Computer simulation of the main gel–fluid phase transition of lipid bilayers

Influence of Temperature on Molecular Adsorption and Transport at Liposome Surfaces Studied by Molecular Dynamics Simulations and Second Harmonic Generation Spectroscopy

A fundamental understanding of the kinetics and thermodynamics of chemical interactions at the phospholipid bilayer interface is crucial for developing potential drug-delivery applications. Here we use molecular dynamics (MD) simulations and surface-sensitive second harmonic generation (SHG) spectroscopy to study the molecular adsorption and transport of a small organic cation, malachite green (MG), at the surface of 1,2-dioleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DOPG) liposomes in water at different temperatures. The temperature-dependent adsorption isotherms, obtained by SHG measurements, provide information on adsorbate concentration, free energy of adsorption, and associated changes in enthalpy and entropy, showing that the adsorption process is exothermic, resulting in increased overall entropy. Additionally, the molecular transport kinetics are found to be more rapid under higher temperatures. Corresponding MD simulations are used to calculate the free energy profiles of the adsorption and the molecular orientation distributions of MG at different temperatures, showing excellent agreement with the experimental results.

Dynamic "Molecular Portraits" of Biomembranes Drawn by Their Lateral Nanoscale Inhomogeneities

To date, it has been reliably shown that the lipid bilayer/water interface can be thoroughly characterized by a sophisticated so-called "dynamic molecular portrait". The latter reflects a combination of time-dependent surface distributions of various physicochemical properties, inherent in both model lipid bilayers and natural multi-component cell membranes. One of the most important features of biomembranes is their mosaicity, which is expressed in the constant presence of lateral inhomogeneities, the sizes and lifetimes of which vary in a wide range-from 1 to 10³ nm and from 0.1 ns to milliseconds. In addition to the relatively well-studied macroscopic domains (so-called "rafts"), the analysis of micro- and nanoclusters (or domains) that form an instantaneous picture of the distribution of structural, dynamic, hydrophobic, electrical, etc., properties at the membrane-water interface is attracting increasing interest. This is because such nanodomains (NDs) have been proven to be crucial for the proper membrane functioning in cells. Therefore, an understanding with atomistic details the phenomena associated with NDs is required. The present mini-review describes the recent results of experimental and in silico studies of spontaneously formed NDs in lipid membranes. The main attention is paid to the methods of ND detection, characterization of their spatiotemporal parameters, the elucidation of the molecular mechanisms of their formation. Biological role of NDs in cell membranes is briefly discussed. Understanding such effects creates the basis for rational design of new prospective drugs, therapeutic approaches, and artificial membrane materials with specified properties.

Thermodynamics of Composition Dependent Ligand Exchange on the Surfaces of Colloidal Indium Phosphide Quantum Dots

Quantum dot surfaces can have a substantial effect on their physical, chemical, and optoelectronic properties. When the chemistry that occurs at the surface of nanocrystals is studied, critical insights can be gained into the fundamental structural, thermodynamic, and optical properties of quantum dot materials providing a valuable guide for how to best adapt them for desired applications. Colloidal quantum dots are often terminated with organic ligands that consist of a long aliphatic chain and a head group that binds tightly to the nanocrystal surface. While extensive work has been done to understand how ligand head groups influence quantum dot properties, studies to unravel the influence of the organic ligand tail on ligands and surface reaction equilibria are incomplete. To further investigate the driving forces of quantum dot surface modification, a series of ligand exchange reactions with oleic acid were performed on indium phosphide quantum dots, initially terminated with straight-chain carboxylates of variable lengths. The reaction was monitored using isothermal titration calorimetry and ¹H NMR to determine the extent of each reaction and its associated thermodynamics. From these measurements, interligand interactions were observed to be dependent on the length of the straight-chain ligand. A modified Ising model was used to investigate the enthalpic and entropic effects contributing to these ligand exchanges and reveal that interligand interactions play a much larger role than previously thought. Additional experimentation with phosphonic acid ligand exchange reveals complexity in the reaction mechanism but further illustrates the significant impact of ligand tail group length on thermodynamics, even in cases where there is a large difference in head group binding energy.

Unsaturated Ligands Seed an Order to Disorder Transition in Mixed Ligand Shells of CdSe/CdS Quantum Dots

A phase transition within the ligand shell of core/shell quantum dots is studied in the prototypical system of colloidal CdSe/CdS quantum dots with a ligand shell composed of bound oleate (OA) and octadecylphosphonate (ODPA). The ligand shell composition is tuned using a ligand exchange procedure and quantified through proton NMR spectroscopy. Temperature-dependent photoluminescence spectroscopy reveals a signature of a phase transition within the organic ligand shell. Surprisingly, the ligand order to disorder phase transition triggers an abrupt increase in the photoluminescence quantum yield (PLQY) and full-width at half-maximum (FWHM) with increasing temperature. The temperature and width of the phase transition show a clear dependence on ligand shell composition, such that QDs with higher ODPA fractions have sharper phase transitions that occur at higher temperatures. In order to gain a molecular understanding of the changes in ligand ordering, Fourier transform infrared and vibrational sum frequency generation spectroscopies are performed. These measurements confirm that an order/disorder transition in the ligand shell tracks with the photoluminescence changes that accompany the ligand phase transition. The phase transition is simulated through a lattice model that suggests that the ligand shell is well-mixed and does not have completely segregated domains of OA and ODPA. Furthermore, we show that the unsaturated chains of OA seed disorder within the ligand shell.

Amphiphilic copolymers change the nature of the ordered-to-disordered phase transition of lipid membranes from discontinuous to continuous

The phase behaviour as a function of temperature is explored for pure phospholipid (DPPC) and hybrid lipid-polymer (DPPC/Pluronic L64) bilayers with the aid of atomistic MD simulations. The range of the fixed-temperature simulations includes temperatures below and above the known melting temperature (Tm) for DPPC membranes. For the pure lipid bilayer, the main phase transition is discontinuous, as verified by the abrupt changes observed in the membrane structure, elasticity and the lipid diffusivity near the critical temperature Tm, which lies in the region 298.15-303.15 K. A pre-transition step is detected at 298.15 K which has been identified as the ripple phase (Pβ'), where ordered and disordered lipids coexist, causing thickness fluctuations. In the ordered gel phase, the positional ordering as assessed by the lipid radial distribution functions is long-range and some degree of hexagonal packing is measured. The hybrid bilayers on the other hand, transform from a more ordered to a disordered phase in a continuous manner, without finite jumps in their properties. No signs of the ripple phase are identified and the ordered phase exhibits very limited hexagonal packing and some positional ordering that decays fast. The effect of the inserted polymers in the two phases is reversed; at low temperatures, they render the membrane thinner, less cohesive and less ordered compared to the pure one, with the lipids assuming faster diffusion rates, whereas at high temperatures, the polymer interaction with the lipids acts reducing their diffusivity, but also increasing the lipid tail ordering and the membrane stiffness. The ability of the amphiphilic L64 copolymers to change the nature of the main phase transition of lipid membranes and their properties both in the ordered and the disordered phase is of vital importance for the prediction of both the efficacy of hybrid lipid/polymer nanoparticles as drug delivery vehicles as well as their potential adverse implications during interactions with healthy cell membranes.

Experimental Evidence of the Existence of Interleaflet Coupled Nanodomains: An MC-FRET Study

Plasma membranes of living cells are compartmentalized into small submicroscopic structures (nanodomains) having potentially relevant biological functions. Despite this, structural features of these nanodomains remain elusive, primarily due to the difficulties in characterizing such small dynamic entities. It is unclear whether nanodomains found in the upper bilayer leaflet are transversally registered with those found in the lower leaflet. Experiments performed on larger microscopic domains indicate that the coupling between the leaflets is strong, forcing the domains to be in perfect registration, but can the same thing be said about the biologically more relevant nanodomains? This work provides experimental evidence that even small nanodomains of variable sizes between 10 and 160 nm are interleaflet coupled. Importantly, the alternative scenarios of partially registered, independent, or antiregistered nanodomains could be excluded.

Phase Transitions in Phospholipid Monolayers: Theory Versus Experiments

The Doniach lattice gas (DLG) represents a ternary-mixture statistical model, whose components, water molecules (w), ordered-chain lipids (o), and disordered-chain lipids (d)-the latter carrying a high degenerescence ω ≫ 1-are located at each site of a two-dimensional lattice. The DLG model was introduced to describe phospholipid Langmuir films at the air-water interface and can be mapped into a spin-1 model, with the single-site states s _i = 0, +1, and -1 representing the three types of molecules in the system (w, o, and d), respectively. The model allows lipid-density fluctuations and has been analyzed at the mean-field approximation (Guidi, H. S.; Henriques, V. B. Phys. Rev. E 2014, 90, 052705) as well as at the pair approximation (de Oliveira, F. O.; Tamashiro, M. N. Phys. Rev. E 2019, 99, 012147). In this work, we focus on performing an explicit comparison of the theoretical predictions obtained for the DLG model at the pair approximation with isothermal monolayer compression experiments (Nielsen, L. K.; Bjørnholm, T.; Mouritsen, O. G. Langmuir 2007, 23, 11684) for the two most commonly studied saturated zwitterionic phospholipids, DMPC (1,2-dimyristoyl- sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl- sn-glycero-3-phosphocholine). The model parameters obtained by fitting to the experimental data yield phase diagrams that are qualitatively consistent with the observed phase transitions on DMPC and DPPC monolayers, with the absence of a low-density gas phase. Quantitative agreement, however, was less significant partially because of the challenging reproducibility of Langmuir monolayer compression experiments, claimed in the literature to be influenced by kinetic effects.

How to Determine Lipid Interactions in Membranes from Experiment Through the Ising Model

The determination and the meaning of interactions in lipid bilayers are discussed and interpreted through the Ising model. Originally developed to understand phase transitions in ferromagnetic systems, the Ising model applies equally well to lipid bilayers. In the case of a membrane, the essence of the Ising model is that each lipid is represented by a site on a lattice and that the interaction of each site with its nearest neighbors is represented by an energy parameter ω. To calculate the thermodynamic properties of the system, such as the enthalpy, the Gibbs energy, and the heat capacity, the partition function is derived. The calculation of the configurational entropy factor in the partition function, however, requires approximations or the use of Monte Carlo (MC) simulations. Those approximations are described. Ultimately, MC simulations are used in combination with experiment to determine the interaction parameters ω in lipid bilayers. Several experimental approaches are described, which can be used to obtain interaction parameters. They include nearest-neighbor recognition, differential scanning calorimetry, and Förster resonance energy transfer. Those approaches are most powerful when used in combination of MC simulations of Ising models. Lipid membranes of different compositions are discussed, which have been studied with these approaches. They include mixtures of cholesterol, saturated (ordered) phospholipids, and unsaturated (disordered) phospholipids. The interactions between those lipid species are examined as a function of molecular properties such as the degree of unsaturation and the acyl chain length. The general rule that emerges is that interactions between different lipids are usually unfavorable. The exception is that cholesterol interacts favorably with saturated (ordered) phospholipids. However, the interaction of cholesterol with unsaturated phospholipids becomes extremely unfavorable as the degree of unsaturation increases.

Phase transitions in phospholipid monolayers: Statistical model at the pair approximation

A Langmuir film, consisting of a phospholipid monolayer at the air-water interface, was modeled as a two-dimensional lattice gas corresponding to a ternary mixture of water molecules (w), ordered-chain lipids (o), and disordered-chain lipids (d). The statistical problem is formulated in terms of a spin-1 model, in which the disordered-chain lipid states possess a high degenerescence ω≫1, and was termed Doniach lattice gas (DLG). Motivated by some open questions in the analysis of the DLG model at the mean-field approximation (MFA) [Phys. Rev. E 90, 052705 (2014)PLEEE81539-375510.1103/PhysRevE.90.052705], we have reconsidered it at the pair-approximation level by solving the model on a Cayley tree of coordination z. The attractors of the corresponding discrete-map problem are associated with the thermodynamic solutions on the Bethe lattice (the central region of an asymptotically infinite Cayley tree). To check the thermodynamic stability of the possible phases, the grand-potential density was obtained by the method proposed by Gujrati [Phys. Rev. Lett. 74, 809 (1995)PRLTAO0031-900710.1103/PhysRevLett.74.809]. In general, the previous MFA results are confirmed at the pair-approximation level, but a novel staggered phase, overlooked in the MFA analysis, was found when the condition ε_{wd}>1/2(ε_{ww}+ε_{dd}) is satisfied, where ε_{xy} represents the nearest-neighbor intermolecular interactions between single-site states x and y. Model parameters obtained by fitting to experimental data for the two most commonly studied zwitterionic phospholipids, 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), yield phase diagrams consistent with the phase transitions observed on Langmuir films of the same lipids under isothermal compression, which present a liquid-condensed to a liquid-expanded first-order transition line ending at a critical point.

Membrane Lipid Nanodomains

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

Phase behavior of supported lipid bilayers: A systematic study by coarse-grained molecular dynamics simulations

Solid-supported lipid bilayers are utilized by experimental scientists as models for biological membranes because of their stability. However, compared to free standing bilayers, their close proximity to the substrate may affect their phase behavior. As this is still poorly understood, and few computational studies have been performed on such systems thus far, here we present the results from a systematic study based on molecular dynamics simulations of an implicit-solvent model for solid-supported lipid bilayers with varying lipid-substrate interactions. The attractive interaction between the substrate and the lipid head groups that are closest to the substrate leads to an increased translocation of the lipids from the distal to the proximal bilayer-leaflet. This thereby leads to a transbilayer imbalance of the lipid density, with the lipid density of the proximal leaflet higher than that of the distal leaflet. Consequently, the order parameter of the proximal leaflet is found to be higher than that of the distal leaflet, the higher the strength of lipid interaction is, the stronger the effect. The proximal leaflet exhibits gel and fluid phases with an abrupt melting transition between the two phases. In contrast, below the melting temperature of the proximal leaflet, the distal leaflet is inhomogeneous with coexisting gel and fluid domains. The size of the fluid domains increases with increasing the strength of the lipid interaction. At low temperatures, the inhomogeneity of the distal leaflet is due to its reduced lipid density.

Interaction of semiochemicals with model lipid membranes: A biophysical approach

Unravelling the chemical language of insects has been the subject of intense research in the field of chemical ecology for the past five decades. Insect communication is mainly based on chemosensation due to the small body size of insects, which limits their ability to produce or perceive auditory and visual signals, especially over large distances. Chemicals involved in insect communication are called semiochemicals. These volatiles and semivolatiles compounds allow to Insects to find a mate, besides the oviposition site in reproduction and food sources. Actually, insect olfaction mechanism is subject to study, but systematic analyses of the role of neural membranes are scarce. In the present work we evaluated the interactions of α-pinene, benzaldehyde, eugenol, and grandlure, among others, with a lipid membrane model using surface pressure experiments and Monte Carlo computational analysis. This allowed us to propose a plausible membranotropic mechanism of interaction between semiochemicals and insect neural membrane.

A model of lipid rearrangements during pore formation in the DPPC lipid bilayer

CONTEXT

The molecular bases of pore formation in the lipid bilayer remain unclear, as do the exact characteristics of their sizes and distributions. To understand this process, numerous studies have been performed on model lipid membranes including cell-sized giant unilamellar vesicles (GUV). The effect of an electric field on DPPC GUV depends on the lipid membrane state: in the liquid crystalline phase the created pores have a cylinder-like shape, whereas in the gel phase a crack has been observed.

OBJECTIVE

The aim of the study was to investigate the geometry of pores created in a lipid bilayer in gel and liquid crystalline phases in reference to literature experimental data.

METHODS

A mathematical model of the pore in a DPPC lipid bilayer developed based on the law of conservation of mass and the assumption of constant volume of lipid molecules, independent of their conformation, allows for analysis of pore shape and accompanying molecular rearrangements.

RESULTS

The membrane area occupied by the pore of a cylinder-like shape is greater than the membrane area occupied by lipid molecules creating the pore structure (before pore appearance). Creation of such pores requires more space, which can be achieved by conformational changes of lipid chains toward a more compact state. This process is impossible for a membrane in the most compact, gel phase.

DISCUSSION AND CONCLUSIONS

We show that the geometry of the pores formed in the lipid bilayer in the gel phase must be different from the cylinder shape formed in the lipid bilayer in a liquid crystalline state, confirming experimental studies. Furthermore, we characterize the occurrence of the 'buffer' zone surrounding pores in the liquid crystalline phase as a mechanism of separation of neighbouring pores.

Dynamics of surface of lipid membranes: theoretical considerations and the ESR experiment

The effect of the surface layer of model membranes on their physical properties was discussed in this paper. The research involved a physical ESR experiment with the use of spin probes and computer simulation based on the Monte Carlo technique. Liposomes formed during the process of sonication of lecithin were scanned in an ESR spectrometer. The membrane surface layer model, represented by the system of electric dipoles arranged in rectangular or hexagonal matrices, was studied. The final states of computer simulations were presented as textures. It was found that in the gel phase some ordered domain structures are formed, while in the liquid–crystal phase we got complex textures comprising a plurality of gaps. The process of forming domain structures during the changing of the temperature and the phase transitions taking place in a dipole system as a function of dipole mobility (k-parameter) was presented. The results obtained imply that the head groups (represented by electric dipoles in the computer model) of the surface layer play a key role in membranes, affecting the properties of the entire membrane, which is particularly essential for transport processes. It also modified the characteristics of the membrane gel-liquid crystalline transition phase.

Lattice solution model for order-disorder transitions in membranes and Langmuir monolayers

Lipid monolayers and bilayers have been used as experimental models for the investigation of membrane thermal transitions. The main transition takes place near ambient temperatures for several lipids and reflects the order-disorder transition of lipid hydrocarbonic chains, which is accompanied by a surface density gap. Equivalence between the transitions in the two systems has been argued by several authors. The two-state statistical model adopted by numerous authors for different properties of the membrane, such as permeability, diffusion, and mixture or insertion of cholesterol or protein, is inadequate for the description of charged membranes, since it lacks a proper description of surface density. We propose a lattice solution model which adds interactions with water molecules to lipid-lipid interactions and obtain its thermal properties under a mean-field approach. Density variations, although concomitant with chain order variations, are independent of the latter. The model presents both chain order and gas-liquid transitions, and extends the range of applicability of previous models, yielding Langmuir isotherms in the full range of pressures and areas.

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Membrane lateral structure: the influence of immobilized particles on domain size

In experiments on model membranes, formation of large domains of different lipid composition is readily observed. However, no such phase separation is observed in the membranes of intact cells. Instead, small transient inhomogeneities called lipid rafts are expected in these systems. One of the numerous attempts to explain small domains refers to the coupling of the membrane to its surroundings, which leads to the immobilization of some of the membrane molecules. These immobilized molecules then act as static obstacles for the remaining mobile ones. We present detailed Molecular Dynamics simulations demonstrating that this can indeed account for small domains. This confirms previous Monte Carlo studies based on simplified models. Furthermore, by directly comparing domain structures obtained using Molecular Dynamics to Monte Carlo simulations of the Ising model, we demonstrate that domain formation in the presence of obstacles is remarkably insensitive to the details of the molecular interactions.

Main transition in the Pink membrane model: finite-size scaling and the influence of surface roughness

We consider the main transition in single-component membranes using computer simulations of the Pink model [D. A. Pink et al., Biochemistry 19, 349 (1980)]. We first show that the accepted parameters of the Pink model yield a main transition temperature that is systematically below experimental values. This resolves an issue that was first pointed out by Corvera and co-workers [Phys. Rev. E 47, 696 (1993)]. In order to yield the correct transition temperature, the strength of the van der Waals coupling in the Pink model must be increased; by using finite-size scaling, a set of optimal values is proposed. We also provide finite-size scaling evidence that the Pink model belongs to the universality class of the two-dimensional Ising model. This finding holds irrespective of the number of conformational states. Finally, we address the main transition in the presence of quenched disorder, which may arise in situations where the membrane is deposited on a rough support. In this case, we observe a stable multidomain structure of gel and fluid domains, and the absence of a sharp transition in the thermodynamic limit.

First order melting transitions of highly ordered dipalmitoyl phosphatidylcholine gel phase membranes in molecular dynamics simulations with atomistic detail

Molecular dynamics simulations with atomistic detail of the gel phase and melting transitions of dipalmitoyl phosphatidylcholine bilayers in water reveal the dependency of many thermodynamic and structural parameters on the initial system ordering. We quantitatively compare different methods to create a gel phase system and we observe that a very high ordering of the gel phase starting system is necessary to observe behavior which reproduces experimental data. We performed heating scans with speeds down to 0.5 K/ns and could observe sharp first order phase transitions. Also, we investigated the transition enthalpy as the natural intrinsic parameter of first order phase transitions, and obtained a quantitative match with experimental values. Furthermore, we performed systematic investigations of the statistical distribution and heating rate dependency of the microscopic phase transition temperature.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment

Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: a statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types--each one associated, respectively, with the polar-headgroup and the acyl-chain states--which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Minimal model of plasma membrane heterogeneity requires coupling cortical actin to criticality

We present a minimal model of plasma membrane heterogeneity that combines criticality with connectivity to cortical cytoskeleton. The development of this model was motivated by recent observations of micron-sized critical fluctuations in plasma membrane vesicles that are detached from their cortical cytoskeleton. We incorporate criticality using a conserved order parameter Ising model coupled to a simple actin cytoskeleton interacting through point-like pinning sites. Using this minimal model, we recapitulate several experimental observations of plasma membrane raft heterogeneity. Small (r ∼ 20 nm) and dynamic fluctuations at physiological temperatures arise from criticality. Including connectivity to the cortical cytoskeleton disrupts large fluctuations, prevents macroscopic phase separation at low temperatures (T ≤ 22°C), and provides a template for long-lived fluctuations at physiological temperature (T = 37°C). Cytoskeleton-stabilized fluctuations produce significant barriers to the diffusion of some membrane components in a manner that is weakly dependent on the number of pinning sites and strongly dependent on criticality. More generally, we demonstrate that critical fluctuations provide a physical mechanism for organizing and spatially segregating membrane components by providing channels for interaction over large distances.

Membrane fluidity and the surface properties of the lipid bilayer: ESR experiment and computer simulation

Penetration of the liposome membranes formed in the gel phase from DPPC (DPPC liposomes) and in the liquid-crystalline phase from egg yolk lecithin (EYL liposomes) by the TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl) and 16 DOXYL (2-ethyl-2-(15-methoxy-oxopentadecyl)-4,4-dimethyl-3-oxazolidinyloxy) spin probes has been investigated. The penetration process was followed by 120 hours at 24(0)C, using the electron spin resonance (ESR) method. The investigation of the kinetics of the TEMPO probe building into the membranes of both types of liposomes revealed differences appearing 30 minutes after the start of the experiment. The number of TEMPO particles built into the EYL liposome membranes began to clearly rise, aiming asymptotically to a constant value after about 100 minutes, whereas the number of the TEMPO particles built into the DPPC liposome membranes was almost constant in time. The interpretation of the obtained experimental results was enriched with those of computer simulation, following the behavior of the polar heads (dipoles) of the lipid particles forming a lipid layer due to the change in the value of the model parameter, k, determining the mobility of the dipoles. The possibility of the formation of an irregular ordering of the polar part of lipid membranes was proved, which leads to the appearance of spaces filled with of water for k > 0.4. The appearance of these defects enables the penetration of the bilayer by the TEMPO particles. The limited mobility of lipid polar heads (k < 0.2) prevents the appearance of such areas facilitating the penetration of the lipid membrane by alien particles in the gel phase.

Main phase transition in lipid bilayers: Phase coexistence and line tension in a soft, solvent-free, coarse-grained model

We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The nonbonded interactions take the form of a weighted-density functional, which allows us to describe the thermodynamics of self-assembly and packing effects of the coarse-grained beads in terms of a density expansion of the equation of state and weighting functions that regularize the microscopic bead densities, respectively. Identifying the length and energy scales via the bilayer thickness and the thermal energy scale, k(B)T, the model qualitatively reproduces key characteristics (e.g., bending rigidity, area per molecule, and compressibility) of lipid membranes. We employ this model to study the main phase transition between the fluid and the gel phase of the bilayer membrane. We accurately locate the phase coexistence using free energy calculations and also obtain estimates for the bare and the thermodynamic line tension.

Crucial roles of charged saccharide moieties in survival of gram negative bacteria against protamine revealed by combination of grazing incidence x-ray structural characterizations and Monte Carlo simulations

Grazing incidence x-ray scattering techniques and Monte Carlo (MC) simulations are combined to reveal the influence of molecular structure (genetic mutation) and divalent cations on the survival of gram negative bacteria against cationic peptides such as protamine. The former yields detailed structures of bacterial lipopolysaccharide (LPS) membranes with minimized radiation damages, while the minimal computer model based on the linearized Poisson-Boltzmann theory allows for the simulation of conformational changes of macromolecules (LPSs and peptides) that occur in the time scale of ms. The complementary combination of the structural characterizations and MC simulation demonstrates that the condensations of divalent ions (Ca2+ or Mg2+) in the negatively charged core saccharides are crucial for bacterial survival.

A pore creation in a triangular network model membrane

Membrane electroporation seems to be a useful method for delivery of biological active compounds into the cell. Although it is known that this phenomenon is sensitive to the electric field intensity, duration of the electric pulse and its shape, it is not fully understood. In some theoretical descriptions it is postulated that a hydrophobic pore appears at an early stage of pore creation. Here we show how to construct a hydrophilic pore structure connecting two parallel triangular networks modeling lipid membrane. It would be useful in Monte Carlo simulation studies on electroporation. In our model the pore appearance requires only movement of one lipid molecule. At the same time the chains of the second lipid molecule should occupy two nodes, one in each network to compensate the differences in chain packing densities when electric field is applied. In consequence the hydrated polar head should be placed in a hydrophobic part of the membrane giving rise to the hydrophilic pore. We also discuss the relation between the pore diameter and its shape.

Molecular studies of the gel to liquid-crystalline phase transition for fully hydrated DPPC and DPPE bilayers

Molecular dynamics simulations were used for a comprehensive study of the structural properties of saturated lipid bilayers, DPPC and DPPE, near the main phase transition. Though the chemical structure of DPPC and DPPE are largely similar (they only differ in the choline and ethanolamine groups), their transformation process from a gel to a liquid-crystalline state is contrasting. For DPPC, three distinct structures can be identified relative to the melting temperature (Tm): below Tm with "mixed" domains consisting of lipids that are tilted with partial overlap of the lipid tails between leaflet; near Tm with a slight increase in the average area per lipid, resulting in a rearrangement of the lipid tails and an increase in the bilayer thickness; and above Tm with unhindered lipid tails in random motion resulting in an increase in %gauche formed and increase in the level of interdigitation between lipid leaflets. For DPPE, the structures identified were below Tm with "ordered" domains consisting of slightly tilted lipid tails and non-overlapping lipid tails between leaflets, near Tm with minimal rearrangement of the lipids as the bilayer thickness reduces slightly with increasing temperature, and above Tm with unhindered lipid tails as that for DPPC. For DPPE, most of the lipid tails do not overlap as observed to DPPC, which is due to the tight packing of the DPPE molecules. The non-overlapping behavior of DPPE above Tm is confirmed from the density profile of the terminal carbon atoms in each leaflet, which shows a narrow distribution near the center of the bilayer core. This study also demonstrates that atomistic simulations are capable of capturing the phase transition behavior of lipid bilayers, providing a rich set of molecular and structural information at and near the transition state.

Modeling the induction of lipid membrane electropermeabilization

Experiments show significant effects of an electric field on lipid membrane, leading to a pore formation when a high intensity field is applied. The phenomenon of electroporation is preceded by the induction and expansion of defects, responsible for the pre-pore excitation. We examine the mechanism of the induction of the field-driven defects by Monte Carlo simulations. The study is based on the improved Pink's model, which includes explicit interactions between the polar heads and energy of interactions between the heads and the field. No anomalous deformation of the molecules is considered. The study, provided for bilayer dipalmitoyl-phosphatidylcholine (DPPC) membrane in the gel (300 K) and fluid (330 K) phases, shows dependence of the membrane conformational and energetical state on the value of the electric field. We observe that the electric field affects the number of molecules in the gel and in the fluid states. In the layer at the negative potential, when the transmembrane voltage is above U(c) approximately 280 mV, lipid heads abruptly reorient and the number of local spots with fluid conformation increases. The other layer slightly tends to tighten its structure, producing additional mechanical stress between layers. Lipids showed complete insensitivity to the electric field within physiological limits, U<70 mV.

Structural and energetic model of the mechanisms for reduced self-diffusion in a lipid bilayer with increasing ionic strength

Ionic concentration of the buffer strongly affects properties of a lipid membrane, such as membrane durability (e.g., in electroporation experiments), lateral diffusion coefficient, and zeta potential. The effect of ionic strength is studied by Monte Carlo simulations based on the improved Pink model with explicitly included interactions between lipid heads. We examine the energetic profile of the membrane, conformation of lipid molecules, and molecular interactions. The study is provided for dipalmitoyl-phosphatidylcholine (DPPC) membrane in the gel (300 K) and fluid (330 K) temperatures for the ionic strength in the range 10-3000 mM at several values of dielectric constant. At high ionic strength, the simulations indicate an increase of the membrane stability due to the screening of the repulsive forces between lipid heads, more stable conformation of lipid chains, and denser packing of the molecules. These effects may account for reduced lateral diffusion in the membrane, as observed in experiments. The simulation also suggests that chains tend to assume a more straightened configuration and the number of standing polar heads increases, which may contribute to thickening of the membrane. An increase of the head tilt dependent on ionic strength may account for the greater value of zeta potential. The model shows stronger electropermebilization of the membrane in external electric field when ionic strength is low.

Diffusion in two-component lipid membranes--a fluorescence correlation spectroscopy and monte carlo simulation study

Using fluorescence correlation spectroscopy, calorimetry, and Monte Carlo simulations, we studied diffusion processes in two-component membranes close to the chain melting transition. The aim is to describe complex diffusion behavior in lipid systems in which gel and fluid domains coexist. Diffusion processes in gel membranes are significantly slower than in fluid membranes. Diffusion processes in mixed phase regions are therefore expected to be complex. Due to statistical fluctuations the gel-fluid domain patterns are not uniform in space and time. No models for such diffusion processes are available. In this article, which is both experimental and theoretical, we investigated the diffusion in DMPC-DSPC lipid mixtures as a function of temperature and composition. We then modeled the fluorescence correlation spectroscopy experiment using Monte Carlo simulations to analyze the diffusion process. It is shown that the simulations yield a very good description of the experimental diffusion processes, and that predicted autocorrelation profiles are superimposable with the experimental curves. We believe that this study adds to the discussion on the physical nature of rafts found in biomembranes.

Analyzing heat capacity profiles of peptide-containing membranes: cluster formation of gramicidin A

The analysis of peptide and protein partitioning in lipid membranes is of high relevance for the understanding of biomembrane function. We used statistical thermodynamics analysis to demonstrate the effect of peptide mixing behavior on heat capacity profiles of lipid membranes with the aim to predict peptide aggregation from c(P)-profiles. This analysis was applied to interpret calorimetric data on the interaction of the antibiotic peptide gramicidin A with lipid membranes. The shape of the heat capacity profiles was found to be consistent with peptide clustering in both gel and fluid phase. Applying atomic force microscopy, we found gramicidin A aggregates and established a close link between thermodynamics data and microscopic imaging. On the basis of these findings we described the effect of proteins on local fluctuations. It is shown that the elastic properties of the membrane are influenced in the peptide environment.

Monte Carlo simulation towards ripple phase modelling

We present a novel approach to analysis of the gel-fluid transition of lipid membrane. The method is based on the Pink's model but in contrast to its standard version the dipole character of the lipid molecules polar part is considered. Moreover, less constrained movement of entire molecules is allowed. Such an approach includes into the model conditions imposed by the adjacent medium such as ionic strength, pH, and other factors affecting biological membranes via the polar part. The results obtained contribute to the explanation of the ripple phase phenomenon.

Histogram method to obtain heat capacities in lipid monolayers, curved bilayers, and membranes containing peptides

Lipid monolayer chain melting transitions were simulated using a two-state Doniach model, and experimental melting profiles of lipid vesicles were analyzed. We sampled the information of a Monte Carlo simulation into a single broad histogram containing complete information about the distribution of states. The information of the monolayer histogram was first used to calculate the melting behavior of a bilayer constructed from two uncoupled monolayers. We then fitted calorimetric heat profiles of various preparations of dipalmitoyl phosphatidylcholine vesicles. This analysis was extended to lipid bilayers. A fixed mean bilayer curvature was shown to result in a broadening of bilayer melting profiles. We furthermore used the histogram method to obtain the chain melting behavior of simple lipid-peptide mixtures.

A macroscopic description of lipid bilayer phase transitions of mixed-chain phosphatidylcholines: chain-length and chain-asymmetry dependence

A macroscopic model is presented to quantitatively describe lipid bilayer gel to fluid phase transitions. In this model, the Gibbs potential of the lipid bilayer is expressed in terms of a single order parameter q, the average chain orientational order parameter. The Gibbs potential is based on molecular mean-field and statistical mechanical calculations of inter and intrachain interactions. Chain-length and chain-asymmetry are incorporated into the Gibbs potential so that one equation provides an accurate description of mixed-chain phosphatidylcholines of a single class. Two general classes of lipids are studied in this work: lipid bilayers of partially or noninterdigitated gel phases, and bilayers of mixed interdigitated gel phases. The model parameters are obtained by fitting the transition temperature and enthalpy data of phosphatidylcholines to the model. The proposed model provides estimates for the transition temperature and enthalpy, van der Waals energy, number of gauche bonds, chain orientational order parameter, and bond rotational and excluded volume entropies, achieving excellent agreement with existing data obtained with various techniques.

Calorimetric and theoretical studies of the effects of lindane on lipid bilayers of different acyl chain length

The effects of the insecticide lindane on the phase transition in multilamellar bilayers of saturated diacylphosphatidylcholines of different acyl chain length (DC14PC, DC16PC, and DC18PC) have been studied by means of differential scanning calorimetry (DSC), as well as computer-simulation calculations on a molecular interaction model. The calorimetric data show that increasing concentrations of lindane lower the transition temperature and lead to a broadening of the specific heat in a systematic way depending on the lipid acyl chain length. Kinetic effects in the observed calorimetric traces indicate that the incorporation of lindane into multilamellar lipid bilayers is slow, but faster for the shorter lipid species. Large unilamellar vesicles do not show such kinetic effects. The transition enthalpy is for all three lipid species found to be independent of the lindane concentration which implies that the entropy of mixing is vanishingly small. This lends support to a microscopic molecular interaction model which assigns the absorbed lindane molecules to interstitial sites in the bilayer. Computer-simulation calculations on this model, which assumes a specific interaction between lindane and certain excited acyl chain configurations, lead to predictions of the lipid-water partition coefficient in qualitative agreement with experimental measurements (Antunes-Madeira and Madeira (1985) Biochim. Biophys. Acta 820, 165-172). The partition coefficient has a peak near the phase transition which is a consequence of enhanced interfacial adsorption of lindane at lipid-domain interfaces.