Modelling general anaesthesia as a first-order phase transition in the cortex

Since 1997 we have been developing a theoretical foundation for general anaesthesia. We have been able to demonstrate that the abrupt change in brain state brought on by anaesthetic drugs can be characterized as a first-order phase transition in the population-average membrane voltage of the cortical neurons. The theory predicts that, as the critical point of phase change into unconsciousness is approached, the electrical fluctuations in cortical activity will grow strongly in amplitude while slowing in frequency, becoming more correlated both in time and in space. Thus the bio-electrical change of brain-state has deep similarities with thermodynamic phase changes of classical physics. The theory further predicts the existence of a second critical point, hysteretically separated from the first, corresponding to the return path from comatose unconsciousness back to normal responsiveness. There is a steadily accumulating body of clinical evidence in support of all of the phase-transition predictions: low-frequency power surge in EEG activity; increased correlation time and correlation length in EEG fluctuations; hysteresis separation, with respect to drug concentration, between the point of induction and the point of emergence.     

Thermotropic and barotropic phase transitions of dilauroylphosphatidylcholine bilayer

The bilayer phase transitions of dilauroylphosphatidylcholine (DLPC), containing two linear acyl chains with 12 carbon atoms, were observed by means of differential scanning calorimetry (DSC) under ambient pressure and light transmittance under high pressure. When the heating scan for the DLPC bilayer in 50 wt.% aqueous ethylene glycol (EG) solution began at -30 degrees C after cold storage, the DSC thermogram showed two endothermic peaks at 1.7 and 4.5 degrees C, which correspond to the transition from the lamellar crystalline (Lc) phase to the intermediate liquid crystalline (Lx) phase and the transition from the Lx phase to the liquid crystalline (L) phase, respectively. Extremely large enthalpy change (32.9 kJ mol(-1)) is characteristic of the Lc/Lx phase transition. The DSC thermogram for the heating scan beginning from -10 degrees C showed a single endothermic peak with 9.2 kJ mol(-1) at -0.4 degrees C, which was assigned as the so-called main transition between the metastable ripple gel (P'(beta)) and metastable Lalpha phases. The DLPC bilayer under high pressure underwent three kinds of transitions in EG solution, whereas only one transition was observed in water under high pressure. The middle-temperature transition in EG solution could be assigned to the main transition because of its consistency with the main transition in water. The lower-temperature transition is probably assigned as transition from the Lc phase to the P'(beta) phase. Since the slope (dT/dp) of the Lc/P'(beta) phase boundary is smaller than that for the main transition, the Lc/P'(beta) phase boundary and the main transition curves crossed each other at 40 MPa on the temperature-pressure phase diagram. The higher-temperature transition in EG solution refers to the transition from the Lx phase to the Lalpha phase. The Lx phase disappeared at about 180 MPa, and the direct transition from the P'(beta) phase to the Lalpha phase was observed at high pressures above 180 MPa.     

Dye permeability at phase transitions in single and binary component phospholipid bilayers

By encapsulating a pH-sensitive dye, phenol red, in multilamellar liposomes of DMPC, DPPC and DMPC/DPPC mixtures, the permeability of these phospholipid bilayers to dye as a function of temperature has been studied. For both DMPC and DPPC liposomes, dye release begins well below the main gel-to-liquid-crystalline phase transition (24°C and 42°C, respectively) at temperatures corresponding to the onset of the pretransition (about 14°C and 36°C, respectively) with DPPC liposomes exhibiting a permeability anomaly at the main phase transition (42°C). The perturbation occurring in the bilayer structure that allows the release of encapsulated phenol red (approx. 5 Å diameter) is not sufficient to permit the release of encapsulated haemoglobin (approx. 20 Å diameter, negatively charged). In liposomes composed of a range of DMPC/DPPC mixtures, dye release commences at the onset of the pretransition range (determined by optical absorbance measurements) and increases with increasing temperature until the first appearance of liquid crystalline phase after which no further dye release occurs. Interestingly, the dye retaining properties of DMPC and DPPC liposomes well below their respective pretransition temperature regions are very different: DMPC liposomes release much encapsulated dye at incubation temperatures of 5°C whilst DPPC liposomes do not.     

Cell-size space effects on phase separation of binary polymer blends

Within living cells, a diverse array of biomolecules is present at high concentrations. To better understand how molecular behavior differs under such conditions (collectively described as macromolecular crowding), the crowding environment has been reproduced inside artificial cells. We have previously shown that the combination of macromolecular crowding and microscale geometries imposed by the artificial cells can alter the molecular behaviors induced by macromolecular crowding in bulk solutions. We have named the effect that makes such a difference the cell-size space effect (CSE). Here, we review the underlying biophysics of CSE for phase separation of binary polymer blends. We discuss how the cell-size space can initiate phase separation, unlike nano-sized spaces, which are known to hinder nucleation and phase separation. Additionally, we discuss how the dimensions of the artificial cell and its membrane characteristics can significantly impact phase separation dynamics and equilibrium composition. Although these findings are, of themselves, very interesting, their real significance may lie in helping to clarify the functions of the cell membrane and space size in the regulation of intracellular phase separation.     

An alternative explanation for phase transitions observed in quick frozen calcium cardiolipin solution

It is demonstrated that the phase changes reported for a quick frozen calcium cardiolipin solution containing CaCl₂ are virtually identical to those seen in pure CaCl₂. This introduces uncertainty as to whether the data in fact reflect the behavior of cardiolipin or of the associated CaCl₂.     

Lateral and transversal diffusion and phase transitions in erythrocyte membranes. An excimer fluorescence study

The lateral diffusion of the excimer-forming probe pyrene decanoic acid has been determined in erythrocyte membranes and in vesicles of the lipid extracts. The random walk of the probe molecules is characterized by their jump frequency, v_j, within the lipid matrix. At T = 35°C a value of v_j = 1.6 · 10³ s^?1 is found in erythrocyte membranes. A somewhat slower mobility is determined in vesicles prepared from lipid extracts of the erythrocyte membrane. Depending on structure and charge of the lipids we obtain jump frequencies between 0.8 · 10⁸ s^?1 and 1.5 · 10⁸ s^?1 at T = 35°C. The results are compared with jump frequencies yielded in model membranes.The mobility of molecules perpendicular to the membrane surface (transversal diffusion) is investigated. Erythrocyte ghosts doped with pyrene phosphatidylcholine were mixed with undoped ghosts in order to study the exchange kinetics of the probe molecule. A fast transfer between the outer layers of the ghost cells ($\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.6}\text{min at}\text{T = 37°}\text{C}$) is found. The exchange process between the inner and the outer layer of one erythrocyte ghost (flip-flop process) following this fast transfer occurs with a half-life time value of $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 100}\text{min at}\text{T = 37°}\text{C}$.The application of excimer-forming probes presumes a fluid state of the membrane. Therefore we investigated the phase transition behaviour using the excimer technique. Beside a thermotropic phase transition at T = 23°C and T = 33°C we observed an additional fluidity change at T = 38°C in erythrocyte ghosts. This transition is attached to a separation of the boundary lipid layer from the intrinsic proteins. No lipid phase transition is observed in liposomes from isolated extracts of the erythrocyte membrane with our methods.     

Phase transitions and cholesterol effects in phospholipid liposomes A new method employing the enhancement of the O-O vibronic transition of pyrene

The enhancement of the weakly allowed O-O vibronic transition in the fluorescence spectrum of the probe pyrene, which we previously showed to result from ground-state complexation with polar groups, has been shown in the present study to offer a new method for determining phase transition temperatures of liposomes and for studying the effects of cholesterol on the structure of their semipolar glycerol backbone. For dipalmitoylphosphatidylcholine it is found that small cholesterol contents (～9 mol%) induce an increase in the polarity of the microenvironment of the probe, whereas contents ?13 mol% induce a decrease in the polarity. The results are discussed in terms of cholesterol effects on the frequency and extent of thermally-induced structural fluctuations which, in turn, affect the penetration of the probe into the bilayer.     

Cholesterol affects divalent cation-induced fusion and isothermal phase transitions of phospholipid membranes

The influence of cholesterol on divalent cation-induced fusion and isothermal phase transitions of large unilamellar vesicles composed of phosphatidylserine (PS) was investigated. Vesicle fusion was monitored by the terbium/dipicolinic acid assay for the intermixing of internal aqueous contents, in the temperature range 10–40°C. The fusogenic activity of the cations decreases in the sequence Ca²⁺ > Ba²⁺ > Sr²⁺ Mg²⁺ for cholesterol concentrations in the range 20–40 mol%, and at all temperatures. Increasing the cholesterol concentration decreases the initial rate of fusion in the presence of Ca²⁺ and Ba²⁺ at 25°C, reaching about 50% of the rate for pure PS at a mole fraction of 0.4. From 10 to 25°C, Mg²⁺ is ineffective in causing fusion at all cholesterol concentrations. However, at 30°C, Mg²⁺-induced fusion is observed with vesicles containing cholesterol. At 40°C, Mg²⁺ induces slow fusion of pure PS vesicles, which is enhanced by the presence of cholesterol. Increasing the temperature also causes a monotonic increase in the rate of fusion induced by Ca²⁺, Ba²⁺ and Sr²⁺. The enhancement of the effect of cholesterol at high temperatures suggests that changes in hydrogen bonding and interbilayer hydration forces may be involved in the modulation of fusion by cholesterol. The phase behavior of PS/cholesterol membranes in the presence of Na⁺ and divalent cations was studied by differential scanning calorimetry. The temperature of the gel-liquid crystalline transition (T_m) in Na⁺ is lowered as the cholesterol content is increased, and the endotherm is broadened. Addition of divalent cations shifts the T_m upward, with a sequence of effectiveness Ba²⁺ > Sr²⁺ > Mg²⁺. The T_m of these complexes decreases as the cholesterol content is increased. Although the transition is not detectable for cholesterol concentrations of 40 and 50 mol% in the presence of Na⁺, Sr²⁺ or Mg²⁺, the addition of Ba²⁺ reveals endotherms with T_m progressively lower than that observed at 30 mol%. Although the presence of cholesterol appears to induce an isothermal gel-liquid crystalline transition by decreasing the T_m, this change in membrane fluidity does not enhance the rate of fusion, but rather decreases it. The effect of cholesterol on the fusion of PS/phosphatidylethanolamine (PE) vesicles was investigated by utilizing a resonance energy transfer assay for lipid mixing. The initial rate of fusion of PS/PE and PS/PE/cholesterol vesicles is saturated at high Mg²⁺ concentrations. With Ca²⁺, saturation is not observed for cholesterol-containing vesicles. The highest rate of fusion for both Ca²⁺- and Mg²⁺-induced fusion is observed with vesicles containing 30 mol% cholesterol.     

Effect of deuterium oxide on the thermodynamic quantities associated with phase transitions of phosphatidylcholine bilayer membranes

The bilayer phase transitions of three kinds of phospholipids, dipalmitoylphosphatidylcholine (DPPC), distearoylphosphatidylcholine (DSPC) and dihexadecylphosphatidylcholine (DHPC), in deuterium oxide (D₂O) and hydrogen oxide (H₂O) were observed by differential scanning calorimetry (DSC) under ambient pressure and light-transmittance measurements under high pressure. The DSC measurements showed that the substitution of H₂O by D₂O affected the pretransition temperatures and the main-transition enthalpies of all PC bilayers. The temperature-pressure phase diagrams for these PC bilayer membranes in both solvents were constructed by use of the data of light-transmittance measurements. Regarding the main transition of all PC bilayer membranes, there was no appreciable difference between the transition temperatures in D₂O and H₂O under high pressure. On the other hand, the phase transitions among the gel phases including the pretransition were significantly affected by the solvent substitution. The thermodynamic quantities of phase transitions for the PC bilayer membranes were evaluated and the differences in thermodynamic properties by the water substitution were considered from the difference of interfacial-free energy per molecule in the bilayer in both solvents. It was proved that the substitution of H₂O by D₂O causes shrinkage of the molecular area of phospholipid at bilayer interface due to the difference in bond strength between deuterium and hydrogen bonds and produces the great influence on the bilayer phase with the smaller area. Further, the induction of bilayer interdigitation in D₂O turned out to need higher pressures than in H₂O.     

Thermotropic and barotropic phase transitions of N-methylated dipalmitoylphosphatidylethanolamine bilayers

In order to understand the effect of polar head group modification on the thermotropic and barotropic phase behavior of phospholipid bilayer membranes, the phase transitions of dipalmitoylphosphatidylethanolamine (DPPE), dipalmitoylphosphatidyl-N-methylethanolamine (DPMePE), dipalmitoylphosphatidyl-N,N-dimethylethanolamine (DPMe₂PE) and dipalmitoylphosphatidylcholine (DPPC) bilayer membranes were observed by differential scanning calorimetry and high-pressure optical methods. The temperatures of the so-called main transition from the gel (L_β) or ripple gel (P_β′) phase to the liquid crystalline (L_α) phase were almost linearly elevated by applying pressure. The slope of the temperature-pressure boundary, dT/dp, was in the range of 0.220-0.264 K MPa⁻¹ depending on the number of methyl groups in the head group of lipids. The main-transition temperatures of N-methylated DPPEs decreased with increasing size of head group by stepwise N-methylation. On the other hand, there was no significant difference in thermodynamic quantities of the main transition between the phospholipids. With respect to the transition from the subgel (L_c) phase to the lamellar gel (L_β or L_β′) phase, the transition temperatures were also elevated by applying pressure. In the case of DPPE bilayer the L_c/L_β transition appeared at a pressure higher than 21.8 MPa. At a pressure below 21.8 MPa the L_c/L_α transition was observed at a temperature higher than the main-transition temperature. The main (L_β/L_α) transition can be recognized as the transformation between metastable phases in the range from ambient pressure to 21.8 MPa. Polymorphism in the gel phase is characteristic of DPPC bilayer membrane unlike other lipid bilayers used in this study: the L_β′, P_β′ and pressure-induced interdigitated gel (L_βI) phases were observed only in the DPPC bilayer. Regarding the bilayers of DPPE, DPMePE and DPMe₂PE, the interdigitation of acyl chain did not appear even at pressures as high as 200 MPa.     

Calorimetric studies of lipid phase transitions in native and heat-denatured membranes of beef heart submitochondrial particles

The lipids in beef heart submitochondrial particles undergo a broad reversible endothermic phase change centered at about −10°C. Following protein denaturation, a new reversible transition centered at about 20°C appears. The extracted lipids from these membranes exhibit thermal behavior that is essentially identical to the lipid transition in the intact membrane after protein denaturation. A role for this latent pool of higher-melting lipids is proposed.     

Membrane phase transitions and succinate oxidase activity in an extremely thermophilic bacterium

ESR and succinate oxidase activity were used to investigate the membrane phase-transitions of an extreme thermophile, Thermus T351, over an 80°C temperature range in whole cells, membrane particles, and extracted lipid suspension. Three phase transitions were observed using both techniques. These occurred at about 19°C, 39°C and 66°C. The transition at 19°C is unusual in that the Arrhenius plot for succinate oxidase is concave upwards, implying an increase in activation energy (E_a) with increased temperature.     

Thermotropic and barotropic phase transitions in bilayer membranes of ether-linked phospholipids with varying alkyl chain lengths

The bilayer phase transitions of a series of ether-linked phospholipids, 1,2-dialkylphosphatidylcholines containing linear saturated alkyl chain (C_n = 12, 14, 16 and 18), were observed by differential scanning calorimetry (DSC) under ambient pressure and light-transmittance measurements under high pressure. The thermodynamic quantities of the pre- and main-transitions for the ether-linked PC bilayer membranes were calculated and compared with those of a series of ester-linked PCs, 1,2-diacylphosphatidylcholines. The thermodynamic quantities of the main transition for the ether-linked PC bilayers showed distinct dependence on alkyl-chain length and were slightly different from those of the ester-linked PC bilayers. From the comparison of thermodynamic quantities for the main transition between both PC bilayers, we revealed that the attractive interaction in the gel phase for the ether-linked PC bilayers is weaker than that for the ester-linked PC bilayers. Regarding the pretransition, although changes in enthalpy and entropy for both PC bilayers were comparable to each other, the volume changes of the ether-linked PC bilayers roughly doubled those of the ester-linked PC bilayers. The larger volume change results from the smallest partial molar volume of the ether-linked PC molecule in the interdigitated gel phase. Further, we constructed the temperature-pressure phase diagrams for the ether-linked PC bilayers by using the phase-transition data. The region of the interdigitated gel phase in the phase diagrams was extended by applying pressure and by increasing the alkyl-chain length of the molecule. Comparing the phase diagrams with those for the ester-linked PC bilayers, it was proved that the phase behavior of the ester-linked PC bilayers under high temperature and pressure is almost equivalent to that of the ether-linked PC bilayers in the vicinity of ambient pressure.     

On a New Method to Study Drastic Change in Ecosystems

We describe a novel method to study drastic change in ecosystems, based on generic functions used in the study of phase transitions and related physical phenomena. We illustrate its use by applying it to the problem of shallow lake eutrophication, and express our results in terms of an interplay between phosphorus content in the water column and fluxes of this substance between the lake and both its biological community and its surroundings. We contrast our solution to this problem with a previous one based on the concept of resilience, and on bifurcation analysis of a dynamical equation that also involves phosphorus concentration and fluxes. We then suggest a generalized dynamical scheme incorporating the generic functions above, that reduces to our original method in the stationary condition, and allows in addition dealing with cyclic and chaotic regimes, as illustrated through a particular example.     

Thermal transitions in dimyristoylphosphatidyleholine foam bilayers

Thermal transitions in the system dimyristoylphosphatidylcholine/water/ethanol/sodium chloride were studied in the temperature range 10–31 °C. The water-ethanol dispersions were investigated by differential scanning calorimetry and the foam bilayers by the microinterferometric method for investigation of thin liquid films. Calorimetry showed that an increase in ethanol content (up to 47.5 vol.% — the concentration used in the experiments with foam bilayers) did not significantly influence the temperature of the main phase transition and led to the disappearance of the pretransition. The microinterferometric study of the foam bilayer thickness showed that there were two thermal transitions — at 13 and 23 °C. An Arrhenius type dependence was obtained for the critical concentration of dimyristoylphosphatidylcholine (DMPC) in the solution, which was necessary for the formation of the foam bilayer. A steep change in the slope of the linearized Arrhenius dependence was found at 23 °C. Values of the binding energy of a DMPC molecule in the foam bilayers were calculated using the hole-nucleation theory of stability and permeability of bilayers. It was proved that the phase transition at 23 °C was due to melting of the hydrocarbon tails of phospholipid molecules. The low-temperature phase transition was assumed to be due to a change in the tilt of the hydrocarbon tails. These experiments demonstrate for the first time the occurrence of phase transitions in foam bilayers. Correspondence to: D. Exerowa     

Bifurcations and phase transitions in spatially extended two-member hypercycles

Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analysed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.     

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.     

Lipid and protein composition and thermotropic lipid phase transitions in fatty acid-homogeneous membranes of Acholeplasma laidlawii B

The membrane composition and lipid physical properties have been systematically investigated as a function of fatty acid composition for a series of Acholeplasma laidlawii B membrane preparations made homogeneous in various fatty acids by growing cells on single fatty acids and avidin, a potent fatty acid synthetic inhibitor. The membrane protein molecular weight distribution is essentially constant as a function of fatty acid composition, but the lipid/protein ratio varies over a 2-fold range when different fatty acid growth supplements are used. The membrane lipid head-group composition varies somewhat under these conditions, particularly in the ratio of the two major neutral glycolipids. Differential thermal analytical investigations of the thermotropic phase transitions of various combinations of membrane components suggest that these compositional changes are unlikely to result in qualitative changes in the nature of lipid-protein or lipid-lipid interactions, although lesser changes of a quantitative nature probably do occur. The total lipids of membranes made homogeneous in their lipid fatty acyl chain composition exhibit sharper than normal gel-to-liquid-crystalline phase transitions of which midpoint temperatures correlate very well with the phase transition temperatures of synthetic hydrated phosphatidylcholines with like acyl chains. Our results indicate that using avidin and suitable fatty acids to grow A. laidlawii B, it is possible to manipulate the position and the sharpness of the membrane lipid phase transition widely and independently without causing major modifications in other aspects of the membrane composition. This fact makes the fatty acid-homogeneous A. laidlawii B membrane a very useful biological membrane preparation in which to study lipid physical properties and their functional consequences.     

Cation binding effects on the pH, thermal and urea denaturation transitions in alpha-lactalbumin

The binding of monovalent (Na+, K+) and divalent (Ca2+, Mg2+) cations to bovine alpha-lactalbumin at 20 and 37 degrees C has been studied by means of intrinsic protein fluorescence. The values of apparent binding constants for these ions obtained at 37 degrees C are about one order of magnitude lower than those measured at 20 degrees C. Urea and alkali (pH greater than 10) induce unfolding transitions which involve stable partially unfolded intermediates for all metal ion-bound forms of alpha-lactalbumin. Heating induces similar partially unfolded states. Nevertheless, the partially unfolded states induced by heating, urea, alkaline or acidic treatments are somewhat different in their tryptophan residue environment properties. The results have been interpreted in terms of a simple scheme of equilibria between metal-free and metal-bound forms in their native, partially unfolded and unfolded states. The scheme provides an approach to the quantitative interpretation of any transition equilibrium shift induced by a low molecular mass species able to be bound by a protein.     

Asymmetric antagonistic effects of an inhalation anesthetic and high pressure on the phase transition temperature of dipalmitoyl phosphatidic acid bilayers

The phase transition temperature ($\text{T}{}_{\mathrm{<mtext>t</mtext>}}$) of dipalmitoyl phosphatidic acid multilamellar liposomes is depressed 10°C by the inhalation anesthetic methoxyflurane at a concentration of 100 mmol/mol lipid. Application of 100 atm of helium pressure to pure phosphatidic acid liposomes increased $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$ only 1.5°C. However, application of 100 atm helium pressure to dipalmitoyl phosphatidic acid lipsomes containing 100 mmol methoxyflurane/mol lipid almost completely antagonized the effect of the anesthetic. A nonlinear pressure effect is observed. In a previous study, a concentration of 60 mmol methoxyflurane/mol dipalmitoyl phosphatidylcholine depressed $\text{T}{}_{\mathrm{<mtext>t</mtext>}}$ only 1.5°C, exhibiting a linear pressure effect. The completely different behavior in the charged membrane is best explained by extrusion of the anesthetic from the lipid phase.