly(ethylene oxide) (PEO) and poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes. The question we attempted to answer was: when the chain grafting points are laterally mobile, how will this lateral mobility influence the structure and phase behavior of the mixed brush? Three different model mixed PEO/PDMAEMA brush systems were prepared: (1) a laterally mobile mixed brush by spreading onto the air-water interface a mixture of poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PnBA) and poly(2-(dimethylamino)ethyl methacrylate)-poly(n-butyl acrylate) (PDMAEMA-PnBA) diblock copolymers (the specific diblock copolymers used will be denoted as PEO113-PnBA100 and PDMAEMA118-PnBA100, where the subscripts refer to the number-average degrees of polymerization of the individual blocks), (2) a mobility-restricted (inseparable) version of the above mixed brush prepared using a PEO-PnBA-PDMAEMA triblock copolymer (denoted as PEO113-PnBA89-PDMAEMA120) having respective brush molecular weights matched with those of the diblock copolymers, and (3) a different laterally mobile mixed PEO and PDMAEMA brush prepared from a PEO113-PnBA100 and PDMAEMA200-PnBA103 diblock copolymer combination, which represents a further more height-mismatched mixed brush situation than described in (1). These three mixed brush systems were investigated by surface pressure-area isotherm and X-ray (XR) reflectivity measurements. These experimental data were analyzed within the theoretical framework of a continuum self-consistent field (SCF) polymer brush model. The combined experimental and theoretical results suggest that the mobile mixed brush derived using the PEO113-PnBA100 and PDMAEMA118-PnBA100 combination (i.e., mixed brush System #1) undergoes a lateral macroscopic phase separation at high chain grafting densities, whereas the more height-mismatched system (System #3) is only microscopically phase separated under comparable brush density conditions even though the lateral mobility of the grafted chains is unrestricted. The macroscopic phase separation observed in the laterally mobile mixed brush system is in contrast with the microphase separation behavior commonly observed in two-dimensional laterally mobile charged small molecule mixtures. Further study is needed to determine the detailed morphologies of the macro- and microphase-separated mixed PEO/PDMAEMA brushes.

Model of a raft in both leaves of an asymmetric lipid bilayer

We present a theory of inhomogeneities in the plasma membrane, or rafts, that can exist in both leaves of the plasma membrane. We note that although neither of the major phospholipid components of the outer leaf, sphingomyelin (SM) nor phosphatidylcholine (PC), evinces a tendency to form phases characterized by nonzero curvature, one of the major components of the inner leaf, phosphatidylethanolamine (PE), displays a strong tendency to do so whereas the other, phosphatidylserine (PS), does not. Therefore, we posit that the concentration difference of PS and PE couples to height fluctuations of the plasma membrane bilayer. This brings about a microemulsion in the inner leaf. Coupling of the concentration difference between PS and PE in the inner leaf and SM and PC in the outer leaf propagates the microemulsion to that leaf as well. The characteristic size of the inhomogeneities is equal to the square-root of the ratio of the bending modulus of the bilayer to its surface tension, a size which is ~100 nm for the plasma membrane. If the coupling between leaves were to be provided by the interchange of cholesterol, then our model raft would consist of SM and cholesterol in the outer leaf and PS and cholesterol in the inner leaf floating in a sea of PC and PE in both leaves.

A lipid bound actin meshwork organizes liquid phase separation in model membranes

The eukaryotic cell membrane is connected to a dense actin rich cortex. We present FCS and STED experiments showing that dense membrane bound actin networks have severe influence on lipid phase separation. A minimal actin cortex was bound to a supported lipid bilayer via biotinylated lipid streptavidin complexes (pinning sites). In general, actin binding to ternary membranes prevented macroscopic liquid-ordered and liquid-disordered domain formation, even at low temperature. Instead, depending on the type of pinning lipid, an actin correlated multi-domain pattern was observed. FCS measurements revealed hindered diffusion of lipids in the presence of an actin network. To explain our experimental findings, a new simulation model is proposed, in which the membrane composition, the membrane curvature, and the actin pinning sites are all coupled. Our results reveal a mechanism how cells may prevent macroscopic demixing of their membrane components, while at the same time regulate the local membrane composition. DOI: http://dx.doi.org/10.7554/eLife.01671.001.

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.

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.

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

When prepared in the liquid-liquid coexistence region, the four-component lipid system distearoyl-phospha-tidylcholine-dioleoyl-phosphatidylcholine-palmitoyl,oleoyl-phosphatidylcholine-cholesterol (DSPC-DOPC-POPC-Cholesterol), with certain ratios of DOPC and POPC, shows striking modulated phase patterns on the surface of giant unilamellar vesicles (GUVs). In this simulation study, we show that the morphology of these patterns can be explained by the competition of line tension (which tends to favor large round domains) and curvature, as specified by the Helfrich energy functional. In this study we use a Monte-Carlo simulation on the surface of a GUV to determine the equilibrium shape and phase morphology. We find that the patterns arising from these competing interactions very closely approximate those observed, that the patterned morphologies represent thermodynamically stable configurations, and that the geometric nature of these patterns is closely tied to the relative and absolute values of the model parameters.

Surface charge dependent nanoparticle disruption and deposition of lipid bilayer assemblies

Electrostatic interaction plays a leading role in nanoparticle interactions with membrane architectures and can lead to effects such as nanoparticle binding and membrane disruption. In this work, the effects of nanoparticles (NPs) interacting with mixed lipid systems were investigated, indicating an ability to tune both NP binding to membranes and membrane disruption. Lipid membrane assemblies (LBAs) were created using a combination of charged, neutral, and gel-phase lipids. Depending on the lipid composition, nanostructured networks could be observed using in situ atomic force microscopy representing an asymmetrical distribution of lipids that rendered varying effects on NP interaction and membrane disruption that were domain-specific. LBA charge could be localized to fluidic domains that were selectively disrupted when interacting with negatively charged Au nanoparticles or quantum dots. Disruption was observed to be related to the charge density of the membrane, with a maximum amount of disruption occurring at ∼40% positively charged lipid membrane concentration. Conversely, particle deposition was determined to begin at charged lipid concentrations greater than 40% and increased with charge density. The results demonstrate that the modulation of NP and membrane charge distribution can play a pivitol role in determining NP-induced membrane disruption and NP surface assembly.

Membrane heterogeneity: manifestation of a curvature-induced microemulsion

To explain the appearance of heterogeneities in the plasma membrane, I propose a hypothesis which begins with the observation that fluctuations in the membrane curvature are coupled to the difference between compositions of one leaf and the other. Because of this coupling, the most easily excited fluctuations can occur at nonzero wave numbers. When the coupling is sufficiently strong, it is well-known that it leads to microphase separation and modulated phases. I note that when the coupling is less strong, the tendency toward modulation remains manifest in a liquid phase that exhibits a transient structure of a characteristic size, that is, it is a microemulsion. The characteristic size of the fluctuating domains is estimated to be on the order of 100 nm, and experiments to verify this hypothesis are proposed.

Control of a nanoscopic-to-macroscopic transition: modulated phases in four-component DSPC/DOPC/POPC/Chol giant unilamellar vesicles

We have found modulated phase morphology in a particular region of composition within the liquid-ordered + liquid-disordered coexistence region in the four-component lipid bilayer mixture DSPC/DOPC/POPC/Chol. By controlling lipid composition, we could see distinct types of modulated liquid-liquid phase morphologies, including linear, irregular, and angular features in giant unilamellar vesicles. We used a combination of confocal, two-photon, wide-field fluorescence, and differential interference contrast microscopies, and used stringent controls to minimize light-induced artifacts. These studies establish that both the size and morphology of membrane rafts can be controlled by the concentration and the type of low-melting lipid in mixtures with cholesterol and a high-melting lipid.

Electrostatic field effects on membrane domain segregation and on lateral diffusion

Natural membranes are organized structures of neutral and charged molecules bearing dipole moments which generate local non-homogeneous electric fields. When subjected to such fields, the molecules experience net forces that can modify the lipid and protein organization, thus modulating cell activities and influencing (or even dominating) the biological functions. The energetics of electrostatic interactions in membranes is a long-range effect which can vary over distance within r^-1 to r^-3. In the case of a dipole interacting with a plane of dipoles, e.g. a protein interacting with a lipid domain, the interaction is stronger than two punctual dipoles and depends on the size of the domain. In this article, we review several contributions on how electrostatic interactions in the membrane plane can modulate the phase behavior, surface topography and mechanical properties in monolayers and bilayers.

Main phase transition in lipid bilayers: Phase coexistence and line tension in a soft, solvent-free, coarse-grained model

We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The nonbonded interactions take the form of a weighted-density functional, which allows us to describe the thermodynamics of self-assembly and packing effects of the coarse-grained beads in terms of a density expansion of the equation of state and weighting functions that regularize the microscopic bead densities, respectively. Identifying the length and energy scales via the bilayer thickness and the thermal energy scale, k(B)T, the model qualitatively reproduces key characteristics (e.g., bending rigidity, area per molecule, and compressibility) of lipid membranes. We employ this model to study the main phase transition between the fluid and the gel phase of the bilayer membrane. We accurately locate the phase coexistence using free energy calculations and also obtain estimates for the bare and the thermodynamic line tension.

Mechanochemical crosstalk during endocytic vesicle formation

Membrane curvature has emerged as a key regulatory factor in endocytic vesicle formation. From a theoretical perspective, we summarize recent progress in understanding how membrane curvature and biochemical pathways are coupled and orchestrated during the coherent process of endocytic vesicle formation. We mainly focus on clathrin-mediated and actin-mediated endocytosis in yeast and in mammalian cells. We further speculate on how mechanochemical feedback could modulate other membrane-remodeling processes.

Surface patterning of low-dimensional systems: the chirality of charged fibres

Charged surfaces are interesting for their ability to have long-range correlations and their ability to be dynamically tuned. While the configurations of charged planar surfaces have been thoroughly mapped and studied, charged cylindrical surfaces show novel features. The surface patterning of cylindrically confined charges is discussed with emphasis on the role of chiral configurations. The origins of surface patterns due to competing interactions in charged monolayers are summarized along with their associated theoretical models. The electrostatically induced patterns described in this paper are important in many low-dimensional biological systems such as plasma membrane organization, filamentous virus capsid structure or microtubule interactions. A simple model effectively predicting some features of chiral patterns in biological systems is presented. We extend our model from helical lamellar patterns to elliptical patterns to consider asymmetrical patterns in assemblies of filamentous aggregates.

Morphology and interaction between lipid domains

Cellular membranes are a heterogeneous mix of lipids, proteins and small molecules. Special groupings enriched in saturated lipids and cholesterol form liquid-ordered domains, known as "lipid rafts," thought to serve as platforms for signaling, trafficking and material transport throughout the secretory pathway. Questions remain as to how the cell maintains small fluid lipid domains, through time, on a length scale consistent with the fact that no large-scale phase separation is observed. Motivated by these examples, we have utilized a combination of mechanical modeling and in vitro experiments to show that membrane morphology plays a key role in maintaining small domain sizes and organizing domains in a model membrane. We demonstrate that lipid domains can adopt a flat or dimpled morphology, where the latter facilitates a repulsive interaction that slows coalescence and helps regulate domain size and tends to laterally organize domains in the membrane.

An introduction to critical points for biophysicists; observations of compositional heterogeneity in lipid membranes

Scaling laws associated with critical points have the power to greatly simplify our description of complex biophysical systems. We first review basic concepts and equations associated with critical phenomena for the general reader. We then apply these concepts to the specific biophysical system of lipid membranes. We recently reported that lipid membranes can contain composition fluctuations that behave in a manner consistent with the two-dimensional Ising universality class. Near the membrane's critical point, these fluctuations are micron-sized, clearly observable by fluorescence microscopy. At higher temperatures, above the critical point, we expect to find submicron fluctuations. In separate work, we have reported that plasma membranes isolated directly from cells exhibit the same Ising behavior as model membranes do. We review other models describing submicron lateral inhomogeneity in membranes, including microemulsions, nanodomains, and mean field critical fluctuations, and we describe experimental tests that may distinguish these models.

Bending mechanics and molecular organization in biological membranes

The underlying structure of cell membranes consists of a highly heterogeneous fluid lipid bilayer. Within this milieu, complexes of proteins transiently assemble and dissolve in the performance of the functions of life. The length scales of these coordinated spatial rearrangements can approach the size of the cell, itself, enabling direct visualization in some cases with tantalizing clarity. There has been much interest in the physical driving forces responsible for the assembly of organized structures in cell membranes. Cholesterol-mediated miscibility phase separation within the lipid bilayer has attracted enormous attention over the past decade. This, however, is not the only ordering principle at play. In the following sections, I review recent experimental observations of bending-mediated force transduction and molecular organization in lipid membranes. These results have emerged largely from new experimental methodologies, which are discussed in parallel.

Composition fluctuations, chemical exchange, and nuclear relaxation in membranes containing cholesterol

A thermodynamic model of cholesterol-phospholipid complexes is used as a starting point for calculating fluctuations in membranes containing cholesterol and phospholipids. The calculations describe fluctuations in the concentration of complexes formed between cholesterol and phospholipids with longer saturated fatty acid chains. The fluctuations in complex concentrations arise by two distinct mechanisms. In one, the chemical composition of the sample varies from point to point, and the concentration of the complexes varies according to local chemical equilibrium. In the second, the composition remains fixed, and the complexes form and dissociate according to chemical reaction kinetics. In both cases the nuclear resonance frequency of a deuterium labeled phospholipid undergoes fluctuations and line broadening as a consequence of the formation and dissociation of complexes. For a specific ternary lipid mixture at its critical composition, deuterium nuclear resonance line broadening of chain labeled phospholipids is calculated for temperatures up to 10 degrees -20 degrees above the miscibility critical temperature. This line broadening is associated with fluctuations in the degree of phospholipid chain ordering related to the formation and dissociation of complexes.

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.

Competing interactions in two dimensional Coulomb systems: Surface charge heterogeneities in coassembled cationic-anionic incompatible mixtures

A binary mixture of oppositely charged components confined to a plane such as cationic and anionic lipid bilayers may exhibit local segregation. The relative strengths of the net short range interactions, which favors macroscopic segregation, and the long range electrostatic interactions, which favors mixing, determine the length scale of the finite size or microphase segregation. The free energy of the system can be examined analytically in two separate regimes, when considering small density fluctuations at high temperatures and when considering the periodic ordering of the system at low temperatures [F. J. Solis, S. I. Stupp, and M. Olvera de la Cruz, J. Chem. Phys. 122, 054905 (2005)]. A simple molecular dynamics simulation of oppositely charged monomers, interacting with a short range Lennard-Jones potential and confined to a two dimensional plane, is examined at different strengths of short and long range interactions. The system exhibits well-defined domains that can be characterized by their periodic length scale as well as the orientational ordering of their interfaces. By adding salt, the ordering of the domains disappears and the mixture macroscopically phase segregates in agreement with analytical predictions.

Kinetic Pathways of Phase Ordering in Lipid Raft Model Systems

We studied kinetic pathways of order-order transitions in bilayer lipid mixtures using a time-dependent Ginzburg-Landau (TDGL) approach. During the stripe-to-hexagonal phase transition in an incompressible two-component system, the stripe phase first develops a pearl-like instability along the phase boundaries, which grows and drives the stripes to break up into droplets that arrange into a hexagonal pattern. These dynamic features are consistent with recent experimental observations. During the disorder-to-hexagonal phase transition in an incompressible three-component system, the disordered state first passes through a transient stripelike structure, which eventually breaks up into a hexagonal droplet phase. Our results suggest experiments with synthetic vesicles where the stripelike patterns could be observed.

'KMC-TDGL'-a coarse-grained methodology for simulating interfacial dynamics in complex fluids: application to protein-mediated membrane processes

In this article, we describe a new multiscale simulation algorithm (which we term the 'KMC-TDGL' method) applicable for the description of equilibrium and dynamic processes associated with a particular class of complex fluids with nanoscale inclusions, namely, biological membranes mediated by membrane-associating and membrane-bound proteins. We adopt a novel strategy of integrating two different phenomenological approaches, namely, a field theoretic (continuum) description for the membrane dynamics given by the time-dependent Ginzburg-Landau equation and a random walk on a discretized lattice description for protein diffusion dynamics. We illustrate that this integrated approach results in a unified description of protein-mediated membrane dynamics.