A theoretical model of the temperature- and pressure-induced phase transition of phospholipid bilayers

A statistical thermodynamic model of phospholipid bilayers is developed. In the model, a new concept of a closely packed system is applied, i.e., a system of hard cylinders of equal radii, the radius being a function of the average number of gauche rotations in a hydrocarbon chain. Using this concept of a closely packed system, reasonable values are obtained for the change in specific volume at the order-disorder transition of lecithin bilayers. In addition to interactions between the lipid matrix and water molecules, between the head groups themselves and between hydrocarbon chains, as well as the intramolecular energy associated with chain conformation, the Hamiltonian of the membrane also includes the energy of the pressure field. Thus, the phase transition of phospholipid membranes induced not only by temperature hut also by hydrostatic pressure is described by this model simultaneously. In accordance with the experimental results, a linear relationship is obtained between the phase transition temperature and phase transition pressure. The other calculated phase transition properties of lecithin homologues. e.g., changes in enthalpy, surface area. thickness and gauche number per chain are in agreement with the available experimental data. The ratio of kink to interstitial conduction of bilayers is also estimated.     

Quantification of phase transitions of lipid mixtures from bilayer to non-bilayer structures: Model,experimental validation and implication on membrane fusion

Lipid bilayers provide a solute-proof barrier that is widely used in living systems. It has long been recognized that the structural changes of lipids during the phase transition from bilayer to non-bilayer have striking similarities with those accompanying membrane fusion processes. In spite of this resemblance, the numerous quantitative studies on pure lipid bilayers are difficult to apply to real membranes. One reason is that in living matter, instead of pure lipids, lipid mixtures are involved and there is currently no model that establishes the connection between pure lipids and lipid mixtures. Here, we make this connection by showing how to obtain (i) the short-range repulsion between bilayers made of lipid mixtures and, (ii) the pressure at which transition from bilayer phase to non-bilayer phases occur. We validated our models by fitting the experimental data of several lipid mixtures to the theoretical data calculated based on our model. These results provide a useful tool to quantitatively predict the behavior of complex membranes at low hydration.     

Lipid-cholesterol interactions in the P beta' phase. Application of a statistical mechanical model.

We describe a statistical mechanical model for lipid-cholesterol mixtures in the P beta' (ripple) phase of lipid bilayers. The model is a simple extension of an earlier model for the ripple phase in pure lipid bilayers. The extension consists of adding a degree of freedom to allow for the occupation of underlying lattice sites by cholesterol molecules, and adding a lipid-cholesterol interaction term to the model Hamiltonian. The interaction term was constructed based on numerical calculations of lipid-cholesterol energies for several different packing juxtapositions of the two molecules. Other than the lipid-cholesterol interactions, the extended model uses the same parameter set as the earlier model, so that comparison of the properties of the extended model with experimental data serves as a test of the validity of the original model. Properties of the model were calculated using the Monte Carlo method. Results are displayed as snapshots of the ripple configurations at different cholesterol concentrations. The spacing of the ripples increases with increasing cholesterol concentration and the rate of increase compares very well with experimental data. The success of this model supports the conclusion drawn earlier that frustration arising from anisotropic packing interactions is responsible for the ripple phase in lipid bilayers. In the extended model these packing interactions are responsible for the selective partitioning of cholesterol in the regions between the ripples.     

Liposomes, disks, and spherical micelles: aggregate structure in mixtures of gel phase phosphatidylcholines and poly(ethylene glycol)-phospholipids

Poly(ethylene glycol) (PEG) decorated lipid bilayers are widely used in biomembrane and pharmaceutical research. The success of PEG-lipid stabilized liposomes in drug delivery is one of the key factors for the interest in these polymer/lipid systems. From a more fundamental point of view, it is essential to understand the effect of the surface grafted polymers on the physical-chemical properties of the lipid bilayer. Herein we have used cryo-transmission electron microscopy and dynamic light scattering to characterize the aggregate structure and phase behavior of mixtures of PEG-lipids and distearoylphosphatidylcholine or dipalmitoylphosphatidylcholine. The PEG-lipids contain PEG of molecular weight 2000 or 5000. We show that the transition from a dispersed lamellar phase (liposomes) to a micellar phase consisting of small spherical micelles occurs via the formation of small discoidal micelles. The onset of disk formation already takes place at low PEG-lipid concentrations (<5 mol %) and the size of the disks decreases as more PEG-lipid is added to the lipid mixture. We show that the results from cryo-transmission electron microscopy correlate well with those obtained from dynamic light scattering and that the disks are well described by an ideal disk model. Increasing the temperature, from 25 degrees C to above the gel-to-liquid crystalline phase transition temperature for the respective lipid mixtures, has a relatively small effect on the aggregate structure.     

Calculation of intermolecular interaction strengths in the P beta' phase in lipid bilayers. Implications for theoretical models.

The existence of the P beta' phase in certain lipid bilayers is evidence that molecular interactions between lipids are capable of producing unusual large-scale structures at or near biological conditions. The problem of identifying the specific intermolecular interactions responsible for the structures requires construction of theoretical models capable of clear predictions of the observable consequences of postulated intermolecular interactions. To this end we have carried out a twofold modeling effort aimed at understanding the ripple phase. First, we have performed detailed numerical calculations of potential energies of interaction between pairs and triplets of lipid molecules having different chain tilt angles and relative vertical alignments. The calculations support the notion that chain tilting in the gel phase is a result of successive 3-5-A displacements of neighboring molecules perpendicular to the bilayer plane rather than long-range cooperative chain tilting. Secondly, we have used these results as a guide to formulate a new lattice model for lipid bilayer condensed phases. The new model is less complex than our earlier model and it includes interactions which are, based on the energy calculations, more likely to be responsible for the ripple phase. In a certain limit the model maps onto the chiral clock model, a model of much interest in condensed matter theory. In this limit the model exhibits a chain-tilted ordered phase followed by (as temperature increases) a modulated phase followed by a disordered phase. Within this limit we discuss the properties of the model and compare structures of the modulated phase exhibited by the model with experimental data for the P beta' phase in lipid bilayers.     

Seeing spots: complex phase behavior in simple membranes

Liquid domains in model lipid bilayers are frequently studied as models of raft domains in cell plasma membranes. Micron-scale liquid domains are easily produced in vesicles composed of ternary mixtures of a high melting temperature lipid, a low melting temperature lipid, and cholesterol. Here, we describe the rich phase behavior observed in binary and ternary systems. We then discuss experimental challenges inherent in mapping phase diagrams of even simple lipid systems. For example, miscibility behavior varies with lipid type, lipid ratio, lipid oxidation, and level of impurity. Liquid domains are often circular, but can become noncircular when membranes are near critical points. Finally, we reflect on applications of phase diagrams in model systems to rafts in cell membranes.     

Studies of short-wavelength collective molecular motions in lipid bilayers using high resolution inelastic X-ray scattering

We summarize a series of experimental results made with the newly developed high resolution X-ray scattering (IXS) instrument on two pure lipid bilayers, including dimyristoylphosphatidylcholine (DMPC) and dilauroylphosphatidylcholine (DLPC) in both gel and liquid crystal phases, and lipid bilayers containing cholesterol. By analyzing the IXS data based on the generalized three effective eigenmode model (GTEE), we obtain dispersion relations of the high frequency density oscillations (phonons) of lipid molecules in these bilayers. We then compare the dispersion relations of pure lipid bilayers of different chain lengths among themselves and the dispersion relations of pure lipid bilayers with those of the cholesterol containing bilayers. We also compare our experimental results with collective dynamics data generated by computer molecular dynamics (MD) simulations for dipalmitoylphosphatidylcholine (DPPC) in gel phase and DMPC in liquid crystal phase.     

Fourier transform infrared spectroscopic studies of the interaction of the antimicrobial peptide gramicidin S with lipid micelles and with lipid monolayer and bilayer membranes

We have utilized Fourier transform infrared spectroscopy to study the interaction of the antimicrobial peptide gramicidin S (GS) with lipid micelles and with lipid monolayer and bilayer membranes as a function of temperature and of the phase state of the lipid. Since the conformation of GS does not change under the experimental conditions employed in this study, we could utilize the dependence of the frequency of the amide I band of the central beta-sheet region of this peptide on the polarity and hydrogen-bonding potential of its environment to probe GS interaction with and location in these lipid model membrane systems. We find that the GS is completely or partially excluded from the gel states of all of the lipid bilayers examined in this study but strongly partitions into lipid micelles, monolayers, or bilayers in the liquid-crystalline state. Moreover, in general, the penetration of GS into zwitterionic and uncharged lipid bilayer coincides closely with the gel to liquid-crystalline phase transition of the lipid. However, GS begins to penetrate into the gel-state bilayers of anionic phospholipids prior to the actual chain-melting phase transition, while in cationic lipid bilayers, GS does not partition strongly into the liquid-crystalline bilayer until temperatures well above the chain-melting phase transition are reached. In the liquid-crystalline state, the polarity of the environment of GS indicates that this peptide is located primarily at the polar/apolar interfacial region of the bilayer near the glycerol backbone region of the lipid molecule. However, the depth of GS penetration into this interfacial region can vary somewhat depending on the structure and charge of the lipid molecule. In general, GS associates most strongly with and penetrates most deeply into more disordered bilayers with a negative surface charge, although the detailed chemical structure of the lipid molecule and physical organization of the lipid aggregate (micelle versus monolayer versus bilayer) also have minor effects on these processes.     

Calculations of the electrostatic potential adjacent to model phospholipid bilayers.

We used the nonlinear Poisson-Boltzmann equation to calculate electrostatic potentials in the aqueous phase adjacent to model phospholipid bilayers containing mixtures of zwitterionic lipids (phosphatidylcholine) and acidic lipids (phosphatidylserine or phosphatidylglycerol). The aqueous phase (relative permittivity, epsilon r = 80) contains 0.1 M monovalent salt. When the bilayers contain < 11% acidic lipid, the -25 mV equipotential surfaces are discrete domes centered over the negatively charged lipids and are approximately twice the value calculated using Debye-Hückel theory. When the bilayers contain > 25% acidic lipid, the -25 mV equipotential profiles are essentially flat and agree well with the values calculated using Gouy-Chapman theory. When the bilayers contain 100% acidic lipid, all of the equipotential surfaces are flat and agree with Gouy-Chapman predictions (including the -100 mV surface, which is located only 1 A from the outermost atoms). Even our model bilayers are not simple systems: the charge on each lipid is distributed over several atoms, these partial charges are non-coplanar, there is a 2 A ion-exclusion region (epsilon r = 80) adjacent to the polar headgroups, and the molecular surface is rough. We investigated the effect of these four factors using smooth (or bumpy) epsilon r = 2 slabs with embedded point charges: these factors had only minor effects on the potential in the aqueous phase.     

Calorimetric and molecular mechanics studies of the thermotropic phase behavior of membrane phospholipids.

In this review, we summarize the results of recent studies on the main phase transition behavior of phospholipid bilayers using the combined approaches of molecular mechanics simulations and high-resolution differential scanning calorimetry. Following a brief overview of the phase transition phenomenon exhibited by the lipid bilayer, we begin with the review by showing how several structural parameters underlying various phospholipids including phosphatidylcholine, phosphatidylethanolamine, and phosphatidylglycerol are defined and determined. Specifically, these structural parameters are obtained with saturated lipids packed in the gel-state bilayer using computer-based molecular mechanics calculations. Then we proceed to present the calorimetric data obtained with the lipid bilayer composed of saturated phospholipids as it undergoes the gel-to-liquid-crystalline phase transition in excess water. The general equations that can correlate the gel-to-liquid-crystalline phase transition temperature (T(m)) of the lipid bilayer with the structural parameters of the lipid molecule constituting the lipid bilayer are subsequently presented. From these equations, two tables of predicated T(m) values for well over 400 molecular species of saturated phosphatidylcholine and saturated phosphatidylethanolamine are generated. We further review the structure and chain-melting behavior of a large number of sn-1 saturated/sn-2 unsaturated phospholipids. Two T(m)-diagrams are shown, from which the effects of the number and the position of one to five cis carbon-carbon double bonds on T(m) can be viewed simultaneously. Finally, in the last part of this review, simple molecular models that have been invoked to interpret the characteristic T(m) trends exhibited by lipid bilayers composed of unsaturated lipids with different numbers and positions of cis carbon-carbon double bonds as seen in the T(m)-diagram are presented.     

Lipid composition regulates the conformation and insertion of the antimicrobial peptide maculatin 1.1

Antimicrobial peptides interact with cell membranes and their selectivity is contingent on the nature of the constituent lipids. Eukaryotic and bacterial membranes are comprised of different proportions of a range of lipid species with different physical properties. Hence, characterisation of antimicrobial peptides with respect to the magnitude of their interactions with model membranes of different lipid types is needed. Maculatin 1.1 is a short antimicrobial peptide secreted from the skin of several Australian tree-frog species. Circular dichroism spectroscopy (CD) was used to explore the interaction of maculatin 1.1 with a wide range of model membrane systems of different head group and acyl chain characteristics. For neutral phosphatidylcholine (PC), unlike anionic phospholipids, the magnitude of the peptide interactions was dependent on the length and degree of saturation of the constituent acyl chains. Oriented circular dichroism (OCD) data indicated that helical structure was likely promoted by peptide insertion into the hydrophobic core of PC bilayers. The addition of cholesterol (30% mol/mol) tended to decrease the membrane interaction of maculatin 1.1. Anionic lipids locked maculatin 1.1 via electrostatic interactions onto the surface of oriented bilayers as seen in OCD spectra. Furthermore, increasing the membrane curvature by reducing the vesicle radii only slightly reduced the proportion of helical structure in all systems by approximately 10%. The peptide-lipid interaction was strongly dependent on both the lipid chain length and head group, which highlights the importance of the lipid composition used to mimic different cell types. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Lipid bilayer arrays: Cyclically formed and measured

Artificial lipid bilayers have many uses. They are well established for scientific studies of reconstituted ion channels, used to host engineered pore proteins for sensing, and can potentially be applied in DNA sequencing. Droplet bilayers have significant technological potential for enabling many of these applications due to their compatibility with automation and array platforms. To further develop this potential, we have simplified the formation and electrical measurement of droplet bilayers using an apparatus that only requires fluid dispensation. We achieved simultaneous bilayer formation and measurement over a 32‐element array with ～80% yield and no operator input following fluid addition. Cycling these arrays resulted in the formation and measurement of 96 out of 120 possible bilayers in 80 minutes, a sustainable rate that could significantly increase with automation and greater parallelization. This turn‐key, high‐yield approach to making artificial lipid bilayers requires no training, making the capability of creating and measuring lipid bilayers and ion channels accessible to a much wider audience. In addition, this approach is low‐cost, parallelizable, and automatable, allowing high‐throughput studies of ion channels and pore proteins in lipid bilayers for sensing or screening applications.     

Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins

Biological membranes are complex and highly cooperative structures. To relate biomembrane structure to their biological function it is often necessary to consider simpler systems. Lipid bilayers composed of one or two lipid species, and with embedded proteins, provide a model system for biological membranes. Here we present a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the help of the dissipative particle dynamics simulation technique. Because hydrophobic matching is believed to be one of the main physical mechanisms regulating lipid-protein interactions in membranes, we considered proteins of different hydrophobic length (as well as different sizes). We studied the cooperative behavior of the lipid-protein system at mesoscopic time- and lengthscales. In particular, we correlated in a systematic way the protein-induced bilayer perturbation, and the lipid-induced protein tilt, with the hydrophobic mismatch (positive and negative) between the protein hydrophobic length and the pure lipid bilayer hydrophobic thickness. The protein-induced bilayer perturbation was quantified in terms of a coherence length, xi(P), of the lipid bilayer hydrophobic thickness profile around the protein. The dependence on temperature of xi(P), and the protein tilt-angle, were studied above the main-transition temperature of the pure system, i.e., in the fluid phase. We found that xi(P) depends on mismatch, i.e., the higher the mismatch is, the longer xi(P) becomes, at least for positive values of mismatch; a dependence on the protein size appears as well. In the case of large model proteins experiencing extreme mismatch conditions, in the region next to the so-called lipid annulus, there appears an undershooting (or overshooting) region where the bilayer hydrophobic thickness is locally lower (or higher) than in the unperturbed bilayer, depending on whether the protein hydrophobic length is longer (or shorter) than the pure lipid bilayer hydrophobic thickness. Proteins may tilt when embedded in a too-thin bilayer. Our simulation data suggest that, when the embedded protein has a small size, the main mechanism to compensate for a large hydrophobic mismatch is the tilt, whereas large proteins react to negative mismatch by causing an increase of the hydrophobic thickness of the nearby bilayer. Furthermore, for the case of small, peptidelike proteins, we found the same type of functional dependence of the protein tilt-angle on mismatch, as was recently detected by fluorescence spectroscopy measurements.     

Interactions between charged, uncharged, and zwitterionic bilayers containing phosphatidylglycerol.

Pressure vs. distance relationships have been obtained for phosphatidylglycerol bilayers, in both charged and uncharged states. Water was removed from the lipid multilayers by the application of osmotic pressures in the range of 0-2.7 x 10(9) dyn/cm2, and the distance between adjacent bilayers was obtained from Fourier analysis of lamellar x-ray diffraction data. For phosphatidylglycerol bilayers made electrically neutral either by lowering the pH or by adding equimolar concentrations of the positively charged lipid stearylamine, the pressure-distance data could be fit with a single exponential. The measured decay lengths were 1.1 A at low pH and 1.5 A with stearylamine, which are similar to decay lengths of the hydration pressure found for gel phases of other neutral bilayers. In addition, the magnitude of this repulsive pressure was proportional to the square of the Volta potential (equivalent to the dipole potential for electrically neutral bilayers) measured in monolayers in equilibrium with bilayers, in agreement with results previously found for the hydration pressure between phosphatidylcholine bilayers. For charged phosphatidylglycerol bilayers, the pressure-distance relation had two distinct regions. For bilayer separations greater than 10 A, the pressure-distance data had an exponential decay length (11 A) and a magnitude consistent with that expected for electrostatic repulsion from double-layer theory. For bilayer separations of 2-10 A, the pressure decayed much more rapidly with increasing bilayer separation (decay length less than 1 A). We interpret these data at low bilayer separations in terms of a combination of hydration repulsion and steric hindrance between the lipid head groups and the sodium ions trapped between apposing bilayers.     

Comparative study of molecular dynamics,diffusion, and permeability for ligands in biomembranes of different lipid composition

A comparative study of several model lipid bilayers of different composition, which included analysis of kinetic parameters of model lipid bilayers and permeability of bilayer membranes for small molecules, has been carried out. The conformity of results of numeric experiments to experimental data (structure of membrane lipid bilayers, lateral diffusion coefficients, and relative permeability of biomembranes for ligands) is discussed in the framework of a standard molecular dynamics protocol.     

Lipid tails modulate antimicrobial peptide membrane incorporation and activity

Membrane disrupting antimicrobial peptides (AMPs) are often amphipathic peptides that interact directly with lipid bilayers. AMPs are generally thought to interact mostly with lipid head groups, but it is less clear how the lipid alkyl chain length and saturation modulate interactions with membranes. Here, we used native mass spectrometry to measure the stoichiometry of three different AMPs—LL-37, indolicidin, and magainin-2—in lipid nanodiscs. We also measured the activity of these AMPs in unilamellar vesicle leakage assays. We found that LL-37 formed specific hexamer complexes but with different intermediates and affinities that depended on the bilayer thickness. LL-37 was also most active in lipid bilayers containing longer, unsaturated lipids. In contrast, indolicidin incorporated to a higher degree into more fluid lipid bilayers but was more active with bilayers with thinner, less fluid lipids. Finally, magainin-2 incorporated to a higher degree into bilayers with longer, unsaturated alkyl chains and showed more activity in these same conditions. Together, these data show that higher amounts of peptide incorporation generally led to higher activity and that AMPs tend to incorporate more into longer unsaturated lipid bilayers. However, the activity of AMPs was not always directly related to amount of peptide incorporated.     

Controlling Anomalous Diffusion in Lipid Membranes

Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.