Computer simulation of the effect of the nodal gap resistance on ionic current measurements in the Ranvier node membrane.

Results are presented of a computer simulation of the effect of the irreducible resistance introduced by the nodal gap, in series with the impedance of the axon membrane. A clamp potential is applied to a structure modeled as an electric circuit composed of a resistance in series with the membrane impedance, and modified nerve equations describing membrane currents are solved to predict the effect of nodal series resistance on these currents. These studies reveal changes in the absolute values and kinetics of the ionic currents (errors greater than 10-20%) for selected values of series resistance.     

Membrane ionic currents in Rhodobacter capsulatus. Evidence for electrophoretic transport of K+, Rb+ and NH4+

1. The cytoplasmic membrane ionic current of cells of Rhodobacter capsulatus, washed to lower the endogenous K+ concentration, had a non-linear dependence on the membrane potential measured during photosynthetic illumination. Treatment of the cells with venturicidin, an inhibitor of the H(+)-ATP synthase, increased the membrane potential and decreased the membrane ionic current at values of membrane potential below a threshold. 2. The addition of K+ or Rb+, but not of Na+, led to an increase in the membrane ionic current and a decrease in the membrane potential in either the presence or absence of venturicidin. Approximately 0.4 mM K+ or 2.0 mM Rb+ led to a half-maximal response. At saturating concentrations of K+ and Rb+, the membrane ionic currents were similar. The membrane ionic currents due to K+ and Rb+ were not additive. The K(+)-dependent and Rb(+)-dependent ionic currents had a non-linear relationship with membrane potential: the alkali cations only increased the ionic current when the membrane potential lay above a threshold value. The presence of 1 mM Cs+ did not lead to an increase in the membrane ionic current but it had the effect of inhibiting the membrane ionic current due to either K+ or Rb+. 3. Photosynthetic illumination in the presence of either K+ or Rb+, and weak acids such as acetate, led to a decrease in light-scattering by the cells. This was attributed to the uptake of potassium or rubidium acetate and a corresponding increase in osmotic strength in the cytoplasm. 4. The addition of NH4+ also led to an increase in membrane ionic current and to a decrease in membrane potential (half-maximal at 2.0 mM NH4+). The relationship between the NH4(+)-dependent ionic currents and the membrane potential was similar to that for K+. The NH4(+)-dependent and K(+)-dependent ionic current were not additive. However, illumination in the presence of NH4+ and acetate did not lead to significant light-scattering changes. The NH4(+)-dependent membrane ionic current was inhibited by 1 mM Cs+ but not by 50 microM methylamine. 5. It is proposed that the K(+)-dependent membrane ionic current is catalysed by a low-affinity K(+)-transport system such as that described in Rb. capsulatus [Jasper, P. (1978) J. Bacteriol. 133, 1314-1322]. The possibility is considered that, as well as Rb+, this transport system can also operate with NH4+. However, in our experimental conditions NH4+ uptake is followed by NH3 efflux.(ABSTRACT TRUNCATED AT 400 WORDS)     

Effects of physostigmine on the voltage dependent ionic conductances of skeletal muscle fibres

The voltage dependent ionic conductances were studied by analysing the phase plane trajectories of action potentials evoked by electrical stimulation of the sartorius muscles of the frog (Rana esculenta). The delayed outward potassium current was measured also under voltage clamp conditions on muscle fibres of either the frog (Rana esculenta) or Xenopus laevis. On analysing the effect of physostigmine decreasing the peak amplitude, the rate of both the rising and falling phases of the action potentials, it was revealed that the alkaloid at a concentration of 1 mmol/l reduced significantly both the delayed potassium conductance and the outward ionic current values during the action potentials. The inhibition of sodium conductance and inward ionic current was less expressed. The maximum value of delayed potassium conductance measured under voltage clamp conditions was decreased by 1 mmol/l physostigmine. The time constant determined from the development of delayed potassium conductance was increased at a given membrane potential. The voltage vs. n relationship describing the membrane potential dependence of the delayed rectifier was not influenced by physostigmine. It has been concluded that physostigmine changes the time course of the action potentials by decreasing the value of both voltage dependent ionic conductances and by slowing down their kinetics. It is discussed that results obtained from the phase plane analysis of complex pharmacological effects can only be accepted with some restrictions.     

Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models

Parallel numerical simulations of excitation and recovery in three-dimensional myocardial domains are presented. The simulations are based on the anisotropic Bidomain and Monodomain models, including intramural fiber rotation and orthotropic or axisymmetric anisotropy of the intra- and extra-cellular conductivity tensors. The Bidomain model consist of a system of two reaction-diffusion equations, while the Monodomain model consists of one reaction-diffusion equation. Both models are coupled with the phase I Luo-Rudy membrane model describing the ionic currents. Simulations of excitation and repolarization sequences on myocardial slabs of different sizes show how the distribution of the action potential durations (APD) is influenced by both the anisotropic electrical conduction and the fiber rotation. This influence occurs in spite of the homogeneous intrinsic properties of the cell membrane. The APD dispersion patterns are closely correlated to the anisotropic curvature of the excitation wavefront.     

Steady state current rectification in potential clamped nodes of Ranvier (Xenopus laevis).

The membrane potential in single nodes of Ranvier was changed in rectangular pulse steps while the membrane currents, associated with the potential steps, were measured. Changes were made in the ionic composition of the external and the internal medium. The latter changes were obtained by free diffusion through a cut internode. The steady state currents, described on the basis of potassium and leak permeability, were affected by the solution composition in a characteristic way. Increased inside concentration of sodium and lithium caused a striking rectification of the outward steady state currents at large potential steps. Instantaneous potassium currents in high [K+]o at a second potential step to E approximately equal to minus 80 mV were not affected by [Na+]1. Neither [Na+]o nor [K+]i affected the potential at which this rectification appeared. Increased [K+]o shifted the region for rectification along the potential axis in positive direction. These findings form strict limitations for satisfactory models describing the mechanism for the steady state current in myelinated nerve.     

An Analysis of the Surface Fixed-Charge Theory of the Squid Giant Axon Membrane

The observed shift in threshold potential, after perfusion of the squid giant axon with solutions of low ionic strength, can be predicted by assuming a fixed negative charge on the inside of the membrane. The constant field equation, together with the double-layer potential due to this charge, has been used to determine the change in resting potential during perfusion with solutions of low ionic strength. Neither the modified constant field equation nor Planck's diffusion equation can successfully predict the observed shift in resting potential. It is suggested that a positive charge distribution exists about the sodium channel on the outside of the membrane. The double-layer potential due to this positive charge, together with the independence principle, has been used to predict the relationship between sodium current and membrane potential when the ionic strength and sodium activity of the external solution are decreased. These predictions have been compared with the available experimental observations.     

Role of nonohmicity in the regulation of electron transport in plant mitochondria

The relationship between the respiratory rate and the membrane ionic current on the protonmotive force has been investigated in percoll purified potato mitochondria. The dependence of the membrane ionic current on the membrane potential was monitored using a methyltriphenylphosphonium-sensitive electrode and determining the maximal net rate of depolarization following the addition of a respiratory inhibitor. We have confirmed that a nonohmic relationship exists between the ionic conductance and membrane potential. Addition of ATPase inhibitors markedly increased the initial rate of dissipation suggesting that in their absence the dissipation rate induced by respiratory inhibitors is partially offset by H⁺-efflux due to the hydrolysis of endogenous ATP. This was corroborated by direct measurement of endogenous ATP levels which decreased significantly following dissipation of the membrane potential. Results are discussed in terms of the regulation of electron transport in plant mitochondria in vivo.     

Ionic concentration profiles and charge distribution for the domain of a polarized spherical cell

Solutions of the Poisson-Boltzmann equation yield potential profiles and equilibrium distributions of ions on either side of a spherical shell membrane across which there exists a separation of ionic charges. For the special case in which the membrane is permeable to only one ion the total charge separation is analyzed in terms of the potential difference given by the Nernst equation. Potential profiles and ionic charge distributions are also given for situations involving a uniform distribution of fixed charges within the membrane.     

An electrophysiological study of the junctional membrane of epidermal cells in Tenebrio molitor

The insect epidermis is normally a coupled network with respect to the movement of inorganic ions through the junctional membranes connecting adjacent cells. The high ionic permeability of the junctional membrane may be reversibly abolished by either the iontophoretic injection of Ca into single cells or by replacing the Na in the external medium with Li. After Ca injection, a concomitant loss in ionic permeability of the junctional membrane and of the membrane potential of the injected cell was recorded within 3 min. Ionic coupling was restored by hyperpolarizing current pulses within a few minutes. Li substitution tripled the resistance of the junctional membrane within 30 min although the membrane potential remained stable during this period. After 60 min exposure to Li the membrane potential had decayed to zero and ionic coupling was unrecordable. Junctional membrane permeability and cell membrane potential were restored within 30 min re-exposure to normal saline. Since Li is thought to act by indirectly raising the free Ca level in the cytoplasm by its interaction with cytoplasmic Na, we suggest that a reduction in junctional permeability is a direct consequence of increased Ca activity in the cytoplasm of the epidermal cells.     

On the state of calcium ions in isolated rat liver mitochondria. I. Ion fluxes and volume changes upon Ca2+ uptake under various ionic conditions

As to functional consequences of Ca2+ uptake in isolated rat liver mitochondria, we simultaneously measured 3H2O and [14C]sucrose spaces, monovalent cation distribution, membrane potential and delta pH across the inner membrane, and [32P]phosphate and 45Ca2+ content in parallel incubations of different ionic composition. Without added Ca2+ and phosphate, mitochondrial matrix volume, membrane potential, and delta pH depended on the concentration and permeability of monovalent cations. Despite large differences in membrane potential, maximal Ca2+ uptake was identical under all conditions. Ca2+ uptake never provoked a volume change from which an osmotic active state of mitochondrial Ca2+ could be concluded. If matrix volume shrunk this could be totally accounted for by the loss of alkali ions exchanging for calcium ions. Even phosphate taken up in conjunction with Ca2+ was osmotically silent. Volume increases here occurring if K+ was permeabilized, solely resulted from K+ uptake, though this condition may give rise to irreversible mitochondrial damage with Ca2+ and phosphate release. As mitochondrial Ca2+ is bound, an electro-chemical equilibrium across the membrane is impossible for this ion. This has to be considered in any model describing equilibria of Ca2+ with mitochondria, though present models neglect this state of mitochondrial Ca2+.     

An electrophysiological study of the non-junctional membrane of epidermal cells in Tenebrio molitor

The contribution of K and Cl to the membrane potential of the epidermal cells of the recently-ecdysed larva of the mealworm was examined. The ionic basis for the membrane potential is complex. Although increasing the external K level depolarized the cell membrane, the relationship obtained suggests that ions other than K contribute largely to the recorded membrane potential. In particular, exposing the cells to K concentrations below the normal level of 40 mM has only slight effects on membrane potential, irrespective of whether K is lowered by direct substitution with Na or under conditions in which Na and Cl levels are held constant. Increasing the external Cl levels from 4 mM to 154 mM while holding K and Na levels constant resulted in a 10 mV hyperpolarization. The slight hyperpolarizing effects of high external Cl could be mimicked by citrate, but not by acetate, the latter drastically hyperpolarizing the cell membrane at levels of K that normally maintain a reduced membrane potential. External Na has little effect on the membrane potential at normal physiological levels of K, but may depolarize the cell at low K levels. The results suggest that several inorganic ions, and possibly organic acids, participate in generating the membrane potential of the epidermal cell. The passive ionic properties of non-junctional epidermal membrane and muscle membrane appear to the similar in this insect.The electrical resistance on the non-junctional membrane is highly dependent on the external K level, and can be reduced by three orders of magnitude by increasing external K from 1 mM to 120 mM. The resistance of the junctional membrane remains constant over this range of external K concentrations.     

Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes.

Ion-carrier complexes and organic ions of similar size and shape have mobilities in lipid bilayer membranes which span several orders of magnitude. In this communication, an examination is made of the hypothesis that the basis for this unusually wide range of ionic mobilities is the potential energy barrier arising from image forces which selectively act on ions according to their polarizability. Using Poisson's equation to evaluate the electrostatic interaction between an ion and its surroundings, the potential energy barrier to ion transport due to image effects is computed, with the result that the potential energy barrier height depends strongly on ionic polarizability. Theoretical membrane potential energy profile calculations are used in conjunction with Nernst-Planck electrodiffusion equation to analyze the available mobility data for several ion-carrier complexes and lipid-soluble ions in lipid bilayer membranes. The variation among the mobilities of different ions is shown to be in agreement with theoretical predictions based on ionic polarizability and size. Furthermore, the important influence exerted by image forces on ion transport in lipid bilayer membranes compared to the frictional effect of membrane viscosity is established by contrasting available data on the activation energy of ionic conductivity with that for membrane fluidity.     

Electrical Activation of Na/K Pumps Can Increase Ionic Concentration Gradient and Membrane Resting Potential

It has been previously demonstrated by our group that our specifically designed synchronization modulation electric field can dynamically entrain the Na/K ATPase molecules, effectively accelerating the pumping action of these molecules. The ATPase molecules are first synchronized by the field, and subsequently their pumping rates are gradually modulated in a stepwise pattern to progressively higher and higher levels. Here, we present results obtained on application of the field to intact twitch skeletal muscle fibers. The ionic concentration gradient across the cell membrane was monitored, with the membrane potential extrapolated using a slow fluorescent probe with a confocal microimaging technique. The applied synchronization-modulation electric field is able to slowly but consistently increase the ionic concentration gradient across the membrane and, hence, hyperpolarize the membrane potential. All of these results were fully eliminated if ouabain was applied to the bathing solution, indicating a correlation with the action of the Na/K pump molecules. These results in combination with our previous results into the entrainment of the pump molecules show that the synchronization-modulation electric field-induced activation of the Na/K pump functions can effectively increase the ionic concentration gradient and the membrane potential.     

Synchronization modulation of Na/K pump molecules can hyperpolarize the membrane resting potential in intact fibers

Previously, we have theoretically studied the possibility of electrical rhythmic entrainment of carrier-mediated ion transporters, and experimentally realized synchronization and acceleration of the Na/K pumping rate in the cell membrane of skeletal muscle fibers by a specially designed synchronization modulation electric field. In these studies we either used cut fibers under a voltage clamp or intact fibers, but in the presence of ion channels blockers. A question remained as to whether the field-induced activation observed in the pump molecules could effectively increase the intracellular ionic concentration and the membrane potential at physiological conditions. In this paper, we studied the effects of the field on intact fibers without any channel blockers. We monitored the field-induced changes in the ionic concentration gradient across the cell membrane and the membrane potential non-invasively by using a fluorescent probe and confocal microscopic imaging techniques. The results clearly show that the entrainment of the pump molecules by the synchronization modulation electric field can effectively increase the ionic concentration gradient, and hence, hyperpolarize the membrane potential.     

On the diffusion of ions in membranes

A simple model of a membrane is used to obtain relations among five measurable quantities: the inward and outward ionic fluxes, the internal and external ionic concentrations, and the difference of electrical potential across the membrane. The Goldman equation is generalized to arbitrary geometrical shapes. Predoctoral Fellow of the National Science Foundation.     

Voltage-Clamp Studies on Uterine Smooth Muscle

These studies have developed and tested an experimental approach to the study of membrane ionic conductance mechanisms in strips of uterine smooth muscle. The experimental and theoretical basis for applying the double sucrose-gap technique is described along with the limitations of this system. Nonpropagating membrane action potentials were produced in response to depolarizing current pulses under current-clamp conditions. The stepwise change of membrane potential under voltage-clamp conditions resulted in a family of ionic currents with voltage- and time-dependent characteristics. In sodium-free solution the peak transient current decreased and its equilibrium potential shifted along the voltage axis toward a more negative internal potential. These studies indicate a sodium-dependent, regenerative excitation mechanism.     

Spring constants for channel-induced lipid bilayer deformations. Estimates using gramicidin channels.

Hydrophobic interactions between a bilayer and its embedded membrane proteins couple protein conformational changes to changes in the packing of the surrounding lipids. The energetic cost of a protein conformational change therefore includes a contribution from the associated bilayer deformation energy (DeltaGdef0), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies based on an elastic liquid-crystal model of the bilayer deformation show that DeltaGdef0 should be quantifiable by a phenomenological linear spring model, in which the bilayer mechanical characteristics are lumped into a single spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurements of the spring constant and thereby evaluate quantitatively the DeltaGdef0 associated with protein conformational changes. Gramicidin channels can be used as such reporter proteins because the channels form by the transmembrane assembly of two nonconducting monomers. The monomerleft arrow over right arrow dimer reaction thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant describing the channel-induced bilayer deformation by examining how DeltaGdef0 varies as a function of a mismatch between the hydrophobic channel length and the unperturbed bilayer thickness. We show this is possible by analyzing experimental studies on the relation between bilayer thickness and gramicidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclusion-induced bilayer deformations using independently measured material constants.     

Surface potential changes of mitoplasts in the presence of pyridoxal phosphate modified cytochromes c.

1. The addition of native cytochrome c to mitoplasts leads to a decrease of surface potential of the mitoplast membrane. However the surface potential is slightly decreased (approximately 3 mV) when PLP(Lys 86)-cytochrome c and PLP(Lys 79)-cytochrome c were added. 2. The native and PLP-modified cytochromes c do not influence the order parameters S and isotropic constant a when both spin probe I and probe II were used. It is shown that cytochrome c binding to the membrane does not affect the hydrophobic intermembrane area as well as the lipid arrangements of the mitoplast membrane. 3. At low ionic strength there was observed a significant difference in the membrane potential when PLP-cytochromes c were added to the mitoplasts. 4. At high ionic strength the addition of native or PLP-modified cytochromes c does not change the membrane potential.