Some models of the evolution of altruistic behaviour between siblings

When a fluid membrane, containing mobile receptors for some ligand, is placed in a diffusion gradient of that ligand, the receptors will redistribute to become more concentrated in those regions of the membrane which are associated with the higher concentrations of ligand. The thermodynamics of this effect are developed. The significance of this effect as a possible step in the transduction of the orientational information content of a diffusion gradient to a cell is discussed. It is pointed out that fluid membrane receptors should potentially be more sensitive transducers of the orientational information content of the gradient than would fixed membrane receptors, and that the transduction sensitivity will rise as the number of ligand binding sites per receptor rises.     

BAR domains and membrane curvature: bringing your curves to the BAR

BAR (bin, amphiphysin and Rvs161/167) domains are a unique class of dimerization domains, whose dimerization interface is edged by a membrane-binding surface. In its dimeric form, the membrane-binding interface is concave, and this gives the ability to bind better to curved membranes, i.e. to sense membrane curvature. When present at higher concentrations, the domain can stabilize membrane curvature, generating lipid tubules. This domain is found in many contexts in a wide variety of proteins, where the dimerization and membrane-binding function of this domain is likely to have a profound effect on protein activity. If these proteins function as predicted, then there will be membrane subdomains based on curvature, and thus there is an additional layer of compartmentalization on membranes. These and other possible functions of the BAR domain are discussed.     

Affinity partitioning of vancomycin

The use of the Flanagan and Barondes model(14) describing affinity partitioning as an aid in designing separation systems is discussed. Experimental studies are described for affinity partitioning of vancomycin, a glycopeptide antibiotic, in a water-methoxypolyethylene glycol-dextran system using methoxypolyethylene glycol-dextran system using methoxypolyethylene glycol bound D-alanyl-Dalanyl-D-alanine or D-alanyl-D-alanine as the reversible affinity ligand. Even for this ideal case of 1:1 binding interaction, the model only qualitatively predicts the affinity effect when all model parameters are measured independently. The discrepancy between measured and predicted values can be attributed to a difference in exposed surface of the free antibiotic and ligand compared to that in the bound state.The effect of experimentally varying model parameters is also described. It was determined that a polymers-ligand which partitions more strongly to the top phase would provide the most significant enhancement to this affinity partitioning system. Such an improvement can be made by increasing the molecular weight of the hydrophobicity of the polymer-ligand. A process for vancomycin recovery from fermentation broth using D--alanyl-D-alanine sepharose as affinity ligand is described.     

Conformational energetics of rhodopsin modulated by nonlamellar-forming lipids

Rhodopsin is an important example of a G protein-coupled receptor (GPCR) in which 11-cis-retinal is the ligand and acts as an inverse agonist. Photolysis of rhodopsin leads to formation of the activated meta II state from its precursor meta I. Various mechanisms have been proposed to explain how the membrane composition affects the meta I-meta II conformational equilibrium in the visual process. For rod disk membranes and recombinant membranes containing rhodopsin, the lipid properties have been discussed in terms of elastic deformation of the bilayer. Here we have investigated the relation of nonlamellar-forming lipids, such as dioleoylphosphatidylethanolamine (DOPE), together with dioleoylphosphatidylcholine (DOPC), to the photochemistry of membrane-bound rhodopsin. We conducted flash photolysis experiments for bovine rhodopsin recombined with DOPE/DOPC mixtures (0:100 to 75:25) as a function of pH to explore the dependence of the photochemical activity on the monolayer curvature free energy of the membrane. It is well-known that DOPC forms bilayers, whereas DOPE has a propensity to adopt the nonlamellar, reverse hexagonal (H(II)) phase. In the case of neutral DOPE/DOPC recombinants, calculations of the membrane surface pH confirmed that an increase in DOPE favored the meta II state. Moreover, doubling the PE headgroup content versus the native rod membranes substituted for the polyunsaturated, docosahexaenoic acyl chains (22:6 omega 3), suggesting rhodopsin function is associated with a balance of forces within the bilayer. The data are interpreted by applying a flexible surface model, in which the meta II state is stabilized by lipids tending to form the H(II) phase, with a negative spontaneous curvature. A simple theory, based on principles of surface chemistry, for coupling the energetics of membrane proteins to material properties of the bilayer lipids is described. For rhodopsin, the free energy balance of the receptor and the lipids is altered by photoisomerization of retinal and involves curvature stress/strain of the membrane (frustration). A new biophysical principle is introduced: matching of the spontaneous curvature of the lipid bilayer to the mean curvature of the lipid/water interface adjacent to the protein, which balances the lipid/protein solvation energy. In this manner, the thermodynamic driving force for the meta I-meta II conformational change of rhodopsin is tightly controlled by mixtures of nonlamellar-forming lipids having distinctive material properties.     

Jumping frequencies in membrane channels. Comparison between stochastic molecular dynamics simulation and rate theory

Permeation of molecules through membrane channels involves local interactions with a limited number of ligand groups. A method for the molecular dynamics simulation of particle movement in small ligand systems is described. It is assumed that the ligand groups carry out thermal vibrations, whereas the rest of the channel molecule and the surroundings act as a heat bath which is coupled via random forces to the motions of the ligands. The simulation technique is applied to a simple system which contains some of the essential features influencing jumping rates in membrane channels, such as flexibility of ligand configuration or inertial effects in the motion of the ligands. Since the simulation is based on strictly microscopic parameters of the particle-ligand system, a rigorous test of the predictions of rate theory is possible. It is found that rate theory describes the general dependence of jumping frequency k' on temperature and on ligand binding strength rather well, although the values of k' obtained by computer simulation are 2-3 times smaller than those predicted by rate theory.     

Regulation of Membrane-Shape Transitions Induced by I-BAR Domains

I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins regulate membrane curvature.     

Thermodynamics and kinetics of co-operative protein-nucleic acid binding: I. General aspects of analysis of data

The process under consideration is the binding of a ligand to a linear polymer of equivalent subunits such that each bound molecule of ligand occupies n subunits. Interactions between bound ligand molecules are also considered. Some useful points regarding the evaluation of raw data without recourse to any specific binding mechanism are discussed first. For a treatment in terms of appropriate thermodynamic parameters a simple model is examined in greater detail. It assumes that interactions are limited to those between ligands bound to nearest-neighbour positions on the polymer.Exact expressions for some basic binding properties of this model at equilibrium are developed. The relations can be considerably simplified in the case of pronounced positive co-operativity which is frequently encountered in practice. Appropriate plots of the data to test the model and to evaluate its parameters are proposed.A simple but consistent kinetic scheme is also introduced. It allows calculation of relaxation times as they can be measured by means of special techniques.     

Flexoelectric origin of nanomechanic deflection in DNA-microcantilever system

The membrane theory is used to study the recently observed nanomechanical bending of cantilevers, which have processed biomolecular adsorption or biochemical reactions. To be different from entropy-controlling bending mechanism discussed before, we propose that the flexoelectric effect induces cantilever bending. With the introduction of flexoelectric spontaneous curvature, the relation between the bending and biopolymer character is constructed by a simple analytical formula. The cantilever motion induced by adsorption of single-strand DNA and DNA hybridization reaction is quantified analytically and our results show good agreement with experiments.     

Spectrin, red cell shape and deformability. II. The antagonistic action of spectrin and sialic acid residues in determining membrane curvature in genetic spectrin deficiency in mice

In a companion paper, the shapes of spectrin deficient mouse erythrocytes were described; in contrast to previous assumptions, spherules with tethered microvesicles rather than true "spherocytes" were found. Thence, spectrin deficient mouse erythrocytes are endowed with an excess of surface area for the given volume but the membrane is assuming a highly positive curvature. Observations during and after the action of enzymes cleaving the red cell surface charge (Neuraminidase, Trypsin, Chymotrypsin) showed that the previously positive membrane curvature, as well as the tendency of the membrane to flow into fingerlike protrusions was completely abolished. The erythrocytes of the spectrin deficient, desialylated mouse erythrocytes assumed a variety of shapes, often discocytic or even stomatocytic, i.e. their membrane presented with negative curvature. However, while these desialylated membranes could be easily deformed (elongated) by shear flow they did not recoil elastically into any definitive configuration after removal of the deforming forces. It is concluded from these observations that spectrin (acting on the inner interface between membrane and cytoplasm) and sialic acid residues (acting on the outer interface between membrane and plasma) exert antagonizing effects on membrane curvature and membrane bending elasticity. Sialic acid residues, strongly charged and situated on the outer side of the cell, produce positive membrane curvature; this observation can most readily be explained by assuming that this mechanical effect is caused by repulsive coulombic forces expanding the outer half of the bilayer. To explain the effect of the spectrin-complex in counteracting positive or in producing negative membrane curvature, a similar expansive coulombic force acting between the highly charged residues has been postulated. Thence, a model for explaining the overall elastic behaviour of the normal mammalian red cell is developed which is based on the assumption of elastic interactions of proteinacous membrane components coupled to the lipid bilayer of the membrane.     

Formation of three-dimensional structures in supported lipid bilayers

The creation of three-dimensional structures in supported lipid bilayers has been examined. In bilayers, shape transformations can be triggered by adjusting a variety of parameters. Here, it is shown that bilayers composed of phosphatidylcholine and phosphatidic acid can be induced to reversibly form cap structures when exposed to an asymmetry in ionic strength. The structures that form depend on the asymmetry in the ionic strength and the amount of anionic lipid. Other factors that may be of importance in the creation of the structures, expansion forces, osmotic forces, and the bilayer-support interaction are discussed. The cap structures have the potential to be of considerable utility in examining the effect that curvature has on membrane processes.     

Mechanisms for the modulation of membrane bilayer properties by amphipathic helical peptides

The amphipathic helix, in which hydrophobia and hydrophilic residues are grouped on opposing faces, is a structural mot if found in many peptides and proteins that bind to membranes. One of the physical properties of membranes that can be altered by the binding of amphipathic helices is membrane monolayer curvature strain. Class A amphipathic helices, which are present in exchangeable plasma lipoproteins, can stabilize membranes by reducing negative monolayer curvature strain; proline-punctuated class A amphipathic helical segments are particularly effective in this regard. This property is suggested to be associated with some of the beneficial biological effects of this protein. On the other hand, lytic amphipathic helical peptides can act by increasing negative curvature strain or by forming pores composed of helical clusters. Thus, different amphipathic helical peptides can be membrane stabilizing or be lytic to membranes, depending on the structural motif of the helix, which in turn determines the nature of its association with membranes. Features of these peptides that are responsible for their specific properties are discussed. © 1994 John Wiley & Sons, Inc.     

The osmotic migration of cells in a solute gradient.

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.     

Manipulating the folding of membrane proteins: using the bilayer to our advantage

The folding mechanisms of integral membrane proteins have largely eluded detailed study. This is owing to the inherent difficulties in folding these hydrophobic proteins in vitro, which, in turn, reflects the often apparently insurmountable problem of mimicking the natural membrane bilayer with lipid or detergent mixtures. There is, however, a large body of information on lipid properties and, in particular, on phosphatidylcholine and phosphatidylethanolamine lipids, which are common to many biological membranes. We have exploited this knowledge to develop efficient in vitro lipid-bilayer folding systems for the membrane protein, bacteriorhodopsin. Furthermore, we have shown that a rate-limiting apoprotein folding step and the overall folding efficiency appear to be controlled by particular properties of the lipid bilayer. The properties of interest are the stored curvature elastic energy within the bilayer, and the lateral pressure that the lipid chains exert on the their neighbouring folding proteins. These are generic properties of the bilayer that can be achieved with simple mixtures of biological lipids, and are not specific to the lipids studied here. These bilayer properties also seem to be important in modulating the function of several membrane proteins, as well as the function of membranes in vivo. Thus, it seems likely that careful manipulations of lipid properties will shed light on the forces that drive membrane protein folding, and will aid the development of bilayer folding systems for other membrane proteins.     

Membrane Curvature Induced by Aggregates of LH2s and Monomeric LH1s

The photosynthetic apparatus of purple bacteria is contained within organelles called chromatophores, which form as extensions of the cytoplasmic membrane. The shape of these chromatophores can be spherical (as in Rhodobacter sphaeroides), lamellar (as in Rhodopseudomonas acidophila and Phaeospirillum molischianum), or tubular (as in certain Rb. sphaeroides mutants). Chromatophore shape is thought to be influenced by the integral membrane proteins Light Harvesting Complexes I and II (LH1 and LH2), which pack tightly together in the chromatophore. It has been suggested that the shape of LH2, together with its close packing in the membrane, induces membrane curvature. The mechanism of LH2-induced curvature is explored via molecular dynamics simulations of multiple LH2 complexes in a membrane patch. LH2s from three species—Rb. sphaeroides, Rps. acidophila, and Phsp. molischianum—were simulated in different packing arrangements. In each case, the LH2s pack together and tilt with respect to neighboring LH2s in a way that produces an overall curvature. This curvature appears to be driven by a combination of LH2's shape and electrostatic forces that are modulated by the presence of well-conserved cytoplasmic charged residues, the removal of which inhibits LH2 curvature. The interaction of LH2s and an LH1 monomer is also explored, and it suggests that curvature is diminished by the presence of LH1 monomers. The implications of our results for chromatophore shape are discussed.     

Shapes of bilayer vesicles with membrane embedded molecules

The interdependence of the lateral distribution of molecules which are embedded in a membrane (such as integral membrane proteins) and the shape of a cell with no internal structure (such as phospholipid vesicles or mammalian erythrocytes) has been studied. The coupling of the lateral distribution of the molecules and the cell shape is introduced by considering that the energy of the membrane embedded molecule at a given site of the membrane depends on the curvature of the membrane at that site. Direct interactions between embedded molecules are not considered. A simple expression for the interaction of the membrane embedded molecule with the local membrane curvature is proposed. Starting from this interaction, the consistently related expressions for the free energy and for the distribution function of the embedded molecules are derived. The equilibrium cell shape and the corresponding lateral distribution of the membrane embedded molecules are determined by minimization of the membrane free energy which includes the free energy of the membrane embedded molecules and the membrane elastic energy. The resulting inhomogeneous distribution of the membrane embedded molecules affects the cell shape in a nontrivial manner. In particular, it is shown that the shape corresponding to the absolute energy minimum at given cell volume and membrane area may be elliptically non-axisymmetric, in contrast to the case of a laterally homogeneous membrane where it is axisymmetric.     

Stability of biphasic vesicles with membrane embedded proteins

The basic physical properties of homogeneous membranes are relatively well known, while the effects of inhomogeneities with membranes are very much an active field of study. In this paper, a biphasic lipid vesicle with membrane embedded proteins is investigated. To take into account the influences of the proteins, a simple phenomenological coupling between the local fraction of proteins and the mean curvature square is suggested. By minimizing the energy of system, the E-L equations and boundary conditions are obtained and solved analytically for vesicle with a simple shape. Besides, stability phase diagrams and stability factor are put forward by linear perturbation analysis. Our results show two different situations which are strongly dependent on the nature of the proteins: a regime of easy instability when the proteins are strongly coupled to the membrane and a regime of difficult instability.     

Physical model of contractile ring initiation in dividing cells

We present a physical mechanism to describe initiation of the contractile ring during cell division. The model couples the membrane curvature with the contractile forces produced by protein clusters attached to the membrane. These protein clusters are mobile on the membrane and possess either an isotropic or an anisotropic spontaneous curvature. Our results show that under these conditions the contraction force gives rise to an instability that corresponds in a closed cellular system to the initiation of the contractile ring. We find a quantization of this process at distinct length-scales, which we compare to available data for different types of eukaryote cells.