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.

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.

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.

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.

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.

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.

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.

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.

The effect of lipid demixing on the electrostatic interaction of planar membranes across a salt solution.

We study the effect of lipid demixing on the electrostatic interaction of two oppositely-charged membranes in solution, modeled here as an incompressible two-dimensional fluid mixture of neutral and charged mobile lipids. We calculate, within linear and nonlinear Poisson-Boltzmann theory, the membrane separation at which the net electrostatic force between the membranes vanishes, for a variety of different system parameters. According to Parsegian and Gingell, contact between oppositely-charged surfaces in an electrolyte is possible only if the two surfaces have exactly the same charge density (sigma(1) = -sigma(2)). If this condition is not fulfilled, the surfaces can repel each other, even though they are oppositely charged. In our model of a membrane, the lipidic charge distribution on the membrane surface is not homogeneous and frozen, but the lipids are allowed to freely move within the plane of the membrane. We show that lipid demixing allows contact between membranes even if there is a certain charge mismatch, /sigma(1)/ not equal /sigma(2)/, and that in certain limiting cases, contact is always possible, regardless of the value of sigma(1)/sigma(2) (if sigma(1)/sigma(2) < 0). We furthermore find that of the two interacting membranes, only one membrane shows a major rearrangement of lipids, whereas the other remains in exactly the same state it has in isolation and that, at zero-disjoining pressure, the electrostatic mean-field potential between the membranes follows a Gouy-Chapman potential from the more strongly charged membrane up to the point of the other, more weakly charged membrane.

Analyzing heat capacity profiles of peptide-containing membranes: cluster formation of gramicidin A.

The analysis of peptide and protein partitioning in lipid membranes is of high relevance for the understanding of biomembrane function. We used statistical thermodynamics analysis to demonstrate the effect of peptide mixing behavior on heat capacity profiles of lipid membranes with the aim to predict peptide aggregation from c(P)-profiles. This analysis was applied to interpret calorimetric data on the interaction of the antibiotic peptide gramicidin A with lipid membranes. The shape of the heat capacity profiles was found to be consistent with peptide clustering in both gel and fluid phase. Applying atomic force microscopy, we found gramicidin A aggregates and established a close link between thermodynamics data and microscopic imaging. On the basis of these findings we described the effect of proteins on local fluctuations. It is shown that the elastic properties of the membrane are influenced in the peptide environment.

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.

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.

Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate-n-octanol

At temperatures between 30 degrees C and 58 degrees C we have recorded the heat capacity of the ionic ethylammonium nitrate-n-octanol mixture of critical composition and also of the constituents. Different samples of the binary mixture have been measured with its upper critical demixing temperature T(c) varying between 41.04 degrees C and 46.87 degrees C, depending on small traces of water within the liquid under test. Almost identical heat capacity profiles result if the data are displayed as a function of the temperature distance to the actual T(c) value. In the homogeneous phase the critical contribution exhibits power-law behavior with the critical exponent alpha=0.11 as theoretically predicted for nonionic liquids and in conformity with our understanding of the ionic criticality as being asymptotically Ising like. The noncritical background part of the heat capacity can be related to the heat capacities of the constituents using a simple mixture relation. In the two-phase regime a series of almost perfectly reproducible events is found which may be taken to indicate the existence of nonequilibrium intermediate states in the ethylammonium nitrate-n-octanol system.

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

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

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

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

FTIR-Spectroscopy of multistranded coiled coil proteins.

Coiled coils of different order were investigated using infrared (IR) spectroscopy. Recently, we demonstrated that dimeric coiled coils display unique vibrational spectra with at least three separable bands instead of only one band of a classical alpha-helix in the amide I region. This was attributed to a distortion of the helical structure by the supercoil bending, giving rise to bands that are not observed in the undistorted helix. Here, we investigated coiled coils forming trimers, tetramers, and pentamers. These higher order coiled coils, in general, possess larger superhelical pitches, resulting in a smaller helical distortion. We found that all coiled coils studied, including the native dimeric GCN4 leucine zipper and its variants leading to parallel trimers and tetramers as well as the rod portions of fibritin (parallel trimer), alpha-actinin (antiparallel spectrin type trimer), and COMP (parallel pentamer), displayed the typical three band pattern of the coiled coil amide I spectra. However, the separation of these three bands and their positional deviation from the classical alpha-helical band position was correlated to the extent of the helical distortion as reflected by the pitch values of the supercoils. The most pronounced spectral anomaly was found for the tropomyosin dimer with a reported helical pitch of 137 A, whereas the smallest spectral distortion was found for the pentameric COMP complex and the tetrameric leucine zipper mutant, both with a pitch of about 205 A.

Binding of peripheral proteins to mixed lipid membranes: effect of lipid demixing upon binding.

Binding isotherms have been determined for the association of horse heart cytochrome c with dioleoyl phosphatidylglycerol (DOPG)/dioleoyl phosphatidylcholine (DOPC) bilayer membranes over a range of lipid compositions and ionic strengths. In the absence of protein, the DOPG and DOPC lipids mix nearly ideally. The binding isotherms have been analyzed using double layer theory to account for the electrostatics, either the Van der Waals or scaled particle theory equation of state to describe the protein surface distribution, and a statistical thermodynamic formulation consistent with the mass-action law to describe the lipid distribution. Basic parameters governing the electrostatics and intrinsic binding are established from the binding to membranes composed of anionic lipid (DOPG) alone. Both the Van der Waals and scaled particle equations of state can describe the effects of protein distribution on the DOPG binding isotherms equally well, but with different values of the maximum binding stoichiometry (13 lipids/protein for Van der Waals and 8 lipids/protein for scaled particle theory). With these parameters set, it is then possible to derive the association constant, Kr, of DOPG relative to DOPC for surface association with bound cytochrome c by using the binding isotherms obtained with the mixed lipid membranes. A value of Kr (DOPG:DOPC) = 3.3-4.8, depending on the lipid stoichiometry, is determined that consistently describes the binding at different lipid compositions and different ionic strengths. Using the value of Kr obtained it is possible to derive the average in-plane lipid distribution and the enhancement in protein binding induced by lipid redistribution using the statistical thermodynamic theory.

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.