Macroion-induced compositional instability of binary fluid membranes

Biomimetic Lipid Raft: Domain Stability and Interaction with Physiologically Active Molecules

The cell membrane, also called the plasma membrane, is the membrane on the cytoplasmic surface that separates the extracellular from the intracellular. It is thin, about 10 nm thick when viewed with an electron microscope, and is composed of two monolayers of phospholipid membranes (lipid bilayers) containing many types of proteins. It is now known that this cell membrane not only separates the extracellular from the intracellular, but is also involved in sensory stimuli such as pain, itching, sedation, and excitement. Since the "Fluid mosaic model" was proposed for cell membranes, molecules have been thought to be homogeneously distributed on the membrane surface. Later, at the end of the twentieth century, the existence of "Phase-separated microdomain structures" consisting of ordered phases rich in saturated lipids and cholesterol was suggested, and these were termed "Lipid rafts." A model in which lipid rafts regulate cell signaling has been proposed and is the subject of active research.This chapter first outlines the physicochemical properties and thermodynamic models of membrane phase separation (lipid rafts), which play an important role in cell signaling. Next, how physiologically active molecules such as local anesthetics, cooling agents (menthol), and warming agents (capsaicin) interact with artificial cell membranes will be presented.It is undeniable that the plasma membrane contains many channels and receptors that are involved in the propagation of sensory stimuli. At the same time, however, it is important to understand that the membrane exerts a significant influence on the intensity and propagation of these stimuli.

Coarse-grained molecular dynamics simulation of cation distribution profiles on negatively charged lipid membranes during phase separation

Revealing the ion distributions on a charged lipid membrane in aqueous solution under the influence of long-range interactions is essential for understanding the origin of the stability of the bilayer structure and the interaction between biomembranes and various electrolytes. However, the ion distributions and their dynamics associated with the phase separation process of the lipid bilayer membrane are still unclear. We perform coarse-grained molecular dynamics simulations to reveal the Na⁺ and Cl^- distributions on charged phospholipid bilayer membranes during phase separation. During the phase separation, cations closely follow the position of negatively charged lipids on a microsecond timescale and are rapidly redistributed parallel to the lipid bilayer. In the homogenous mixture of zwitterionic and negatively charged lipids, cations weakly follow negatively charged lipids, indicating the strong interaction between cations and negatively charged lipids. We also compare cation concentrations as a function of surface charge density obtained by our simulation with those obtained by a modified Poisson-Boltzmann theory. Including the ion finite size makes the statistical results consistent, suggesting the importance of the ion-ion interactions in aqueous solution. Our simulation results advance our understanding of ion distribution during phase separation.

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

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

Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties

In this study we derived a model for a multicomponent lipid monolayer in contact with an aqueous solution by means of a generalized classical density functional theory and Monte Carlo simulations. Some of the important biological lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, additional internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler–Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the electric double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the electric double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge density of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concentration in the system.

Three-Phase Coexistence in Binary Charged Lipid Membranes in a Hypotonic Solution

We investigated the phase separation of dioleoylphosphatidylserine (DOPS) and dipalmitoylphosphatidylcholine (DPPC) in giant unilamellar vesicles in a hypotonic solution using fluorescence and confocal laser scanning microscopy. Although phase separation in charged lipid membranes is generally suppressed by the electrostatic repulsion between the charged headgroups, osmotic stress can promote the formation of charged lipid domains. Interestingly, we observed a three-phase coexistence even in the DOPS/DPPC binary lipid mixtures. The three phases were DPPC-rich, dissociated DOPS-rich, and nondissociated DOPS-rich phases. The two forms of DOPS were found to coexist owing to the ionization of the DOPS headgroup, such that the system could be regarded as quasi-ternary. The three formed phases with differently ionized DOPS domains were successfully identified experimentally by monitoring the adsorption of positively charged particles. In addition, coarse-grained molecular dynamics simulations confirmed the stability of the three-phase coexistence. Attraction mediated by hydrogen bonding between protonated DOPS molecules and reduction of the electrostatic interactions at the domain boundaries stabilized the three-phase coexistence.

The impact of non-ideality of lipid mixing on peptide induced lipid clustering

The influence of several antimicrobial trivalent cyclic hexapeptides on the mixing behavior of bilayer lipid membranes containing phosphatidylglycerol (PG) and phosphatidylethanolamine (PE) with varying composition was studied using DSC and ITC. The peptides contained three arginines and three aromatic amino acids and had different sequences. All of them induce clustering of PG-rich clusters with bound peptides after binding. In a previous publication we could show that a correlation between clustering efficacy and the antimicrobial activity of the peptides exists (S. Finger et al., Biochim. Biophys. Acta 1848 (2015) 2998-3006). In the current study we investigated whether the non-ideality of the lipid mixture had any effect on the clustering efficacy and the critical peptide/lipid clustering ratio. We could show that for PG/PE membranes containing 1:1 M ratios and lipids with equal or unequal chain lengths, the amount of clustered PG depended only slightly on the absolute chain length and on the chain length difference between PG and PE. Much larger differences were observed when the PG/ PE mixing ratio was changed. In mixtures of DPPG/DPPE with high PG content, the amount of clustered PG per added peptide was much higher than in PE-rich mixtures. The ITC experiments showed that the critical peptide/lipid ratio for cluster formation is also strongly dependent on the PG/PE ratio in the mixture. In the PG/PE 3:1 mixture, the formation of clusters with bound peptide is much more likely than for mixtures with less PG. For 1:1 and 1:3 lipid mixtures, the critical peptide/lipid ratio for demixing is between 0.002 and 0.004. Therefore, even in these mixtures clustering occurs way below charge saturation of the PG in the mixture and the PG-rich clusters are not charge compensated either. The peptide concentration necessary for inducing clustering amounts to ~8 μM, a value well within the range of minimal inhibitory concentration values observed for the cyclic peptides studied here. Our results show that not only the structure of the cyclic peptide influences the clustering efficacy but also the mixing behavior of the lipids in the bilayers has an influence on the amount of clustering induced by binding of cyclic peptides.

Toward building a physical model for membrane selectivity of antimicrobial peptides: making a quantitative sense of the selectivity

Antimicrobial peptides (AMPs) are naturally-occurring peptide antibiotics. AMPs are typically cationic and utilize their electrostatic interactions with the bacterial membrane to selectively attack bacteria. The way they work has inspired a vigorous search for optimized peptides for fighting resistant bacteria. Here, we present a physical model of membrane selectivity of AMPs. The challenge for theoretical modeling of membrane-peptide systems arises from the simultaneous presence of several competing effects, including lipid demixing and peptide-peptide interactions on the membrane surface. We first examine critically a number of models of peptide-membrane interactions and map out one, which incorporates adequately these competing effects as well as the geometry of various regions in membranes, occupied by bound peptides, anionic lipids within the interaction range of each peptide, and those outside this range. This effort leads to a systematically-improved model for peptide selectivity. Using the model, we relate peptide's intrinsic (Ccell-independent) selectivity to an apparent, Ccell-dependent one, and clarify the relative roles of peptide parameters and cell densities in determining their selectivity. This relationship suggests that the selectivity is more sensitive to peptide parameters at low cell densities; as a result, the optimal peptide charge, at which the selectivity is maximized, increases with the cell density in such a manner that this notion becomes less meaningful at high cell densities.

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

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

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

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

Mesoscale Computational Modeling of Protein-Membrane Interactions Based on Continuum Mean-Field Theory

Quantitative computational modeling of protein-membrane interactions is of great importance as it aids in the interpretation of experimental results and enables design and exploration of new experimental systems. This review describes one such computational approach conceived specifically to treat electrostatically driven interactions between a lipid membrane and a protein (or protein domains) adsorbing onto the membrane. The methodology is based on self-consistent minimization of the governing free energy functional which is expressed in the mean-field approximation and has contributions from electrostatic interactions as well as from mixing entropy of lipids in the membrane and ions in the solution. The method enables calculation of the free energy of the binding process and quantification of the steady-state lipid distribution around the adsorbing protein. The extension of the method to include membrane deformation degrees of freedom further allows calculation of the equilibrium bilayer shape upon the protein binding.

Regulation of phase boundaries and phase-segregated patterns in model membranes

Demixing of components has long been described in model membranes. It is a consequence of non-ideal lateral interactions between membrane components, and it causes the presence of segregated phases, forming patches (domains) of different properties, thus introducing heterogeneity into the membrane. In the present review we first describe the processes through which domains are generated, how they grow, and why they are rounded, striped or fractal-like, as well as why they get distributed forming defined patterns. Next, we focus on the effect of an additive on a lipid mixture, which usually induces shifts in demixing points, thus stabilizing or destabilizing the phase-segregated state. Results found for different model membranes are summarized, detailing the ways in which phase segregation and the generated patterns may be modulated. We focus on which are, from our viewpoint, the most relevant regulating factors affecting the surface texture observed in model membranes. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

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

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

Physical properties of the hybrid lipid POPC on micrometer-sized domains in mixed lipid membranes

In a DPPC/DOPC/POPC ternary mixture, hybrid lipids are localized at the solid-ordered domain boundary. On the other hand, in a DPPC/DOPC/POPC/Chol four-component mixture, they are included in the liquid-ordered domain and disturb the chain ordering of lipids in the domain.

Charge-induced phase separation in lipid membranes

Phase separation in lipid bilayers that include negatively charged lipids is examined experimentally. We observed phase-separated structures and determined the membrane miscibility temperatures in several binary and ternary lipid mixtures of unsaturated neutral lipid, dioleoylphosphatidylcholine (DOPC), saturated neutral lipid, dipalmitoylphosphatidylcholine (DPPC), unsaturated charged lipid, dioleoylphosphatidylglycerol (DOPG((-))), saturated charged lipid, dipalmitoylphosphatidylglycerol (DPPG((-))), and cholesterol. In binary mixtures of saturated and unsaturated charged lipids, the combination of the charged head with the saturation of the hydrocarbon tail is a dominant factor in the stability of membrane phase separation. DPPG((-)) enhances phase separation, while DOPG((-)) suppresses it. Furthermore, the addition of DPPG((-)) to a binary mixture of DPPC/cholesterol induces phase separation between DPPG((-))-rich and cholesterol-rich phases. This indicates that cholesterol localization depends strongly on the electric charge on the hydrophilic head group rather than on the ordering of the hydrocarbon tails. Finally, when DPPG((-)) was added to a neutral ternary system of DOPC/DPPC/cholesterol (a conventional model of membrane rafts), a three-phase coexistence was produced. We conclude by discussing some qualitative features of the phase behaviour in charged membranes using a free energy approach.

Compositional redistribution and dynamic heterogeneity in mixed lipid membrane induced by polyelectrolyte adsorption: effects of chain rigidity

Monte Carlo simulation is employed to investigate the interaction between a polyelectrolyte and a fluid mixed membrane containing neutral (phosphatidyl-choline, PC), monovalent anionic (phosphatidylserine, PS), and multivalent anionic (phosphatidylinositol, PIP2) lipids. The effects of the intrinsic polyelectrolyte rigidity and solution ionic strength on the lateral rearrangement and dynamics of different anionic lipid species are systematically studied. Our results show that, the increase of polyelectrolyte chain rigidity reduces the loss of polyelectrolyte conformational entropy and the energy gains in electrostatic interaction, but raises the demixing entropy loss of the segregated anionic lipids. Therefore, the polyelectrolyte/membrane adsorption strength exhibits a non-monotonic dependence on the polyelectrolyte rigid parameter k ang, and there exists a certain optimal k ang for which the adsorption strength is maximal. Because the less loss of chain conformational entropy dominates the increase of the demixing entropy loss of the segregated anionic lipids and the decreases of the electrostatic energy gains, the semiflexible polyelectrolyte adsorbs onto the membrane more firmly than the flexible one. Whereas, for the adsorption of rigid polyelectrolyte, larger anionic lipid demixing entropy loss and less energy gain in the electrostatic interaction dominate over the decrease of the polyelectrolyte conformation entropy loss, leading to the desorption of the chain from the membrane. By decreasing the ionic concentration of the salt solution, the certain optimal k ang shifts to larger values. The cooperative effects of the adsorbing polyelectrolyte beads determine the concentration gradients and hierarchical mobility of the bound anionic lipids, as well as the polyelectrolyte dynamics.

Charged bilayer membranes in asymmetric ionic solutions: phase diagrams and critical behavior

We consider the phase separation in an asymmetrically charged lipid bilayer membrane consisting of neutral and negatively charged lipids that are in contact with in and out ionic solutions having different ionic strengths. The two asymmetric leaflets are coupled through electrostatic interactions. Based on a free-energy approach, the critical point and phase diagrams are calculated for different ionic strengths of the two solutions and coupling parameter. An increase of the coupling constant or asymmetry in the salt concentration between the in and out solutions yields a higher phase-separation temperature because of electrostatic interactions. As a consequence, the phase-coexistence region increases for strong screening (small Debye length). Finally, possible three-phase coexistence regions in the phase diagram are predicted.

Membrane composition-mediated protein-protein interactions

The authors investigate membrane composition-mediated interactions between proteins adsorbed onto a two-component lipid bilayer close to critical demixing using coarse-grained molecular dynamics simulations and a phenomenological Ginzburg-Landau theory. The simulations consist of three-bead lipids and platelike proteins, which adsorb onto the membrane by binding preferentially to one of the two lipid species. The composition profile around one protein and the pair correlation function between two proteins are measured and compared to the analytical predictions. The theoretical framework is applicable to any scalar field embedded in the membrane, and although in this work the authors treat flat membranes, the methodology extends readily to curved geometries. Neglecting fluctuations, both lipid composition profile and induced protein pair potential are predicted to follow a zeroth order modified Bessel function of the second kind with the same characteristic decay length. These predictions are consistent with our molecular dynamics simulations, except that the interaction range is found to be larger than the single profile correlation length.

Stability of protein-decorated mixed lipid membranes: The interplay of lipid-lipid, lipid-protein, and protein-protein interactions

Membrane-associated proteins are likely to contribute to the regulation of the phase behavior of mixed lipid membranes. To gain insight into the underlying mechanism, we study a thermodynamic model for the stability of a protein-decorated binary lipid layer. Here, proteins interact preferentially with one lipid species and thus locally sequester that species. We aim to specify conditions that lead to an additional macroscopic phase separation of the protein-decorated lipid membrane. Our model is based on a standard mean-field lattice-gas description for both the lipid mixture and the adsorbed protein layer. Besides accounting for the lipid-protein binding strength, we also include attractive lipid-lipid and protein-protein interactions. Our analysis characterizes the decrease in the membrane's critical interaction parameter as a function of the lipid-protein binding strength. For small and large binding strengths we provide analytical expressions; numerical results cover the intermediate range. Our results reiterate the crucial importance of the line tension associated with protein-induced compositional gradients and the presence of attractive lipid-lipid interactions within the membrane. Direct protein-protein attraction effectively increases the line tension and thus tends to further destabilize the membrane.

The "electrostatic-switch" mechanism: Monte Carlo study of MARCKS-membrane interaction

The binding of the myristoylated alanine-rich C kinase substrate (MARCKS) to mixed, fluid, phospholipid membranes is modeled with a recently developed Monte Carlo simulation scheme. The central domain of MARCKS is both basic (zeta = +13) and hydrophobic (five Phe residues), and is flanked with two long chains, one ending with the myristoylated N-terminus. This natively unfolded protein is modeled as a flexible chain of "beads" representing the amino acid residues. The membranes contain neutral (zeta = 0), monovalent (zeta = -1), and tetravalent (zeta = -4) lipids, all of which are laterally mobile. MARCKS-membrane interaction is modeled by Debye-Hückel electrostatic potentials and semiempirical hydrophobic energies. In agreement with experiment, we find that membrane binding is mediated by electrostatic attraction of the basic domain to acidic lipids and membrane penetration of its hydrophobic moieties. The binding is opposed by configurational entropy losses and electrostatic membrane repulsion of the two long chains, and by lipid demixing upon adsorption. The simulations provide a physical model for how membrane-adsorbed MARCKS attracts several PIP(2) lipids (zeta = -4) to its vicinity, and how phosphorylation of the central domain (zeta = +13 to zeta = +7) triggers an "electrostatic switch", which weakens both the membrane interaction and PIP(2) sequestration. This scheme captures the essence of "discreteness of charge" at membrane surfaces and can examine the formation of membrane-mediated multicomponent macromolecular complexes that function in many cellular processes.

Protein diffusion on charged membranes: a dynamic mean-field model describes time evolution and lipid reorganization

As charged macromolecules adsorb and diffuse on cell membranes in a large variety of cell signaling processes, they can attract or repel oppositely charged lipids. This results in lateral membrane rearrangement and affects the dynamics of protein function. To address such processes quantitatively we introduce a dynamic mean-field scheme that allows self-consistent calculations of the equilibrium state of membrane-protein complexes after such lateral reorganization of the membrane components, and serves to probe kinetic details of the process. Applicable to membranes with heterogeneous compositions containing several types of lipids, this comprehensive method accounts for mobile salt ions and charged macromolecules in three dimensions, as well as for lateral demixing of charged and net-neutral lipids in the membrane plane. In our model, the mobility of membrane components is governed by the diffusion-like Cahn-Hilliard equation, while the local electrochemical potential is based on nonlinear Poisson-Boltzmann theory. We illustrate the method by applying it to the adsorption of the anionic polypeptide poly-Lysine on negatively charged lipid membranes composed of binary mixtures of neutral and monovalent lipids, or onto ternary mixtures of neutral, monovalent, and multivalent lipids. Consistent with previous calculations and experiments, our results show that at steady-state multivalent lipids (such as PIP(2)), but not monovalent lipid (such as phosphatidylserine), will segregate near the adsorbing macromolecules. To address the corresponding diffusion of the adsorbing protein in the membrane plane, we couple lipid mobility with the propagation of the adsorbing protein through a dynamic Monte Carlo scheme. We find that due to their higher mobility dictated by the electrochemical potential, multivalent lipids such as PIP(2) more quickly segregate near oppositely charged proteins than do monovalent lipids, even though their diffusion constants may be similar. The segregation, in turn, slows protein diffusion, as lipids introduce an effective drag on the motion of the adsorbate. In contrast, monovalent lipids such as phosphatidylserine only weakly segregate, and the diffusions of protein and lipid remain largely uncorrelated.

Ion induced lamellar-lamellar phase transition in charged surfactant systems

We propose a model for the liquid-liquid (L(alpha)-->L(alpha(') )) phase transition observed in osmotic pressure measurements of certain charged lamellae-forming amphiphiles. The model free energy combines mean-field electrostatic and phenomenological nonelectrostatic interactions, while the number of dissociated counterions is treated as a variable degree of freedom that is determined self-consistently. The model, therefore, joins two well-known theories: the Poisson-Boltzmann theory for ionic solutions between charged lamellae and the Langmuir-Frumkin-Davies adsorption isotherm modified to account for charged adsorbing species. Minimizing the appropriate free energy for each interlamellar spacing, we find the ionic density profiles and the resulting osmotic pressure. While in the simple Poisson-Boltzmann theory the osmotic pressure isotherms are always smooth, we observe a discontinuous liquid-liquid phase transition when the Poisson-Boltzmann theory is self-consistently augmented by the Langmuir-Frumkin-Davies adsorption. This phase transition depends on the area per amphiphilic head group, as well as on nonelectrostatic interactions of the counterions with the lamellae and interactions between counterion-bound and counterion-dissociated surfactants. Coupling the lateral phase transition in the bilayer plane with electrostatic interactions in the bulk, our results offer a qualitative explanation for the existence of the L(alpha)-->L(alpha(') ) phase transition of didodecyldimethylammonium bromide (DDABr), but the transition's apparent absence for the chloride and the iodide homologs. More quantitative comparisons with experiment require better understanding of the microscopic basis of the phenomenological model parameters.

Effective attraction interactions between like-charge macroions bound to binary fluid lipid membranes

Using integral equation theory of liquids to a binary mixed fluid lipid membrane, the authors study the membrane-mediated interactions between binding macroions and the redistribution of neutral and charged lipids due to the macroions. The authors find that when the concentration of binding macroions is infinitely dilute, the main contribution to the attractive potential between macroions is the line tension between neutral and charged lipids of the membrane. As the relative concentration of charged lipids is increased, the authors observe a repulsive-attractive-repulsive potential transition due to the competition between the line tension of mixed lipids and screened electrostatic macroion-macroion interactions. For the finite concentration of macroions, the main feature of the attraction is similar to the infinite-diluted case. However, the corresponding line tension of binary lipids under single macroion is lowered with the formation of multicomplexes by the charged lipids and the macroions, and the maximum of attractive potential will shift toward the higher values of charged lipid concentration.

Grafting of polylysine with polyethylenoxide prevents demixing of O-pyromellitylgramicidin in lipid membranes

Both natural and synthetic polycations can induce demixing of negatively charged components in artificial and possibly in natural membranes. This process can result in formation of clusters (binding of several components to a polycation chain) and/or domains (aggregation of clusters and formation of a separate phase enriched in some particular component). In order to distinguish between these two phenomena, a model lipid membrane system containing ion channels, formed by a negatively charged peptide, O-pyromellitylgramicidin, and polycations of different structures was used. Microelectrophoresis of liposomes, changes in boundary potential of planar bilayers, the shape of compression curves and potentials of lipid and lipid/peptide monolayers were used to monitor the electrostatic factors in polymer adsorption to the membrane and peptide-polymer interactions. The synthesized PEO-grafted polylysine, PLL-PEO20000, did not induce peptide demixing monitored by stabilization of the gramicidin channels, in contrast to parent polylysine (PLL). Both polymers were shown to bind effectively to negatively charged liposomes and lipid monolayers, suggesting that the ineffectiveness of PLL-PEO20000 was not due to reduction of its binding. It was hypothesized that PLL-PEO20000 could not induce domain formation due to steric hindrance of long PEO chains preventing lateral fusion of clusters. Another copolymer, PLL-PEO4000, having four PEO chains of 4000 Da, exhibited intermediate effect between PLL and PLL-PEO20000, which shows the importance of the copolymer architecture for the effect on the lateral distribution of OPg channels. The model system can be relevant to regulation of lateral organization of ion channels and other components in natural membrane systems.

Phase behavior of polyelectrolyte-surfactant complexes at planar surfaces

We investigate theoretically the phase diagram of an insoluble charged surfactant monolayer in contact with a semidilute polyelectrolyte solution (of opposite charge). The polyelectrolytes are assumed to have long-range and attractive (electrostatic) interaction with the surfactant molecules. In addition, we introduce a short-range (chemical) interaction which is either attractive or repulsive. The surfactant monolayer can have a lateral phase separation between dilute and condensed phases. Three different regimes of the coupled system are investigated depending on system parameters. A regime where the polyelectrolyte is depleted due to short range repulsion from the surface, and two adsorption regimes, one being dominated by electrostatics, whereas the other by short range chemical attraction (similar to neutral polymers). When the polyelectrolyte is more attracted (or at least less repelled) by the surfactant molecules as compared with the bare water-air interface, it will shift upwards the surfactant critical temperature. For repulsive short-range interactions the effect is opposite. Finally, the addition of salt to the solution is found to increase the critical temperature for attractive surfaces, but does not show any significant effect for repulsive surfaces.

Cooperative adsorption of proteins onto lipid membranes

The adsorption of proteins onto a lipid membrane depends on and thus reflects the energetics of the underlying substrate. This is particularly relevant for mixed membranes that contain lipid species with different affinities for the adsorbed proteins. In this case, there is an intricate interplay between lateral membrane organization and the number of adsorbed proteins. Most importantly, proteins often tend to enhance the propensity of the lipid mixture to form clusters, domains, or to macroscopically phase separate. Sigmoidal binding isotherms are the typical signature of the corresponding cooperativity in protein adsorption. We discuss the underlying thermodynamic basis, and compare various theoretical binding models for protein adsorption onto mixed membranes. We also present experimental data for the adsorption of the C2A protein motif and analyse to what extent these data reflect cooperative binding.

Modelling of proteins in membranes

This review describes some recent theories and simulations of mesoscopic and microscopic models of lipid membranes with embedded or attached proteins. We summarize results supporting our understanding of phenomena for which the activities of proteins in membranes are expected to be significantly affected by the lipid environment. Theoretical predictions are pointed out, and compared to experimental findings, if available. Among others, the following phenomena are discussed: interactions of interfacially adsorbed peptides, pore-forming amphipathic peptides, adsorption of charged proteins onto oppositely charged lipid membranes, lipid-induced tilting of proteins embedded in lipid bilayers, protein-induced bilayer deformations, protein insertion and assembly, and lipid-controlled functioning of membrane proteins.

Composition dependence of vesicle morphology and mixing properties in a bacterial model membrane system

We have determined the mixing properties and lamellar organization of bacterial membrane mimetics composed of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE) and -phosphatidylglycerol (POPG) at various molar ratios applying differential scanning calorimetry, small and wide-angle X-ray scattering, as well as optical phase contrast microscopy. Combining the experimental thermodynamic data with a simulation of the liquidus and solidus lines, we were able to construct a phase diagram. Using this approach, we find that the lipids mix in all phases non-ideally in the thermodynamic sense. As expected, pure POPE assembles into multilamellar and pure POPG into unilamellar vesicles, respectively, which are stable within the studied temperature range. In contrast, mixtures of the two components form oligolamellar vesicles consisting of about three to five bilayers. The layers within these oligolamellar liposomes are positionally correlated within the gel phase, but become uncorrelated within the fluid phase exhibiting freely fluctuating bilayers, while the vesicles as a whole remain intact and do not break up into unilamellar forms. X-ray, as well as DSC data, respectively, reveal a miscibility gap due to a lateral phase segregation at POPG concentrations above about 70 mol%, similar to previously reported data on mixtures composed of disaturated PEs and PGs. Hence, the existence of a region of immiscibility is a general feature of PE/PG mixtures and the mixing properties are dominated by PE/PG headgroup interactions, but are largely independent of the composition of the hydrocarbon chains. This is in accordance with a recent theoretical prediction.

Alternative mechanisms of structuring biomembranes: self-assembly versus self-organization

We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to a nonequilibrium biochemical reaction cycle of proteins near the membrane. While both processes lead eventually to quite similar patterns, their evolution occurs on very different length and time scales. Self-assembly produces periodic protein patterns on a spatial scale below 0.1 microm in a few seconds followed by extremely slow coarsening, whereas self-organization results in a pattern wavelength comparable to the typical cell size of 100 microm within a few minutes suggesting different biological functions for the two processes.

Flexible charged macromolecules on mixed fluid lipid membranes: theory and Monte Carlo simulations

Fluid membranes containing charged lipids enhance binding of oppositely charged proteins by mobilizing these lipids into the interaction zone, overcoming the concomitant entropic losses due to lipid segregation and lower conformational freedom upon macromolecule adsorption. We study this energetic-entropic interplay using Monte Carlo simulations and theory. Our model system consists of a flexible cationic polyelectrolyte, interacting, via Debye-Hückel and short-ranged repulsive potentials, with membranes containing neutral lipids, 1% tetravalent, and 10% (or 1%) monovalent anionic lipids. Adsorption onto a fluid membrane is invariably stronger than to an equally charged frozen or uniform membrane. Although monovalent lipids may suffice for binding rigid macromolecules, polyvalent counter-lipids (e.g., phosphatidylinositol 4,5 bisphosphate), whose entropy loss upon localization is negligible, are crucial for binding flexible macromolecules, which lose conformational entropy upon adsorption. Extending Rosenbluth's Monte Carlo scheme we directly simulate polymer adsorption on fluid membranes. Yet, we argue that similar information could be derived from a biased superposition of quenched membrane simulations. Using a simple cell model we account for surface concentration effects, and show that the average adsorption probabilities on annealed and quenched membranes coincide at vanishing surface concentrations. We discuss the relevance of our model to the electrostatic-switch mechanism of, e.g., the myristoylated alanine-rich C kinase substrate protein.

Travelling lipid domains in a dynamic model for protein-induced pattern formation in biomembranes

Cell membranes are composed of a mixture of lipids. Many biological processes require the formation of spatial domains in the lipid distribution of the plasma membrane. We have developed a mathematical model that describes the dynamic spatial distribution of acidic lipids in response to the presence of GMC proteins and regulating enzymes. The model encompasses diffusion of lipids and GMC proteins, electrostatic attraction between acidic lipids and GMC proteins as well as the kinetics of membrane attachment/detachment of GMC proteins. If the lipid-protein interaction is strong enough, phase separation occurs in the membrane as a result of free energy minimization and protein/lipid domains are formed. The picture is changed if a constant activity of enzymes is included into the model. We chose the myristoyl-electrostatic switch as a regulatory module. It consists of a protein kinase C that phosphorylates and removes the GMC proteins from the membrane and a phosphatase that dephosphorylates the proteins and enables them to rebind to the membrane. For sufficiently high enzymatic activity, the phase separation is replaced by travelling domains of acidic lipids and proteins. The latter active process is typical for nonequilibrium systems. It allows for a faster restructuring and polarization of the membrane since it acts on a larger length scale than the passive phase separation. The travelling domains can be pinned by spatial gradients in the activity; thus the membrane is able to detect spatial clues and can adapt its polarity dynamically to changes in the environment.

Domain formation induced by the adsorption of charged proteins on mixed lipid membranes

Peripheral proteins can trigger the formation of domains in mixed fluid-like lipid membranes. We analyze the mechanism underlying this process for proteins that bind electrostatically onto a flat two-component membrane, composed of charged and neutral lipid species. Of particular interest are membranes in which the hydrocarbon lipid tails tend to segregate owing to nonideal chain mixing, but the (protein-free) lipid membrane is nevertheless stable due to the electrostatic repulsion between the charged lipid headgroups. The adsorption of charged, say basic, proteins onto a membrane containing anionic lipids induces local lipid demixing, whereby charged lipids migrate toward (or away from) the adsorption site, so as to minimize the electrostatic binding free energy. Apart from reducing lipid headgroup repulsion, this process creates a gradient in lipid composition around the adsorption zone, and hence a line energy whose magnitude depends on the protein's size and charge and the extent of lipid chain nonideality. Above a certain critical lipid nonideality, the line energy is large enough to induce domain formation, i.e., protein aggregation and, concomitantly, macroscopic lipid phase separation. We quantitatively analyze the thermodynamic stability of the dressed membrane based on nonlinear Poisson-Boltzmann theory, accounting for both the microscopic characteristics of the proteins and lipid composition modulations at and around the adsorption zone. Spinodal surfaces and critical points of the dressed membranes are calculated for several different model proteins of spherical and disk-like shapes. Among the models studied we find the most substantial protein-induced membrane destabilization for disk-like proteins whose charges are concentrated in the membrane-facing surface. If additional charges reside on the side faces of the proteins, direct protein-protein repulsion diminishes considerably the propensity for domain formation. Generally, a highly charged flat face of a macroion appears most efficient in inducing large compositional gradients, hence a large and unfavorable line energy and consequently lateral macroion aggregation and, concomitantly, macroscopic lipid phase separation.

Increased concentration of polyvalent phospholipids in the adsorption domain of a charged protein

We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the electrochemical potentials of the lipids in the two blocks yields an expression for the relations among the various lipid fractions in the adsorption domain, indicating a sensitive dependence of lipid fraction on valence. This expression is a result of the two-block picture but does not depend on further details of the protein-membrane interaction. We subsequently calculated the lipid fractions themselves using the Poisson-Boltzmann theory. We examined the dependence of lipid enrichment, i.e., the ratio between the lipid fractions inside and outside the adsorption domain, on various parameters such as ionic strength and lipid valence. Maximum enrichment was found for lipid valence in the range between -3 and -4 in physiological conditions. Our results are in qualitative agreement with recent experimental studies on the interactions between peptides having a domain of basic residues and membranes containing a small fraction of the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study provides theoretical support for the suggestion that proteins adsorbed onto membranes through a cluster of basic residues may sequester PIP2 and other polyvalent lipids.

A computational model for the electrostatic sequestration of PI(4,5)P2 by membrane-adsorbed basic peptides

The multivalent acidic phospholipid phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) plays a key role in many biological processes. Recent studies show that unstructured clusters of basic residues from a number of peripheral proteins can laterally sequester PI(4,5)P2 in membranes. Specifically, experiments suggest that the basic effector domain of the myristoylated alanine-rich C kinase substrate (MARCKS), or a peptide corresponding to this domain, MARCKS(151-175), sequesters several PI(4,5)P2 and that this sequestration is due to nonspecific electrostatic interactions. Here, we use the finite difference Poisson-Boltzmann method to test this hypothesis by calculating the electrostatic free energy of lateral sequestration of PI(4,5)P2 by membrane-adsorbed basic peptides: Lys-7, Lys-13, and FA-MARCKS(151-175), a peptide based on MARCKS(151-175). In agreement with experiments, we find that the electrostatic free energy becomes more favorable when: 1), Lys-13 and FA-MARCKS(151-175) sequester several PI(4,5)P2; 2), the linear charge density of the basic peptide increases; 3), the mol percent monovalent acidic lipid in the membrane decreases; and 4), the ionic strength of the solution decreases. In addition, the electrostatic sequestration free energy is in excess of the entropic penalty associated with localizing PI(4,5)P2. Our calculations, thus, provide a structural and quantitative description of the observed interaction of PI(4,5)P2 with membrane-adsorbed basic sequences.