Monte Carlo simulations of membranes: phase transition of small unilamellar dipalmitoylphosphatidylcholine vesicles

The excitable fluid mosaic

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10-20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.¹.

Simulation of fluid/gel phase equilibrium in lipid vesicles

Simulation of single component dipalmitoylphosphatidylcholine (DPPC) coarse-grained DRY-MARTINI lipid vesicles of diameter 10 nm (1350 lipids), 20 nm (5100 lipids) and 40 nm (17 600 lipids) is performed using statistical temperature molecular dynamics (STMD), to study finite size effects upon the order-disorder gel/fluid transition. STMD obtains enhanced sampling using a generalized ensemble, obtaining a flat energy distribution between upper and lower cutoffs, with little computational cost over canonical molecular dynamics. A single STMD trajectory of moderate length is sufficient to sample 20+ transition events, without trapping in the gel phase, and obtain well averaged properties. Phase transitions are analyzed via the energy-dependence of the statistical temperature, T_S(U). The transition temperature decreases with decreasing diameter, in agreement with experiment, and the transition changes from first order to borderline first-second order. The size- and layer-dependence of the structure of both stable phases, and of the pathway of the phase transition, are determined. It is argued that the finite size effects are primarily caused by the disruption of the gel packing by curvature. Inhomogeneous states with faceted gel patches connected by unusual fluid seams are observed at high curvature, with visually different structure in the inner and outer layers due to the different curvatures. Thus a simple physical picture describes phase transitions in nanoscale finite systems far from the thermodynamic limit.

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.

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.

Modeling order-disorder transition in Low-Density Lipoprotein

Low Density Lipoproteins (LDL) undergo a reversible order-disorder thermal transition close to biological temperature due to cooperative melting of the cholesteryl esters (CE) in the core of the LDL particle. We have noticed that chain-chain interactions between CE molecules are responsible for the stability of the ordered smectic phase; thus, we formulated a simple "coarse-grained" two-state model to describe the melting process. In this model only nearest neighbor interactions are allowed. On the basis of these assumptions we performed Metropolis Monte Carlo (MC) simulation in order to obtain the heat capacity curve. The resulting profile reveals well-known features of the systems with a finite size.

Sorting of lipidated peptides in fluid bilayers: a molecular-level investigation

Nearest-neighbor recognition (NNR) measurements have been made for two lipidated forms of GlyCys, interacting with analogues of cholesterol and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) in the liquid-ordered (l(o)) and liquid-disordered (l(d)) phases. Interaction free energies that have been determined from these measurements have been used in Monte Carlo simulations to quantify the distribution of the peptides between liquid-ordered and liquid-disordered regions. These simulations have shown that significant differences in the lipid chains have a very weak influence on the partitioning of the peptide between these two phases. They have also revealed an insensitivity of the peptide partition coefficient, K(p), to the size of the l(o) and l(d) domains that are present. In a broader context, these findings strongly suggest that the sorting of peripheral proteins in cellular membranes via differential lipidation may be more subtle than previously thought.

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.

Monte Carlo simulation of protein-induced lipid demixing in a membrane with interactions derived from experiment

Lipid domain formation induced by annexin was investigated in mixtures of phosphatidylcholine (PC), phosphatidylserine (PS), and cholesterol (Chol), which were selected to mimic the inner leaflet of a eukaryotic plasma membrane. Annexins are ubiquitous and abundant cytoplasmic, peripheral proteins, which bind to membranes containing PS in the presence of calcium ions (Ca(2+)), but whose function is unknown. Prompted by indications of interplay between the presence of cholesterol in PS/PC mixtures and the binding of annexins, we used Monte Carlo simulations to investigate protein and lipid domain formation in these mixtures. The set of interaction parameters between lipids and proteins was assigned by matching experimental observables to corresponding variables in the calculations. In the case of monounsaturated phospholipids, the PS-PC and PC-Chol interactions are weakly repulsive. The interaction between protein and PS was determined based on experiments of annexin binding to PC/PS mixtures in the presence of Ca(2+). Based on the proposal that PS and cholesterol form a complex in model membranes, a favorable PS-Chol interaction was postulated. Finally, protein-protein favorable interactions were also included, which are consistent with observations of large, two-dimensional, regular arrays of annexins on membranes. Those net interactions between pairs of lipids, proteins and lipids, and between proteins are all small, of the order of the average kinetic energy. We found that annexin a5 can induce formation of large PS domains, coincident with protein domains, but only if cholesterol is present.

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.

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.

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.

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.

Lateral organization of cholesterol molecules in lipid-cholesterol assemblies

We present results of an off-lattice simulation of a two-component planar system, as a model for lateral organization of cholesterol molecules in lipid-cholesterol assemblies. We explore the existence of "superlattice" structures even in fluid systems, in the absence of an underlying translational long-range order, and study their coupling to hexatic or bond-orientational order. We discuss our results in context of geometric superlattice theories and "condensation complexes" in understanding a variety of experiments in artificial lipid-cholesterol assemblies.

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.

Relaxation kinetics of lipid membranes and its relation to the heat capacity

We investigated the relaxation behavior of lipid membranes close to the chain-melting transition using pressure jump calorimetry with a temperature accuracy of approximately 10(-3) K. We found relaxation times in the range from seconds up to about a minute, depending on vesicular state. The relaxation times are within error proportional to the heat capacity. We provide a statistical thermodynamics theory that rationalizes the close relation between heat capacity and relaxation times. It is based on our recent finding that enthalpy and volume changes close to the melting transition are proportional functions.

Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer-size gel clusters co-exist with one large gel cluster of size comparable with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increases with increasing cluster size, S, according to a power function of 0.00427 x S(1.3); 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(-0.0072xS)). By means of the equations describing the average geometry of the clusters the process of the association of clusters is investigated.

Association of a fluorescent amphiphile with lipid bilayer vesicles in regions of solid-liquid-disordered phase coexistence

The effects of solid-fluid phase separations on the kinetics of association of a single-chain fluorescent amphiphile were investigated in two different systems: pure DMPC (dimyristoylphosphatidylcholine) and a 1:1 mixture of DMPC and DSPC (distearoylphosphatidylcholine). In pure DMPC vesicles, solid (s) and fluid (l(d)) phases coexist at the phase transition temperature, T(m), whereas a 1:1 mixture of DMPC and DSPC shows a stable s-l(d) phase separation over a large temperature interval. We found that in single-component bilayers, within the main phase transition, the experimental kinetics of association are clearly not single-exponential, the deviation from that function becoming maximal at the T(m). This observation can be accounted for by a rate of desorption that is slower than desorption from either fluid or solid phases, leaving the rates of insertion unchanged, but a treatment in terms of stable fluid and solid domains may not be adequate for the analysis of the association of an amphiphile with pure DMPC vesicles at the T(m). In DMPC/DSPC mixtures with solid-fluid phase coexistence, association occurs overall faster than expected based on phase composition. The observed kinetics can be described by an increase in the rate of insertion, leaving the desorption rates unchanged. The fast kinetics of insertion of the amphiphile into two-phase bilayers in two-component vesicles is attributed to a more rapid insertion into defect-rich regions, which are most likely phase boundaries between solid and fluid domains. A two-component mixture of lipids that shows a stable phase separation between l(d)-s phases over a large temperature interval thus behaves very differently from a single-component bilayer at the T(m), with respect to insertion of amphiphiles.

A model for the lipid pretransition: coupling of ripple formation with the chain-melting transition

Below the thermotropic chain-melting transition, lipid membrane c(P) traces display a transition of low enthalpy called the lipid pretransition. It is linked to the formation of periodic membrane ripples. In the literature, these two transitions are usually regarded as independent events. Here, we present a model that is based on the assumption that both pretransition and main transition are caused by the same physical effect, namely chain melting. The splitting of the melting process into two peaks is found to be a consequence of the coupling of structural changes and chain-melting events. On the basis of this concept, we performed Monte Carlo simulations using two coupled monolayer lattices. In this calculation, ripples are considered to be one-dimensional defects of fluid lipid molecules. Because lipids change their area by approximately 24% upon melting, line defects are the only ones that are topologically possible in a triangular lattice. The formation of a fluid line defect on one monolayer leads to a local bending of the membrane. Geometric constraints result in the formation of periodic patterns of gel and fluid domains. This model, for the first time, is able to predict heat capacity profiles, which are comparable to the experimental c(P) traces that we obtained using calorimetry. The basic assumptions are in agreement with a large number of experimental observations.

Network formation of lipid membranes: triggering structural transitions by chain melting

Phospholipids when dispersed in excess water generally form vesicular membrane structures. Cryo-transmission and freeze-fracture electron microscopy are combined here with calorimetry and viscometry to demonstrate the reversible conversion of phosphatidylglycerol aqueous vesicle suspensions to a three-dimensional structure that consists of extended bilayer networks. Thermodynamic analysis indicates that the structural transitions arise from two effects: (i) the enhanced membrane elasticity accompanying the lipid state fluctuations on chain melting and (ii) solvent-associated interactions (including electrostatics) that favor a change in membrane curvature. The material properties of the hydrogels and their reversible formation offer the possibility of future applications, for example in drug delivery, the design of structural switches, or for understanding vesicle fusion or fission processes.

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

In this paper, we describe a relatively simple lattice model of a two-component, two-state phospholipid bilayer. Application of Monte Carlo methods to this model permits simulation of the observed excess heat capacity versus temperature curves of dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) mixtures as well as the lateral distributions of the components and properties related to these distributions. The analysis of the bilayer energy distribution functions reveals that the gel-fluid transition is a continuous transition for DMPC, DSPC, and all DMPC/DSPC mixtures. A comparison of the thermodynamic properties of DMPC/DSPC mixtures with the configurational properties shows that the temperatures characteristics of the configurational properties correlate well with the maxima in the excess heat capacity curves rather than with the onset and completion temperatures of the gel-fluid transition. In the gel-fluid coexistence region, we also found excellent agreement between the threshold temperatures at different system compositions detected in fluorescence recovery after photobleaching experiments and the temperatures at which the percolation probability of the gel clusters is 0.36. At every composition, the calculated mole fraction of gel state molecules at the fluorescence recovery after photobleaching threshold is 0.34 and, at the percolation threshold of gel clusters, it is 0.24. The percolation threshold mole fraction of gel or fluid lipid depends on the packing geometry of the molecules and the interchain interactions. However, it is independent of temperature, system composition, and state of the percolating cluster.

The relationship between compositional phase separation and vesicle morphology: implications for the regulation of phospholipase A2 by membrane structure

The action of phospholipase A2 (PLA2) on bilayer substrates causes the accumulation of reaction products, lyso-phospholipid and fatty acid. These reaction products and the phospholipid substrate generate compositional heterogeneities and then apparently phase separate when a critical mole fraction of reaction product accumulates in the membrane. This putative phase separation drives an abrupt morphologic rearrangement of the vesicle, which may be in turn responsible for modulating the activity of PLA2. Here we examine the thermotropic properties of the phase-separated lipid system formed upon hydrating colyophilized reaction products (1:1 palmitic acid:1-palmitoyl-2-lyso-phosphatidylcholine) and substrate, dipalmitoylphosphatidylcholine. The mixture forms structures which are not canonical spherical vesicles and appear to be disks in the gel-state. The main gel-liquid transition of these structures is hysteretic. This hysteresis is apparent using several techniques, each selected for its sensitivity to different aspects of a lipid aggregate's structure. The thermotropic hysteresis reflects the coupling between phase separation and changes in vesicle morphology.

Simulation of the gel-fluid transition in a membrane composed of lipids with two connected acyl chains: application of a dimer-move step

Phospholipids have been treated as dimers on a hexagonal lattice, and a move has been introduced that allows the dimers to move and change their orientation on the lattice. Simulations have been performed in which phospholipid chains have been treated as being either independent or infinitely coupled thermodynamically with regard to their conformational state. Both types of simulation have reproduced well experimental heat-capacity curves of dipalmitoyl phosphatidylcholine small unilamellar vesicles. Apart from a different gel-fluid interaction parameter and a different number of unlike nearest-neighbor contacts, most of the averages and thermodynamic quantities were essentially the same in the two types of simulation. These results indicate that the transition is not first order and validate those of previous Monte Carlo simulations that have neglected the dimeric nature of phospholipids in the sense that they show that for the thermotropic transition the approximation of phospholipids as monomers is valid.

A Monte Carlo simulation study of protein-induced heat capacity changes and lipid-induced protein clustering

Monte Carlo simulations were used to describe the interaction of peripheral and integral proteins with lipids in terms of heat capacity profiles and protein distribution. The simulations were based on a two-state model for the lipid, representing the lipid state as being either gel or fluid. The interaction between neighboring lipids has been taken into account through an unlike nearest neighbor free energy term delta omega, which is a measure of the cooperativity of the lipid transition. Lipid/protein interaction was considered using the experimental observation that the transition midpoints of lipid membranes are shifted upon protein binding, a thermodynamic consequence of different binding constants of protein with fluid or gel lipids. The difference of the binding free energies was used as an additional parameter to describe lipid-protein interaction. The heat capacity profiles of lipid/protein complexes could be well described for both peripheral and integral proteins. Binding of proteins results in a shift and an asymmetric broadening of the melting profile. The model results in a coexistence of gel and fluid lipid domains in the proximity of the thermotropic transition. As a consequence, bound peripheral proteins aggregate in the temperature range of the lipid transition. Integral proteins induce calorimetric melting curves that are qualitatively different from that of peripheral proteins and aggregate in either gel or liquid crystalline lipid phase. The results presented here are in good agreement with calorimetric experiments on lipid-protein complexes and have implementations for the functional control of proteins.