Autorhythmicity and entrainment in excitable membranes

Low calcium increases the excitability of neurones and can induce autorhythmicity in excitable cells. Numerical solutions of the Hodgkin-Huxley membrane equations, and numerical evaluations of the small-signal impedance and admittance are used to illustrate the increase in resonance produced by low [Ca²⁺]₀. The resonant frequency may be located either by the peak of the amplitude of the impedance, or by the frequency at which the phase angle is zero for 1:1 entrained action potentials. Autorhythmicity is produced by any mechanism which increases the resonant peak of the amplitude of the membrane impedance.     

Ionic processes in excitable membranes

The dynamical theory of ionized media is applied to the semi-electrolyte component of an excitable cell membrane, and the adjacent electrolytes. The equations of conservation of charge and momentum for the ions, and Poisson's equation for the electrostatic potential, are applied first to investigate the steady states of the membrane, and then transient effects in the membrane. A dispersion equation is derived, and the characteristic modes of relaxation within the membrane are determined. Among these are oscillating modes whose frequencies and amplitudes are of the correct order of magnitude to explain the observed excitation phenomena.A pair of coupled non-linear equations in the ionic potentials, with action potential solutions, is derived from the time-dependent electrodiffusion equations, and calculations are presented which model the behaviour of the excitable membrane during the voltage clamp. It is not necessary to postulate large changes in the ionic permeabilities in the course of the action potential and the voltage clamp to account for the large transient membrane conductances. It is suggested that the sodium hypothesis be replaced by one which attributes the action potential to non-linear plasma oscillations.     

Palytoxin-induced permeability changes in excitable membranes

Palytoxin, a toxin isolated from the Caribean corrall Palythoa caribaeorum, increases the cation permeability of excitable membranes in vitro. Three membrane systems have been investigated: axonal membranes from crayfish walking leg nerves, membranes rich in nicotinic acetylcholine receptor isolated from Torpedo californica electric tissue and, for control, artificial liposomes. Ion permeability of the latter was not affected by palytoxin, but with both biological membranes an increase in cation permeability was observed at a palytoxin concentration of 0.14 microM. Palytoxin-induced cation flow through the axonal membrane was not inhibited by tetrodotoxin, indicating that the voltage-dependent sodium channels were not involved. The effect of palytoxin on the receptor-rich membranes was not blocked by alpha-bungarotoxin, a competitive antagonist of the nicotinic acetylcholine receptor, nor by triphenylmethylphosphonium, a blocker of the receptor-ion channel. But with both the axonal and the receptor-rich membranes ouabain was an inhibitor of the palytoxin-induced cation flow. Evidence is presented that it is not the (Na+ + K+)-ATPase which is affected by palytoxin as has been postulated for similar observations with non-neuronal membranes (Chhatwal, G.S., Hessler, H.-J. and Habermann, E. (1983) Naunyn-Schmiedeberg's Arch. Pharmacol. 323, 261-268).     

Voltage-noise-induced transitions in electrically excitable membranes.

A quantitative study of the steady-state behavior of the sodium and potassium conductance for the Hodgkin-Huxley axon under the influence of an externally driven voltage noise is reported. The dichotomous Markov noise (random telegraph signal) considered allows for an exact evaluation of the stationary probability density of the conductances. Phase diagrams are constructed to represent the response of the system as a function of the amplitude and the correlation time of the noise. The results obtained for the Hodgkin-Huxley axon are compared with some molecular models used in the literature.     

A possible model for receptors in excitable membranes

A model is proposed for receptors in excitable membranes based on the following assumptions. The receptor site and the process it excites in the membrane are located close to each other. The change of the electrostatic potential in the neighbourhood of the receptor site on the adsorption of a molecule (or ion) influences a potential dependent process in the membrane, such as ion permeability, rate of enzymatic reactions, ion binding etc. A comment is also made about the connection between measured physiological activity of a molecule and its ?real” physical activity.     

Biochemical investigations of ionic channels in excitable membranes

Summary Ion channels of excitable membranes are composed of a gating device and a selectivity filter. Two strategies are discussed in this review for the biochemical isolation and characterization of these two functional subunits of channels: Membrane molecules involved in ion translocation can be identified in vitro by their pharmacological properties, i.e. by binding assays with radioactive drugs known to selectively affect a special channel in vivo. More desirable is an assay of their true biological function, i.e. translocation of ions through a membrane. Ion flux measurements with natural and reconstituted membrane systems in vitro are recently available.This article summarizes our present knowledge of electrically excitable sodium and potassium channels of nerve membranes and of the chemically excitable sodium/potassium channel of cholinergic synapses, the acetylcholine receptor complex (AChR). Because of the availability of a great variety of drugs binding with high affinity to axonal sodium channels its investigation is more advanced than that of the axonal potassium channel. The lack of high affinity labels for the latter can be possibly overcome by photoaffinity labels which label components of the channel in situ. Initial success is reported with a photoafinity label derived from the potassium channel blocker TEA.Most advanced is the biochemical investigation of the acetylcholine receptor (AChR) which has been purified in milligram quantities. It represents a protein complex composed of different polypeptide chains with different functions regulating the sodium/potassium permeability of cholinergic postsynaptic membranes. Experiments are described to elucidate the quaternary structure, the site of binding of cholinergic ligands and neurotoxins and to prove dynamic conformation changes of the protein which may be the cause for permeability changes of the membrane. The gating device and the ion translocation system (selectivity filter, ionophor) appear to be present in the receptor complex though located possible in different subunits. This is evidenced by reconstitution of excitable membranes from purified AChR and exogenous lipids by a novel and reproducible method.An invited review article.     

Retardation currents in excitable membranes and models of flicker noise

We have presented (Holden and Rubio, 1976) a model for flicker noise in nerve membranes in which there are interactions between adjacent ionic channels. These interactions are proposed to be mediated by order-disorder transitions in the membrane matrix. In this paper we explore the relaxation behaviour of our model, and, using transition state theory, predict a new class of membrane ionic currents which we call retardation currents. Such retardation currents have slow (hundreds of ms) kinetics, a low temperature dependence and appear as inactivation processes. We consider some candidate retardation currents.     

Lipid--protein multiple binding equilibria in membranes

Phospholipids at the lipid--protein interface of membrane proteins are in dynamic equilibrium with fluid bilayer. In order to express the number of binding sites (N) and the relative binding constants (K) in terms of measurable quantities, the equilibrium is formulated as an exchange reaction between lipid molecules competing for hydrophobic sites on the protein surface. Experimental data are reported on two integral membrane proteins, cytochrome oxidase and (Na,-K)-ATPase, reconstituted into defined phospholipids. Electron spin resonance measurements on reconstituted preparations of beef heart cytochrome oxidase in 1,2-dioleoyl-sn-3-phosphatidylcholine containing small quantities of the spin-labeled phospholipid 1-palmitoyl-2-(14-proxylstearoyl)-sn-3-phosphatidylcholine (PC*) gave a linear plot of bilayer/bound PC* vs. the lipid/protein ratio as predicted by the theory, with K congruent to 1 and N = 40 (normalized to heme aa3). This demonstrates that the spin-label moiety attached to the hydrocarbon chain does not significantly perturb the binding equilibria. In the second experimental system, (Na,K)-ATPase purified from rectal glands of Squalus acanthias was reconstituted with defined phosphatidylcholines as the lipid solvent and spin-labeled phospholipids with choline or serine head groups (PC*, PS*) as the solute. The (Na,K)-ATPase has a larger number of lipid binding or contact sites (N = 60-65 per alpha 2 beta 2 dimer) and exhibits a detectably larger average binding constant for the negatively charged phosphatidylserine than for the corresponding phosphatidylcholine. These results show that a multiple equilibria, noninteracting site binding treatment can account for the behavior of lipids exchanging between the protein surface and the lipid bilayer. Selective sites among a background of nonselective sites are experimentally detectable as a change in the measured relative binding constant.     

Compensation for resistance in series with excitable membranes.

Extracellular resistance in series (Rs) with excitable membranes can give rise to significant voltage errors that distort the current records in voltage-clamped membranes. Electrical methods for measurement of and compensation for such resistances are described and evaluated. Measurement of Rs by the conventional voltage jump in response to a current step is accurate but the measurement of sine-wave admittance under voltage-clamp conditions is better, having about a fivefold improvement in resolution (+/- 0.1 omega cm2) over the conventional method. Conventional feedback of the membrane current signal to correct the Rs error signal leads to instability of the voltage clamp when approximately two-thirds of the error is corrected. We describe an active electronic bridge circuit that subtracts membrane capacitance from the total membrane current and allows full, yet stable, compensation for the voltage error due to ionic currents. Furthermore, this method provides not only fast and accurate control of the membrane potential in response to a command step, but also fast recovery following an abrupt change in the membrane conductance. Marked changes in the kinetics and amplitude of ionic currents resulting from full compensation for Rs are shown for several typical potential patterns.     

The problem of nonstationary ion fluxes in excitable membranes

Time-dependent electrodiffusion through a membrane is analysed within a simple model treating the boundary-layers in a consistent manner. It is shown that time-independent reversal potentials for the ion fluxes exist only under steady-state conditions. We argue that this result holds very generally. Therefore nonstationary effects like ion storage and depletion inside the membrane should not contribute to the phenomena of excitability.Glossary of Symbols A _mv [V] functional cf. Equation (3) - C membrane capacitance - d one half the thickness of the membrane - F[V] functional cf. Equation (1) - g _i electrochemical potential inside membrane - g _i electrochemical potentials outside membrane at x ±d, respectively - i (index) refers to i-th ionic species - J electric current across membrane - j = j ^} = j ^< current density measured by external electrodes - j _i (x) current density inside membrane in x-direction - j _i ^inst(x) instantaneous current density - J _i ^stat steady-state current density - k Boltzmann constant - m (index) is used in Sec. 2 to denote the independent diffusion currents - n ^< ionic strength of electrolyte at x = - - n _i density of ions inside membrane - n _i density of ions outside membrane at x = ±, respectively - Q charge per unit area of boundary layers at x ± d, respectively - Q ₀ fixed charge per unit area of membrane - q elementary charge - q _i ionic charges - T temperature - it time - V membrane potential (= (-)-()) - V _i Nernst potential - V potential drops inside boundary layers (can be neglected, see Appendix II) - V ^± potential steps at x = ± d, cf. Equation (29) - V ₀ = V ^–-V ⁺ - w _i activation energy inside membrane - x spatial coordinate perpendicular to membrane - y, z spatial coordinates parallel to membrane - dielecric constant - ₀ dielectric constant of electrolyte solution ( 80) - _m dielectric constant of membrane ( 5) - (x) electrostatic potential - charge density of boundary layers - ⁰ fixed charge density inside membrane - spatial average, cf. Equation (12)