Lateral organization of membranes and cell shapes.

The relations among membrane structure, mechanical properties, and cell shape have been investigated. The fluid mosaic membrane models used contains several components that move freely in the membrane plane. These components interact with each other and determine properties of the membrane such as curvature and elasticity. A free energy equation is postulated for such a multicomponent membrane and the condition of free energy minimum is used to obtain differential equations relating the distribution of membrane components and the local membrane curvature. The force that moves membrane components along the membrane in a variable curvature field is calculated. A change in the intramembrane interactions can bring about phase separation or particle clustering. This, in turn, may strongly affect the local curvature. The numerical solution of the set of equations for the two dimensional case allows determination of the cell shape and the component distribution along the membrane. The model has been applied to describe certain erythrocytes shape transformations.     

Mechanical stability of membrane nanotubular protrusions influenced by attachment of flexible rod-like proteins

It is indicated that nonhomogeneous lateral distribution of membrane attached and flexible rod-like proteins (MRPs) may stabilize nanotubular membrane protrusions. We have shown that curvature induced accumulation of MRPs in the nanotubular membrane protrusion and the corresponding reduction of the membrane free energy are possible if the decrease of the deviatoric free energy of MRPs in the nanotubular protrusions is large enough to overcome the increase of the free energy due to decrease of configurational entropy in the process of lateral sorting of MRPs. The decrease of isotropic curvature energy of MRPs in the region of membrane protrusion is usually not sufficient for substantial MRPs sorting and consequent stabilization of the nanotubular membrane protrusions.     

Statistical mechanics of lipid membranes. Protein correlation functions and lipid ordering

An expression is derived for the lipid-mediated intermolecular interaction between protein molecules embedded in a lipid bilayer. It is assumed that protein particles are accommodated by the bilayer, but they distort the lipids in some manner from their equilibrium protein-free configuration. We treat this situation by expanding the free energy density in the plane of the membrane as a Taylor series in some arbitrary parameter and its gradient. Minimization of the total membrane energy for a given particle configuration yields the interparticle interaction energy for that configuration. A test of the model is provided by measurement of the protein-protein pair distribution function from freeze-fracture micrographs of partially aggregated membranes. The measured functions can be simulated by adjustment of two parameters (a) a lipid correlation length that characterizes the distance over which a distortion of the bilayers is transmitted laterally through the bilayer, and (b) a term quantifying the energy of the protein-lipid interaction at the protein-lipid boundary. Correlation lengths obtained by fitting the calculated particle distribution functions to the data are found to be several nanometers. Protein-lipid interaction energies are of the order of a few kT.     

Electrostatic free energy and spontaneous curvature of spherical charged layered membrane

A biophysical model for the equilibrium curvature of a composite membrane element is derived taking into account the mechanical bilayer properties and the adjacent charged protein layers. The minimum of the total free energy density with respect to the curvature of such a membrane curved was estimated from the sum of the electrostatic free energy density of the charges of the membrane and the elastic surface energy density due to bending the lipid bilayer membrane. It was shown that the equilibrium curvature, i.e. the spontaneous curvature, of such a charged composite sandwich-like membrane depends inversely on the bending stiffness of the lipid membrane itself and directly on the charge amount inside and outside the membrane to the second power. Furthermore the geometric and electrostatic structure of the protein layers and the physico-chemical environment conditions are involved. Corresponding to the model developed a "standard RBC" membrane element has a negative spontaneous curvature, accounting for a discocyte RBC shape. The shape change from a discocyte to a more stomatocytic shape (increase in the negative spontaneous curvature) after reducing the charges in the glycocalyx is also explained within this model.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

Estimation of the maximum change in stability of globular proteins upon mutation of a hydrophobic residue to another of smaller size.

Although the hydrophobic effect is generally considered to be one of the most important forces in stabilizing the folded structure of a globular protein molecule, there is a lack of consensus on the precise magnitude of this effect. The magnitude of the hydrophobic effect is most directly measured by observing the change in stability of a protein molecule when an internal hydrophobic residue is mutated to another of smaller size. Results of such measurements have, however, been confusing because they vary greatly and are generally considerably larger than expected from the transfer free energies of corresponding small molecules. In this article, a thermodynamic argument is presented to show (1) that the variation is mainly due to that in the flexibility of the protein molecule at the site of mutation, (2) that the maximum destabilization occurs when the protein at the site of mutation is rigid, in which case the value of the destabilization is approximately given by the work of cavity formation in water, and (3) that the transfer free energy approximately gives the minimum of the range of variations. The best numerical agreements between the small molecule and the protein systems are obtained when the data from the small molecule system are expressed as the molarity-based standard free energies without other corrections.     

Membrane shape changes at initial stage of membrane fusion under the action of proteins inducing spontaneous curvature

This paper studies change of membrane shape at the initial stage of the fusion process due to the fusion proteins inducing spontaneous curvature in the membrane. As protein inclusions are embedded into the membrane, a highly curved surface forms in the center of the membrane; it facilitates the formation of short-lived hydrophobic defects and leads to the merger of the contact monolayers of the membranes. Membrane is considered as continuous liquid-crystal medium subject to elastic deformations. One deformational mode of splay is taken into account; energy is calculated in the quadratic approximation on this deformation. In case of positive spontaneous curvature induced by the protein there is no bulge on the top of the membrane despite high deviation of membrane shape from the equilibrium state. In case of negative spontaneous curvature a bulge is formed and its height and curvature increase with the increase of the membrane curvature in the initial state.     

Lipid phase transitions in membranes involving intrinsic periodic curvature

A conformation of the lipid bilayer of membranes is proposed, with periodic curvature corresponding to the minimal surface structure of cubic lipid phases. Evidence is given indicating that activities of lipid synthesis/modification enzymes embedded in the membrane are controlled by the lateral "packing-pressure", so that the lipid bilayer is close to a transition from the lamellar (L alpha) type of conformation to this periodically curved conformation. Such a phase transition mechanism is assumed to be involved in numerous cooperative membrane functions.     

Evidence of cholesterol accumulated in high curvature regions: implication to the curvature elastic energy for lipid mixtures

Recent experiments suggested that cholesterol and other lipid components of high negative spontaneous curvature facilitate membrane fusion. This is taken as evidence supporting the stalk-pore model of membrane fusion in which the lipid bilayers go through intermediate structures of high curvature. How do the high-curvature lipid components lower the free energy of the curved structure? Do the high-curvature lipid components modify the average spontaneous curvature of the relevant monolayer, thereby facilitate its bending, or do the lipid components redistribute in the curved structure so as to lower the free energy? This question is fundamental to the curvature elastic energy for lipid mixtures. Here we investigate the lipid distribution in a monolayer of a binary lipid mixture before and after bending, or more precisely in the lamellar, hexagonal, and distorted hexagonal phases. The lipid mixture is composed of 2:1 ratio of brominated di18:0PC and cholesterol. Using a newly developed procedure for the multiwavelength anomalous diffraction method, we are able to isolate the bromine distribution and reconstruct the electron density distribution of the lipid mixture in the three phases. We found that the lipid distribution is homogenous and uniform in the lamellar and hexagonal phases. But in the distorted hexagonal phase, the lipid monolayer has nonuniform curvature, and cholesterol almost entirely concentrates in the high curvature region. This finding demonstrates that the association energies between lipid molecules vary with the curvature of membrane. Thus, lipid components in a mixture may redistribute under conditions of nonuniform curvature, such as in the stalk structure. In such cases, the spontaneous curvature depends on the local lipid composition and the free energy minimum is determined by lipid distribution as well as curvature.     

Action of surface-active substances on biological membranes IV. Hemolytic and membrane-perturbing action of homologous series of β-d-glucopyranosyl-1-alkylphosphates

The hemolytic action of a homologous series of β-d-glucopyranosyl-1-alkylphosphates on human erythrocytes has been examined. The agent's affinity for the red cell membrane and the mean number of the agent's molecules which, upon interaction with an erythrocyte, make it undergo hemolysis have been measured. The contribution of the head group and that of a CH₂ group of the surfactants to the free energy of the agents' binding to the cell membrane have been estimated. The effect of the surfactants on the red cell volume and the lytic concentrations of the agents have been measured. The contribution of a CH₂ group to the free energy of the interaction of the amphiphiles embedded in the membrane bilayer with their environment has been evaluated and is proposed to be used as a measure of the membrane matrix stability.     

Distribution functions, describing the binding of extended ligands with DNA molecules. Possible use for cases of DNA condensation

Due to noncooperative binding of ligands to DNA molecules, DNA molecules are in equilibrium with different numbers of adsorbed ligands. This equilibrium for a given concentration of the free ligand in the solution is characterized by the distribution function, which describes the probability of revealing the DNA molecule with a definite number of adsorbed ligands. If polycations act as ligands, DNA molecules with the number of ligands sufficient for neutralizing the charges on phosphates may undergo a phase transition. One example of this transition is the formation of liquid-crystalline dispersions during the binding of DNA to chitosan. We analyzed the binding of chitosan to DNA on the assumption that this binding is due to equilibrium adsorption. At a definite concentration of chitosan in solution, DNA molecules are in equilibrium with different numbers of adsorbed molecules of chitosan. If the number of adsorbed ligands exceeds some critical value, the DNA molecule covered with chitosan becomes capable of interacting with other DNA molecules. As a result of this interaction (attraction), liquid-crystalline dispersions can form. Equations describing the dependence of the concentration of DNA molecules on the concentration of the ligand in solution were derived. It was shown that, at given parameters of the model, it is possible to describe experimental data characterizing the formation of cholesteric liquid-crystalline dispersions. The analysis of the data makes it possible to reconstitute both the size of the binding site occupied by chitosan on the DNA and the energy of interaction of chitosan with DNA.     

Nanoscale dynamics of actin filaments in the red blood cell membrane skeleton

Red blood cell (RBC) shape and deformability are supported by a planar network of short actin filament (F-actin) nodes (∼37 nm length, 15–18 subunits) interconnected by long spectrin strands at the inner surface of the plasma membrane. Spectrin-F-actin network structure underlies quantitative modeling of forces controlling RBC shape, membrane curvature, and deformation, yet the nanoscale organization and dynamics of the F-actin nodes in situ are not well understood. We examined F-actin distribution and dynamics in RBCs using fluorescent-phalloidin labeling of F-actin imaged by multiple microscopy modalities. Total internal reflection fluorescence and Zeiss Airyscan confocal microscopy demonstrate that F-actin is concentrated in multiple brightly stained F-actin foci ∼200–300 nm apart interspersed with dimmer F-actin staining regions. Single molecule stochastic optical reconstruction microscopy imaging of Alexa 647-phalloidin-labeled F-actin and computational analysis also indicates an irregular, nonrandom distribution of F-actin nodes. Treatment of RBCs with latrunculin A and cytochalasin D indicates that F-actin foci distribution depends on actin polymerization, while live cell imaging reveals dynamic local motions of F-actin foci, with lateral movements, appearance and disappearance. Regulation of F-actin node distribution and dynamics via actin assembly/disassembly pathways and/or via local extension and retraction of spectrin strands may provide a new mechanism to control spectrin-F-actin network connectivity, RBC shape, and membrane deformability.     

Packing analysis of crystalline myosin subfragment-1. Implications for the size and shape of the myosin head

Crystals of myosin subfragment-1 have been examined by X-ray diffraction and electron microscopy to determine how the molecules pack in the unit cell and to gain preliminary information on the size and shape of the myosin head. Subfragment-1 crystallizes in space group P212121. Analysis of the X-ray diffraction photographs shows that there are eight molecules in the unit cell with two in the asymmetric unit related by a non-crystallographic or local 2-fold axis. It also indicates that in projection down the a axis, two molecules of myosin subfragment-1 lie almost directly on top of one another except for a translation of about 9 A along c. Small crystals were fixed and embedded in the presence of tannic acid, and thin sections were cut perpendicular to each of the three crystallographic axes. Image analysis of micrographs recorded from these sections confirm the packing arrangement deduced from X-ray diffraction, and give the approximate size and shape of the molecule in the crystal lattice. They show that the molecule is at least 160 A long with a maximum thickness of about 60 A, and that it has marked curvature in the unit cell.     

Crenation and cupping of the red cell: A new theoretical approach. Part II. Cupping

Typical, axisymmetrical cup shaped cells have been carefully measured and the shapes analyzed mathematically. The results show that the strain energy of a cup shaped cell is always higher than that of a biconcave cell except when the two layers of the membrane involved in resistance to bending are free to slide over one another. This is true whether intrinsic curvature of the membrane is positive, negative or zero. If the two layers can slide over one another, the cup shape becomes the lower energy form. Shear resistance, if appreciable, must cause the cup cell to buckle. Photomicrographs of cup shaped cells show buckled configurations characteristic of those of a partly deflated thin-walled rubber ball, which is a similar object having a low ratio of bending/shear strength.In light of these findings, the cup shape of the red cell can no longer be considered as evidence of intrinsic membrane curvature of opposite sign to that of the crenated cell, but appears to indicate a phase change either in the hydrophobic interior of the bimolecular membrane or in some equivalent interface.     

Calorimetric detection of curvature strain in phospholipid bilayers.

Phospholipids in biological membranes are arranged as bilayers. When constrained to pack into planar bilayers, certain phospholipids will form unstable structures as a consequence of their molecular shape and noncovalent bonding. This produces curvature strain which may provide energy for certain membrane processes. We demonstrate that an exothermic process associated with the relief of curvature strain can be detected calorimetrically. The enthalpy for the incorporation of a few percent lysophosphatidylcholine into large unilamellar vesicles of monomethyldioleoylphosphatidylethanolamine at pH 7.4 is exothermic but it is endothermic for stable bilayers such as this same lipid at pH 9 or dioleoylphosphatidylcholine at pH 7.4 or 9. The addition of lysophosphatidylcholine to monomethyldioleoylphosphatidylethanolamine at pH 7.4 is exothermic only for the addition of the first few percent of lysophosphatidylcholine and then it becomes endothermic. The size of the exothermic heat change is sensitive to changes in temperature, while the endothermic processes are relatively temperature-insensitive. The exothermic heat is also larger when 1 or 2 mol % of diolein is incorporated into vesicles of monomethyldioleoylphosphatidylethanolamine. These results are all consistent with the exothermic process corresponding to the relief of curvature strain in bilayers having a tendency to convert to the hexagonal phase. It provides a demonstration that considerable energy may be released upon the incorporation of certain molecules into membranes which have a low radius of spontaneous curvature.     

Effect of oligosaccharides and their monosaccharide mixtures on the stability of proteins: a scaled particle study

Experimental results of RNase-A stabilization by sugar osmolytes show that the change in the Gibbs free energy (ΔGD) associated with the equilibrium, N (native) state ? D (denatured) state of the protein in the presence of equimolar mixture of monosaccharides is larger than that of the corresponding oligosaccharides at a given temperature and pH. However, at the molar scale, ΔGD obtained in the presence of an oligosaccharide is much higher as compared with ΔGD obtained using individual monosaccharide. We used scaled particle theory (SPT) to explain these experimental observations. The effective length, called Tolman's length that describes the curvature correlations to a surface area or surface tension and in turn contributes to the change in free energy, is discussed. Tolman's length is higher for corresponding monomer mixture than the oligosaccharide molecules. Based on SPT analysis, a geometrical model is proposed for clustering of monosaccharides in the mixture due to high particle density. The cluster is presumed to have weak interaction among them due to larger hydrodynamic radius than that of the bonded molecules of oligosaccharides.     

Differential regulation of the lateral mobility of plasma membrane phospholipids by the extracellular matrix and cholesterol

In this study, we compared qualitative and quantitative changes in the lateral mobility of phospholipid molecules in the plasma membrane of intact cells under various conditions of specific interaction of integrins in the cell membrane with two extracellular matrix (ECM) components viz. fibronectin (FN) and laminin (LN). We found a strong and specific correlation between the lower lateral mobility of phosphatidylcholine (PC) and higher lateral mobility of phosphatidylethanolamine (PE) when cells were expressing high levels of alpha5beta1 integrin and thus were adherent and motile on FN. The interaction between PC and FN in alpha5 integrin expressing cells was aided by the strong affinity of alpha5 integrin to the FN matrix. Cholesterol was involved in regulating the lateral mobility of PC to a great extent and of PE to a lesser extent without affecting the overall microviscosity of the plasma membrane or the distribution of caveolin-marked domains. The distribution and mobility of PC and PE molecules in the lamellipodial regions differed from that in the rest of the membrane and also in the more motile and in the less motile cells. We propose that these differences in distribution of PC and PE in different regions of cell membrane and their respective lateral mobility are observed due to the specific interaction of PC molecules with FN molecules in the ECM. Our results outline a new role of integrin-matrix interactions in the regulation of membrane phospholipid behavior.     

Three-dimensional reconstruction of a membrane-bending complex: the RC-LH1-PufX core dimer of Rhodobacter sphaeroides

A three-dimensional model of the dimeric reaction center-light harvesting I-PufX (RC-LH1-PufX) complex from Rhodobacter sphaeroides, calculated from electron microscope single particle analysis of negatively stained complexes, shows that the two halves of the dimer molecule incline toward each other on the periplasmic side, creating a remarkable V-shaped structure. The distribution of negative stain is consistent with loose packing of the LH1 ring near the 14th LH1 alpha/beta pair, which could facilitate the migration of quinone and quinol molecules across the LH1 boundary. The three-dimensional model encloses a space near the reaction center Q(B) site and the 14th LH1 alpha/beta pair, which is approximately 20 angstroms in diameter, sufficient to sequester a quinone pool. Helical arrays of dimers were used to construct a three-dimensional membrane model, which matches the packing lattice deduced from electron microscope analysis of the tubular dimer-only membranes found in mutants of Rba. sphaeroides lacking the LH2 complex. The intrinsic curvature of the dimer explains the shape and approximately 70-nm diameter of these membrane tubules, and at least partially accounts for the spherical membrane invaginations found in wild-type Rba. sphaeroides. A model of dimer aggregation and membrane curvature in these spherical membrane invaginations is presented.     

A self-consistent chain model for the phase transitions in lipid bilayer membranes

We presented a mechanical model of a lipid bilayer membrane. The internal conformations of a polar head group and double hydrocarbon chains in a lipid molecule were described on the basis of the isomeric bond-rotation scheme. The thermodynamic properties of the lipid membranes were represented by a density matrix that described the rotational isomeric states of the head groups and chains. The parameters that determined the density matrix were obtained in the presence of the intermolecular interactions, which depend on the conformation of the molecules. The interchain interaction was given by the Kihara potential, which depends on the shape of the chains. The Coulomb interaction between the polar head groups and the lateral pressure were considered. The calculation was made for the three lipid molecules corresponding to DMPC, DPPC, and DSPC. The model agreed well with the following experimental results: the temperature, the latent heat of the gel-to-liquid crystalline phase transition, the temperature dependencies of (a) the intermolecular distance, (b) the number of gauche bonds in a hydrocarbon chain, (c) the order parameter for the bond orientation, (d) the volume of the membrane, (e) the thermal expansion coefficients, and (f) the birefringence.     

Quantitative characterization of the lateral distribution of membrane proteins within the lipid bilayer.

The dependence of the lateral distribution of membrane proteins on the size, protein/lipoid molar ratio, and the magnitude of the interaction potentials has been investigated by computer modeling protein-lipid distributions with Monte Carlo calculations. These results have allowed us to develop a quantitative characterization of the distribution of membrane proteins and to correlate these distributions with experimental observables. The topological arrangement of protein domains, protein plus annular lipid domains, and free lipid domains is described in terms of radial distribution, pair connectedness, and cluster distribution functions. The radial distribution functions are used to measure the distribution of intermolecular distances between protein molecules, whereas the pair connectedness functions are used to estimate the physical extension of compositional domains. It is shown that, at characteristic protein/lipid molar ratios, previously isolated domains become connected, forming domain networks that extend over the entire membrane surface. These changes in the lateral connectivity of compositional domains are paralleled by changes in the calculated lateral diffusion coefficients and might have important implications for the regulation of diffusion controlled processes within the membrane.