Membrane-mediated interactions measured using membrane domains

"Head-to-Toe" Lipid Properties Govern the Binding and Cargo Transfer of High-Density Lipoprotein

The viscoelastic properties of biological membranes are crucial in controlling cellular functions and are determined primarily by the lipids' composition and structure. This work studies these properties by varying the structure of the constituting lipids in order to influence their interaction with high-density lipoprotein (HDL) particles. Various fluorescence-based techniques were applied to study lipid domains, membrane order, and the overall lateral as well as the molecule-internal glycerol region mobility in HDL-membrane interactions (i.e., binding and/or cargo transfer). The analysis of interactions with HDL particles and various lipid phases revealed that both fully fluid and some gel-phase lipids preferentially interact with HDL particles, although differences were observed in protein binding and cargo exchange. Both interactions were reduced with ordered lipid mixtures containing cholesterol. To investigate the mechanism, membranes were prepared from single-lipid components, enabling step-by-step modification of the lipid building blocks. On a biophysical level, the different mixtures displayed varying stiffness, fluidity, and hydrogen bond network changes. Increased glycerol mobility and a strengthened hydrogen bond network enhanced anchoring interactions, while fluid membranes with a reduced water network facilitated cargo transfer. In summary, the data indicate that different lipid classes are involved depending on the type of interaction, whether anchoring or cargo transfer.

Bending-driven patterning of solid inclusions in lipid membranes: Colloidal assembly and transitions in elastic 2D fluids

Biological or biomimetic membranes are examples within the larger material class of flexible ultrathin lamellae and contoured fluid sheets that require work or energy to impose bending deformations. Bending elasticity also dictates the interactions and assembly of integrated phases or molecular clusters within fluid lamellae, for instance enabling critical cell functions in biomembranes. More broadly, lamella and other thin fluids that integrate dispersed objects, inclusions, and phases behave as contoured 2D colloidal suspensions governed by elastic interactions. To elucidate the breadth of interactions and assembled patterns accessible through elastic interactions, we consider the bending elasticity-driven assembly of 1-10 μm solid plate-shaped Brownian domains (the 2D colloids), integrated into a fluid phospholipid membrane (the 2D fluid). Here, the fluid membranes of giant unilamellar vesicles, 20-50 μm in diameter, each contain 4-100 monodisperse plate-domains at an overall solid area fraction of 17 ± 3%. Three types of reversible plate arrangements are found: persistent vesicle-encompassing quasi-hexagonal lattices, persistent closely associated chains or concentrated lattices, and a dynamic disordered state. The interdomain distances evidence combined attractive and repulsive elastic interactions up to 10 μm, far exceeding the ranges of physio-chemical interactions. Bending contributions are controlled through membrane slack (excess area) producing, for a fixed composition, a sharp cooperative multibody transition in plate arrangement, while domain size and number contribute intricacy.

Glycan-Driven Formation of Raft-Like Domains with Hierarchical Periodic Nanoarrays on Dendrimersome Synthetic Cells

The accurate spatial segregation into distinct phases within cell membranes coordinates vital biochemical processes and functionalities in living organisms. One of nature's strategies to localize reactivity is the formation of dynamic raft domains. Most raft models rely on liquid-ordered L0 phases in a liquid-disordered Ld phase lacking correlation and remaining static, often necessitating external agents for phase separation. Here, we introduce a synthetic system of bicomponent glycodendrimersomes coassembled from Janus dendrimers and Janus glycodendrimers (JGDs), where lactose-lactose interactions exclusively drive lateral organization. This mechanism results in modulated phases across two length scales, yielding raft-like microdomains featuring nanoarrays at the nanoscale. By varying the density of lactose and molecular architecture of JGDs, the nanoarray type and size, shape, and spacing of the domains were controlled. Our findings offer insight into the potential primordial origins of rudimentary raft domains and highlight the crucial role of glycans within the glycocalyx.

Kinetic control of shape deformations and membrane phase separation inside giant vesicles

A variety of cellular processes use liquid-liquid phase separation (LLPS) to create functional levels of organization, but the kinetic pathways by which it proceeds remain incompletely understood. Here in real time, we monitor the dynamics of LLPS of mixtures of segregatively phase-separating polymers inside all-synthetic, giant unilamellar vesicles. After dynamically triggering phase separation, we find that the ensuing relaxation-en route to the new equilibrium-is non-trivially modulated by a dynamic interplay between the coarsening of the evolving droplet phase and the interactive membrane boundary. The membrane boundary is preferentially wetted by one of the incipient phases, dynamically arresting the progression of coarsening and deforming the membrane. When the vesicles are composed of phase-separating mixtures of common lipids, LLPS within the vesicular interior becomes coupled to the membrane's compositional degrees of freedom, producing microphase-separated membrane textures. This coupling of bulk and surface phase-separation processes suggests a physical principle by which LLPS inside living cells might be dynamically regulated and communicated to the cellular boundaries.

Tailoring a Solvent-Assisted Method for Solid-Supported Hybrid Lipid-Polymer Membranes

Combining amphiphilic block copolymers and phospholipids opens new opportunities for the preparation of artificial membranes. The chemical versatility and mechanical robustness of polymers together with the fluidity and biocompatibility of lipids afford hybrid membranes with unique properties that are of great interest in the field of bioengineering. Owing to its straightforwardness, the solvent-assisted method (SA) is particularly attractive for obtaining solid-supported membranes. While the SA method was first developed for lipids and very recently extended to amphiphilic block copolymers, its potential to develop hybrid membranes has not yet been explored. Here, we tailor the SA method to prepare solid-supported polymer-lipid hybrid membranes by combining a small library of amphiphilic diblock copolymers poly(dimethyl siloxane)-poly(2-methyl-2-oxazoline) and poly(butylene oxide)-block-poly(glycidol) with phospholipids commonly found in cell membranes including 1,2-dihexadecanoyl-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine, sphingomyelin, and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(glutaryl). The optimization of the conditions under which the SA method was applied allowed for the formation of hybrid polymer-lipid solid-supported membranes. The real-time formation and morphology of these hybrid membranes were evaluated using a combination of quartz crystal microbalance and atomic force microscopy. Depending on the type of polymer-lipid combination, significant differences in membrane coverage, formation of domains, and quality of membranes were obtained. The use of the SA method for a rapid and controlled formation of solid-supported hybrid membranes provides the basis for developing customized artificial hybrid membranes.

Switchable positioning of plate-like inclusions in lipid membranes: Elastically mediated interactions of planar colloids in 2D fluids

We demonstrate how manipulating curvature in an elastic fluid lamella enables the reversible relative positioning of flat, rigid, plate-like micrometer-scale inclusions, with spacings from about a micrometer to tens of micrometers. In an experimental model comprising giant unilamellar vesicles containing solid domain pairs coexisting in a fluid membrane, we adjusted vesicle inflation to manipulate membrane curvature and mapped the interdomain separation. A two-dimensional model of the pair potential predicts the salient experimental observations and reveals both attractions and repulsions, producing a potential minimum entirely a result of the solid domain rigidity and bending energy in the fluid membrane. The impact of vesicle inflation on domain separation in vesicles containing two solid domains was qualitatively consistent with observations in vesicles containing many domains. The behavior differs qualitatively from the pure repulsions between fluid membrane domains or interactions between nanoscopic inclusions whose repulsive or attractive character is not switchable.

Defining the Diffusion in Model Membranes Using Line Fluorescence Recovery after Photobleaching

In this study, we explore the use of line FRAP to detect diffusion in synthetic lipid membranes. The study of the dynamics of these membrane lipids can, however, be challenging. The diffusion in two different synthetic membranes consisting of the lipid mixtures 1:1 DOPC:DPPC and 2:2:1 DOPC:DPPC:Cholesterol was studied with line FRAP. A correlation between diffusion coefficient and temperature was found to be dependent on the morphology of the membrane. We suggest line FRAP as a promising accessible and simple technique to study diffusion in plasma membranes.

Shape morphology of dipolar domains in planar and spherical monolayers

We present a continuum theory for predicting the equilibrium shape and size of dipolar domains formed during liquid-liquid phase coexistence in planar and spherical monolayers. Our main objective is to assess the impact of the monolayer surface curvature on domain morphology. Following previous investigators, we base our analysis around minimizing the free energy, with contributions from line tension and electrostatic dipolar repulsions. Assuming a monodisperse system of circularly symmetric domains, we calculate self-energies and interaction energies for planar and spherical monolayers and determine the equilibrium domain size from the energy minima. We subsequently evaluate the stability of the circularly symmetric domain shapes to an arbitrary, circumferential distortion of the perimeter via a linear stability analysis. We find that the surface curvature generally promotes the formation of smaller, circularly symmetric domains instead of larger, elongated domains. We rationalize these results by examining the effect of the curvature on the intra- and inter-domain dipolar repulsions. We then present a phase diagram of domain shape morphologies, parameterized in terms of the domain area fraction and the monolayer curvature. For typical domain dimensions of 1-30 µm, our theoretical results are relevant to monolayers (and possibly also bilayers) in liquid-liquid phase coexistence with radii of curvature of 1-100 µm.

Conformational switching of chiral colloidal rafts regulates raft-raft attractions and repulsions

Membrane-mediated particle interactions depend both on the properties of the particles themselves and the membrane environment in which they are suspended. Experiments have shown that chiral rod-like inclusions dissolved in a colloidal membrane of opposite handedness assemble into colloidal rafts, which are finite-sized reconfigurable droplets consisting of a large but precisely defined number of rods. We systematically tune the chirality of the background membrane and find that, in the achiral limit, colloidal rafts acquire complex structural properties and interactions. In particular, rafts can switch between 2 chiral states of opposite handedness, which alters the nature of the membrane-mediated raft-raft interactions. Rafts with the same chirality have long-ranged repulsions, while those with opposite chirality acquire attractions with a well-defined minimum. Both attractive and repulsive interactions are qualitatively explained by a continuum model that accounts for the coupling between the membrane thickness and the local tilt of the constituent rods. These switchable interactions enable assembly of colloidal rafts into intricate higher-order architectures, including stable tetrameric clusters and "ionic crystallites" of counter-twisting domains organized on a binary square lattice. Furthermore, the properties of individual rafts, such as their sizes, are controlled by their complexation with other rafts. The emergence of these complex behaviors can be rationalized purely in terms of generic couplings between compositional and orientational order of fluids of rod-like elements. Thus, the uncovered principles might have relevance for conventional lipid bilayers, in which the assembly of higher-order structures is also mediated by complex membrane-mediated interactions.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Why Enveloped Viruses Need Cores-The Contribution of a Nucleocapsid Core to Viral Budding

During the lifecycle of many enveloped viruses, a nucleocapsid core buds through the cell membrane to acquire an outer envelope of lipid membrane and viral glycoproteins. However, the presence of a nucleocapsid core is not required for assembly of infectious particles. To determine the role of the nucleocapsid core, we develop a coarse-grained computational model with which we investigate budding dynamics as a function of glycoprotein and nucleocapsid interactions, as well as budding in the absence of a nucleocapsid. We find that there is a transition between glycoprotein-directed budding and nucleocapsid-directed budding that occurs above a threshold strength of nucleocapsid interactions. The simulations predict that glycoprotein-directed budding leads to significantly increased size polydispersity and particle polymorphism. This polydispersity can be explained by a theoretical model accounting for the competition between bending energy of the membrane and the glycoprotein shell. The simulations also show that the geometry of a budding particle leads to a barrier to subunit diffusion, which can result in a stalled, partially budded state. We present a phase diagram for this and other morphologies of budded particles. Comparison of these structures against experiments could establish bounds on whether budding is directed by glycoprotein or nucleocapsid interactions. Although our model is motivated by alphaviruses, we discuss implications of our results for other enveloped viruses.

Directed tubule growth from giant unilamellar vesicles in a thermal gradient

We demonstrate experimental control over tubule growth in giant unilamellar vesicles with liquid-liquid phase coexistence, using a thermal gradient to redistribute lipid phase domains on the membrane. As studied previously, the domains of the less abundant phase always partition towards hotter temperatures, depleting the cold side of the vesicle of domains. We couple this mechanism of domain migration with the inclusion of negative-curvature lipids within the membrane, resulting in control of tubule growth direction towards the high temperature. Control of composition determines the interior/exterior growth of tubules, whereas the thermal gradient regulates the length of the tubule relative to the vesicle radius. Maintaining lipid membranes under non-equilibrium conditions, such as thermal gradients, allows the creation of thermally-oriented protrusions, which could be a key step towards developing functional materials or artificial tissues. Interconnected vesicle compartments or ejected daughter vesicles as transport intermediaries towards hot/cold are just two possibilities.

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.

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.

Formation of modulated phases and domain rigidification in fatty acid-containing lipid membranes

We investigated the phase behavior of lipid membranes containing fatty acids (FAs) by microscopy and differential scanning calorimetry. We used palmitic acid (saturated FA), oleic acid (cis-isomer of unsaturated FA), elaidic acid (trans-isomer of unsaturated FA), and phytanic acid (branched FA) and examined the effects of FAs on phase-separated structures in lipid bilayer membranes consisting of dioleolylphosphocholine (DOPC)/dipalmitoylphosphocholine (DPPC)/cholesterol (Chol). Palmitic acid and elaidic acid exclude Chol from the DPPC-rich phase. As a result, the liquid-ordered phase formed by DPPC and Chol transforms into a solid-ordered phase. Oleic acid and phytanic acid significantly reduce the line tension at the liquid domain boundary. This decrease in line tension leads to the formation of modulated phases, such as striped, hexagonal, and polygonal domains. We measured the line tension and the interdomain interaction in these specific domains by an image analysis. The result showed that oleic acid and phytanic acid-containing vesicles as well as palmitic acid-containing vesicles are not spherical, and this domain-induced deformation is explained theoretically.

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.

Modulation of phase separation at the micron scale and nanoscale in giant polymer/lipid hybrid unilamellar vesicles (GHUVs)

Phase separation in giant polymer/lipid hybrid unilamellar vesicles (GHUVs) has been described over the last few years. However there is still a lack of understanding on the physical and molecular factors governing the phase separation in such systems. Among these parameters it has been suggested that in analogy to multicomponent lipid vesicles hydrophobic mismatches as well as lipid fluidity play a role. In this work, we aim to map a global picture of phase separation and domain formation in the membrane of GHUVs by using various copolymers based on poly(dimethylsiloxane) (PDMS) and poly(ethylene glycol) (PEO) with different architectures (grafted, triblock) and molar masses, combined with phospholipids in the fluid (POPC) or gel state (DPPC) at room temperature. From confocal imaging and fluorescence lifetime imaging microscopy (FLIM) techniques, the phase separation into either micro- or nano-domains within GHUVs was studied. In particular, our systematic studies demonstrate that in addition to the lipid/polymer fraction or the lipid physical state, important factors such as line tension at lipid polymer/lipid boundaries can be finely modulated by the molar mass and the architecture of the copolymer and lead to the formation of stable lipid domains with different sizes and morphologies in such GHUVs.

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.

Lipid membrane-mediated attraction between curvature inducing objects

The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.

Bending Rigidities and Interdomain Forces in Membranes with Coexisting Lipid Domains

To precisely quantify the fundamental interactions between heterogeneous lipid membranes with coexisting liquid-ordered (Lo) and liquid-disordered (Ld) domains, we performed detailed osmotic stress small-angle x-ray scattering experiments by exploiting the domain alignment in raft-mimicking lipid multibilayers. Performing a Monte Carlo-based analysis allowed us to determine with high reliability the magnitude and functional dependence of interdomain forces concurrently with the bending elasticity moduli. In contrast to previous methodologies, this approach enabled us to consider the entropic undulation repulsions on a fundamental level, without having to take recourse to crudely justified mean-field-like additivity assumptions. Our detailed Hamaker-coefficient calculations indicated only small differences in the van der Waals attractions of coexisting Lo and Ld phases. In contrast, the repulsive hydration and undulation interactions differed significantly, with the latter dominating the overall repulsions in the Ld phase. Thus, alignment of like domains in multibilayers appears to originate from both, hydration and undulation repulsions.

High-order power series expansion of the elastic interaction between conical membrane inclusions

We revisit the problem of the long-range interaction between two conical proteins inserted into a lipid membrane and interacting via the induced deformation of the membrane, first considered by Goulian et al. (M. Goulian, R. Bruinsma, P. Pincus, Europhys. Lett. 22, 145 (1993); Europhys. Lett. 23, 155 (1993)). By means of a complex variables formulation and an iterative solution, we determine analytically an arbitrary high-order expansion of the interaction energy in powers of the inverse distance between two inclusions of different sizes. At leading order and for inclusions of equal sizes, we recover the result obtained by Goulian et al.. We generalize the development to inclusions of different sizes and give explicit formulas that increase the precision by ten orders in the inverse distance.

Confinement without boundaries: anisotropic diffusion on the surface of a cylinder

Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly affected by physical confinement, e.g., by the walls. In this work, we explore the effects of confinement by shape, not rigid boundaries, on the diffusion of discs by confining them to the surface of a cylinder. We find that both the magnitude and the directionality of lateral diffusion is strongly influenced by the radius of the cylinder. An anisotropy between diffusion in the longitudinal and circumferential direction of the cylinder develops. We demonstrate that the origin of this effect lies in the fact that screw-like packings of mono- and oligodisperse discs on the surface of a cylinder induce preferential collective motions in the circumferential direction, but also show that even in polydisperse systems lacking such order an intrinsic finite size confinement effect increases diffusivity in the circumferential direction.

Lipid domains in model membranes: a brief historical perspective

All biological membranes consist of a complex composite of macromolecules and macromolecular assemblies, of which the fluid lipid-bilayer component is a core element with regard to cell encapsulation and barrier properties. The fluid lipid bilayer also supports the functional machinery of receptors, channels and pumps that are associated with the membrane. This bilayer is stabilized by weak physical and colloidal forces, and its nature is that of a self-assembled system of amphiphiles in water. Being only approximately 5 nm in thickness and still encapsulating a cell that is three orders of magnitude larger in diameter, the lipid bilayer as a material has very unusual physical properties, both in terms of structure and dynamics. Although the lipid bilayer is a fluid, it has a distinct and structured trans-bilayer profile, and in the plane of the bilayer the various molecular components, viz different lipid species and membrane proteins, have the capacity to organize laterally in terms of differentiated domains on different length and time scales. These elements of small-scale structure and order are crucial for the functioning of the membrane. It has turned out to be difficult to quantitatively study the small-scale structure of biological membranes. A major part of the insight into membrane micro- and nano-domains and the concepts used to describe them have hence come from studies of simple lipid bilayers as models of membranes, by use of a wide range of theoretical, experimental and simulational approaches. Many questions remain to be answered as to which extent the result from model studies can carry over to real biological membranes.

Simulations show that virus assembly and budding are facilitated by membrane microdomains

For many viruses, assembly and budding occur simultaneously during virion formation. Understanding the mechanisms underlying this process could promote biomedical efforts to block viral propagation and enable use of capsids in nanomaterials applications. To this end, we have performed molecular dynamics simulations on a coarse-grained model that describes virus assembly on a fluctuating lipid membrane. Our simulations show that the membrane can promote association of adsorbed subunits through dimensional reduction, but it also introduces thermodynamic and kinetic effects that can inhibit complete assembly. We find several mechanisms by which membrane microdomains, such as lipid rafts, reduce these effects, and thus, enhance assembly. We show how these predicted mechanisms can be experimentally tested. Furthermore, the simulations demonstrate that assembly and budding depend crucially on the system dynamics via multiple timescales related to membrane deformation, protein diffusion, association, and adsorption onto the membrane.

The Effective Field Theory approach towards membrane-mediated interactions between particles

Fluid lipid membranes can mediate forces between particles bound to them: A local deformation of the surface geometry created by some object spreads to distant regions, where other objects can respond to it. The physical characteristics of these geometric interactions, and how they are affected by thermal fluctuations, are well described by the simple continuum curvature-elastic Hamiltonian proposed 40 years ago by Wolfgang Helfrich. Unfortunately, while the underlying principles are conceptually straightforward, the corresponding calculations are not-largely because one must enforce boundary conditions for finite-sized objects. This challenge has inspired several heuristic approaches for expressing the problem in a point particle language. While streamlining the calculations of leading order results and enabling predictions for higher order corrections, the ad hoc nature of the reformulation leaves its domain of validity unclear. In contrast, the framework of Effective Field Theory (EFT) provides a systematic way to construct a completely equivalent point particle description. In this review we present a detailed account for how this is accomplished. In particular, we use a familiar example from electrostatics as an analogy to motivate the key steps needed to construct an EFT, most notably capturing finite size information in point-like "polarizabilities," and determining their value through a suitable "matching procedure." The interaction (free) energy then emerges as a systematic cumulant expansion, for which powerful diagrammatic techniques exist, which we also briefly revisit. We then apply this formalism to derive series expansions for interactions between flat and curved particle pairs, multibody interactions, as well as corrections to all these interactions due to thermal fluctuations.

Growth kinetics of circular liquid domains on vesicles by diffusion-controlled coalescence

Motivated by recent experiments on multicomponent membranes, the growth kinetics of domains on vesicles are theoretically studied. It is known that the steady-state rate of coalescence cannot be obtained by taking the long-time limit of the coalescence rate when the membrane is regarded as an infinite two-dimensional (2D) system. The steady-state rate of coalescence is obtained by explicitly taking into account the spherical vesicle shape. Using the expression for the 2D diffusion coefficient obtained in the limit of small domain size, an analytical expression for domain growth kinetics is obtained when a circular shape is always maintained. For large domains, the growth kinetics are discussed by investigating the size dependence of the coalescence rate, using the expression for the diffusion coefficient of arbitrary domain size.

Multidomain and ground state configurations of two-phase vesicles

A simple model is used to study the equilibrium of lipid domains on two-phase vesicles. Two classes of configurations are considered: multidomain and ground state configurations. For multidomain configurations, the vesicle has a finite number of identical lipid domains. For ground state configurations, the vesicle is fully phase separated into two coexisting domains. Whereas the volume enclosed by a vesicle with multidomains is fixed, the volume enclosed by a vesicle in a ground state is allowed to vary with the osmotic pressure. Guided by experimental observations, all domains are assumed to be spherical caps. In a multidomain configuration, the line tension is found to decrease with the number of domains present, with possible exceptions when the number of domains is very small. The importance of a critical osmotic pressure and a critical excess radius on ground state configurations is explored. Emphasis is placed on understanding the variations of these critical quantities with relevant parameters.

Polka-dotted vesicles: lipid bilayer dynamics and cross-linking effects

We have investigated the effects of cross-linking perturbations on lipid phase-domain coalescence. Our model system explores cross-linking in the fluid-disordered phase of two-phase vesicles. Here, we quantify the vesicle population shift from the expected predominance of two-domain, two-phase configuration to a multidomain vesicle majority. We have found that the increase in multidomain vesicles is a distinct outcome from the cross-linking of biotinylated lipids and avidin. Analysis of our cross-linking data suggests that avidin forms clusters on the surface of the fluid-disordered domains, resulting in a large immobile fraction and restricted diffusion. In cellular membranes, receptor concentrations are similar to our experimental model, and we expect similar cluster formations, leading to nonideal mixing and lateral heterogeneity. We have induced and quantified a global response by cross-linking only a small percentage of lipids in our system, similar to receptor-ligand interactions on the cell membrane. Common activities, such as ligand-receptor coupling, contribute to lateral heterogeneity and membrane protein clustering, adding to cell membrane complexity. Fundamental studies into subtle shifts such as cross-linking events, which induce global cellular response, are pertinent to understanding membrane activities and effects of external stimuli.

Bilayer thickness mismatch controls domain size in model membranes

The observation of lateral phase separation in lipid bilayers has received considerable attention, especially in connection to lipid raft phenomena in cells. It is widely accepted that rafts play a central role in cellular processes, notably signal transduction. While micrometer-sized domains are observed with some model membrane mixtures, rafts much smaller than 100 nm-beyond the reach of optical microscopy-are now thought to exist, both in vitro and in vivo. We have used small-angle neutron scattering, a probe free technique, to measure the size of nanoscopic membrane domains in unilamellar vesicles with unprecedented accuracy. These experiments were performed using a four-component model system containing fixed proportions of cholesterol and the saturated phospholipid 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), mixed with varying amounts of the unsaturated phospholipids 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). We find that liquid domain size increases with the extent of acyl chain unsaturation (DOPC:POPC ratio). Furthermore, we find a direct correlation between domain size and the mismatch in bilayer thickness of the coexisting liquid-ordered and liquid-disordered phases, suggesting a dominant role for line tension in controlling domain size. While this result is expected from line tension theories, we provide the first experimental verification in free-floating bilayers. Importantly, we also find that changes in bilayer thickness, which accompany changes in the degree of lipid chain unsaturation, are entirely confined to the disordered phase. Together, these results suggest how the size of functional domains in homeothermic cells may be regulated through changes in lipid composition.

Membrane-mediated interactions between rigid inclusions: an effective field theory

An approach based on effective field theory (EFT) is discussed and applied to the problem of surface-mediated interactions between rigid inclusions of circular footprint on a membrane. Instead of explicitly constraining the surface fluctuations in accord with the boundary conditions around the inclusions, the EFT formalism rewrites the theory; the Hamiltonian of a freely fluctuating surface is augmented by pointwise localized terms that capture the same constraints. This allows one to compute the interaction free energy as an asymptotic expansion in inverse separations in a systematic, efficient, and transparent way. Both entropic (fluctuation-induced, Casimir-like) and curvature-elastic (ground-state) forces are considered. Our findings include higher-order corrections to known asymptotic results, on both the pair and the multibody levels. We also show that the few previous attempts in the literature at predicting subleading orders missed some terms due to an uncontrolled point-particle approximation.

Lipids of plant membrane rafts

Lipids tend to organize in mono or bilayer phases in a hydrophilic environment. While they have long been thought to be incapable of coherent lateral segregation, it is now clear that spontaneous assembly of these compounds can confer microdomain organization beyond spontaneous fluidity. Membrane raft microdomains have the ability to influence spatiotemporal organization of protein complexes, thereby allowing regulation of cellular processes. In this review, we aim at summarizing briefly: (i) the history of raft discovery in animals and plants, (ii) the main findings about structural and signalling plant lipids involved in raft segregation, (iii) imaging of plant membrane domains, and their biochemical purification through detergent-insoluble membranes, as well as the existing debate on the topic. We also discuss the potential involvement of rafts in the regulation of plant physiological processes, and further discuss the prospects of future research into plant membrane rafts.

Protein sorting and membrane-mediated interactions

Sorting of membrane proteins is of vital importance for living cells. Indeed, roughly one-third of a eukaryotic cell's proteome consists of peripheral and transmembrane proteins. These need to be properly distributed and dynamically maintained at distinct locations in the compartmentalized cell, and one may wonder how proteins determine where, when, and how to travel to reach a specific organelle. While specific binary interactions between proteins have been invoked in explaining the trafficking and sorting processes, a more active role of lipids in this context has become visible in recent years. In particular, membrane-mediated interactions have been suggested to serve as a robust physicochemical mechanism to facilitate protein sorting. Here, we will review some recent insights into these aspects.

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.

Lipids, curvature, and nano-medicine

The physical properties of the lamellar lipid-bilayer component of biological membranes are controlled by a host of thermodynamic forces leading to overall tensionless bilayers with a conspicuous lateral pressure profile and build-in curvature-stress instabilities that may be released locally or globally in terms of morphological changes. In particular, the average molecular shape and the propensity of the different lipid and protein species for forming non-lamellar and curved structures are a source of structural transitions and control of biological function. The effects of different lipids, sterols, and proteins on membrane structure are discussed and it is shown how one can take advantage of the curvature-stress modulations brought about by specific molecular agents, such as fatty acids, lysolipids, and other amphiphilic solutes, to construct intelligent drug-delivery systems that function by enzymatic triggering via curvature.Practical applications: The simple concept of lipid molecular shape and how it impacts on the structure of lipid aggregates, in particular the curvature and curvature stress in lipid bilayers and liposomes, can be exploited to construct liposome-based drug-delivery systems, e.g., for use as nano-medicine in cancer therapy. Non-lamellar-forming lysolipids and fatty acids, some of which may be designed to be prodrugs, can be created by phospholipase action in diseased tissues thereby providing for targeted drug release and proliferation of molecular entities with conical shape that break down the permeability barrier of the target cells and may hence enhance efficacy.

Amphiphilic properties of dumbbell-shaped inorganic-organic-inorganic molecular hybrid materials in solution and at an interface

Five novel dumbbell-shaped polyoxometalate (POM)-based inorganic-organic-inorganic molecular hybrids are investigated both in polar solvents and at interfaces for potential amphiphilic properties, which are compared with those of conventional surfactants. These hybrids with the general formula {P(2)V(3)W(15)}(2)-bis(TRIS)-linker are formed by linking two Wells-Dawson-type clusters, [P(2)V(3)W(15)O(62)](9-), with different linear bis(TRIS) linker ligands between the two TRIS moieties. Laser light scattering (LLS) studies reveal the presence of self-assembled vesicular structures in water/acetone mixed solvents, and the vesicle size increases with increasing acetone content, suggesting a charge-regulated process. The elastic constants, which are used to calculate the bending energy during vesicle formation, reveal that the organic ligands play an important role in determining the self-assembly process and that the hybrids do demonstrate amphiphilic behavior at the water/air interface. Furthermore, it is shown that some of the hybrids form monolayers at the interface, with an average molecular area that can be correlated with their organic linkers, as determined from their π-A isotherms. Finally, the hybrids not only display amphiphilic behavior akin to that of a surfactant but also exhibit an unusually high entropy contribution to vesicle formation as a result of their unique large, polar head groups, complex organic linkers, and their special molecular architectures as well as because of the involvement of the amphiphilic tetrabutylammonium (TBA) counterions.

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.

Near-critical fluctuations and cytoskeleton-assisted phase separation lead to subdiffusion in cell membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out Monte Carlo simulations of two-component lipid membranes. We find that near-critical fluctuations in the membrane lead to transient subdiffusion, while membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, we present a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion.

Phase separation in lipid membranes

Cell membranes show complex behavior, in part because of the large number of different components that interact with each other in different ways. One aspect of this complex behavior is lateral organization of components on a range of spatial scales. We found that lipid-only mixtures can model the range of size scales, from approximately 2 nm up to microns. Furthermore, the size of compositional heterogeneities can be controlled entirely by lipid composition for mixtures such as 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 or sphingomyelin (SM)/DOPC/POPC/cholesterol. In one region of special interest, because of its connection to cell membrane rafts, nanometer-scale domains of liquid-disordered phase and liquid-ordered phase coexist over a wide range of compositions.

Comparison of three ternary lipid bilayer mixtures: FRET and ESR reveal nanodomains

Phase diagrams of ternary lipid mixtures containing cholesterol have provided valuable insight into cell membrane behaviors, especially by describing regions of coexisting liquid-disordered (Ld) and liquid-ordered (Lo) phases. Fluorescence microscopy imaging of giant unilamellar vesicles has greatly assisted the determination of phase behavior in these systems. However, the requirement for optically resolved Ld + Lo domains can lead to the incorrect inference that in lipid-only mixtures, Ld + Lo domain coexistence generally shows macroscopic domains. Here we show this inference is incorrect for the low melting temperature phosphatidylcholines abundant in mammalian plasma membranes. By use of high compositional resolution Förster resonance energy transfer measurements, together with electron spin resonance data and spectral simulation, we find that ternary mixtures of DSPC and cholesterol together with either POPC or SOPC, do indeed have regions of Ld + Lo coexistence. However, phase domains are much smaller than the optical resolution limit, likely on the order of the Förster distance for energy transfer (R(0), ∼2-8 nm).