The thermodynamic soliton theory of the nervous impulse and possible medical implications.

The textbook picture of nerve activity is that of a propagating voltage pulse driven by electrical currents through ion channel proteins, which are gated by changes in voltage, temperature, pressure or by drugs. All function is directly attributed to single molecules. We show that this leaves out many important thermodynamic couplings between different variables. A more recent alternative picture for the nerve pulse is of thermodynamic nature. It considers the nerve pulse as a soliton, i.e., a macroscopic excited region with properties that are influenced by thermodynamic variables including voltage, temperature, pressure and chemical potentials of membrane components. All thermodynamic variables are strictly coupled. We discuss the consequences for medical treatment in a view where one can compensate a maladjustment of one variable by adjusting another variable. For instance, one can explain why anesthesia can be counteracted by hydrostatic pressure and decrease in pH, suggest reasons why lithium over-dose may lead to tremor, and how tremor is related to alcohol intoxication. Lithium action as well as the effect of ethanol and the anesthetic ketamine in bipolar patients may fall in similar thermodynamic patterns. Such couplings remain obscure in a purely molecular picture. Other fields of application are the response of nerve activity to muscle stretching and the possibility of neural stimulation by ultrasound.

The stability of solitons in biomembranes and nerves.

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.

Melting of individual lipid components in binary lipid mixtures studied by FTIR spectroscopy, DSC and Monte Carlo simulations.

Monte Carlo (MC) simulations, Differential Scanning Calorimetry (DSC) and Fourier Transform InfraRed (FTIR) spectroscopy were used to study the melting behavior of individual lipid components in two-component membranes made of DMPC and DSPC. We employed Monte Carlo simulations based on parameters obtained from DSC profiles to simulate the melting of the different lipids as a function of temperature. The simulations show good agreement with the FTIR data recorded for deuterated and non-deuterated lipids, which demonstrates that the information on the differential melting of the individual components is already contained in the calorimetric profiles. In mixtures, both lipids melt over a wide temperature range. As expected, the lipid melting events of the lipid with the lower melting temperature occur on average at lower temperatures. The simulations also yield information on the lateral distribution of the lipids that is neither directly contained in the DSC nor in the FTIR data. In the phase coexistence region, liquid disordered domains are typically richer in the lower-melting-temperature lipid species.

Diffusion and partitioning of fluorescent lipid probes in phospholipid monolayers.

The pressure-dependent diffusion and partitioning of single lipid fluorophores in DMPC and DPPC monolayers were investigated with the use of a custom-made monolayer trough mounted on a combined fluorescence correlation spectroscopy (FCS) and wide-field microscopy setup. It is shown that lipid diffusion, which is essential for the function of biological membranes, is heavily influenced by the lateral pressure and phase of the lipid structure. Both of these may change dynamically during, e.g., protein adsorption and desorption processes. Using FCS, we measured lipid diffusion coefficients over a wide range of lateral pressures in DMPC monolayers and fitted them to a free-area model as well as the direct experimental observable mean molecular area. FCS measurements on DPPC monolayers were also performed below the onset of the phase transition (Pi < 5 mN/m). At higher pressures, FCS was not applicable for measuring diffusion coefficients in DPPC monolayers. Single-molecule fluorescence microscopy and differential scanning calorimetry clearly showed that this was due to heterogeneous partitioning of the lipid fluorophores in condensed phases. The results were compared with dye partitioning in giant lipid vesicles. These findings are significant in relation to the application of lipid fluorophores to study diffusion in both model systems and biological systems.

Phase-state dependent current fluctuations in pure lipid membranes.

Current fluctuations in pure lipid membranes have been shown to occur under the influence of transmembrane electric fields (electroporation) as well as a result from structural rearrangements of the lipid bilayer during phase transition (soft perforation). We demonstrate that the ion permeability during lipid phase transition exhibits the same qualitative temperature dependence as the macroscopic heat capacity of a D15PC/DOPC vesicle suspension. Microscopic current fluctuations show distinct characteristics for each individual phase state. Although current fluctuations in the fluid phase show spikelike behavior of short timescales (approximately 2 ms) with a narrow amplitude distribution, the current fluctuations during lipid phase transition appear in distinct steps with timescales of approximately 20 ms. We propose a theoretical explanation for the origin of timescales and permeability based on a linear relationship between lipid membrane susceptibilities and relaxation times near the phase transition.

Calcium electroporation and electrochemotherapy for cancer treatment: Importance of cell membrane composition investigated by lipidomics, calorimetry and in vitro efficacy.

Calcium electroporation is a novel anti-cancer treatment investigated in clinical trials. We explored cell sensitivity to calcium electroporation and electroporation with bleomycin, using viability assays at different time and temperature points, as well as heat calorimetry, lipidomics, and flow cytometry. Three cell lines: HT29 (colon cancer), MDA-MB231 (breast cancer), and HDF-n (normal fibroblasts) were investigated for; (a) cell survival dependent on time of addition of drug relative to electroporation (1.2 kV/cm, 8 pulses, 99 µs, 1 Hz), at different temperatures (37 °C, 27 °C, 17 °C); (b) heat capacity profiles obtained by differential scanning calorimetry without added calcium; (c) lipid composition by mass spectrometry; (d) phosphatidylserine in the plasma membrane outer leaflet using flow cytometry. Temperature as well as time of drug administration affected treatment efficacy in HT29 and HDF-n cells, but not MDA-MB231 cells. Interestingly the HT29 cell line displayed a higher phase transition temperature (approximately 20 °C) versus 14 °C (HDF-n) and 15 °C (MDA-MB231). Furthermore the HT29 cell membranes had a higher ratio of ethers to esters, and a higher expression of phosphatidylserine in the outer leaflet. In conclusion, lipid composition and heat capacity of the membrane might influence permeabilisation of cells and thereby the effect of calcium electroporation and electrochemotherapy.

Thermodynamics of lipid multi-lamellar vesicles in presence of sterols at high hydrostatic pressure.

We compared the effect of cholesterol at different concentration on the phase behaviour of DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) multilamellar vesicles. We used pressure perturbation differential scanning calorimetry (PPC) that studies a system on the whole by giving access to relevant thermodynamic quantities, and elastic incoherent neutron scattering (EINS) that probes local motions of a system at the atomic level by allowing extraction of dynamical parameters. PPC revealed that the volume expansion coefficient of DMPC and DMPC/Cholesterol samples with 13 and 25 mol% cholesterol is a linear function of the heat capacity measured by differential scanning calorimetry. Neutron backscattering spectroscopy showed that the mean square displacements of H atoms do exhibit an increase with temperature and a decrease under increasing pressure. Cholesterol added at concentrations of 25 and 50 mol% led to suppression of the main phase transition. Taking advantage of these results, the present study aims (i) to show that calorimetry and EINS using the Bicout and Zaccai model equally permit to get access to thermodynamic quantities characterizing pure DMPC and DMPC/cholesterol mixtures, thus directly confirming the theoretical method, and (ii) to validate our approach as function of temperature and of pressure, as both are equally important and complementary thermodynamic variables.

Solitary electromechanical pulses in lobster neurons.

Investigations of nerve activity have focused predominantly on electrical phenomena. Nerves, however, are thermodynamic systems, and changes in temperature and in the dimensions of the nerve can also be observed during the action potential. Measurements of heat changes during the action potential suggest that the nerve pulse shares many characteristics with an adiabatic pulse. First experiments in the 1980s suggested small changes in nerve thickness and length during the action potential. Such findings have led to the suggestion that the action potential may be related to electromechanical solitons traveling without dissipation. However, there have been no modern attempts to study mechanical phenomena in nerves. Here, we present ultrasensitive AFM recordings of mechanical changes on the order of 2-12Å in the giant axons of the lobster. We show that the nerve thickness changes in phase with voltage changes. When stimulated at opposite ends of the same axon, colliding action potentials pass through one another and do not annihilate. These observations are consistent with a mechanical interpretation of the nervous impulse.

Mechanical aspects of membrane thermodynamics. Estimation of the mechanical properties of lipid membranes close to the chain melting transition from calorimetry.

Changes in the internal energy of lipids with temperature are related to both lipid volume and area changes. Close to the chain melting transition of lipid bilayers volume and enthalpy fluctuations generally follow proportional functions. This makes it possible to calculate the relationship between membrane excess heat capacity with lipid volume, area compressibility and the membrane bending modulus, if the area fluctuations of the two monolayers are assumed to be mainly decoupled. Thus, compressibility and elasticity display pronounced maxima at the chain melting transition. These maxima can also be related to pronounced minima of the sound velocity in the lipid transition range, which were found in ultrasonic experiments. In the present study heat capacity profiles and volume changes were obtained. The compressibilities and the bending modulus were then deduced from the specific heat. The relevance of these findings for structural transitions and for the curvature dependence of heat capacities is discussed.

Phase transition from a gel to a fluid phase of cubic symmetry in dimyristoylphosphatidylcholine/myristic acid (1:2, mol/mol) bilayers.

Aqueous dispersions (pH 4.0) of a 2:1 (mol/mol) mixture of myristic acid with dimyristoylphosphatidylcholine undergo a sharp transition at 45-47 degrees C from a lamellar gel phase to a fluid phase which is optically isotropic. This fluid phase gives rise to 31P-NMR spectra, and 2H-NMR spectra of the chain-deuterated components, which are also isotropic. X-ray diffraction studies of the fluid phase at 49 degrees C, reveal reflections with spacings in the ratio square root of 2: (square root of 3): square root of 4: square root of 6: square root of 8, accompanied by a strong diffuse scatter. These reflections index on a cubic lattice of primitive space group Pn3 or Pn3m, or possibly the body-centered group Im3m, with a lattice constant of 21.2 nm. The dimensions of the phase are consistent with a structure composed of two systems of tetrahedrally (octahedrally) oriented inverted lipid cylinders, found for other cubic lipid phases with Pn3m (Im3m) symmetry. At higher temperatures the cubic phase gradually converts, with increasing temperature, to a coexisting inverted hexagonal phase.

Histogram method to obtain heat capacities in lipid monolayers, curved bilayers, and membranes containing peptides.

Lipid monolayer chain melting transitions were simulated using a two-state Doniach model, and experimental melting profiles of lipid vesicles were analyzed. We sampled the information of a Monte Carlo simulation into a single broad histogram containing complete information about the distribution of states. The information of the monolayer histogram was first used to calculate the melting behavior of a bilayer constructed from two uncoupled monolayers. We then fitted calorimetric heat profiles of various preparations of dipalmitoyl phosphatidylcholine vesicles. This analysis was extended to lipid bilayers. A fixed mean bilayer curvature was shown to result in a broadening of bilayer melting profiles. We furthermore used the histogram method to obtain the chain melting behavior of simple lipid-peptide mixtures.

Lipid ion channels.

The interpretation of electrical phenomena in biomembranes is usually based on the assumption that the experimentally found discrete ion conduction events are due to a particular class of proteins called ion channels while the lipid membrane is considered being an inert electrical insulator. The particular protein structure is thought to be related to ion specificity, specific recognition of drugs by receptors and to macroscopic phenomena as nerve pulse propagation. However, lipid membranes in their chain melting regime are known to be highly permeable to ions, water and small molecules, and are therefore not always inert. In voltage-clamp experiments one finds quantized conduction events through protein-free membranes in their melting regime similar to or even undistinguishable from those attributed to proteins. This constitutes a conceptual problem for the interpretation of electrophysiological data obtained from biological membrane preparations. Here, we review the experimental evidence for lipid ion channels, their properties and the physical chemistry underlying their creation. We introduce into the thermodynamic theory of membrane fluctuations from which the lipid channels originate. Furthermore, we demonstrate how the appearance of lipid channels can be influenced by the alteration of the thermodynamic variables (e.g., temperature, pressure, tension and chemical potentials) in a coherent description that is free of parameters. This description leads to pores that display dwell times closely coupled to the fluctuation lifetime via the fluctuation-dissipation theorem. Drugs as anesthetics and neurotransmitters are shown to influence the channel likelihood and their lifetimes in a predictable manner. We also discuss the role of proteins in influencing the likelihood of lipid channel formation.

Critical behavior of 2,6-dimethylpyridine-water: measurements of specific heat, dynamic light scattering, and shear viscosity.

The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.

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.

Protein surface-distribution and protein-protein interactions in the binding of peripheral proteins to charged lipid membranes.

The binding of native cytochrome c to negatively charged lipid dispersions of dioleoyl phosphatidylglycerol has been studied over a wide range of ionic strengths. Not only is the strength of protein binding found to decrease rapidly with increasing ionic strength, but also the binding curves reach an apparent saturation level that decreases rapidly with increasing ionic strength. Analysis of the binding isotherms with a general statistical thermodynamic model that takes into account not only the free energy of the electrostatic double layer, but also the free energy of the surface distribution of the protein, demonstrates that the apparent saturation effects could arise from a competition between the out-of-plane binding reaction and the lateral in-plane interactions between proteins at the surface. It is found that association with nonlocalized sites results in binding isotherms that display the apparent saturation effect to a much more pronounced extent than does the Langmuir adsorption isotherm for binding to localized sites. With the model for nonlocalized sites, the binding isotherms of native cytochrome c can be described adequately by taking into account only the entropy of the surface distribution of the protein, without appreciable enthalpic interactions between the bound proteins. The binding of cytochrome c to dioleoyl phosphatidylglycerol dispersions at a temperature at which the bound protein is denatured on the lipid surface, but is nondenatured when free in solution, has also been studied. The binding curves for the surface-denatured protein differ from those for the native protein in that the apparent saturation at high ionic strength is less pronounced. This indicates the tendency of the denatured protein to aggregate on the lipid surface, and can be described by the binding isotherms for nonlocalized sites only if attractive interactions between the surface-bound proteins are included in addition to the distributional entropic terms. Additionally, it is found that the binding capacity for the native protein is increased at low ionic strength to a value that is greater than that for complete surface coverage, and that corresponds more closely to neutralization of the effective charge (determined from the ionic strength dependence), rather than of the total net charge, on the protein. Electron spin resonance experiments with spin-labeled lipids indicate that this different mode of binding arises from a penetration or disturbance of the bilayer surface by the protein that may alleviate the effects of in-plane interactions under conditions of strong binding.

Investigation of secondary and tertiary structural changes of cytochrome c in complexes with anionic lipids using amide hydrogen exchange measurements: an FTIR study.

The structure of cytochrome c bound to anionic lipid membranes composed of dimyristoyl, dipalmitoyl, or dioleoyl phosphatidylglycerols, or of bovine heart cardiolipin, has been investigated by Fourier transform infrared spectroscopy. Only small changes in secondary structure, as registered by the amide I band of cytochrome c, were observed upon binding at temperatures below that of denaturation of the protein, and these were not coupled to the thermotropic phase transitions of the lipid. The denaturation temperature of the protein decreased by approximately 25-30 degrees upon binding, in a progression which correlated with that of the lipid phase transition temperatures, being approximately 7 degrees lower for complexes with dioleoyl than with dipalmitoyl phosphatidylglycerol. Large changes in the amide proton exchange characteristics, as monitored by the spectral shifts in the amide I band of the protein in D2O, were observed on binding cytochrome c to the lipid membranes. For the slowly exchanging population, the amide deuteration rates of the free protein were nearly independent of temperature, whereas those of the bound protein increased by up to two orders of magnitude over the temperature range from 10 to 40 degrees C. In addition, the extent of exchange differed between the bound and unbound protein. A structural transition in the bound protein was detected as a discontinuous step in Arrhenius plots of the deuterium exchange rates which occurred at a temperature in the region of 22 to 29 degrees C, depending on the lipid, far below that of denaturation. The temperature of this transition was determined by the physical state of the lipid, being 7 degrees lower for the lipids in the fluid state than for those in the gel state, and, for complexes with dimyristoyl phosphatidylglycerol, occurred at an intermediate temperature, being controlled by the lipid chain-melting transition at 27-28 degrees C. These results provide evidence for a coupling of the tertiary structure of the membrane-bound protein with the physical state of the membrane lipids.

Quantitative conformational analysis of cytochrome c bound to phospholipid vesicles studied by resonance Raman spectroscopy.

Resonance Raman spectra have been recorded from ferri-cytochrome c bound to phospholipid vesicles composed of dimyristoyl phosphatidylglycerol (DMPG), dioleoyl phosphatidylglycerol (DOPG) or dioleoyl phosphatidylglycerol-dioleoyl phosphatidylcholine (DOPG-DOPC) (70:30 mole/mole). Lipid binding induces very significant conformational changes in the protein molecule. The resonance Raman spectra differ in their content of bands originating from two different conformational species, I and II, of the protein, and from two different spin and coordination states of the heme in conformation II. Data of sufficiently high precision were obtained that the spectra of the individual species could be quantitated by a constraint interactive fitting routine using single Lorentzian profiles. In the high frequency, or marker band region (1200 to 1700 cm-1), the frequencies, half widths and relative intensities of the individual bands could be estimated from previous surface enhanced resonance Raman measurements on cytochrome c adsorbed on a silver electrode. These were then further optimized to yield both the spectral parameters and relative contents of the different species. In the low frequency, or fingerprint, region (200 to 800 cm-1), the spectral parameters of the individual species were obtained from difference spectra derived by sequential subtraction between the spectra of ferri-cytochrome c in the three different lipid systems, using the relative proportions of the species derived from the marker band region. These parameters were then subsequently refined by iterative optimization. The optimized spectral parameters in both frequency regions for the six-coordinated low spin states I and II, and for the five-coordinated high spin state II are presented.(ABSTRACT TRUNCATED AT 250 WORDS)

Binary phase diagram of hydrated dimyristoylglycerol-dimyristoylphosphatidylcholine mixtures.

The thermotropic phase behavior of binary mixtures of dimyristoylphosphatidylcholine with dimyristoyl glycerol (DMPC-DMG) has been studied in aqueous dispersion by using differential scanning calorimetry and spin label electron spin resonance spectroscopy. Phase identifications have been made by means of (31)P nuclear magnetic resonance spectroscopy and x-ray diffraction. The binary phase diagram of DMPC-DMG mixtures displays three regions corresponding to the existence of compounds (C1 and C2, respectively) with approximately 1:1 and 1:2 mol/mol DMPC:DMG stoichiometries. The first region displays immiscibility between DMPC and C1 in the low temperature lamellar phase and miscibility of the components in the fluid phase that is lamellar. The second region displays immiscibility between C1 and C2 in the low temperature phase that is lamellar, whereas the fluid phase is of the inverted hexagonal type (H(II)). The third region displays immiscibility between C2 and DMG in the low temperature phase that is lamellar, whereas the fluid phase is isotropic. The presence of immiscible DMG in the low temperature phase of the third region is indicated by hysteresis in the temperature scans corresponding to conversion between the stable and metastable crystalline polymorphs. Analysis of the first region of the phase diagram using regular solution theory further demonstrates the existence of a DMPC:DMG complex with approximately 1:1 stoichiometry and provides parameters for the nonideality of mixing in the fluid phase.

Insertion and pore formation driven by adsorption of proteins onto lipid bilayer membrane-water interfaces.

We describe the binding of proteins to lipid bilayers in the case for which binding can occur either by adsorption to the lipid bilayer membrane-water interface or by direct insertion into the bilayer itself. We examine in particular the case when the insertion and pore formation are driven by the adsorption process using scaled particle theory. The adsorbed proteins form a two-dimensional "surface gas" at the lipid bilayer membrane-water interface that exerts a lateral pressure on the lipid bilayer membrane. Under conditions of strong intrinsic binding and a high degree of interfacial converge, this pressure can become high enough to overcome the energy barrier for protein insertion. Under these conditions, a subtle equilibrium exists between the adsorbed and inserted proteins. We propose that this provides a control mechanism for reversible insertion and pore formation of proteins such as melittin and magainin. Next, we discuss experimental data for the binding isotherms of cytochrome c to charged lipid membranes in the light of our theory and predict that cytochrome c inserts into charged lipid bilayers at low ionic strength. This prediction is supported by titration calorimetry results that are reported here. We were furthermore able to describe the observed binding isotherms of the pore-forming peptides endotoxin (alpha 5-helix) and of pardaxin to zwitterionic vesicles from our theory by assuming adsorption/insertion equilibrium.