The excitable fluid mosaic.

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10-20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.1.

The effect of stretching on nerve excitability.

Nerves are frequently stretched during movement. We investigate here the effect of stretch on nerve excitability within the framework of the soliton theory. This thermodynamic theory for nerve pulse propagation relies on the presence of a melting transition in the nerve membrane. In this transition, the area of the nerve membrane and the nerve thickness change. It depends on thermodynamic variables including temperature, the chemical potentials of anesthetics and on hydrostatic pressure. A further variable relevant for movement science is the the stretching of nerves, i.e., a tension in the nerve caused by muscle contraction, the bending of joints and the pulling on extremities. We show here that the soliton theory predicts a decrease in nerve excitability upon stretching. This becomes evident in a reduction of the amplitude of compound action potentials and in the suppression of reflexes. We compare these predictions with medical findings.

The important consequences of the reversible heat production in nerves and the adiabaticity of the action potential.

It has long been known that there is no measurable heat production associated with the nerve pulse. Rather, one finds that heat production is biphasic, and a heat release during the first phase of the action potential is followed by the reabsorption of a similar amount of heat during the second phase. We review the long history the measurement of heat production in nerves and provide a new analysis of these findings focusing on the thermodynamics of adiabatic and isentropic processes. We begin by considering adiabatic oscillations in gases, waves in layers, oscillations of springs and the reversible (or irreversible) charging and discharging of capacitors. We then apply these ideas to the heat signature of nerve pulses. Finally, we compare the temperature changes expected from the Hodgkin-Huxley model and the soliton theory for nerves. We demonstrate that heat production in nerves cannot be explained as an irreversible charging and discharging of a membrane capacitor as it is proposed in the Hodgkin-Huxley model. Instead, we conclude that it is consistent with an adiabatic pulse. However, if the nerve pulse is adiabatic, completely different physics is required to explain its features. Membrane processes must then be reversible and resemble the oscillation of springs more than resembling "a burning fuse of gunpowder" (quote A. L. Hodgkin). Theories acknowledging the adiabatic nature of the nerve pulse have recently been discussed by various authors. It forms the central core of the soliton model, which considers the nerve pulse as a localized sound pulse.

Non-linear Conductance, Rectification, and Mechanosensitive Channel Formation of Lipid Membranes.

There is mounting evidence that lipid bilayers display conductive properties. However, when interpreting the electrical response of biological membranes to voltage changes, they are commonly considered as inert insulators. Lipid bilayers under voltage-clamp conditions display current traces with discrete conduction-steps, which are indistinguishable from those attributed to the presence of protein channels. In current-voltage (I-V) plots they may also display outward rectification, i.e., voltage-gating. Surprisingly, this has even been observed in chemically symmetric lipid bilayers. Here, we investigate this phenomenon using a theoretical framework that models the electrostrictive effect of voltage on lipid membranes in the presence of a spontaneous polarization, which can be recognized by a voltage offset in electrical measurements. It can arise from an asymmetry of the membrane, for example from a non-zero spontaneous curvature of the membrane. This curvature can be caused by voltage via the flexoelectric effect, or by hydrostatic pressure differences across the membrane. Here, we describe I-V relations for lipid membranes formed at the tip of patch pipettes situated close to an aqueous surface. We measured at different depths relative to air/water surface, resulting in different pressure gradients across the membrane. Both linear and non-linear I-V profiles were observed. Non-linear conduction consistently takes the form of outward rectified currents. We explain the conductance properties by two mechanisms: One leak current with constant conductance without pores, and a second process that is due to voltage-gated pore opening correlating with the appearance of channel-like conduction steps. In some instances, these non-linear I-V relations display a voltage regime in which dI/dV is negative. This has also been previously observed in the presence of sodium channels. Experiments at different depths reveal channel formation that depends on pressure gradients. Therefore, we find that the channels in the lipid membrane are both voltage-gated and mechanosensitive. We also report measurements on black lipid membranes that also display rectification. In contrast to the patch experiments they are always symmetric and do not display a voltage offset.

Melting transitions in biomembranes.

We investigated melting transitions in native biological membranes containing their membrane proteins. The membranes originated from E. coli, B. subtilis, lung surfactant and nerve tissue from the spinal cord of several mammals. For some preparations, we studied the pressure, pH and ionic strength dependence of the transition. For porcine spine, we compared the transition of the native membrane to that of the extracted lipids. All preparations displayed melting transitions of 10-20° below physiological or growth temperature, independent of the organism of origin and the respective cell type. We found that the position of the transitions in E. coli membranes depends on the growth temperature. We discuss these findings in the context of the thermodynamic theory of membrane fluctuations close to transition that predicts largely altered elastic constants, an increase in fluctuation lifetime and in membrane permeability. We also discuss how to distinguish lipid melting from protein unfolding transitions. Since the feature of a transition slightly below physiological temperature is conserved even when growth conditions change, we conclude that the transitions are likely to be of major biological importance for the survival and the function of the cell.

Is a constant low-entropy process at the root of glycolytic oscillations?

We measured temporal oscillations in thermodynamic variables such as temperature, heat flux, and cellular volume in suspensions of non-dividing yeast cells which exhibit temporal glycolytic oscillations. Oscillations in these variables have the same frequency as oscillations in the activity of intracellular metabolites, suggesting strong coupling between them. These results can be interpreted in light of a recently proposed theoretical formalism in which isentropic thermodynamic systems can display coupled oscillations in all extensive and intensive variables, reminiscent of adiabatic waves. This interpretation suggests that oscillations may be a consequence of the requirement of living cells for a constant low-entropy state while simultaneously performing biochemical transformations, i.e., remaining metabolically active. This hypothesis, which is in line with the view of the cellular interior as a highly structured and near equilibrium system where energy inputs can be low and sustain regular oscillatory regimes, calls into question the notion that metabolic processes are essentially dissipative.

The free energy of biomembrane and nerve excitation and the role of anesthetics.

In the electromechanical theory of nerve stimulation, the nerve impulse consists of a traveling region of solid membrane in a liquid environment. Therefore, the free energy necessary to stimulate a pulse is directly related to the free energy difference necessary to induce a phase transition in the nerve membrane. It is a function of temperature and pressure, and it is sensitively dependent on the presence of anesthetics which lower melting transitions. We investigate the free energy difference of solid and liquid membrane phases under the influence of anesthetics. We calculate stimulus-response curves of electromechanical pulses and compare them to measured stimulus-response profiles in lobster and earthworm axons. We also compare them to stimulus-response experiments on human median nerve and frog sciatic nerve published in the literature.

Linear nonequilibrium thermodynamics of reversible periodic processes and chemical oscillations.

Onsager's phenomenological equations successfully describe irreversible thermodynamic processes. They assume a symmetric coupling matrix between thermodynamic fluxes and forces. It is easily shown that the antisymmetric part of a coupling matrix does not contribute to dissipation. Therefore, entropy production is exclusively governed by the symmetric matrix even in the presence of antisymmetric terms. In this paper we focus on the antisymmetric contributions which describe isentropic oscillations with well-defined equations of motion. The formalism contains variables that are equivalent to momenta and coefficients that are analogous to inertial mass. We apply this formalism to simple problems with known answers such as an oscillating piston containing an ideal gas, and oscillations in an LC-circuit. One can extend this formalism to other pairs of variables, including chemical systems with oscillations. In isentropic thermodynamic systems all extensive and intensive variables including temperature can display oscillations reminiscent of adiabatic waves.

Non-invasive detection of animal nerve impulses with an atomic magnetometer operating near quantum limited sensitivity.

Magnetic fields generated by human and animal organs, such as the heart, brain and nervous system carry information useful for biological and medical purposes. These magnetic fields are most commonly detected using cryogenically-cooled superconducting magnetometers. Here we present the first detection of action potentials from an animal nerve using an optical atomic magnetometer. Using an optimal design we are able to achieve the sensitivity dominated by the quantum shot noise of light and quantum projection noise of atomic spins. Such sensitivity allows us to measure the nerve impulse with a miniature room-temperature sensor which is a critical advantage for biomedical applications. Positioning the sensor at a distance of a few millimeters from the nerve, corresponding to the distance between the skin and nerves in biological studies, we detect the magnetic field generated by an action potential of a frog sciatic nerve. From the magnetic field measurements we determine the activity of the nerve and the temporal shape of the nerve impulse. This work opens new ways towards implementing optical magnetometers as practical devices for medical diagnostics.

The Effect of the Nonlinearity of the Response of Lipid Membranes to Voltage Perturbations on the Interpretation of Their Electrical Properties. A New Theoretical Description.

Our understanding of the electrical properties of cell membranes is derived from experiments where the membrane is exposed to a perturbation (in the form of a time-dependent voltage or current change) and information is extracted from the measured output. The interpretation of such electrical recordings consists in finding an electronic equivalent that would show the same or similar response as the biological system. In general, however, there is no unique circuit configuration, which can explain a single electrical recording and the choice of an electric model for a biological system is based on complementary information (most commonly structural information) of the system investigated. Most of the electrophysiological data on cell membranes address the functional role of protein channels while assuming that the lipid matrix is an insulator with constant capacitance. However, close to their melting transition the lipid bilayers are no inert insulators. Their conductivity and their capacitance are nonlinear functions of both voltage, area and volume density. This has to be considered when interpreting electrical data. Here we show how electric data commonly interpreted as gating currents of proteins and inductance can be explained by the nonlinear dynamics of the lipid matrix itself.

Mechano-capacitive properties of polarized membranes.

Biological membranes are capacitors that can be charged by applying a field across the membrane. The charges on the capacitor exert a force on the membrane that leads to electrostriction, i.e. a thinning of the membrane. Since the force is quadratic in voltage, negative and positive voltage have an identical influence on the physics of symmetric membranes. However, this is not the case for a membrane with an asymmetry leading to a permanent electric polarization. Positive and negative voltages of identical magnitude lead to different properties. Such an asymmetry can originate from a lipid composition that is different on the two monolayers of the membrane, or from membrane curvature. The latter effect is called 'flexoelectricity'. As a consequence of permanent polarization, the membrane capacitor is discharged at a voltage different from zero. This leads to interesting electrical phenomena such as outward or inward rectification of membrane permeability. Here, we introduce a generalized theoretical framework, that treats capacitance, polarization, flexoelectricity, piezoelectricity and thermoelectricity in the same language. We show applications to electrostriction, membrane permeability and piezoelectricity and thermoelectricity close to melting transitions, where such effects are especially pronounced.

Protein reconstitution into freestanding planar lipid membranes for electrophysiological characterization.

The reconstitution of channel-forming proteins into planar lipid bilayers enables their functional characterization at very low (sometimes below attomolar) concentrations. We describe the three main approaches used in our laboratories (the Mueller-Rudin technique, in which the bilayers contain an organic solvent, the Montal-Mueller or solvent-free technique, and a method for membrane reconstitution via liposome formation), and we discuss their respective advantages and limitations. Despite the differences in the reconstitution procedures, subsequent protein characterization is based on the same electrophysiological technique. A transmembrane electric field is applied, inducing an ion current and allowing conclusions to be drawn on apparent pore sizes, or suggesting functional properties such as channel opening and closing upon ligand binding, pH-induced conformational changes, ion selectivity or substrate specificity.

The thermodynamics of general and local anesthesia.

General anesthetics are known to cause depression of the freezing point of transitions in biomembranes. This is a consequence of ideal mixing of the anesthetic drugs in the membrane fluid phase and exclusion from the solid phase. Such a generic law provides physical justification of the famous Meyer-Overton rule. We show here that general anesthetics, barbiturates, and local anesthetics all display the same effect on melting transitions. Their effect is reversed by hydrostatic pressure. Thus, the thermodynamic behavior of local anesthetics is very similar to that of general anesthetics. We present a detailed thermodynamic analysis of heat capacity profiles of membranes in the presence of anesthetics. Using this analysis, we are able to describe experimentally observed calorimetric profiles and predict the anesthetic features of arbitrary molecules. In addition, we discuss the thermodynamic origin of the cutoff effect of long-chain alcohols and the additivity of the effect of general and local anesthetics.

Fluctuations of systems in finite heat reservoirs with applications to phase transitions in lipid membranes.

In an adiabatically shielded system, the total enthalpy is conserved. Enthalpy fluctuations of an arbitrarily chosen subsystem must be buffered by the remainder of the total system which serves as a heat reservoir. The magnitude of these fluctuations depends on the size of the reservoir. This leads to various interesting consequences for the physical behavior of the subsystem. As an example, we treat a lipid membrane with a phase transition that is embedded in an aqueous reservoir. We find that large fluctuations are attenuated when the reservoir has finite size. This has consequences for the compressibility of the membrane since volume and area fluctuations are also attenuated. We compare the equilibrium fluctuations of subsystems in finite reservoirs with those in periodically driven systems. In such systems, the subsystem has only finite time available to exchange heat with the surrounding medium. A larger frequency therefore reduces the volume of the accessible heat reservoir. Consequently, the fluctuations of the subsystem display a frequency dependence. While this work is of particular interest for a subsystem displaying a transition such as a lipid membrane, some of the results are of a generic nature and may contribute to a better understanding of relaxation processes in general.

Lipid ion channels and the role of proteins.

In the absence of proteins, synthetic lipid membranes can display quantized conduction events for ions that are virtually indistinguishable from those of protein channels. The phenomenological similarities between typical conductances are striking: they are of equal order and show similar lifetime distributions and current histograms. They can include conduction bursts, flickering, and multistep conductance. Lipid channels can be gated by voltage and blocked by drugs. They respond to changes in lateral membrane tension and temperature. Thus, they behave like voltage-gated, temperature-gated, and mechano-sensitive protein channels, or like receptors. The similarity between lipid and protein channels poses an important problem for the interpretation of protein channel data. For example, the Hodgkin-Huxley theory for nerve pulse conduction requires a selective mechanism for the conduction of sodium and potassium ions. To this end, the lipid membrane must act both as a capacitor and as an insulator. Nonselective ion conductance by mechanisms other than the gated protein channels challenges the proposed mechanism for pulse propagation. Nevertheless, textbooks rarely describe the properties of the lipid membrane surrounding the proteins in their discussions of membrane models. These similarities lead to important questions: Do these similarities in lipid and protein channels result from a common mechanism, or are these similarities fortuitous? What distinguishes protein channels from lipid channels, if anything? In this Account, we document experimental and theoretical findings that show the similarity between lipid and protein channels. We discuss important cases where protein channel function strongly correlates with the properties of the lipid. Based on statistical thermodynamics simulations, we discuss how such correlations could come about. We suggest that proteins can act as catalysts for lipid channel formation and that this hypothesis can explain some of the unexplained correlations between protein and lipid membrane function.

Voltage-Gated Lipid Ion Channels.

Synthetic lipid membranes can display channel-like ion conduction events even in the absence of proteins. We show here that these events are voltage-gated with a quadratic voltage dependence as expected from electrostatic theory of capacitors. To this end, we recorded channel traces and current histograms in patch-experiments on lipid membranes. We derived a theoretical current-voltage relationship for pores in lipid membranes that describes the experimental data very well when assuming an asymmetric membrane. We determined the equilibrium constant between closed and open state and the open probability as a function of voltage. The voltage-dependence of the lipid pores is found comparable to that of protein channels. Lifetime distributions of open and closed events indicate that the channel open distribution does not follow exponential statistics but rather power law behavior for long open times.

Variations in interpulse interval of double action potentials during propagation in single neurons.

In this work, we analyzed the interpulse interval (IPI) of doublets and triplets in single neurons of three biological models. Pulse trains with two or three spikes originate from the process of sensory mechanotransduction in neurons of the locust femoral nerve, as well as through spontaneous activity both in the abdominal motor neurons and the caudal photoreceptor of the crayfish. We show that the IPI for successive low-frequency single action potentials, as recorded with two electrodes at two different points along a nerve axon, remains constant. On the other hand, IPI in doublets either remains constant, increases or decreases by up to about 3 ms as the pair propagates. When IPI increases, the succeeding pulse travels at a slower speed than the preceding one. When IPI is reduced, the succeeding pulse travels faster than the preceding one and may exceed the normal value for the specific neuron. In both cases, IPI increase and reduction, the speed of the preceding pulse differs slightly from the normal value, therefore the two pulses travel at different speeds in the same nerve axon. On the basis of our results, we may state that the effect of attraction or repulsion in doublets suggests a tendency of the spikes to reach a stable configuration. We strongly suggest that the change in IPI during spike propagation of doublets opens up a whole new realm of possibilities for neural coding and may have major implications for understanding information processing in nervous systems.

The capacitance and electromechanical coupling of lipid membranes close to transitions: the effect of electrostriction.

Biomembranes are thin capacitors with the unique feature of displaying phase transitions in a physiologically relevant regime. We investigate the voltage and lateral pressure dependence of their capacitance close to their chain melting transition. Because the gel and the fluid membrane have different area and thickness, the capacitance of the two membrane phases is different. In the presence of external fields, charges exert forces that can influence the state of the membrane, thereby influencing the transition temperature. This phenomenon is called "electrostriction". We show that this effect allows us to introduce a capacitive susceptibility that assumes a maximum in the melting transition with an associated excess charge. As a consequence, voltage regimes exist in which a small change in voltage can lead to a large uptake of charge and a large capacitive current. Furthermore, we consider electromechanical behavior such as pressure-induced changes in capacitance, and the application of such concepts in biology.

Comparing ion conductance recordings of synthetic lipid bilayers with cell membranes containing TRP channels.

In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel activity is characterized by typical patterns of current events dependent on the type of protein expressed. Synthetic lipid bilayers show a wide spectrum of electrical phenomena that are considered typical for the activity of protein ion channels. We find unitary currents, burst behavior, flickering, multistep-conductances, and spikes behavior in both preparations. Moreover, we report conductances and lifetimes for lipid channels as described for protein channels. Non-linear and asymmetric current-voltage relationships are seen in both systems. Without further knowledge of the recording conditions, no easy decision can be made whether short current traces originate from a channel protein or from a pure lipid membrane.