Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures

Interaction Energy between Two Separated Charged Spheres Surrounded Inside and Outside by Electrolyte

By using the recently generalized version of Newton's shell theorem, analytical equations are derived to calculate the electric interaction energy between two separated, charged spheres surrounded outside and inside by electrolyte. This electric interaction energy is calculated as a function of the electrolyte's ion concentration, temperature, distance between the spheres and size of the spheres. At the same distance between the spheres, the absolute value of the interaction energy decreases with increasing electrolyte ion concentration and increases with increasing temperature. At zero electrolyte ion concentration, the derived analytical equation transforms into the Coulomb Equation Finally, the analytical equation is generalized to calculate the electric interaction energy of N separated, charged spheres surrounded by electrolyte.

Revealing local molecular distribution, orientation, phase separation, and formation of domains in artificial lipid layers: Towards comprehensive characterization of biological membranes

Lipids, together with molecules such as DNA and proteins, are one of the most relevant systems responsible for the existence of life. Selected lipids are able to assembly into various organized structures, such as lipid membranes. The unique properties of lipid membranes determine their complex functions, not only to separate biological environments, but also to participate in regulatory functions, absorption of nutrients, cell-cell communication, endocytosis, cell signaling, and many others. Despite numerous scientific efforts, still little is known about the reason underlying the variability within lipid membranes, and its biochemical significance. In this review, we discuss the structural complexity of lipid membranes, as well as the importance to simplify studied systems in order to understand phenomena occurring in natural, complex membranes. Such systems require a model interface to be analyzed. Therefore, here we focused on analytical studies of artificial systems at various interfaces. The molecular structure of lipid membranes, specifically the nanometric thickens of molecular bilayer, limits in a major extent the choice of highly sensitive methods suitable to study such structures. Therefore, we focused on methods that combine high sensitivity, and/or chemical selectivity, and/or nanometric spatial resolution, such as atomic force microscopy, nanospectroscopy (tip-enhanced Raman spectroscopy, infrared nanospectroscopy), phase modulation infrared reflection-absorption spectroscopy, sum-frequency generation spectroscopy. We summarized experimental and theoretical approaches providing information about molecular structure and composition, lipid spatial distribution (phase separation), organization (domain shape, molecular orientation) of lipid membranes, and real-time visualization of the influence of various molecules (proteins, drugs) on their integrity. An integral part of this review discusses the latest achievements in the field of lipid layer-based biosensors.

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.

Cellular absorption of small molecules: free energy landscapes of melatonin binding at phospholipid membranes

Free energy calculations are essential to unveil mechanisms at the atomic scale such as binding of small solutes and their translocation across cell membranes, eventually producing cellular absorption. Melatonin regulates biological rhythms and is directly related to carcinogenesis and neurodegenerative disorders. Free energy landscapes obtained from well-tempered metadynamics simulations precisely describe the characteristics of melatonin binding to specific sites in the membrane and reveal the role of cholesterol in free energy barrier crossing. A specific molecular torsional angle and the distance between melatonin and the center of the membrane along the normal to the membrane Z-axis have been considered as suitable reaction coordinates. Free energy barriers between two particular orientations of the molecular structure (folded and extended) have been found to be of about 18 kJ/mol for z-distances of about 1–2 nm. The ability of cholesterol to expel melatonin out of the internal regions of the membrane towards the interface and the external solvent is explained from a free energy perspective. The calculations reported here offer detailed free energy landscapes of melatonin embedded in model cell membranes and reveal microscopic information on its transition between free energy minima, including the location of relevant transition states, and provide clues on the role of cholesterol in the cellular absorption of small molecules.

A machine learning study of the two states model for lipid bilayer phase transitions

Machine learning algorithms can identify fluid and gel conformation states of individual lipid molecules.

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.

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.

Heat Capacity of DPPC/Cholesterol Mixtures: Comparison of Single Bilayers with Multibilayers and Simulations

The excess heat capacity (Δ C _p) of mixtures of dipalmitoylphosphatidylcholine (DPPC) and cholesterol (Chol) is examined in detail in large unilamellar vesicles (LUVs), both experimentally, using differential scanning calorimetry (DSC), and theoretically, using a three-state Ising model. The model postulates that DPPC can access three conformational states: gel, liquid-disordered (L_d), and liquid-ordered (L_o). The L_o state, however, is only available if coupled with interaction with an adjacent Chol. Δ C _p was calculated using Monte Carlo simulations on a lattice and compared to experiment. The DSC results in LUVs are compared with literature data on multilamellar vesicles (MLVs). The enthalpy change of the complete phase transition from gel to L_d is identical in LUVs and MLVs, and the melting temperatures ( T_m) are similar. However, the DSC curves in LUVs are significantly broader, and the maxima of Δ C _p are accordingly smaller. The parameters in the Ising model were chosen to match the DSC curves in LUVs and the nearest-neighbor recognition (NNR) data. The model reproduces the NNR data very well. It also reproduces the phase transition in DPPC, the freezing point depression induced by Chol, and the broad component of Δ C _p in DPPC/Chol LUVs. However, there is a sharp component, between 5 and 15 mol % Chol, that the model does not reproduce. The broad component of Δ C _p becomes dominant as Chol concentration increases, indicating that it involves melting of the L_o phase. Because the simulations reproduce this component, the conclusions regarding the nature of the phase transition at high Chol concentrations and the structure of the L_o phase are important: there is no true phase separation in DPPC/Chol LUVs. There are large domains of gel and L_o phase coexisting below T_m of DPPC, but above T_m the three states of DPPC are mixed with Chol, although clusters persist.

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.

Crowding-Induced Mixing Behavior of Lipid Bilayers: Examination of Mixing Energy, Phase, Packing Geometry, and Reversibility

In an effort to develop a general thermodynamic model from first-principles to describe the mixing behavior of lipid membranes, we examined lipid mixing induced by targeted binding of small (Green Fluorescent Protein (GFP)) and large (nanolipoprotein particles (NLPs)) structures to specific phases of phase-separated lipid bilayers. Phases were targeted by incorporation of phase-partitioning iminodiacetic acid (IDA)-functionalized lipids into ternary lipid mixtures consisting of DPPC, DOPC, and cholesterol. GFP and NLPs, containing histidine tags, bound the IDA portion of these lipids via a metal, Cu(2+), chelating mechanism. In giant unilamellar vesicles (GUVs), GFP and NLPs bound to the Lo domains of bilayers containing DPIDA, and bound to the Ld region of bilayers containing DOIDA. At sufficiently large concentrations of DPIDA or DOIDA, lipid mixing was induced by bound GFP and NLPs. The validity of the thermodynamic model was confirmed when it was found that the statistical mixing distribution as a function of crowding energy for smaller GFP and larger NLPs collapsed to the same trend line for each GUV composition. Moreover, results of this analysis show that the free energy of mixing for a ternary lipid bilayer consisting of DOPC, DPPC, and cholesterol varied from 7.9 × 10(-22) to 1.5 × 10(-20) J/lipid at the compositions observed, decreasing as the relative cholesterol concentration was increased. It was discovered that there appears to be a maximum packing density, and associated maximum crowding pressure, of the NLPs, suggestive of circular packing. A similarity in mixing induced by NLP1 and NLP3 despite large difference in projected areas was analytically consistent with monovalent (one histidine tag) versus divalent (two histidine tags) surface interactions, respectively. In addition to GUVs, binding and induced mixing behavior of NLPs was also observed on planar, supported lipid multibilayers. The mixing process was reversible, with Lo domains reappearing after addition of EDTA for NLP removal.

The use of zeta potential as a tool to study phase transitions in binary phosphatidylcholines mixtures

Temperature dependence of the zeta potential (ZP) is proposed as a tool to analyze the thermotropic behavior of unilamellar liposomes prepared from binary mixtures of phosphatidylcholines in the absence or presence of ions in aqueous suspensions. Since the lipid phase transition influences the surface potential of the liposome reflecting a sharp change in the ZP during the transition, it is proposed as a screening method for transition temperatures in complex systems, given its high sensitivity and small amount of sample required, that is, 70% less than that required in the use of conventional calorimeters. The sensitivity is also reflected in the pre-transition detection in the presence of ions. Plots of phase boundaries for these mixed-lipid vesicles were constructed by plotting the delimiting temperatures of both main phase transition and pre-transition vs. the lipid composition of the vesicle. Differential scanning calorimetry (DSC) studies, although subject to uncertainties in interpretation due to broad bands in lipid mixtures, allowed the validation of the temperature dependence of the ZP method for determining the phase transition and pre-transition temperatures. The system chosen was dipalmitoylphosphatidylcholine/dimyristoyl phosphatidylcholine (DMPC/DPPC), the most common combination in biological membranes. This work may be considered as a starting point for further research into more complex lipid mixtures with functional biological importance.

Use of DMPC and DSPC lipids for verapamil and naproxen permeability studies by PAMPA

Verapamil and naproxen Parallel Artificial Membrane Permeability Assay (PAMPA) permeability was studied using lipids not yet reported for this model in order to facilitate the quantification of drug permeability. These lipids are 1,2-distearoyl-sn-glycero-3-phosphatidylcholine (DSPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and an equimolar mixture of DMPC/DSPC, both in the absence and in the presence of 33.3 mol% of cholesterol. PAMPA drug permeability using the lipids mentioned above was compared with lecithin-PC. The results show that verapamil permeability depends on the kind of lipid used, in the order DMPC > DMPC/DSPC > DSPC. The permeability of the drugs was between 1.3 and 3.5-times larger than those obtained in lecithin-PC for all the concentrations of the drug used. Naproxen shows similar permeability than verapamil; however, the permeability increased with respect to lecithin-PC only when DMPC and DMPC/DSPC were used. This behavior could be explained by a difference between the drug net charge at pH 7.4. On the other hand, in the presence of cholesterol, verapamil permeability increases in all lipid systems; however, the relative verapamil permeability respect to lecithin-PC did not show any significant increase. This result is likely due to the promoting effect of cholesterol, which is not able to compensate for the large increase in verapamil permeability observed in lecithin-PC. With respect to naproxen, its permeability value and relative permeability respect lecithin-PC not always increased in the presence of cholesterol. This result is probably attributed to the negative charge of naproxen rather than its molecular weight. The lipid systems studied have an advantage in drug permeability quantification, which is mainly related to the charge of the molecule and not to its molecular weight or to cholesterol used as an absorption promoter.

Complex roles of hybrid lipids in the composition, order, and size of lipid membrane domains

Hybrid lipids (HL) are phospholipids with one saturated chain and one unsaturated chain. HL are hypothesized to act as linactants (i.e., 2D surfactants) in cell membranes, reducing line tension and creating nanoscopic lipid domains. Here we compare three hybrid lipids of different chain unsaturation (16:0-18:1PC (POPC), 16:0-18:2PC (PLPC), and 16:0-20:4PC (PAPC)) in their abilities to alter the composition, line tension, order, and compactness of lipid domains. We found that the liquid-ordered (Lo) and liquid-disordered (Ld) lipid domains in PAPC/di18:0PC(DSPC)/cholesterol and PLPC/DSPC/cholesterol mixtures are micrometer-sized, and only the POPC/DSPC/cholesterol system has nanoscopic domains. The results indicate that some HLs with polyunsaturated chains are not linactants, and the monounsaturated POPC displays both properties of weak linactants and "Ld-phase" lipids such as di18:1PC (DOPC). The obtained phase boundaries from giant unilamellar vesicles (GUV) show that both POPC and PLPC partition well in the Lo phases. Our MD simulations reveal that these hybrid lipids decrease the order and compactness of Lo domains. Thus, hybrid lipids distinguish themselves from other lipid groups in this combined "partitioning and loosening" ability, which could explain why the Lo domains of GUVs, which often do not contain HL, are more compact than the raft domains in cell membranes. Our line tension measurement and Monte Carlo simulation both show that even the monounsaturated POPC is a weak linactant with only modest ability to occupy domain boundaries and reduce line tension. A more important property of HLs is that they can reduce physical property differences of Lo and Ld bulk domains, which also reduces line tension at domain boundaries.

Quantifying disorder through conditional entropy: an application to fluid mixing

In this paper, we present a method to quantify the extent of disorder in a system by using conditional entropies. Our approach is especially useful when other global, or mean field, measures of disorder fail. The method is equally suited for both continuum and lattice models, and it can be made rigorous for the latter. We apply it to mixing and demixing in multicomponent fluid membranes, and show that it has advantages over previous measures based on Shannon entropies, such as a much diminished dependence on binning and the ability to capture local correlations. Further potential applications are very diverse, and could include the study of local and global order in fluid mixtures, liquid crystals, magnetic materials, and particularly biomolecular systems.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Phase separation and fluctuations in mixtures of a saturated and an unsaturated phospholipid

We describe quantitatively the interactions in a mixture of a saturated and an unsaturated phospholipid, and their consequences to the phase behavior at macroscopic and microscopic levels. This type of lipid-lipid interaction is fundamental in determining the organization and physical behavior of biological membranes. Mixtures of dipalmitoylphosphatidylcholine (DPPC) and 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) are examined in detail by multiple experimental approaches (differential scanning calorimetry (DSC), fluorescence resonance energy transfer, and confocal fluorescence microscopy) in combination with Monte Carlo simulations in a lattice. The interactions between all possible pairs of lipid species and states are determined by matching the heat capacity calculated through Monte Carlo simulations to that measured experimentally by DSC. Only for one other lipid system, a mixture between two saturated phosphatidylcholines, is a similar quantitative description available. The interactions in the two systems and different representations used to model them are compared. Phase separation occurs in DPPC/POPC at about the center of the phase diagram mapped by DSC, but not at all compositions and temperatures in the coexistence region. Close to the extremes of composition, the phase behavior is best described by large fluctuations. At the heat capacity maxima in the mixtures, the domain size distributions change remarkably; large domains disappear and cooperative fluctuations increase.

A statistical mechanical model of cholesterol/phospholipid mixtures: linking condensed complexes, superlattices, and the phase diagram

Despite extensive studies for nearly three decades, lateral distribution of molecules in cholesterol/phospholipid bilayers remains elusive. Here we present a statistical mechanical model of cholesterol/phospholipid mixtures that is able to rationalize almost every critical mole fraction (X(cr)) value previously reported for sterol superlattice formation as well as the observed biphasic changes in membrane properties at X(cr). This model is able to explain how cholesterol superlattices and cholesterol/phospholipid condensed complexes are interrelated. It gives a more detailed characterization of the LG(I)region (a broader region than the liquid disordered-liquid ordered mixed-phase region), which is considered to be a sludgelike mixture of fluid phase and aggregates of rigid clusters. A rigid cluster is formed by a cholesterol molecule and phospholipid molecules that are condensed to the cholesterol. Rigid clusters of similar size tend to form aggregates, in which cholesterol molecules are regularly distributed into superlattices. According to this model, the extent and type of sterol superlattices, thus the lateral distribution of the entire membrane, should vary with cholesterol mole fraction in a delicate, predictable, and nonmonotonic manner, which should have profound functional implications.

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.

Enhanced Lipid Diffusion and Mixing in Accelerated Molecular Dynamics

Accelerated molecular dynamics (aMD) is an enhanced sampling technique that expedites conformational space sampling by reducing the barriers separating various low-energy states of a system. Here, we present the first application of the aMD method on lipid membranes. Altogether, ∼1.5 μs simulations were performed on three systems: a pure POPC bilayer, a pure DMPC bilayer, and a mixed POPC:DMPC bilayer. Overall, the aMD simulations are found to produce significant speedup in trans–gauche isomerization and lipid lateral diffusion versus those in conventional MD (cMD) simulations. Further comparison of a 70-ns aMD run and a 300-ns cMD run of the mixed POPC:DMPC bilayer shows that the two simulations yield similar lipid mixing behaviors, with aMD generating a 2–3-fold speedup compared to cMD. Our results demonstrate that the aMD method is an efficient approach for the study of bilayer structural and dynamic properties. On the basis of simulations of the three bilayer systems, we also discuss the impact of aMD parameters on various lipid properties, which can be used as a guideline for future aMD simulations of membrane systems.

A simple thermodynamic model of the liquid-ordered state and the interactions between phospholipids and cholesterol

A theoretical model is proposed to describe the heat capacity function and the phase behavior of binary mixtures of phospholipids and cholesterol. The central idea is that the liquid-ordered state (L(o)) is a thermodynamic state or an ensemble of conformations of the phospholipid, characterized by enthalpy and entropy functions that are intermediate between those of the solid and the liquid-disordered (L(d)) states. The values of those thermodynamic functions are such that the L(o) state is not appreciably populated in the pure phospholipid, at any temperature, because either the solid or the L(d) state have much lower free energies. Cholesterol stabilizes the L(o) state by nearest-neighbor interactions, giving rise to the appearance of the L(o) phase. The model is studied by Monte Carlo simulations on a lattice with nearest-neighbor interactions, which are derived from experiment as much as possible. The calculated heat capacity function closely resembles that obtained by calorimetry. The phase behavior produced by the model is also in agreement with experimental data. The simulations indicate that separation between solid and L(o) phases occurs below the melting temperature of the phospholipid (T(m)). Above T(m), small L(d) and L(o) domains do exist, but there is no phase separation.

Near-critical fluctuations and cytoskeleton-assisted phase separation lead to subdiffusion in cell membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out Monte Carlo simulations of two-component lipid membranes. We find that near-critical fluctuations in the membrane lead to transient subdiffusion, while membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, we present a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion.

FCS diffusion laws in two-phase lipid membranes: determination of domain mean size by experiments and Monte Carlo simulations

Many efforts have been undertaken over the last few decades to characterize the diffusion process in model and cellular lipid membranes. One of the techniques developed for this purpose, fluorescence correlation spectroscopy (FCS), has proved to be a very efficient approach, especially if the analysis is extended to measurements on different spatial scales (referred to as FCS diffusion laws). In this work, we examine the relevance of FCS diffusion laws for probing the behavior of a pure lipid and a lipid mixture at temperatures below, within and above the phase transitions, both experimentally and numerically. The accuracy of the microscopic description of the lipid mixtures found here extends previous work to a more complex model in which the geometry is unknown and the molecular motion is driven only by the thermodynamic parameters of the system itself. For multilamellar vesicles of both pure lipid and lipid mixtures, the FCS diffusion laws recorded at different temperatures exhibit large deviations from pure Brownian motion and reveal the existence of nanodomains. The variation of the mean size of these domains with temperature is in perfect correlation with the enthalpy fluctuation. This study highlights the advantages of using FCS diffusion laws in complex lipid systems to describe their temporal and spatial structure.

Simulation of the lo-ld phase boundary in DSPC/DOPC/cholesterol ternary mixtures using pairwise interactions

Recently, a number of ternary phase diagrams of lipid mixtures have been constructed using various experimental techniques with a common goal of understanding the nature of lipid domains. An accurate experimental phase diagram can provide rich thermodynamic information and can also be used to extract molecular interactions using computer simulation. In this study, the liquid-ordered and liquid-disordered (l(o)-l(d)) phase boundary of DSPC/DOPC/Cholesterol ternary mixtures is simulated in a lattice model using pairwise interactions. The block composition distribution (BCD) technique was used to locate accurately the compositions of coexisting phases and thermodynamics tie-lines in the two-phase region, and the Binder ratio method was used to determine the phase boundary in the critical region. In simulations performed along a thermodynamic tie-line, the BCD method correctly samples the compositions as well as the relative amounts of coexisting phases, which is in excellent agreement with the lever rule. A "best-fit" phase boundary was obtained that has a top boundary closely resembling the experimental boundary. However, the width of the simulated two-phase region is significantly wider than the experimental one. The results show that pairwise interactions alone are not sufficient to describe the complexity of molecular interactions in the ternary lipid mixtures; more complex forms of interactions, possibly multibody interaction or domain interfacial energy, should be included in the simulation.

A liposomal formulation able to incorporate a high content of Paclitaxel and exert promising anticancer effect

A liposome formulation for paclitaxel was developed in this study. The liposomes, composed of naturally unsaturated and hydrogenated phosphatidylcholines, with significant phase transition temperature difference, were prepared and characterized. The liposomes exhibited a high content of paclitaxel, which was incorporated within the segregated microdomains coexisting on phospholipid bilayer of liposomes. As much as 15% paclitaxel to phospholipid molar ratio were attained without precipitates observed during preparation. In addition, the liposomes remained stable in liquid form at 4°C for at least 6 months. The special composition of liposomal membrane which could reduce paclitaxel aggregation could account for such a capacity and stability. The cytotoxicity of prepared paclitaxel liposomes on the colon cancer C-26 cell culture was comparable to Taxol. Acute toxicity test revealed that LD₅₀ for intravenous bolus injection in mice exceeded by 40 mg/kg. In antitumor efficacy study, the prepared liposomal paclitaxel demonstrated the increase in the efficacy against human cancer in animal model. Taken together, the novel formulated liposomes can incorporate high content of paclitaxel, remaining stable for long-term storage. These animal data also demonstrate that the liposomal paclitaxel is promising for further clinical use.

Rheological properties of a two phase lipid monolayer at the air/water interface: effect of the composition of the mixture

Many biologically relevant monolayers show coexistence of discrete domains of a long-range ordered condensed phase dispersed in a continuous, disordered, liquid-expanded phase. In this work, we determined the viscous and elastic components of the compressibility modulus and the shear viscosity of monolayers exhibiting phase coexistence with the aim at elucidating the contribution of each phase to the observed monolayer mechanical properties. To this purpose, mixed monolayers with different proportions of distearoylphosphatidylcholine (DSPC) and dimyristoylphosphatidylcholine (DMPC) were prepared and their rheological properties were analyzed. The relationship between the phase diagram of the mixture at 10 mN m(-1) and the rheological properties was studied. We found that the monolayer shear viscosity is highly dependent on the presence of domains and on the domain density. In turn, the monolayer compressibility is only influenced by the presence of domains for high domain densities. For monolayers that look homogeneous on the micrometer scale (DSPC amount lower that 23 mol %), all the analyzed rheological properties remain similar to those observed for pure DMPC monolayers, indicating that in this proportion range the DSPC molecules contribute as DMPC to the surface rheology in spite of having hydrocarbon chains four carbons longer.

Atomistic simulations of mixed-lipid bilayers in gel and fluid phases

The slow rate of diffusive mixing poses a challenge for molecular dynamics (MD) simulation studies of mixed-lipid bilayers. A mixed Monte Carlo-molecular dynamics (MC-MD) approach, which uses mutation moves to swap lipid types throughout the system within the semi-grand canonical ensemble, is here applied to a comparison of binary mixtures in the gel and liquid crystalline phases. The two lipid components modeled, distearoylphosphatidylcholine (DSPC) and dimyristoylphosphatidylcholine (DMPC), differ by four carbons in the lengths of their acyl tails and are investigated here at full hydration at a temperature (313 K) between their transition temperatures, where coexistence between a DSPC-rich gel phase and a DMPC-rich liquid crystalline phase is expected. An analysis of DSPC-DMPC mixtures in the gel phase indicates strong deviation from ideality in the thermodynamics of mixing, accompanied by a tendency of the shorter-tailed component DMPC to associate laterally and for DMPC headgroups to be displaced toward the bilayer midplane. The liquid crystal phase mixtures, in contrast, show more mild deviation from thermodynamically ideal mixing with no apparent tendency for similar lipids to cluster laterally and no difference in headgroup normal distribution profiles.

Raftlike mixtures of sphingomyelin and cholesterol investigated by solid-state 2H NMR spectroscopy

Sphingomyelin is a lipid that is abundant in the nervous systems of mammals, where it is associated with putative microdomains in cellular membranes and undergoes alterations due to aging or neurodegeneration. We investigated the effect of varying the concentration of cholesterol in binary and ternary mixtures with N-palmitoylsphingomyelin (PSM) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) using deuterium nuclear magnetic resonance ((2)H NMR) spectroscopy in both macroscopically aligned and unoriented multilamellar dispersions. In our experiments, we used PSM and POPC perdeuterated on the N-acyl and sn-1 acyl chains, respectively. By measuring solid-state (2)H NMR spectra of the two lipids separately in mixtures with the same compositions as a function of cholesterol mole fraction and temperature, we obtained clear evidence for the coexistence of two liquid-crystalline domains in distinct regions of the phase diagram. According to our analysis of the first moments M1 and the observed (2)H NMR spectra, one of the domains appears to be a liquid-ordered phase. We applied a mean-torque potential model as an additional tool to calculate the average hydrocarbon thickness, the area per lipid, and structural parameters such as chain extension and thermal expansion coefficient in order to further define the two coexisting phases. Our data imply that phase separation takes place in raftlike ternary PSM/POPC/cholesterol mixtures over a broad temperature range but vanishes at cholesterol concentrations equal to or greater than a mole fraction of 0.33. Cholesterol interacts preferentially with sphingomyelin only at smaller mole fractions, above which a homogeneous liquid-ordered phase is present. The reasons for these phase separation phenomena seem to be differences in the effects of cholesterol on the configurational order of the palmitoyl chains in PSM-d31 and POPC-d31 and a difference in the affinity of cholesterol for sphingomyelin observed at low temperatures. Hydrophobic matching explains the occurrence of raftlike domains in cellular membranes at intermediate cholesterol concentrations but not saturating amounts of cholesterol.

On the inner structure and topology of clusters in two-component lipid bilayers. Comparison of monomer and dimer Ising models

It has been shown on model and biological systems that membrane clusters can affect in-plane membrane reactions and can control biochemical reaction cascades. Clusters of two-component phospholipid bilayers have been simulated by two Ising-type lattice models: the monomer and the dimer model. In each model the plane of one layer of the bilayer is represented by a triangular lattice, each site of which is occupied by an acyl chain of either a component 1 or a component 2 lipid molecule. The dimer model assumes that pairs of acyl chains (lipid molecules) are permanently connected, forming dimers on the lattice, while in the case of the monomer model this covalent connection between acyl chains is ignored. Phase diagrams of two-component phospholipid bilayers were successfully calculated by both models. In this work, we use Monte Carlo techniques to calculate thermodynamic averages of global and local characteristics of the largest component 2 cluster (such as outer/inner perimeter, percolation, minimal linear size, and local density) and compare the results obtained by the two models. A new method is developed to characterize the inner structure of the clusters. Each point of a cluster is classified based on its shortest distance (or depth) from the cluster's outer perimeter. Then local cluster properties, such as density, are calculated as a function of the depth. The depth analysis reveals that toward the cluster interior the average density usually decreases in midsize clusters and remains constant in very large clusters. On the basis of the simulations the following typical cluster topologies are identified at different cluster sizes and cooperativity parameter values: (i) branch-like, (ii) circular, (iii) band-like, and (iv) planar.We did not find qualitative differences between the cluster structures in the dimer and monomer model. However, at the same cluster size and cooperativity parameter value the cluster of the dimer model is more compact. The cluster properties of the dimer model are different from that of the monomer model because of the lower mixing entropy and higher formation energy of an elementary inner island.

Thermodynamics of lipid interactions in complex bilayers

The mutual interactions between lipids in bilayers are reviewed, including mixtures of phospholipids, and mixtures of phospholipids and cholesterol (Chol). Binary mixtures and ternary mixtures are considered, with special emphasis on membranes containing Chol, an ordered phospholipid, and a disordered phospholipid. Typically the ordered phospholipid is a sphingomyelin (SM) or a long-chain saturated phosphatidylcholine (PC), both of which have high phase transitions temperatures; the disordered phospholipid is 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) or dioleoylphosphatidylcholine (DOPC). The unlike nearest-neighbor interaction free energies (omega(AB)) between lipids (including Chol), obtained by an variety of unrelated methods, are typically in the range of 0-400 cal/mol in absolute value. Most are positive, meaning that the interaction is unfavorable, but some are negative, meaning it is favorable. It is of special interest that favorable interactions occur mainly between ordered phospholipids and Chol. The interpretation of domain formation in complex mixtures of Chol and phospholipids in terms of phase separation or condensed complexes is discussed in the light of the values of lipid mutual interactions.

Critical temperatures and a critical chain length in saturated diacylphosphatidylcholines: calorimetric, ultrasonic and Monte Carlo simulation study of chain-melting/ordering in aqueous lipid dispersions

Chain-ordering/melting transition in a series of saturated diacylphosphatidylcholines (PCs) in aqueous dispersions have been studied experimentally (calorimetric and ultrasonic techniques) and theoretically (an Ising-like lattice model). The shape of the calorimetric curves was compared with the theoretical data and interpreted in terms of the lateral interactions and critical temperatures determined for each lipid studied. A critical chain length has been found (between 16 and 17 C-atoms per chain) which subdivides PCs into two classes with different phase behavior. In shorter lipids, the transition takes place above their critical temperatures meaning that this is an intrinsically continuous transition. In longer lipids, the transition occurs below the critical temperatures of the lipids, meaning that the transition is intrinsically discontinuous (first-order). This conclusion was supported independently by the ultrasonic relaxation sensitive to density fluctuations. Interestingly, it is this length that is the most abundant among the saturated chains in biological membranes.

Phase and mixing behavior in two-component lipid bilayers: a molecular dynamics study in DLPC/DSPC mixtures

Phase and mixing behavior of dilauroylphosphatidylcholine (DLPC)/distearoylphosphatidylcholine (DSPC) lipid mixtures are studied by molecular dynamics simulations with use of a coarse-grained model over a wide range of concentrations. The results reveal that phase transformations from the fluid to the gel state can be followed over a microsecond time scale. The changes in structure suggest regions of phase coexistence allowing us to outline the entire phase diagram for this lipid mixture using a molecular based model. We show that simulations yield good agreement with the experimental phase diagram. We also address the effect of macroscopic phase separation on the determination of the transition temperature, different leaflet composition, and finite size effects. This study may have implications on lateral membrane organization and the associated processes dependent on these membrane regions on different time and length scales.

Lateral diffusion of molecules in two-component lipid bilayer: a Monte Carlo simulation study

Lateral diffusion of membrane components makes possible any in-plane membrane reaction and has a key role in signaling in cell membranes. In this report the equilibrium lateral diffusion of intrinsic molecules in an equimolar DMPC/DSPC mixture is simulated using a thoroughly tested two-state model of two-component phospholipid bilayers. The model has been successful in calculating the excess heat capacity function, the most frequent center-to-center distances between DSPC clusters, and the fractal dimensions of gel clusters (Sugar, I. P., Thompson, T. E., Biltonen, R. L. Biophys. J. 1999, 76, 2099-2110). In the gel/fluid mixed phase region, a diffusing intrinsic molecule may change its state from fluid to gel (or from gel to fluid) at any time. A common characterization of the diffusion of intrinsic molecules is given by the simulated average first-passage time curves. We find that these curves can be described as power functions containing two parameters, alpha and beta, except near the percolation threshold of gel/fluid or compositional clusters. We find also that the intrinsic molecules are involved in approximately normal diffusion, i.e., beta approximately 2 in the extreme gel and fluid phase regions, while in the gel/fluid and gel/gel mixed phase regions the diffusion is anomalous, i.e., beta not equal 2. In the mixed phase regions, when the initial local state of the diffusing molecule is not specified, each component is involved in sub-diffusion (beta > 2). In the gel/fluid mixed phase region molecules situated initially inside a fluid cluster are involved in sub-diffusion, but DMPC molecules situated initially inside a gel cluster are involved in super-diffusion (beta < 2). The possibility of anomalous diffusion in membranes apparently arises because the diffusing molecule visits a variety of different environments characterized by its relative proximity to various membrane components. The diffusion is actually anomalous when the components of the bilayer are nonrandomly distributed. The deviation from random distribution is strongly correlated with beta. Similar to the results of the NMR experiments, the calculated relative diffusion coefficient continuously decreases in the gel/fluid mixed phase region with decreasing temperature. In apparent contradiction, diffusion measured by fluorescence recovery after photobleaching (FRAP) demonstrates the existence of a threshold temperature, below which long-range diffusion of FRAP probe molecules is essentially blocked. This threshold temperature is highly correlated with the percolation temperature of gel clusters.

Equilibrium distributions of dipalmitoyl phosphatidylcholine and dilauroyl phosphatidylcholine in a mixed lipid bilayer: atomistic semigrand canonical ensemble simulations

Conventional molecular dynamics (MD) simulations are seriously limited by the slow rate of diffusive mixing in their ability to predict lateral distributions of different lipid types within mixed-lipid bilayers using atomistic models. A method to overcome this limitation, using configuration-bias Monte Carlo (MC) "mutation" moves to transform lipids from one type to another in dynamic equilibrium, is demonstrated in binary fluid-phase mixtures of lipids whose tails differ in length by four carbons. The hybrid MC-MD method operates within a semigrand canonical ensemble, so that an equilibrium composition of the mixture is determined by a constant difference in chemical potential (Delta(mu)) chosen for the components. Within several nanoseconds, bilayer structures initiated as pure dipalmitoyl phosphatidylcholine (DPPC) or pure dilauroyl phosphatidylcholine (DLPC) converge to a common composition and structure in independent simulations conducted at the same Delta(mu). Trends in bilayer thickness, area per lipid, density distributions across the bilayer, and order parameters have been investigated at three mixture compositions and compared with results from the pure bilayers at 323 K. The mixtures showed a moderate increase in DPPC acyl tail sites crossing the bilayer midplane relative to pure DPPC. Correlations between lateral positions of the two lipid types within or across the bilayer were found to be weak or absent. While the lateral distribution is consistent with nearly ideal mixing, the dependence of composition on Delta(mu) indicates a positive excess free energy of mixing.

Investigation of domain formation in sphingomyelin/cholesterol/POPC mixtures by fluorescence resonance energy transfer and Monte Carlo simulations

We have recently proposed a phase diagram for mixtures of porcine brain sphingomyelin (BSM), cholesterol (Chol), and 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) on the basis of kinetics of carboxyfluorescein efflux induced by the amphipathic peptide δ-lysin. Although that study indicated the existence of domains, phase separations in the micrometer scale have not been observed by fluorescence microscopy in BSM/Chol/POPC mixtures, though they have for some other sphingomyelins (SM). Here we examine the same BSM/Chol/POPC system by a combination of fluorescence resonance energy transfer (FRET) and Monte Carlo simulations. The results clearly demonstrate that domains are formed in this system. Comparison of the FRET experimental data with the computer simulations allows the estimate of lipid-lipid interaction Gibbs energies between SM/Chol, SM/POPC, and Chol/POPC. The latter two interactions are weakly repulsive, but the interaction between SM and Chol is favorable. Furthermore, those three unlike lipid interaction parameters between the three possible lipid pairs are sufficient for the existence of a closed loop in the ternary phase diagram, without the need to involve multibody interactions. The calculations also indicate that the largest POPC domains contain several thousand lipids, corresponding to linear sizes of the order of a few hundred nanometers.

Thermodynamics of membrane domains

The concept of lipid rafts and the intense work toward their characterization in biological membranes has spurred a renewed interest in the understanding of domain formation, particularly in the case of cholesterol-containing membranes. The thermodynamic principles underlying formation of domains, rafts, or cholesterol/phospholipid complexes are reviewed here, along with recent work in model and biological membranes. A major motivation for this review was to present those concepts in a way appropriate for the broad readership that has been drawn to the field. Evidence from a number of different techniques points to the conclusion that lipid-lipid interactions are generally weak; therefore, in most cases, massive phase separations are not to be expected in membranes. On the contrary, small, dynamic lipid domains, possibly stabilized by proteins are the most likely outcome. The results on mixed lipid bilayers are used to discuss recent experiments in biological membranes. The clear indication is that proteins partition preferentially into fluid, disordered lipid domains, which is contrary to their localization in ordered, cholesterol/sphingomyelin rafts inferred from detergent extraction experiments on cell membranes. Globally, the evidence appears most consistent with a membrane model in which the majority of the lipid is in a liquid-ordered phase, with dispersed, small, liquid-disordered domains, where most proteins reside. Co-clustering of proteins and their concentration in some membrane areas may occur because of similar preferences for a particular domain but also because of simultaneous exclusion from other lipid phases. Specialized structures, such as caveolae, which contain high concentrations of cholesterol and caveolin are not necessarily similar to bulk liquid-ordered phase.

Nonequilibrium raftlike membrane domains under continuous recycling

We present a model for the kinetics of spontaneous membrane domain (raft) assembly that includes the effect of membrane recycling ubiquitous in living cells. We show that domains can have a broad power-law distribution with an average radius that scales with the 1/4 power of the domain lifetime when the line tension at the domain edges is large. For biologically reasonable recycling and diffusion rates, the average domain radius is in the tens of nm range, consistent with observations. This represents one possible link between signaling (involving rafts) and traffic (recycling) in cells. Finally, we present evidence that suggests that the average raft size may be the same for all scale-free recycling schemes.

Anomalous diffusion in a gel-fluid lipid environment: a combined solid-state NMR and obstructed random-walk perspective

Lateral diffusion is an essential process for the functioning of biological membranes. Solid-state nuclear magnetic resonance (NMR) is, a priori, a well-suited technique to study lateral diffusion within a heterogeneous environment such as the cell membrane. Moreover, restriction of lateral motions by lateral heterogeneities can be used as a means to characterize their geometry. The goal of this work is to understand the advantages and limitations of solid-state NMR exchange experiments in the study of obstructed lateral diffusion in model membranes. For this purpose, simulations of lateral diffusion on a sphere with varying numbers and sizes of immobile obstacles and different percolation properties were performed. From the results of these simulations, two-dimensional 31P NMR exchange maps and time-dependent autocorrelation functions were calculated. The results indicate that the technique is highly sensitive to percolation properties, total obstacle area, and, within certain limits, obstacle size. A practical example is shown, namely the study of the well-characterized DMPC-DSPC binary mixture. The comparison of experimental and simulated results yielded obstacle sizes in the range of hundreds of nanometers, therefore bridging the gap between previously published NMR and fluorescence recovery after photobleaching results. The method could also be applied to the study of membrane protein lateral diffusion in model membranes.

Temperature and pressure dependent growth and morphology of DMPC/DSPC domains studied by Brewster angle microscopy

In this work, the temperature and pressure dependent growth of domains in DMPC/DSPC monolayers at various molar ratios was studied by Brewster angle microscopy. Upon compression, roughly discoidal domains with some branching are formed. Further compression leads to an increase in both the number and the average size of the domains, which range between ca. 5 and 20 microm. The isobaric heating of the monolayers results in a gradual decrease of the domain size until their disappearance. The size and morphology of the domains depend not only on equilibrium parameters such as temperature, pressure and composition, but appear to be also strongly dependent on non-equilibrium parameters such as the rate of perturbation. The comparison between our results and those previously published for bilayers allows us to infer that the growth behaviour in monolayers can be qualitatively but not quantitatively extrapolated to bilayers.