A theoretical model for lipid monolayer phase transitions.

We present a theoretical model for the liquid-expanded to liquid-condensed phase transition observed in many phospholipid monolayer films. The total two-dimensional pressure in the model is the sum of the hydrocarbon chain pressure and the surface pressure. The hydrocarbon chain pressure is calculated in an exteded version of a model published earlier. The surface pressure results from a lowering of the surface tension in the monolayer over that of pure water, thus producing a force on a Langmuir float. When these two contributions are added, pi/A isotherms are obtained which have slope discontinuities very similar to those observed experimentally. The results indicate that a successful model for lipid phase behavior must consider the interactions between head groups and water as well as cooperative hydrocarbon chain melting.     

A theoretical model for lipid monolayer phase transitions

We present a theoretical model for the liquid-expanded to liquid-condensed phase transition observed in many phospholipid monolayer films. The total two-dimensional pressure in the model is the sum of the hydrocarbon chain pressure and the surface pressure. The hydrocarbon chain pressure is calculated in an extended version of a model published earlier. The surface pressure results from a lowering of the surface tension in the monolayer over that of pure water, thus producing a force on a Langmuir float. When these two contributions are added, $\text{π/A}$ isotherms are obtained which have slope discontinuities very similar to those observed experimentally. These results indicate that a successful model for lipid phase behavior must consider the interactions between head groups and water as well as cooperative hydrocarbon chain melting.     

A model for phase transitions in lipid bilayers and biological membranes

We wish to present an order-disorder model for the observed phase transitions in lipid bilayers and biological membranes. We show that the model may, under certain circumstances, exhibit two phase transitions, one corresponding to positional disordering of entire lipid molecules, and the other corresponding to orientational disordering in the hydrocarbon chains. We then give results of our numerical analysis of the model and compare them with experimental data. Shortcomings of the model and future directions for analyses of this type are also discussed.     

A theoretical model of phase transitions in human hand movements

Earlier experimental studies by one of us (Kelso, 1981a, 1984) have shown that abrupt phase transitions occur in human hand movements under the influence of scalar changes in cycling frequency. Beyond a critical frequency the originally prepared out-of-phase, antisymmetric mode is replaced by a symmetrical, in-phase mode involving simultaneous activation of homologous muscle groups. Qualitavely, these phase transitions are analogous to gait shifts in animal locomotion as well as phenomena common to other physical and biological systems in which new modes or spatiotemporal patterns arise when the system is parametrically scaled beyond its equilibrium state (Haken, 1983). In this paper a theoretical model, using concepts central to the interdisciplinary field of synergetics and nonlinear oscillator theory, is developed, which reproduces (among other features) the dramatic change in coordinative pattern observed between the hands.     

A theoretical model of phase transitions in the human brain

An experiment using a multisensor SQUID (superconducting quantum interference device) array was performed by Kelso and colleagues (1992) which combined information from three different sources: perception, motor response, and brain signals. When an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency in both motor behavior and brain signals. Qualitatively analogous transitions are known for physical and biological systems such as changes in the coordination of human hand movements (Kelso 1981, 1984). In this paper we develop a theoretical model based on methods from the interdisciplinary field of synergetics (Haken 1983, 1987) and nonlinear oscillator theory that reproduces the main experimental features very well and suggests a formulation of a fundamental biophysical coupling. Received: 8 September 1993     

A self-consistent chain model for the phase transitions in lipid bilayer membranes

We presented a mechanical model of a lipid bilayer membrane. The internal conformations of a polar head group and double hydrocarbon chains in a lipid molecule were described on the basis of the isomeric bond-rotation scheme. The thermodynamic properties of the lipid membranes were represented by a density matrix that described the rotational isomeric states of the head groups and chains. The parameters that determined the density matrix were obtained in the presence of the intermolecular interactions, which depend on the conformation of the molecules. The interchain interaction was given by the Kihara potential, which depends on the shape of the chains. The Coulomb interaction between the polar head groups and the lateral pressure were considered. The calculation was made for the three lipid molecules corresponding to DMPC, DPPC, and DSPC. The model agreed well with the following experimental results: the temperature, the latent heat of the gel-to-liquid crystalline phase transition, the temperature dependencies of (a) the intermolecular distance, (b) the number of gauche bonds in a hydrocarbon chain, (c) the order parameter for the bond orientation, (d) the volume of the membrane, (e) the thermal expansion coefficients, and (f) the birefringence.     

Phase diagrams for impure lipid systems. Application to lipid/anaesthetic mixtures

A physical model is presented to describe theoretically the temperature-dependent interactions of lipid bilayers with small molecules such as anaesthetics. Based on an earlier model, a triangular lattice in which each site is occupied by a single lipid chain is constructed and the small (anaesthetic) molecules are assumed to occupy interstitial sites in the centre of each lattice triangle. The phase characteristics of such lipid/anaesthetic mixtures are described in terms of the interaction parameters between lipid-lipid, lipid-anaesthetic and anaesthetic-anaesthetic molecules. Depending on the chemical nature of the interacting species the following three models are formulated: Model I. An interstitial model in which the only perturbation is in the head-group region of the bilayer and direct interactions between neighbouring anaesthetic molecules are taken into account. Model II. Here, only hydrophobic interactions between anaesthetics and lipids are considered. Model III. Both van der Waals' and coulombic interactions are taken into account. Phase diagrams for the three models are obtained by numerical calculation over a wide range of interaction parameters. It is shown that in all three models, lateral phase separation takes place due to the presence of anaesthetics. The heat of transition, however, is found to be virtually independent of the anaesthetic concentration.     

Phase diagrams and lipid domains in multicomponent lipid bilayer mixtures

Understanding the phase behavior of biological membranes is helped by the study of more simple systems. Model membranes that have as few as 3 components exhibit complex phase behavior that can be well described, providing insight for biological membranes. A number of different studies are in agreement on general findings for some compositional phase diagrams, in particular, those that model the outer leaflet of animal cell plasma membranes. These model mixtures include cholesterol, together with one high-melting lipid and one low-melting lipid. An interesting finding is of two categories of such 3-component mixtures, leading to what we term Type I and Type II compositional phase diagrams. The latter have phase regions of macroscopic coexisting domains of {Lα + Lβ + Lo} and of {Lα + Lo}, with domains resolved under the light microscope. Type I mixtures have the same phase coexistence regions, but the domains seem to be nanoscopic. Type I mixtures are likely to be better models for biological membranes.     

Fluorescence studies of chlorophyll a incorporated into lipid mixtures, and the interpretation of "phase" diagrams.

The fluorescence of chlorophyll a incorporated into liposomes of mixtures of phosphatidylcholines and phosphatidylethanolamines is reported. Plots of fluorescence intensities against temperature show breaks at characteristic temperatures which can be attributed to the onset and completion of solid phase lipid formation. These temperatures can be plotted to give diagrams analogous to the phase diagrams obtained for macroscopic systems. Complications due to "small-system effects" are discussed, and the experimental diagrams are compared with theoretical phase diagrams calculated for ideal mixing. Introduction of cholesterol leads to a reduction in fluorescence intensity, most readily explained by a 1:1 lipid:cholesterol interaction with exclusion of monomeric, fluorescent, chlorophyll a. Interaction of divalent ions with mixtures of dipalmitoyl phosphatidylcholine and dipalmitoyl phosphatidylserine leads to exclusion of chlorophyll a from the phosphatidylserine.     

Cold-induced lipid phase transitions

The structural organization of biological membranes is largely determined by the weak interactions existing between their components and between these components and their aqueous environment. These interactions are particularly sensitive to changes in temperature and hydration. The factors influencing membrane lipid phase behaviour are briefly reviewed and used to develop a phase-separation model describing the response of biological membranes to stress. The factors affecting the interaction of cryoprotectants with membrane lipids are explored and their role in the stabilization of membrane organization at low temperatures discussed. It is suggested that the basis of their protective action lies in an ability to preserve the balance of interactions between membrane components at low temperatures at a level similar to that existing under physiological conditions.     

Isothermal lipid phase transitions

In liotropic lipid systems phase transitions can be induced isothermally by changing the solvent concentration or composition; alternatively, lipid composition can be modified by (bio)chemical means. The probability for isothermal phase transitions increases with the decreasing transition entropy; it is proportional to the magnitude of the transition temperature shift caused by transformation-inducing system variation. Manipulations causing large thermodynamic effects, such as lipid (de)hydration, binding of protons or divalent ions and macromolecular adsorption, but also close bilayer approach are, therefore, likely to cause structural lipid change(s) at a constant temperature. Net lipid charges enhance the membrane susceptibility to salt-induced isothermal phase transitions; a large proportion of this effect is due to the bilayer dehydration, however, rather than being a consequence of the decreased Coulombic electrostatic interactions. Membrane propensity for isothermal phase transitions, consequently, always increases with the hydrophilicity of the lipid heads, as well as with the desaturation and shortening of the lipid chains. Upon a phase change at a constant temperature, some of the interfacially bound solutes (e.g. protons or calcium) are released in the solution. Membrane permeability and fusogenicity simultaneously increase. In mixed systems, isothermal phase transitions, moreover, may result in lateral phase separation. All this opens up ways for the involvement of isothermal phase transitions in the regulation of biological processes.     

An index of lipid phase diagrams

There is a growing awareness of the utility of lipid phase behavior data in studies of membrane-related phenomena. Such miscibility information is commonly reported in the form of temperature-composition (T-C) phase diagrams. The current index is a conduit to the relevant literature. It lists lipid phase diagrams, their components and conditions of measurement, and complete bibliographic information. The main focus of the index is on lipids of membrane origin where water is the dispersing medium. However, it also includes records on acylglycerols, fatty acids, cationic lipids, and detergent-containing systems. The miscibility of synthetic and natural lipids with other lipids, with water, and with biomolecules (proteins, nucleic acids, carbohydrates, etc.) and non-biological materials (drugs, anesthetics, organic solvents, etc.) is within the purview of the index. There are 2188 phase diagram records in the index, the bulk (81%) of which refers to binary (two-component) T-C phase diagrams. The remainder is made up of more complex (ternary, quaternary) systems, pressure-T phase diagrams, and other more exotic miscibility studies. The index covers the period from 1965 through to July, 2001.     

Distinguishing individual lipid headgroup mobility and phase transitions in raft-forming lipid mixtures with 31P MAS NMR

A model membrane system composed of egg sphingomyelin (SM), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and cholesterol was studied with static and magic angle spinning (31)P NMR spectroscopy. This model membrane system is of significant biological relevance since it is known to form lipid rafts. (31)P NMR under magic angle spinning conditions resolves the SM and DOPC headgroup resonances allowing for extraction of the (31)P NMR parameters for the individual lipid components. The isotropic chemical shift, chemical shift anisotropy, and asymmetry parameter can be extracted from the spinning side band manifold of the individual components that form liquid-ordered and liquid-disordered domains. The magnitude of the (31)P chemical shift anisotropy and the line width is used to determine headgroup mobility and monitor the gel-to-gel and gel-to-liquid crystalline phase transitions of SM as a function of temperature in these mixtures. Spin-spin relaxation measurements are in agreement with the line width results, reflecting mobility differences and some heterogeneities. It will be shown that the presence of DOPC and/or cholesterol greatly impacts the headgroup mobility of SM both above and below the liquid crystalline phase transition temperature, whereas DOPC displays only minor variations in these lipid mixtures.     

A theoretical framework of ecological phase transitions for characterizing tree-grass dynamics

This paper describes a theoretical framework of ecological phase transitions for modeling tree-grass dynamics and analyzing the shifts or phase transitions from one vegetation structure to another in the southern Texas landscape. This framework implements the integration of percolation theory, fractal geometry and phase transition theory as a method for modeling the spatial patterns of tree-grass dynamics, and nonlinear Markov non-equilibrium thermodynamic stability theory as a method for characterizing temporal tree-grass dynamics and phase transition. An historical sequence of aerial photographs at a Prosopis - thornscrub savanna parkland site in southern Texas was used to determine the parameters of the models. The preliminary analytical result accords well with current understanding and field survey of vegetation dynamics in the southern Texas landscape. The potential of such approaches and other relevant theories such as self-organized criticality and synergetics to vegetation dynamics is also discussed.     

Effect of lipid composition on the structure and theoretical phase diagrams of DC-Chol/DOPE-DNA lipoplexes

Lipoplexes constituted by calf-thymus DNA (CT-DNA) and mixed cationic liposomes consisting of varying proportions of the cationic lipid 3β-[N-(N',N'-dimethylaminoethane)-carbamoyl]cholesterol hydrochloride (DC-Chol) and the zwitterionic lipid, 1,2-dioleoyl-sn-glycero-3-phosphoetanolamine (DOPE) have been analyzed by means of electrophoretic mobility, SAXS, and fluorescence anisotropy experiments, as well as by theoretically calculated phase diagrams. Both experimental and theoretical studies have been run at several liposome and lipoplex compositions, defined in terms of cationic lipid molar fraction, α, and either the mass or charge ratios of the lipoplex, respectively. The experimental electrochemical results indicate that DC-Chol/DOPE liposomes, with a mean hydrodynamic diameter of around (120 ± 10) nm, compact and condense DNA fragments at their cationic surfaces by means of a strong entropically driven electrostatic interaction. Furthermore, the positive charges of cationic liposomes are compensated by the negative charges of DNA phosphate groups at the isoneutrality L/D ratio, (L/D)(?), which decreases with the cationic lipid content of the mixed liposome, for a given DNA concentration. This inversion of sign process has been also studied by means of the phase diagrams calculated with the theoretical model, which confirms all the experimental results. SAXS diffractograms, run at several lipoplex compositions, reveal that, irrespectively of the lipoplex charge ratio, DC-Chol/DOPE-DNA lipoplexes show a lamellar structure, L(α), when the cationic lipid content on the mixed liposomes α ≥ 0.4, while for a lower content (α = 0.2) the lipoplexes show an inverted hexagonal structure, H(II), usually related with improved cell transfection efficiency. A similar conclusion is reached from fluorescence anisotropy results, which indicate that the fluidity on liposome and lipoplexes membrane, also related with better transfection results, increases as long as the cationic lipid content decreases.     

A new method for the demonstration of phase transitions in lipid films

Monolayers of l-α-lecithin (β,γ-dimyristoyl), l-α-lecithin (β,γ-dipalmitoyl) and egg phosphatidylethanolamine were formed on a water surface at a sufficiently low temperature. The rate of evaporation of water was measured as a function ofincreasing temperature.In agreement with previous reports, the monomolecular films had a marked influence on the rate of evaporation of water, and the passage of water molecules through the monolayer was retarded.Using films in which phase transitions can be observed at a specific transition temperature [l-α-lecithin (β,γ-dimyristoyl) at 23°C and l-α-lecithin (β,γ-dipalmitoyl) at 41 °C], an unexpected decrease of water permeability was measured at this particular temperature. The retardation suggests that water transport through the film is hindered. It is thought that these results are best explained by an enhanced interaction between the water molecules and the chains of the lipid molecules above the phase transition temperature.