Phase behaviour and structure of a model biomolecular condensate.

Phase separation of immiscible fluids is a common phenomenon in polymer chemistry, and is recognized as an important mechanism by which cells compartmentalize their biochemical reactions. Biomolecular condensates are condensed fluid droplets in cells that form by liquid-liquid phase separation of intrinsically-disordered proteins. They have a wide range of functions and are associated with chronic neurodegenerative diseases in which they become pathologically rigid. However, it remains unclear how their material properties depend on the molecular structure of the proteins. Here we explore the phase behaviour and structure of a model biomolecular condensate composed of semi-flexible polymers with attractive end-caps using coarse-grained simulations. The model contains the minimal molecular features that are sufficient to observe liquid-liquid phase separation of soluble polymers into a porous, three-dimensional network in which their end-caps reversibly bind at junctions. The distance between connected junctions scales with the polymer length as a self-avoiding random walk over a wide range of concentration with a weak affinity-dependent prefactor. By contrast, the average number of polymers that meet at the junctions depends on the end-cap affinity but only weakly on the polymer length. The structured porosity of the condensed phase suggests a mechanism for cells to regulate biomolecular condensates. Protein interaction sites may be turned on or off to modulate the condensate's porosity and therefore the diffusion and interaction of additional proteins.

C24 Sphingolipids Govern the Transbilayer Asymmetry of Cholesterol and Lateral Organization of Model and Live-Cell Plasma Membranes.

Mammalian sphingolipids, primarily with C24 or C16 acyl chains, reside in the outer leaflet of the plasma membrane. Curiously, little is known how C24 sphingolipids impact cholesterol and membrane microdomains. Here, we present evidence that C24 sphingomyelin, when placed in the outer leaflet, suppresses microdomains in giant unilamellar vesicles and also suppresses submicron domains in the plasma membrane of HeLa cells. Free energy calculations suggested that cholesterol has a preference for the inner leaflet if C24 sphingomyelin is in the outer leaflet. We indeed observe that cholesterol enriches in the inner leaflet (80%) if C24 sphingomyelin is in the outer leaflet. Similarly, cholesterol primarily resides in the cytoplasmic leaflet (80%) in the plasma membrane of human erythrocytes where C24 sphingolipids are naturally abundant in the outer leaflet. We conclude that C24 sphingomyelin uniquely interacts with cholesterol and regulates the lateral organization in asymmetric membranes, potentially by generating cholesterol asymmetry.

Numerical insights into the phase diagram of p-atic membranes with spherical topology.

The properties of self-avoiding p-atic membranes restricted to spherical topology have been studied by Monte Carlo simulations of a triangulated random surface model. Spherically shaped p-atic membranes undergo a Kosterlitz-Thouless transition as expected with topology induced mutually repelling disclinations of the p-atic ordered phase. For flexible membranes the phase behaviour bears some resemblance to the spherically shaped case with a p-atic disordered crumpled phase and p-atic ordered, conformationally ordered (crinkled) phase separated by a KT-like transition with proliferation of disclinations. We confirm the proposed buckling of disclinations in the p-atic ordered phase, while the expected associated disordering (crumpling) transition at low bending rigidities is absent in the phase diagram.

Exploring the raft-hypothesis by probing planar bilayer patches of free-standing giant vesicles at nanoscale resolution, with and without Na,K-ATPase.

The structure of functional lipid domains (rafts) in biological membranes has for long time been unresolved due to their small length scales and transient nature. These cooperative properties of the lipid bilayer matrix are modelled by free-standing giant unilammellar vesicles (GUVs) with well-characterized lipid composition. We review a series of recent advances in preparation and analysis of GUVs, which allows for characterization of small domains by high-resolution imaging techniques. These includes a new GUV preparation method with a desired overall lipid composition achieved by mixing small unilammellar vesicles (SUVs), test of the lipids compositional uniformity in GUVs and swift adsorption of GUVs to solid support by kinetically arresting the lateral structure of membrane prior to collapse for subsequent imaging. The techniques are applied to the analysis of membrane domains in GUVs formed from mixtures of DOPC/DPPC/cholesterol with and without Na,K-ATPase (NKA), a transmembrane protein known to be associated with rafts. Two mechanisms of domain formation are revealed: 1) close to lo/ld phase coexistence, domains in size up to 100nm appear as thermally induced droplet fluctuations, 2) NKA shows interfacial activity and cluster in lo/ld micro-emulsion droplets. Some perspectives for the application of the techniques and the understanding of the nature of raft domains are outlined.

Membrane invagination induced by Shiga toxin B-subunit: from molecular structure to tube formation.

The bacterial Shiga toxin is composed of an enzymatically active A-subunit, and a receptor-binding homopentameric B-subunit (STxB) that mediates intracellular toxin trafficking. Upon STxB-mediated binding to the glycolipid globotriaosylceramide (Gb3) at the plasma membrane of target cells, Shiga toxin is internalized by clathrin-dependent and independent endocytosis. The formation of tubular membrane invaginations is an essential step in the clathrin-independent STxB uptake process. However, the mechanism by which STxB induces these invaginations has remained unclear. Using a combination of all-atom molecular dynamics and Monte Carlo simulations we show that the molecular architecture of STxB enables the following sequence of events: the Gb3 binding sites on STxB are arranged such that tight avidity-based binding results in a small increment of local curvature. Membrane-mediated clustering of several toxin molecules then creates a tubular membrane invagination that drives toxin entry into the cell. This mechanism requires: (1) a precise molecular architecture of the STxB binding sites; (2) a fluid bilayer in order for the tubular invagination to form. Although, STxB binding to the membrane requires specific interactions with Gb3 lipids, our study points to a generic molecular design principle for clathrin-independent endocytosis of nanoparticles.

Advantages of statistical analysis of giant vesicle flickering for bending elasticity measurements.

We show how to greatly improve precision when determining bending elasticity of giant unilamellar vesicles. Taking advantage of the well-known quasi-spherical model of liposome flickering, we analyze the full probability distributions of the configurational fluctuations instead of limiting the analysis to the second moment measurements only as usually done in previously published works. This leads to objective criteria to reject vesicles that do not behave according to the model. As a result, the confidence in the bending elasticity determination of individual vesicles that fit the model is improved and, consequently, the reproducibility of this measurement for a given membrane system. This approach uncovers new possibilities for bending elasticity studies like detection of minute influences by solutes in the buffer or into the membrane. In the same way, we are now able to detect the inhomogeneous behavior of giant vesicle systems such as the hazardous production of peroxide in bilayers containing fluorescent dyes.

Lipid domains in giant unilamellar vesicles and their correspondence with equilibrium thermodynamic phases: a quantitative fluorescence microscopy imaging approach.

We report a novel analytical procedure to measure the surface areas of coexisting lipid domains in giant unilamellar vesicles (GUVs) based on image processing of 3D fluorescence microscopy data. The procedure involves the segmentation of lipid domains from fluorescent image stacks and reconstruction of 3D domain morphology using active surface models. This method permits the reconstruction of the spherical surface of GUVs and determination of the area fractions of coexisting lipid domains at the level of single vesicles. Obtaining area fractions enables the scrutiny of the lever rule along lipid phase diagram's tie lines and to test whether or not the coexistence of lipid domains in GUVs correspond to equilibrium thermodynamic phases. The analysis was applied to DLPC/DPPC GUVs displaying coexistence of lipid domains. Our results confirm the lever rule, demonstrating that the observed membrane domains correspond to equilibrium thermodynamic phases (i.e., solid ordered and liquid disordered phases). In addition, the fact that the lever rule is validated from 11 to 14 randomly selected GUVs per molar fraction indicates homogeneity in the lipid composition among the explored GUV populations. In conclusion, our study shows that GUVs are reliable model systems to perform equilibrium thermodynamic studies of membranes.

Mechanical properties of the cell nucleus and the effect of emerin deficiency.

Nuclear structure and mechanics are gaining recognition as important factors that affect gene expression, development, and differentiation in normal function and disease, yet the physical mechanisms that govern nuclear mechanical stability remain unclear. Here we examined the physical properties of the cell nucleus by imaging fluorescently labeled components of the inner nucleus (chromatin and nucleoli) and the nuclear envelope (lamins and membranes) in nuclei deformed by micropipette aspiration (confocal imaged microdeformation). We investigated nuclei, both isolated and in intact, living cells, and found that nuclear volume significantly decreased by 60-70% during aspiration. While nuclear membranes exhibited blebbing and fluid characteristics during aspiration, the nuclear lamina exhibited behavior of a solid-elastic shell. Under large deformations of GFP-lamin A-labeled nuclei, we observed a decay of fluorescence intensity into the tip of the deformed tongue that we interpreted in terms of nonlinear, two-dimensional elasticity theory. Here we applied this method to study nuclear envelope stability in disease and found that mouse embryo fibroblasts lacking the inner nuclear membrane protein, emerin, had a significantly decreased ratio of the area expansion to shear moduli (K/mu) compared to wild-type cells (2.1 +/- 0.2 versus 5.1 +/- 1.3). These data suggest that altered nuclear envelope elasticity caused by loss of emerin could contribute to increased nuclear fragility in Emery-Dreifuss muscular dystrophy patients with mutations in the emerin gene. Based on our experimental results and theoretical considerations, we present a model describing how the nucleus is stabilized in the pipette. Such a model is essential for interpreting the results of any micropipette study of the nucleus and porous materials in general.

Universal behavior of membranes with sterols.

Lanosterol is the biosynthetic precursor of cholesterol and ergosterol, sterols that predominate in the membranes of mammals and lower eukaryotes, respectively. These three sterols are structurally quite similar, yet their relative effects on membranes have been shown to differ. Here we study the effects of cholesterol, lanosterol, and ergosterol on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine lipid bilayers at room temperature. Micropipette aspiration is used to determine membrane material properties (area compressibility modulus), and information about lipid chain order (first moments) is obtained from deuterium nuclear magnetic resonance. We compare these results, along with data for membrane-bending rigidity, to explore the relationship between membrane hydrophobic thickness and elastic properties. Together, such diverse approaches demonstrate that membrane properties are affected to different degrees by these structurally distinct sterols, yet nonetheless exhibit universal behavior.

Characterization of the elastic properties of the nuclear envelope.

Underlying the nuclear envelope (NE) of most eukaryotic cells is the nuclear lamina, a meshwork consisting largely of coiled-coil nuclear intermediate filament proteins that play a critical role in nuclear organization and gene expression, and are vital for the structural stability of the NE/nucleus. By confocal microscopy and micromanipulation of the NE in living cells and isolated nuclei, we show that the NE undergoes deformations without large-scale rupture and maintains structural stability when exposed to mechanical stress. In conjunction with image analysis, we have developed theory for a two-dimensional elastic material to quantify NE elastic behaviour. We show that the NE is elastic and exhibits characteristics of a continuous two-dimensional solid, including connections between lamins and the embedded nuclear pore complexes. Correlating models of NE lateral organization to the experimental findings indicates a heterogeneous lateral distribution of NE components on a mesoscopic scale.

Measurement of membrane elasticity by micro-pipette aspiration.

The classical micro-pipette aspiration technique, applied for measuring the membrane bending elasticity, is in the present work reviewed and extended to span the range of pipette aspiration pressures going through the flaccid (low pressures) to tense (high pressures) membrane regime. The quality of the conventional methods for analysing data is evaluated using numerically generated data and a new method for data analysis, based on thermodynamic analysis and detailed statistical mechanical modelling, is introduced. The analysis of the classical method, where the membrane bending modulus is obtained from micro-pipette aspiration data acquired in the low-pressure regime, reveals a significant correction from membrane stretching elasticity. The new description, which includes the full vesicle geometry and both the membrane bending and stretching elasticity, is used for the interpretation of micro-pipette aspiration experiments conducted on SOPC (stearoyl-oleoyl-phosphatidyl-choline) lipid vesicles in the fluid phase. The data analysis, which is extended by detailed image analysis and a fitting procedure based on Monte Carlo integration, gives an estimate of the bending modulus, that agrees with previously published results obtained by the use of shape fluctuation analysis of giant unilamellar vesicles. The obtained estimate of the area expansion modulus, is automatically corrected for contributions from residual thermal undulations and the equilibrium area of the vesicle is resolved.

Thermal undulations of quasi-spherical vesicles stabilized by gravity.

The classical treatment of quasi-spherical vesicle undulations has, in the present work, been reviewed and extended to systems, which are affected by a gravitational field caused by a density difference across the membrane. The effects have been studied by the use of perturbation theory leading to corrections to the mean shape and the fluctuation correlation matrix. These corrections have been included in an analytical expression for the flicker spectrum to probe how the experimentally accessible spectrum changes with gravity. The results are represented in terms of the gravitational parameter, g(0) = Delta(rho)g R(4)/kappa. The contributions from gravity are in most experimental situations small and thus negligible, but for values of g(0) above a certain limit, the perturbational corrections must be included. Expressions for the relative error on the flicker spectrum have been worked out, so that it is possible to define the regime where gravity is negligible. An upper limit of g(0) has also been identified, where the error in all modes of the flicker spectrum is significant due to distortion of the mean shape.

Off-lattice model for the phase behavior of lipid-cholesterol bilayers.

Lipid bilayers exhibit a phase behavior that involves two distinct, but coupled, order-disorder processes, one in terms of lipid-chain crystalline packing (translational degrees of freedom) and the other in terms of lipid-chain conformational ordering (internal degrees of freedom). Experiments and previous approximate theories have suggested that cholesterol incorporated into lipid bilayers has different microscopic effects on lipid-chain packing and conformations and that cholesterol thereby leads to decoupling of the two ordering processes, manifested by a special equilibrium phase, "liquid-ordered phase," where bilayers are liquid (with translational disorder) but lipid chains are conformationally ordered. We present in this paper a microscopic model that describes this decoupling phenomena and which yields a phase diagram consistent with experimental observations. The model is an off-lattice model based on a two-dimensional random triangulation algorithm and represents lipid and cholesterol molecules by hard-core particles with internal (spin-type) degrees of freedom that have nearest-neighbor interactions. The phase equilibria described by the model, specifically in terms of phase diagrams and structure factors characterizing different phases, are calculated by using several Monte Carlo simulation techniques, including histogram and thermodynamic reweighting techniques, finite-size scaling as well as non-Boltzmann sampling techniques (in order to overcome severe hysteresis effects associated with strongly first-order phase transitions). The results provide a consistent interpretation of the various phases of phospholipid-cholesterol binary mixtures based on the microscopic dual action of cholesterol on the lipid-chain degrees of freedom. In particular, a distinct small-scale structure of the liquid-ordered phase has been identified and characterized. The generic nature of the model proposed holds a promise for a unifying description for a whole series of different lipid-sterol mixtures.

Theoretical analysis of protein organization in lipid membranes.

The fundamental physical principles of the lateral organization of trans-membrane proteins and peptides as well as peripheral membrane proteins and enzymes are considered from the point of view of the lipid-bilayer membrane, its structure, dynamics, and cooperative phenomena. Based on a variety of theoretical considerations and model calculations, the nature of lipid-protein interactions is considered both for a single protein and an assembly of proteins that can lead to aggregation and protein crystallization in the plane of the membrane. Phenomena discussed include lipid sorting and selectivity at protein surfaces, protein-lipid phase equilibria, lipid-mediated protein-protein interactions, wetting and capillary condensation as means of protein organization, mechanisms of two-dimensional protein crystallization, as well as non-equilibrium organization of active proteins in membranes. The theoretical findings are compared with a variety of experimental data.

Wetting and capillary condensation as means of protein organization in membranes.

Wetting and capillary condensation are thermodynamic phenomena in which the special affinity of interfaces to a thermodynamic phase, relative to the stable bulk phase, leads to the stabilization of a wetting phase at the interfaces. Wetting and capillary condensation are here proposed as mechanisms that in membranes may serve to induce special lipid phases in between integral membrane proteins leading to long-range lipid-mediated joining forces acting between the proteins and hence providing a means of protein organization. The consequences of wetting in terms of protein aggregation and protein clustering are derived both within a simple phenomenological theory as well as within a concrete calculation on a microscopic model of lipid-protein interactions that accounts for the lipid bilayer phase equilibria and direct lipid-protein interactions governed by hydrophobic matching between the lipid bilayer hydrophobic thickness and the length of the hydrophobic membrane domain. The theoretical results are expected to be relevant for optimizing the experimental conditions required for forming protein aggregates and regular protein arrays in membranes.

The effect of cholesterol in small amounts on lipid-bilayer softness in the region of the main phase transition.

The temperature dependence of the small-angle neutron scattering from aqueous multilammellar DMPC lipid bilayers, containing small amounts of cholesterol, is analyzed near the main phase transition by means of a simple geometric model which yields the lamellar repeat distance, the hydrophobic thickness of the bilayer, the interlamellar aqueous spacing, as well as fluctuation parameters. The observation of anomalous swelling behavior in the transition region is interpreted as an indication of bilayer softening and thermally reduced bending rigidity. Our results indicate that the effect of small amounts of cholesterol, ≲3 mole%, is a softening of the bilayers in the transition region, whereas cholesterol contents above this range lead to the well-known effect of rigidification. The possible biological relevance of this result is discussed.

Model of a sub-main transition in phospholipid bilayers.

A recently discovered submain phase transition in multi-lamellar bilayers of long-chain saturated diacyl phosphatidylcholines (Jørgensen, K. (1995) Biochim. Biophys. Acta 1240, 111-114) is discussed in terms of a theoretical molecular interaction model using computer simulation techniques. The model interprets the transition to be due to a decoupling of the acyl-chain melting from the melting of the pseudo-two-dimensional crystalline lattice of the P beta' phase. A two-stage melting process is predicted by the calculations suggesting that the sub-main transition involves a lattice melting whereas the acyl-chain melting takes place at a higher temperature at the main transition. The calculated heat contents of the two transitions as well as the chain-length dependence compare favorably with experimental data for multi-lamellar phosphatidylcholine lipid bilayers.

The computer as a laboratory for the physical chemistry of membranes.

A mini-review is given of some recent advances in the use of computer-simulation approaches to the study of physico-chemical properties of lipid bilayers and biological membranes. The simulations are based on microscopic molecular interaction models as well as random-surface models of fluid membranes. Particular emphasis is put on those properties that are controlled by the many-particle character of the lamellar membrane, i.e. correlations and fluctuations in density, composition and large-scale conformational structure. It is discussed how dynamic membrane heterogeneity arises and how it is affected by various molecular species interacting with membranes, such as cholesterol, drugs, insecticides, as well as polypeptides and integral membrane proteins. The influence of bending rigidity and osmotic-pressure gradients on large-scale membrane conformation and topology is described.

The effect of anaesthetics on the dynamic heterogeneity of lipid membranes.

The influence of membrane-perturbing drugs such as anaesthetics on the lipid membrane properties is analyzed theoretically on the basis of a general microscopic interaction model of the gel-to-fluid chain melting transition of one-component phospholipid membranes and phospholipid membranes with a low content of cholesterol. Monte Carlo computer simulation of the model shows that the gel-to-fluid transition of the lipid membrane, manifested in the formation of dynamically coexisting domains of gel and fluid lipids, is strongly influenced by the presence of anaesthetics. Macroscopically the effect of anaesthetics on the membrane properties is seen in a depression of the transition temperature and a smearing of thermodynamic response functions like the specific heat. Microscopically the calculations reveal that anaesthetics have a high affinity to the fluctuating domain interfaces that are dominated by kink-like lipid-chain conformations. This leads to formation of more interfaces and to a locally high concentration of anaesthetics in the interfacial regions, which is much larger than the global concentration in the membrane. Important membrane components like cholesterol, which also has been shown to be interfacially active, are found to decrease the absorption of anaesthetics and to squeeze out anaesthetics from the interfaces. The results of the general model study of anaesthetics-membrane interactions are discussed in relation to both general anaesthetics, like halothane, and local anaesthetics like cocaine-derivatives.

Phase equilibria and local structure in binary lipid bilayers.

A molecular interaction model is used to describe the phase diagram of two-component phospholipid bilayer membranes of saturated phospholipids, DCnPC, with different acyl-chain lengths, n = 12,14,18,20. The interaction between acyl chains of different length is formulated in terms of a hydrophobic mismatch which permits the series of binary phase diagrams to be calculated in terms of a single 'universal' interaction parameter. The properties of the model are calculated by computer-simulation techniques which not only permit determination of the specific-heat function and the phase diagram but also reveal the local structure of the mixture in the different parts of the phase diagram. The local structure is described pictorially and characterized quantitatively in terms of a correlation function. It is shown that the non-ideal mixing of lipid species due to mismatch in the hydrophobic lengths leads to a progressively increasing local ordering as the chain-length difference is increased. A pronounced local structure is found to persist deep inside the fluid phase of the mixture. The local structure is discussed in relation to the features observed in the specific-heat function, for which theoretical data, as well as experimental data obtained from differential-scanning calorimetry are presented.