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

The Importance of Bilayer Asymmetry in Biological Membranes: Insights from Model Membranes

This mini-review intends to highlight the importance of bilayer asymmetry. Biological membranes are complex structures that are a physical barrier separating the external environment from the cellular content. This complex bilayer comprises an extensive lipid repertory, suggesting that the different lipid structures might play a role in the membrane. Interestingly, this vast repertory of lipids is asymmetrically distributed between leaflets that form the lipid bilayer. Here, we discuss the properties of the plasma membrane from the perspective of experimental model membranes, consisting of simplified and controlled in vitro systems. We summarize some crucial features of the exoplasmic (outer) and cytoplasmic (inner) leaflets observed through investigations using symmetric and asymmetric membranes. Symmetric model membranes for the exoplasmic leaflet have a unique lipid composition that might form a coexistence of phases, namely the liquid disordered and liquid order phases. These phase domains may appear in different sizes and shapes depending on lipid composition and lipid-lipid interactions. In contrast, symmetric model membranes for the cytoplasmic leaflet form a fluid phase. We discuss the outcomes reported in the literature for asymmetric bilayers, which vary according to lipid compositions and, consequently, reflect different intra- and inter-leaflet interactions. Interestingly, the asymmetric bilayer could show induced domains in the inner leaflet, or it could decrease the tendency of the outer leaflet to phase separation. If cells regulate the lipid composition of the plasma membrane, they can adjust the existence and sizes of the domains by tuning the lipid composition.

Dipole Potential of Monolayers with Biologically Relevant Lipid Compositions

The membrane dipole potential that arises from the interfacial water and constitutive dipolar groups of lipid molecules modulates the interaction of amphiphiles and proteins with membranes. Consequently, its determination for lipid mixtures resembling the existing diversity in biological membranes is very relevant. In this work, the dipole potentials of monolayers, formed at the air-water interface, from pure or mixed lipids (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidyserine (POPS), sphingomyelin (SpM) and cholesterol) were measured and correlated with the mean area per lipid. The results showed that, as previously observed, cholesterol increases the dipole potential in correspondence with the decrease in the average area per lipid. At the small mole fractions encountered in biomembranes, the presence of the negatively charged lipid POPS increases the dipole potentials of monolayers despite inducing an increase in the average area per lipid. Additionally, the inclusion of POPE in POPC:cholesterol monolayers disrupts the area condensation induced by cholesterol while increasing the membrane dipole moment, leading to a small reduction in the dipole potential. This trend is reinforced for the quaternary POPC:cholesterol:POPE:POPS 4:3:2:1 system, which mimics the inner leaflets of eukaryotic plasma membranes. In agreement with previous works, the replacement of phosphocholine lipids with sphingomyelin leads to a decrease in the dipole potential. Together, this results in a lower dipole potential for the SpM-enriched outer leaflet, generating a non-zero transbilayer dipole potential in the asymmetric plasma membranes of eukaryotic cells.

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

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

There and back again: bridging meso- and nano-scales to understand lipid vesicle patterning

We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale. Simulating the as-obtained mesoscale system enables us to equilibrate the long wavelengths of the vesicles of interest, up to the vesicle size. Conversely, we then backmap from the meso- to the nano-scale, which enables us to equilibrate in turn the short wavelengths down to the molecular length-scales. By applying our approach to the specific situation of patterning a vesicle membrane, we show that macroscopic membranes can thus be equilibrated at all length-scales in achievable computational time offering an original strategy to address the fundamental challenge of timescale in simulations of large bio-membrane systems.

Nano-scale domains in the plasma membrane are like macroscopic domains in asymmetric bilayers

Unfavorable lipid-lipid pairwise interactions between HiTm and LowTm lipids drive liquid-disordered (Ld) + liquid-ordered (Lo) phase separation. Large size of phase domains is opposed by lipid dipole repulsions, which are more significant compared with the pairwise interactions for naturally abundant LowTm lipids such as palmitoyl oleoyl phosphatidylcholine. During the nano-to-macro domain size transition, no lipid phase transition occurs, and measured properties of Ld + Lo nanodomains are found to be essentially the same as those of macrodomains. Use of macrodomains in mixtures to model cell plasma membranes (PM) is helpful, enabling study by optical microscopy. Use of asymmetric giant unilamellar vesicles to model a PM reveals that ordered phase domains in one leaflet induce ordered domains in an otherwise uniform phase in the apposing leaflet that models a cytoplasmic leaflet. Because macro and nano phase properties are so similar, we conclude that a cell PM that has nano-scale Ld + Lo phase domains in the exoplasmic leaflet is likely to induce nano-scale ordered domains in the cytoplasmic leaflet.

A Small-Angle Neutron Scattering, Calorimetry and Densitometry Study to Detect Phase Boundaries and Nanoscale Domain Structure in a Binary Lipid Mixture

Techniques that can probe nanometer length scales, such as small-angle neutron scattering (SANS), have become increasingly popular to detect phase separation in membranes. But to extract the phase composition and domain structure from the SANS traces, complementary information is needed. Here, we present a SANS, calorimetry and densitometry study of a mixture of two saturated lipids that exhibits solidus-liquidus phase coexistence: 1,2-dipalmitoyl-d62-sn-glycero-3-phosphocholine (dDPPC, tail-deuterated DPPC) and 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC). With calorimetry, we investigated the phase diagram for this system and found that the boundary traces for both multilamellar vesicles (MLVs) as well as 50 nm unilamellar vesicles overlap. Because the solidus boundary was mostly inaccessible by calorimetry, we investigated it by both SANS and molecular volume measurements for a 1:1 dDPPC:DLPC lipid mixture. From the temperature behavior of the molecular volume for the 1:1 dDPPC:DLPC mixture, as well as the individual molecular volume of each lipid species, we inferred that the liquidus phase consists of only fluid-state lipids while the solidus phase consists of lipids that are in gel-like states. Using this solidus-liquidus phase model, the SANS data were analyzed with an unrestricted shape model analysis software: MONSA. The resulting fits show irregular domains with dendrite-like features as those previously observed on giant unilamellar vesicles (GUVs). The surface pair correlation function describes a characteristic domain size for the minority phase that decreases with temperature, a behavior found to be consistent with a concomitant decrease in membrane mismatch between the liquidus and solidus phases.

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.

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

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

Pollen wall patterns as a model for biological self-assembly

We are still far from being able to predict organisms' shapes purely from their genetic codes. While it is imperative to identify which encoded macromolecules contribute to a phenotype, determining how macromolecules self-assemble independently of the genetic code may be equally crucial for understanding shape development. Pollen grains are typically single-celled microgametophytes that have decorated walls of various shapes and patterns. The accumulation of morphological data and a comprehensive understanding of the wall development makes this system ripe for mathematical and physical modeling. Therefore, pollen walls are an excellent system for identifying both the genetic products and the physical processes that result in a huge diversity of extracellular morphologies. In this piece, I highlight the current understanding of pollen wall biology relevant for quantification studies and enumerate the modellable aspects of pollen wall patterning and specific approaches that one may take to elucidate how pollen grains build their beautifully patterned walls.

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.

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

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

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].

Cholesterol Effects on the Physical Properties of Lipid Membranes Viewed by Solid-state NMR Spectroscopy

In this chapter, we review the physical properties of lipid/cholesterol mixtures involving studies of model membranes using solid-state NMR spectroscopy. The approach allows one to quantify the average membrane structure, fluctuations, and elastic deformation upon cholesterol interaction. Emphasis is placed on understanding the membrane structural deformation and emergent fluctuations at an atomistic level. Lineshape measurements using solid-state NMR spectroscopy give equilibrium structural properties, while relaxation time measurements study the molecular dynamics over a wide timescale range. The equilibrium properties of glycerophospholipids, sphingolipids, and their binary and tertiary mixtures with cholesterol are accessible. Nonideal mixing of cholesterol with other lipids explains the occurrence of liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids, and may drive formation of lipid rafts. The functional dependence of ²H NMR spin-lattice relaxation (R _1Z) rates on segmental order parameters (S _CD) for lipid membranes is indicative of emergent viscoelastic properties. Addition of cholesterol shows stiffening of the bilayer relative to the pure lipids and this effect is diminished for lanosterol. Opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale can potentially affect lipid raft formation in cellular membranes.

Membrane Lipid Nanodomains

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

A Rationale for Mesoscopic Domain Formation in Biomembranes

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

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

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

Orientational ordering of lamellar structures on closed surfaces

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

Domain size polydispersity effects on the structural and dynamical properties in lipid monolayers with phase coexistence

In lipid monolayers with phase coexistence, domains of the liquid-condensed phase always present size polydispersity. However, very few theoretical works consider size distribution effects on the monolayer properties. Because of the difference in surface densities, domains have excess dipolar density with respect to the surrounding liquid expanded phase, originating a dipolar inter-domain interaction. This interaction depends on the domain area, and hence the presence of a domain size distribution is associated with interaction polydispersity. Inter-domain interactions are fundamental to understanding the structure and dynamics of the monolayer. For this reason, it is expected that polydispersity significantly alters monolayer properties. By means of Brownian dynamics simulations, we study the radial distribution function (RDF), the average mean square displacement and the average time-dependent self-diffusion coefficient, D(t), of lipid monolayers with normally distributed size domains. For this purpose, we vary the relevant system parameters, polydispersity and interaction strength, within a range of experimental interest. We also analyze the consequences of using a monodisperse model to determine the interaction strength from an experimental RDF. We find that polydispersity strongly affects the value of the interaction strength, which is greatly underestimated if polydispersity is not considered. However, within a certain range of parameters, the RDF obtained from a polydisperse model can be well approximated by that of a monodisperse model, by suitably fitting the interaction strength, even for 40% polydispersities. For small interaction strengths or small polydispersities, the polydisperse systems obtained from fitting the experimental RDF have an average mean square displacement and D(t) in good agreement with that of the monodisperse system.

Composition Fluctuations in Lipid Bilayers

Cell membranes contain multiple lipid and protein components having heterogeneous in-plane (lateral) distribution. Nanoscale rafts are believed to play an important functional role, but their phase state—domains of coexisting phases or composition fluctuations—is unknown. As a step toward understanding lateral organization of cell membranes, we investigate the difference between nanoscale domains of coexisting phases and composition fluctuations in lipid bilayers. We simulate model lipid bilayers with the MARTINI coarse-grained force field on length scales of tens of nanometers and timescales of tens of microseconds. We use a binary and a ternary mixture: a saturated and an unsaturated lipid, or a saturated lipid, an unsaturated lipid, and cholesterol, respectively. In these mixtures, the phase behavior can be tuned from a mixed state to a coexistence of a liquid-crystalline and a gel, or a liquid-ordered and a liquid-disordered phase. Transition from a two-phase to a one-phase state is achieved by raising the temperature and adding a hybrid lipid (with a saturated and an unsaturated chain). We analyze the evolution of bilayer properties along this transition: domains of two phases transform to fluctuations with local ordering and compositional demixing. Nanoscale domains and fluctuations differ in several properties, including interleaflet overlap and boundary length. Hybrid lipids show no enrichment at the boundary, but decrease the difference between the coexisting phases by ordering the disordered phase, which could explain their role in cell membranes.

Partitioning of nanoscale particles on a heterogeneous multicomponent lipid bilayer

Partitioning of nanoparticles into different lipid phases of a cell membrane is regulated by the physical properties of both the membrane and nanoparticles.

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

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

Complex biomembrane mimetics on the sub-nanometer scale

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

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

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

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

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

Modulation of lipid membrane structural and mechanical properties by a peptidomimetic derived from reduced amide scaffold

Understanding how antimicrobial peptidomimetics interact with lipid membranes is important in battling multidrug resistant bacterial pathogens. We study the effects of a recently reported peptidomimetic on lipid bilayer structural and mechanical properties. The compound referred to as E107-3 is synthesized based on the acylated reduced amide scaffold and has been shown to exhibit good antimicrobial potency. Our vesicle leakage assay indicates that the compound increases lipid bilayer permeability. We use micropipette aspiration to explore the kinetic response of giant unilamellar vesicles (GUVs). Exposure to the compound causes the GUV protrusion length L_P to spontaneously increase and then decrease, followed by GUV rupture. Solution atomic force microscopy (AFM) is used to visualize lipid bilayer structural modulation within a nanoscopic regime. Unlike melittin, which produces pore-like structures, the peptidomimetic compound is found to induce nanoscopic heterogeneous structures. Finally, we use AFM-based force spectroscopy to study the impact of the compound on lipid bilayer mechanical properties. We find that incremental addition of the compound to planar lipid bilayers results in a moderate decrease of the bilayer puncture force F_P and a 39% decrease of the bilayer area compressibility modulus K_A. To explain our experimental data, we propose a membrane interaction model encompassing disruption of lipid chain packing and extraction of lipid molecules. The later action mode is supported by our observation of a double-bilayer structure in the presence of fusogenic calcium ions.

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.

Cholesterol-induced suppression of membrane elastic fluctuations at the atomistic level

Applications of solid-state NMR spectroscopy for investigating the influences of lipid-cholesterol interactions on membrane fluctuations are reviewed in this paper. Emphasis is placed on understanding the energy landscapes and fluctuations at an emergent atomistic level. Solid-state (2)H NMR spectroscopy directly measures residual quadrupolar couplings (RQCs) due to individual C-(2)H labeled segments of the lipid molecules. Moreover, residual dipolar couplings (RDCs) of (13)C-(1)H bonds are obtained in separated local-field NMR spectroscopy. The distributions of RQC or RDC values give nearly complete profiles of the order parameters as a function of acyl segment position. Measured equilibrium properties of glycerophospholipids and sphingolipids including their binary and tertiary mixtures with cholesterol show unequal mixing associated with liquid-ordered domains. The entropic loss upon addition of cholesterol to sphingolipids is less than for glycerophospholipids and may drive the formation of lipid rafts. In addition relaxation time measurements enable one to study the molecular dynamics over a wide time-scale range. For (2)H NMR the experimental spin-lattice (R1Z) relaxation rates follow a theoretical square-law dependence on segmental order parameters (SCD) due to collective slow dynamics over mesoscopic length scales. The functional dependence for the liquid-crystalline lipid membranes is indicative of viscoelastic properties as they emerge from atomistic-level interactions. A striking decrease in square-law slope upon addition of cholesterol denotes stiffening relative to the pure lipid bilayers that is diminished in the case of lanosterol. Measured equilibrium properties and relaxation rates infer opposite influences of cholesterol and detergents on collective dynamics and elasticity at an atomistic scale that potentially affects lipid raft formation in cellular membranes.

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

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

Are Molecular Vibration Patterns of Cell Structural Elements Used for Intracellular Signalling?

BACKGROUND

To date the manner in which information reaches the nucleus on that part within the three-dimensional structure where specific restorative processes of structural components of the cell are required is unknown. The soluble signalling molecules generated in the course of destructive and restorative processes communicate only as needed.

HYPOTHESIS

All molecules show temperature-dependent molecular vibration creating a radiation in the infrared region. Each molecule species has in its turn a specific frequency pattern under given specific conditions. Changes in their structural composition result in modified frequency patterns of the molecules in question. The main structural elements of the cell membrane, of the endoplasmic reticulum, of the Golgi apparatus, and of the different microsomes representing the great variety of polar lipids show characteristic frequency patterns with peaks in the region characterised by low water absorption. These structural elements are very dynamic, mainly caused by the creation of signal molecules and transport containers. By means of the characteristic radiation, the area where repair or substitution services are needed could be identified; this spatial information complements the signalling of the soluble signal molecules. Based on their resonance properties receptors located on the outer leaflet of the nuclear envelope should be able to read typical frequencies and pass them into the nucleus. Clearly this physical signalling must be blocked by the cell membrane to obviate the flow of information into adjacent cells.

CONCLUSION

If the hypothesis can be proved experimentally, it should be possible to identify and verify characteristic infrared frequency patterns. The application of these signal frequencies onto cells would open entirely new possibilities in medicine and all biological disciplines specifically to influence cell growth and metabolism. Similar to this intracellular system, an extracellular signalling system with many new therapeutic options has to be discussed.

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

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

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

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

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

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

Mixed lipid bilayers with locally varying spontaneous curvature and bending

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

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

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