Physical aspects of heterogeneities in multi-component lipid membranes

Characterizing the heterogeneity of membrane liquid-ordered domains

We use a lattice model of a ternary mixture containing saturated and unsaturated lipids with cholesterol (Chol), to study the structural properties characterizing the coexistence between the liquid-disordered and liquid-ordered phases. Depending on the affinity of the saturated and unsaturated lipids, the system may exhibit macroscopic (thermodynamic) liquid-liquid phase separation or be divided into small-size liquid-ordered domains surrounded by a liquid-disordered matrix. In both cases, it is found that the nanoscale structure of the liquid-ordered regions is heterogeneous, and that they are partitioned into Chol-rich sub-domains and Chol-free, gel-like, nano-clusters. This emerges as a characteristic feature of the liquid-ordered state, which helps distinguishing between liquid-ordered domains in a two-phase mixture, and similar-looking domains in a one-phase mixture that are rich in saturated lipids and Chol, but are merely thermal density fluctuations. The nano-structure heterogeneity of the liquid-ordered phase can be detected by suitable experimental spectroscopic methods and is observed also in atomistic computer simulations.

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Physical Concept to Explain the Regulation of Lipid Membrane Phase Separation under Isothermal Conditions

Lateral phase separation within lipid bilayer membranes has attracted considerable attention in the fields of biophysics and cell biology. Living cells organize laterally segregated compartments, such as raft domains in an ordered phase, and regulate their dynamic structures under isothermal conditions to promote cellular functions. Model membrane systems with minimum components are powerful tools for investigating the basic phenomena of membrane phase separation. With the use of such model systems, several physicochemical characteristics of phase separation have been revealed. This review focuses on the isothermal triggering of membrane phase separation from a physical point of view. We consider the free energy of the membrane that describes lateral phase separation and explain the experimental results of model membranes to regulate domain formation under isothermal conditions. Three possible regulation factors are discussed: electrostatic interactions, chemical reactions and membrane tension. These findings may contribute to a better understanding of membrane lateral organization within living cells that function under isothermal conditions and could be useful for the development of artificial cell engineering.

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

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

Control of Line Tension at Phase-Separated Lipid Domain Boundaries: Monounsaturated Fatty Acids with Different Chain Lengths and Osmotic Pressure

Line tension at phase-separated lipid domain boundaries is an important factor that governs the stability of the phase separation. We studied the control of the line tension in lipid membranes composed of dioleoylphosphocholine (DOPC), dipalmitoylphosphocholine (DPPC), and cholesterol (Chol) by the addition of the following three monounsaturated fatty acids (MUFAs) with different chain lengths: palmitoleic acid (PaA), oleic acid (OA), and eicosenoic acid (EiA). In addition, we attempted to alter the line tension by applying osmotic pressure. The phase behavior of the MUFA-containing lipid membranes in the presence and absence of osmotic stress was observed by fluorescence and confocal laser scanning microscopy. The line tension was quantitatively measured from the domain boundary fluctuation by flicker spectroscopy, and the interactions between the lipids and MUFAs were examined by differential scanning calorimetry. PaA and OA, which are shorter MUFAs, decreased the line tension, whereas EiA changed the liquid domain to a solid domain. The osmotic pressure increased the line tension, even in the presence of MUFAs. It may be possible to control the line tension by combining the chemical approach of MUFA addition and the physical approach of applying osmotic pressure.

Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity

We discuss hydrodynamic forces acting on a two-dimensional liquid domain that moves laterally within a supported fluid membrane in the presence of odd viscosity. Since active rotating proteins can accumulate inside the domain, we focus on the difference in odd viscosity between the inside and outside of the domain. Taking into account the momentum leakage from a two-dimensional incompressible fluid to the underlying substrate, we analytically obtain the fluid flow induced by the lateral domain motion and calculate the drag and lift forces acting on the moving liquid domain. In contrast to the passive case without odd viscosity, the lateral lift arises in the active case only when the in and out odd viscosities are different. The in-out contrast in the odd viscosity leads to nonreciprocal hydrodynamic responses of an active liquid domain.

Domain formation in bicomponent vesicles induced by composition-curvature coupling

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

Modulated and spiral surface patterns on deformable lipid vesicles

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

Label-free, chronological and selective detection of aggregation and fibrillization of amyloid β protein in serum by microcantilever sensor immobilizing cholesterol-incorporated liposome

To facilitate the early diagnosis of Alzheimer's disease and mild cognitive impairment patients, we developed a cantilever-based microsensor that immobilized liposomes of various phospholipids to detect a trace amount of amyloid β (Aβ) protein, and investigated its aggregation and fibrillization on model cell membranes in human serum. Three species of liposomes composed of different phospholipids of 1,2-dipalmtoyl-sn-glycero-3-phosphocholine (DPPC), DPPC/phosphatidyl ethanolamine and 1,2-dipalmitoyl-sn-glycero-3-phosphorylglycerol having varied hydrophilic groups were applied, which showed different chronological interactions with Aβ(1-40) protein and varied sensitivities of the cantilever sensor, depending on their specific electrostatic charged conditions, hydrophilicity, and membrane fluidity. 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) having short hydrophobic carbon chains confirmed to show a large interaction with Aβ(1-40) and a high sensitivity. Furthermore, the incorporation of cholesterol into DMPC was effective to selectively detect Aβ(1-40) in human serum, which effect was also checked by quartz crystal microbalance. Finally, Aβ detection of 100-pM order was expected selectively in the serum by using the developed biosensor.

A molecular dynamics study proposing the existence of statistical structural heterogeneity due to chain orientation in the POPC-cholesterol bilayer

We performed molecular dynamics simulations of a lipid bilayer consisting of POPC and cholesterol at temperatures from 283 to 308K and cholesterol concentrations from 0 to 50% mol/mol. The purpose of this study was to look for the existence of structural differences in the region delimited by these parameters and, in particular, in a region where coexistence of liquid disordered and liquid ordered phases has been proposed. Our interest in this range of concentration and temperature responds to the fact that polyene ionophore activity varies considerably along it. Two force fields, CHARMM36 and Slipids, were compared in order to determine the most suitable. Both force fields predict non-monotonic behaviors consistent with the existence of phase transitions. We found the presence of lateral structural heterogeneity, statistical in nature, in some of the bilayers occurring in this range of temperatures and sterol concentrations. This heterogeneity was produced by correlated ordering of the POPC tails and not due to cholesterol enrichment, and lasts for tens of nanoseconds. We relate these observations to the action of polyenes in these membranes.

Fluid Phase Coexistence in Biological Membrane: Insights from Local Nonaffine Deformation of Lipids

Lateral heterogeneities in biomembranes play a crucial role in various physiological functions of the cell. Such heterogeneities lead to demixing of lipid constituents and formation of distinct liquid domains in the membrane. We study lateral heterogeneities in terms of topological rearrangements of lipids to identify the liquid-liquid phase coexistence in model membranes. Using ideas from the physics of amorphous systems and glasses, we calculate the degree of nonaffine deformation associated with individual lipids to characterize the liquid-ordered (L_o) and liquid-disordered (L_d) regions in model lipid bilayers. We explore the usage of this method on all-atom and coarse-grained lipid bilayer trajectories. This method is helpful in defining the instantaneous L_o-L_d domain boundaries in complex multicomponent bilayer systems. The characterization is also used to highlight the effect of line-active molecules on the phase boundaries and domain mixing. Overall, we propose a framework to explore the molecular origin of spatial and dynamical heterogeneity in biomembrane systems, which can be exploited not only in computer simulations but also in experiments.

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

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

Coarse-grained molecular dynamics simulation for uptake of nanoparticles into a charged lipid vesicle dominated by electrostatic interactions

We use a coarse-grained molecular dynamics simulation to investigate the interaction between neutral or charged nanoparticles (NPs) and a vesicle consisting of neutral and negatively charged lipids. We focus on the interaction strengths of hydrophilic and hydrophobic attraction and electrostatic interactions between a lipid molecule and an NP. A neutral NP passes through the lipid membrane when the hydrophobic interaction is sufficiently strong. As the valence of the positively charged NP increases, the membrane permeation speed of the NP is increased compared with the neutral NP and charged lipids are accumulated around the charged NP. A charged NP with a high valence passes through the lipid membrane via a transient channel formed by charged lipids or transportlike endocytosis. These permeation processes can be classified based on analyses of the density correlation function. When the nonelectrostatic interaction parameters are large enough, a negatively charged NP can be adsorbed on the membrane and a neutral lipid-rich region is formed directly below the NP. The NP is spontaneously incorporated into the vesicle under various conditions and the incorporation is mediated by the membrane curvature. We reveal how the NP's behavior depends on the NP valence, size, and the nonelectrostatic interaction parameters.

Recent Lipid Membrane-Based Biosensing Platforms

The investigation of lipid films for the construction of biosensors has recently given the opportunity to manufacture devices to selectively detect a wide range of food toxicants, environmental pollutants, and compounds of clinical interest. Biosensor miniaturization using nanotechnological tools has provided novel routes to immobilize various “receptors” within the lipid film. This chapter reviews and exploits platforms in biosensors based on lipid membrane technology that are used in food, environmental, and clinical chemistry to detect various toxicants. Examples of applications are described with an emphasis on novel systems, new sensing techniques, and nanotechnology-based transduction schemes. The compounds that can be monitored are insecticides, pesticides, herbicides, metals, toxins, antibiotics, microorganisms, hormones, dioxins, etc.

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].

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.

Field-Embedded Particles Driven by Active Flips

Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite of the surrounding one. Our approach combines Monte Carlo simulations with analytical methods based on dynamical density functional approaches.

Three-disk microswimmer in a supported fluid membrane

A model of three-disk micromachine swimming in a quasi-two-dimensional supported membrane is proposed. We calculate the average swimming velocity as a function of the disk size and the arm length. Due to the presence of the hydrodynamic screening length in the quasi-two-dimensional fluid, the geometric factor appearing in the average velocity exhibits three different asymptotic behaviors depending on the microswimmer size and the hydrodynamic screening length. This is in sharp contrast with a microswimmer in a three-dimensional bulk fluid that shows only a single scaling behavior. We also find that the maximum velocity is obtained when the disks are equal-sized, whereas it is minimized when the average arm lengths are identical. The intrinsic drag of the disks on the substrate does not alter the scaling behaviors of the geometric factor.

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.

Noise-induced drift in two-dimensional anisotropic systems

We study the isothermal Brownian dynamics of a particle in a system with spatially varying diffusivity. Due to the heterogeneity of the system, the particle's mean displacement does not vanish even if it does not experience any physical force. This phenomenon has been termed "noise-induced drift," and has been extensively studied for one-dimensional systems. Here, we examine the noise-induced drift in a two-dimensional anisotropic system, characterized by a symmetric diffusion tensor with unequal diagonal elements. A general expression for the mean displacement vector is derived and presented as a sum of two vectors, depicting two distinct drifting effects. The first vector describes the tendency of the particle to drift toward the high diffusivity side in each orthogonal principal diffusion direction. This is a generalization of the well-known expression for the noise-induced drift in one-dimensional systems. The second vector represents a novel drifting effect, not found in one-dimensional systems, originating from the spatial rotation in the directions of the principal axes. The validity of the derived expressions is verified by using Langevin dynamics simulations. As a specific example, we consider the relative diffusion of two transmembrane proteins, and demonstrate that the average distance between them increases at a surprisingly fast rate of several tens of micrometers per second.

Lateral diffusion induced by active proteins in a biomembrane

We discuss the hydrodynamic collective effects due to active protein molecules that are immersed in lipid bilayer membranes and modeled as stochastic force dipoles. We specifically take into account the presence of the bulk solvent that surrounds the two-dimensional fluid membrane. Two membrane geometries are considered: the free membrane case and the confined membrane case. Using the generalized membrane mobility tensors, we estimate the active diffusion coefficient and the drift velocity as a function of the size of a diffusing object. The hydrodynamic screening lengths distinguish the two asymptotic regimes of these quantities. Furthermore, the competition between the thermal and nonthermal contributions in the total diffusion coefficient is characterized by two length scales corresponding to the two membrane geometries. These characteristic lengths describe the crossover between different asymptotic behaviors when they are larger than the hydrodynamic screening lengths.

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.

Budding transition of asymmetric two-component lipid domains

We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Assuming a coupling between the local curvature and local lipid composition in each of the leaflets, we discuss the morphology and thermodynamic behavior of asymmetric lipid domains. The membrane free-energy contains three contributions: the bending energy, the line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams containing fully budded, dimpled, and flat states as a function of the two leaflet compositions. The global phase behavior is analyzed, and depending on system parameters, the phase diagrams include one-phase, two-phase, and three-phase regions. In particular, we predict various phase coexistence regions between different morphologies of domains, which may be observed in multicomponent membranes or vesicles.

Coarse-grained molecular dynamics simulation of binary charged lipid membranes: Phase separation and morphological dynamics

Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover, the electrostatic repulsion causes morphological changes, such as pore formation, and further transformations into disk, string, and bicelle structures, which are spatiotemporally coupled to the lateral segregation of charged lipids. Based on our coarse-grained MD simulation, we propose a plausible mechanism of pore formation at the molecular level. The pore formation in a charged-lipid-rich domain is initiated by the prior disturbance of the local molecular orientation in the domain.

Correlated lateral phase separations in stacks of lipid membranes

Motivated by the experimental study of Tayebi et al. [Nat. Mater. 11, 1074 (2012)] on phase separation of stacked multi-component lipid bilayers, we propose a model composed of stacked two-dimensional Ising spins. We study both its static and dynamical features using Monte Carlo simulations with Kawasaki spin exchange dynamics that conserves the order parameter. We show that at thermodynamical equilibrium, due to strong inter-layer correlations, the system forms a continuous columnar structure for any finite interaction across adjacent layers. Furthermore, the phase separation shows a faster dynamics as the inter-layer interaction is increased. This temporal behavior is mainly due to an effective deeper temperature quench because of the larger value of the critical temperature, Tc, for larger inter-layer interaction. When the temperature ratio, T/Tc, is kept fixed, the temporal growth exponent does not increase and even slightly decreases as a function of the increased inter-layer interaction.

Transbilayer Colocalization of Lipid Domains Explained via Measurement of Strong Coupling Parameters

When micron-scale compositional heterogeneity develops in membranes, the distribution of lipids on one face of the membrane strongly affects the distribution on the other. Specifically, when lipid membranes phase separate into coexisting liquid phases, domains in each monolayer leaflet of the membrane are colocalized with domains in the opposite leaflet. Colocalized domains have never been observed to spontaneously move out of registry. This result indicates that the lipid compositions in one leaflet are strongly coupled to compositions in the opposing leaflet. Predictions of the interleaflet coupling parameter, Λ, vary by a factor of 50. We measure the value of Λ by applying high shear forces to supported lipid bilayers. This causes the upper leaflet to slide over the lower leaflet, moving domains out of registry. We find that the threshold shear stress required to deregister domains in the upper and lower leaflets increases with the inverse length of domains. We derive a simple, closed-form expression relating the threshold shear to Λ, and find Λ = 0.016 ± 0.004 kBT/nm2.

Relaxation dynamics of two-component fluid bilayer membranes

We theoretically investigate the relaxation dynamics of a nearly flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion. Mutual diffusion is the collective irreversible process that leads to homogenization of the density difference between the two lipid species. We find that two relaxation modes associated with the mutual diffusion appear in addition to the three previously discussed relaxation modes reflecting the bending and compression of the membrane. Because of the symmetry, only one of the two diffusive modes is coupled to the bending mode. The two diffusive modes are much slower than the bending and compression modes in the entire realistic wave number range. This means that the long time relaxation behavior is dominated by the mutual diffusion in binary membranes. The two diffusive modes become even slower in the vicinity of the unstable region towards phase separation, while the other modes are almost unchanged. In short time scales, on the other hand, the lipid composition heterogeneity induces in-plane compression and bending of the bilayer.

Non-Brownian diffusion in lipid membranes: Experiments and simulations

The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Quantifying Lateral Inhomogeneity of Cholesterol-Containing Membranes

Lateral inhomogeneity plays a critical role for many properties of cholesterol-containing membranes, yet the thermodynamic forces involved in inhomogeneity remain poorly understood. Based on coarse-grained simulations of cholesterol in four increasingly unsaturated phospholipids, we computed lateral density fluctuations and free energies of domain formation, and we quantitatively relate those to variations in the chemical potential of cholesterol. Our simulations suggest that the lateral organization is dominated by weak repulsive cholesterol interactions, leading to a significantly more homogeneous distribution as compared to a two-dimensional ideal gas. Hence, phospholipids provide a "good" solvent for cholesterol. Unexpectedly, the degree of unsaturation of the phospholipid has only a minor effect on the lateral inhomogeneity of cholesterol in binary lipid mixtures. These results provide a link between functional properties and thermal fluctuations in lipid membranes.

Modeling Lipid-Lipid Correlations across a Bilayer Membrane Using the Quasi-chemical Approximation

Mixed fluid-like lipid membranes exhibit interactions not only among the lipids within a given leaflet but also across the bilayer. The ensuing collective interleaflet coupling of entire membrane domains has been modeled previously using various mean-field approaches. Yet, also on the level of individual lipids have correlations across the bilayer been observed experimentally for binary mixtures of charged/uncharged lipids with mismatching combinations of short and long acyl chain lengths. The present study proposes a lattice gas model to quantify these correlations. To this end, we represent a macroscopically homogeneous lipid bilayer by two coupled two-dimensional lattice gases that we study using the quasi-chemical approximation. We demonstrate that the rationalization of previous experimental results is only possible if besides two-body lipid-lipid interactions within and across the bilayer our model also accounts for an additional multibody interaction mechanism, namely the local hydrophobic height mismatch created by pairing short and long chain lipids together. The robustness of the quasi-chemical approximation is verified by comparison with Monte Carlo simulations.

Budding of domains in mixed bilayer membranes

We propose a model that accounts for the budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and the local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free energy contains three contributions: the bending energy, the line tension, and a Landau free energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully budded, dimpled, and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as a three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.

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

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

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

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

Raft formation in lipid bilayers coupled to curvature

We present computer simulations of a membrane in which the local composition is coupled to the local membrane curvature. At high temperatures (i.e., above the temperature of macroscopic phase separation), finite-sized transient domains are observed, reminiscent of lipid rafts. The domain size is in the range of hundred nanometers, and set by the membrane elastic properties. These findings are in line with the notion of the membrane as a curvature-induced microemulsion. At low temperature, the membrane phase separates. The transition to the phase-separated regime is continuous and belongs to the two-dimensional Ising universality class when the coupling to curvature is weak, but becomes first-order for strong curvature-composition coupling.

Membrane binding and bending in Ebola VP40 assembly and egress

Lipid-enveloped viruses contain a lipid bilayer coat that protects their genome and helps to facilitate entry into the host cell. Filoviruses are lipid-enveloped viruses that have up to 90% clinical fatality and include Marbug (MARV) and Ebola (EBOV). These pleomorphic filamentous viruses enter the host cell through their membrane-embedded glycoprotein and then replicate using just seven genes encoded in their negative-sense RNA genome. EBOV budding occurs from the inner leaflet of the plasma membrane (PM) and is driven by the matrix protein VP40, which is the most abundantly expressed protein of the virus. VP40 expressed in mammalian cells alone can trigger budding of filamentous virus-like particles (VLPs) that are nearly indistinguishable from authentic EBOV. VP40, such as matrix proteins from other viruses, has been shown to bind anionic lipid membranes. However, how VP40 selectively interacts with the inner leaflet of the PM and assembles into a filamentous lipid enveloped particle is mostly unknown. This article describes what is known regarding VP40 membrane interactions and what answers will fill the gaps.

The Role of the Actin Cytoskeleton and Lipid Rafts in the Localization and Function of the ABCC1 Transporter

ATP-binding cassette (ABC) transporters are known to be important factors in multidrug resistance of tumor cells. Lipid rafts have been implicated in their localization in the plasma membrane, where they function as drug efflux pumps. This specific localization in rafts may support the activity of ABC/Abc transporters. This raises questions regarding the nature and composition of the lipid rafts that harbor ABC/Abc transporters and the dependence of ABC/Abc transporters—concerning their localization and activity—on lipid raft constituents. Here we review our work of the past 10 years aimed at evaluating whether ABC/Abc transporters are dependent on a particular membrane environment for their function. What is the nature of this membrane environment and which of the lipid raft constituents are important for this dependency? It turns out that cortical actin is of major importance for stabilizing the localization and function of the ABC/Abc transporter, provided it is localized in an actin-dependent subtype of lipid rafts, as is the case for human ABCC1/multidrug resistance-related protein 1 (MRP1) and rodent Abcc1/Mrp1 but not human ABCB1/P-glycoprotein (PGP). On the other hand, sphingolipids do not appear to be modulators of ABCC1/MRP1 (or Abcc1/Mrp1), even though they are coregulated during drug resistance development.