Effects of external currents on duration and amplitude of normal and prolonged action potentials from single nodes of Ranvier

Duration and amplitude of normal and prolonged action potentials from single nodes of Ranvier vary as functions of potential changes induced by currents from an external source. The quantitative relations between externally applied potential and the resulting potential generated within the system are analyzed in order to obtain information about the kinetics of the electromotance,—potential,—and chemical changes taking place during excitation. The following preliminary conclusions are drawn: A depolarizing and a repolarizing process (positive and negative electromotance) increase and decrease with the potential. For a sudden potential displacement the negative electromotance reaches its new value at a faster rate than the positive electromotance. Since the individual values of the two electromotances depend on the potential and since they both generate a potential which is proportional to the difference of their absolute values, the values of either electromotance are determined by this difference as well as by any externally induced potential change.     

On the Concept of Resting Potential—Pumping Ratio of the Na+/K+ Pump and Concentration Ratios of Potassium Ions Outside and Inside the Cell to Sodium Ions Inside and Outside the Cell

In animal cells, the resting potential is established by the concentration gradients of sodium and potassium ions and the different permeabilities of the cell membrane to them. The large concentration gradients of sodium and potassium ions are maintained by the Na⁺/K⁺ pump. Under physiological conditions, the pump transports three sodium ions out of and two potassium ions into the cell per ATP hydrolyzed. However, unlike other primary or secondary active transporters, the Na⁺/K⁺ pump does not work at the equilibrium state, so the pumping ratio is not a thermodynamic property of the pump. In this article, I propose a dipole-charging model of the Na⁺/K⁺ pump to prove that the three Na⁺ to two K⁺ pumping ratio of the Na⁺/K⁺ pump is determined by the ratio of the ionic mobilities of potassium to sodium ions, which is to ensure the time constant τ and the τ-dependent processes, such as the normal working state of the Na⁺/K⁺ pump and the propagation of an action potential. Further, the concentration ratios of potassium ions outside and inside the cell to sodium ions inside and outside the cell are 0.3027 and 0.9788, respectively, and the sum of the potassium and sodium equilibrium potentials is ?30.3 mV. A comparative study on these constants is made for some marine, freshwater and terrestrial animals. These findings suggest that the pumping ratio of the Na⁺/K⁺ pump and the ion concentration ratios play a role in the evolution of animal cells.     

A three-state model for inactivation of sodium permeability

The inactivation of Na⁺ permeability in single myelinated motor nerve fibres of Rana esculenta was investigated under voltage and current clamp conditions at 20°C in Ringer's solution and under blocked K⁺ currents. Development of inactivation and its recovery was described by two potential-dependent time constants: The smaller time constant followed the usual bell-shaped function of membrane potential, whereas the larger one was monotone-increasing with more negative potentials. Several three-state models for inactivation were investigated. The experiments could best be approximated by a model with two open and one closed state for inactivation following: open ? closed ? open. Rate constants were determined for all transitions shown from the voltage clamp experiments. The action potentials computed by means of the proposed model were in good agreement with those measured, both in Ringer's solution and under blocked K⁺ current conditions.     

Electrochemical State of Potassium and Sodium in Free Cells of Acer pseudoplatanus

The intracellular distribution of K⁺ and Na⁺ ions has been determined by compartmental analysis of isotope exchange. The simultaneous measurement of electrical potentials allowed us to show that the distribution of K⁺ was close to thermodynamic equilibrium while the internal concentration of Na⁺ was well below the value predicted for the equilibrium. The efflux of Na⁺ was more sensitive to temperature than its influx. Both ouabain and variations in the external levels of KCl produced weak and inconsistent effects, observations which would emphasize the difference between the Na⁺ extrusion mechanism of plants and animals. The Na⁺ extrusion system of Acer cells ceased to be functional in Na⁺-depleted cells but recovered its function if the cells were placed in 10 mM NaCl, which suggests that the extrusion system was induced by the level of internal Na⁺ ions.     

The oxidizing power of the glutathione thiyl radical as measured by its electrode potential at physiological pH

The oxidizing power of the thiyl radical (GS*) produced on oxidation of glutathione (GSH) was determined as the mid-point electrode potential (reduction potential) of the one-electron couple E(m)(GS*,H+/GSH) in water, as a function of pH over the physiological range. The method involved measuring the equilibrium constants for electron-transfer equilibria with aniline or phenothiazine redox indicators of known electrode potential. Thiyl and indicator radicals were generated in microseconds by pulse radiolysis, and the position of equilibrium measured by fast kinetic spectrophotometry. The electrode potential E(m)(GS*,H+/GSH) showed the expected decrease by approximately 0.06 V/pH as pH was increased from approximately 6 to 8, reflecting thiol/thiolate dissociation and yielding a value of the reduction potential of GS*=0.92+/-0.03 V at pH 7.4. An apparently almost invariant potential between pH approximately 3 and 6, with potentials significantly lower than expected, is ascribed at least in part to errors arising from radical decay during the approach to the redox equilibrium and slow electron transfer of thiol compared to thiolate.     

Active transport,ion movements,and pH changes

The transport of substances across cell membranes may be the most fundamental activity of living things. When the substance transported is any ion there can be a change in the concentration of hydrogen ions on the two sides of the membrane. These hydrogen ion concentration changes are not caused by fluxes of hydrogen ions although fluxes of hydrogen ions may sometimes be involved. The reason for the apparent contradiction is quite simple. All aqueous systems are subject to two constraints: (1) to maintain the charge balance, the sum of the cationic charges must equal the sum of the anionic charges and (2) the product of the molar concentration of H⁺ and the molar concentration of OH⁻, established and maintained by the association and the dissociation of water, remains always at 10⁻¹⁴. As a consequence the concentrations of H⁺ and OH⁻ are determined uniquely by differences between the concentrations of the other cations and anions, with [H⁺] and [OH⁻] being dependent variables. Hydrogen ions and hydroxyl ions can be produced or consumed in local reactions whereas any strong ions such as Cl⁻, Mg²⁺, or K⁺ can be neither produced nor consumed in biological reactions. Further consequences of these truisms are outlined here in terms of the chemistry of the kinds of reactions which can lead to pH changes.     

Genetic and physiological evidence concerning the development of chemically sensitive voltage-dependent ionophores in L6 cells

The electrophysiological properties of a tissue culture muscle line, L₆, and a K⁺ resistant mutant (MK₁) derived from L₆ were determined to elucidate certain aspects of membrane differentiation and function. MK₁ was selected as a clone of myoblasts resistant to the toxic effects of 55 mM K⁺. The resting potentials of L₆ and MK₁ myoblasts and myotubes were K⁺ dependent and equal. The amplitudes of the action potentials were equal in normal medium, but 27.7 mM K⁺ interfered with or eliminated the ability of L₆ myotubes to produce action potentials. MK₁ myotubes produced nearly normal action potentials under these conditions. Thus, the K⁺ resistant myoblasts differentiate into myotubes which have an action potential generating mechanism much less sensitive to K⁺ than the normal mechanism. Also, both d-tubocurarine and α-bungarotoxin enhance the amplitude of the action potentials produced by L₆ myotubes in the presence of 27.7 mM K⁺; these compounds do not enhance the amplitude of the action potentials produced by MK₁ myotubes under the same conditions. It is proposed that as a consequence of differentiation a type of ionophore present in myoblasts becomes a voltage-dependent ionophore in myotubes. Furthermore, these voltage-dependent ionophores can be chemically sensitive.     

Soft- and hard-modeling approaches for the determination of stability constants of metal-peptide systems by voltammetry

The Zn(2+)-glutathione system is studied as a model for metal-peptide systems where some critical factors must be considered when using voltammetric techniques for the determination of stability constants. These factors are the presence of side reactions (in this case, both the protonation of glutathione and the hydrolysis of Zn(2+)), the association-dissociation rates of the complexes compared with the time scales of the measurements (which makes the complexes electrochemically labile or inert), and the electron transfer kinetics on the electrode surface (which makes the metal ion reduction reversible or irreversible). For the study of these factors, three data treatment approaches have been applied: (i) the electrochemical hard-modeling approach (modelization of both chemical equilibrium and electrochemical processes), (ii) a chemical hard-modeling approach (modelization of chemical equilibria only, based on the least-squares curve-fitting program SQUAD), and (iii) a previously developed model-free soft-modeling approach based on multivariate curve resolution with a constrained alternating least-squares optimization. By analyzing differential pulse polarographic data obtained under different experimental conditions, the influence of the mentioned factors on every approach is discussed and, if possible, the corresponding stability constants are computed. The results of this study showed the potential usefulness of voltammetry in combination with hard- and soft-modeling data analysis for the study of peptide complexation equilibria of metal ions such as Zn which have neither relevant spectroscopic properties nor proper isotopes for NMR measurements.     

p-CMBS Modifies Extrafacial Sulfhydryl Groups at the Chara Plasma Membrane: Activation of Ca2+ Influx and Inhibition of Two Different K+ Currents

The effect of the membrane impermeant sulfhydryl group (SH) reagent, p-chloromercuribenzenesulfonic acid (p-CMBS), on electrical membrane transport properties of the giant alga, Chara corallina, was determined. In an external medium with a high K⁺ concentration (5 mM) cells typically exhibited stable membrane potentials close to the K⁺equilibrium potential. The steady-state current-voltage (I-V) relation could be dissected into two distinct components: an almost linear ohmic leak current and a voltage-dependent K⁺ current. Adding 0.5 mM p-CMBS to the external medium resulted in an immediate, short depolarization transient (resembling the time course of an action potential) and was associated with a slow down of the cytoplasmic streaming velocity. The depolarization, as well as the streaming inhibition, could be abolished by pretreating cells with the Ca²⁺ channel inhibitor, LaCl₃. This suggests that the depolarization transient reflected a p-CMBS induced Ca²⁺ influx, a scenario known to trigger membrane excitation and slow down of cytoplasmic streaming. From the I-V analysis it appeared that p-CMBS also caused a reversible inhibition of two additional transmembrane currents: (1) a reduction of a leak current and (2) a modification of the deactivation kinetics of the voltage-dependent K⁺ channels. From the I-V difference analysis, the inhibited leak current was identified as a K⁺ current, because the reversal potential was close to the estimated K⁺ equilibrium potential. Control experiments have furthermore shown that the mercapto reagent, dithiothreitol, partly reversed the effect of p-CMBS. This strengthens the view that the action of the mercurial is related to a specific and direct modification of SH groups. The p-CMBS-evoked inhibition of K⁺ currents was not abolished by the LaCl₃ pretreatment, which suggests that the effect of the SH reagent is not induced indirectly by p-CMBS-triggered Ca²⁺ influx. Therefore, it is suggested that the mercurial interacts direcly with the K⁺ transport protein.     

A respiration-dependent primary sodium extrusion system functioning at alkaline pH in the marine bacterium Vibrioalginolyticus

The membrane potential generated at pH 8.5 by K⁺-depleted and Na⁺-loaded $\text{Vibrio}\text{alginolyticus}$ is not collapsed by proton conductors which, instead, induce the accumulation of protons in equilibrium with the membrane potential. The generation of such a membrane potential and the accumulation of protons are specific to Na⁺-loaded cells at alkaline pH and are dependent on respiration. Extrusion of Na⁺ at pH 8.5 occurs in the presence of proton conductors unless respiration is inhibited while it is abolished by proton conductors at acidic pH. The uptake of α-aminoisobutyric acid, which is driven by the Na⁺-electrochemical gradient, is observed even in the presence of proton conductors at pH 8.5 but not at acidic pH. We conclude that a respiration-dependent primary electrogenic Na⁺ extrusion system is functioning at alkaline pH to generate the proton conductor-insensitive membrane potential and Na⁺ chemical gradient.     

Ionic dependence and transmission of epidermal action potentials in a newt embryo

The ionic dependency and transmission of epidermal action potentials have been examined from tailbud to hatching stages of newt embryos. Previously we have reported that the epidermal action potential is composed of a fast- and slow-action component; only the slow-action component, however, is transmitted to other cells. We address in this report the mechanism by which these responses are mediated. The slow-action potential is not produced in Na⁺-free saline, tricaine saline, or following the application of TTX, and thus appears to be Na⁺ dependent. The fast-action potential on the other hand is blocked by application of Co²⁺ and verapamil saline and thus appears to be Ca²⁺ dependent. The slow-action potentials appear to be chemically transmitted since they are transmitted even to those cells which are electrically uncoupled at low intracellular pH (NaHCO₃ + HCl, pH 6.2). Furthermore 1 μM curare and atropine are inhibitory to transmission of the slow potential. Epidermal cells of the newt embryo are sensitive to acetylcholine (ACh) applied by hydrostatic ejection through a micropipet. The latter observation further suggests that propagation of the slow-action potential is, in part, a chemical event.     

Fluorescence correlation spectroscopy. II. An experimental realization

This paper describes the first experimental application of fluorescence correlation spectroscopy, a new method for determining chemical kinetic constants and diffusion coefficients. These quantities are measured by observing the time behaviour of the tiny concentration fluctuations which occur spontaneously in the reaction system even when it is in equilibrium. The equilibrium of the system is not disturbed during the experiment. The diffusion coefficients and chemical rate constants which determine the average time behaviour of these spontaneous fluctuations are the same as those sought by more conventional methods including temperature-jump or other perturbation techniques. The experiment consists essentially in measuring the variation with time of the number of molecules of specified reactants in a defined open volume of solution. The concentration of a reactant is measured by its fluorescence; the sample volume is defined by a focused laser beam which excites the fluorescence. The fluorescent emission fluctuates in proportion with the changes in the number of fluorescent molecules as they diffuse into and out of the sample volume and as they are created or eliminated by the chemical reactions. The number of these reactant molecules must be small to permit detection of the concentration fluctuations. Hence the sample volume is small (10^?8 ml) and the concentration of the solutes is low (～ 10^?9 M). We have applied this technique to the study of two prototype systems: the simple example of pure diffusion of a single fluorescent species, rhodamine 6G, and the more interesting but more challenging example of the reaction of macromolecular DNA with the drug ethidium bromide to form a fluorescent complex. The increase of the fluorescence of the ethidium bromide upon formation of the complex permits the observation of the decay of concentration fluctuations via the chemical reaction and consequently the determination of chemical rate constants.     

Nitrilotris(methylenephosphonates) in aqueous solution and solid state - dilatometric, potentiometric and NMR investigations

Dissociation and alkali complex formation equilibria of nitrilotris(methylenephosphonic acid) (NTMP, H₆L) have been studied by dilatometric, potentiometric and ³¹P NMR-controlled titrations. Dilatometry indicated the formation of alkali complexes ML (M=Li, Na, K, Rb, Cs) at high pH with a stability decreasing from Li to Cs. An efficient combination of potentiometric and NMR methods confirmed two types of alkali metal complexes MHL and ML. Stability constants for the equilibria following M⁺ + HL⁵⁻ ? MHL⁴⁻ and M⁺ + L⁶⁻ ? ML⁵⁻, respectively, were determined: logK_NaHL=1.08(0.07), logK_KHL=0.86(0.08), logK_NaL=2.24(0.03). Systematic errors are introduced by using alkali metal hydroxides as titrants for routine potentiometric determinations of dissociation constants pK_a5^app and pK_a6^app. Correction formulae were derived to convert actual dissociation constants pK_a into apparent dissociation constants pK_a^app (or vice versa). The actual dissociation constants were found: pK_a5(H₂L⁴⁻ ? H⁺ + HL⁵⁻)=7.47(0.03) and pK_a6(HL⁵⁻ ? H⁺ + L⁶⁻)=14.1(0.1). The anisotropy of ³¹P chemical shifts of salts M_nH_6 − nL (M=Li, Na, n=0-5) is more sensitive towards titration (n) than isotropic solution state chemical shifts.     

Relaxation studies on complex formation of macrocyclic and open chain antibiotics with monovalent cations

The stability constants for the 1 : 1 complexes of macrocyclic antibiotics (nonactin, monactin, dinactin and trinactin) with Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, NH⁺₄ and for the Na⁺-complexes with the open chain compounds nigericin and monensin in methanol solution have been determined. The relaxation amplitude method was employed to obtain both the equilibrium constants and the enthalpies of reaction. The kinetics were studied with the help of temperature-jump, electric-field pulse and ultrasonic absorption techniques. Although complex formation of the metal ions with the antibiotics involves multidentate ligand chelation, the formation rates are in general very high, i.e. close to the limits imposed for diffusion controlled processes. The data for the macrotetrolides indicate the existence of conformational transition prior to complexation. A sequential substitution or “redressing” mechanism is proposed which is in accord with the high rates of complex formation. The selectivity patterns, as expressed by the equilibrium constants, are similar to those observed for the transport of metal ions across membranes in presence of the antibiotics. Selectivity results from an optimal balance between the strength of metal ion solvation and the stability of the individual metal complex, which in turn is governed by the conformational flexibility of the antibiotics.     

Influence of surface charge and transmembrane potential on rubidium-86 efflux of human red blood cells

Summary The dependence of the rate constant of Rb⁺ efflux on extracellular cation concentration was measured. At low ionic strengths Rb⁺ efflux increased strongly. Permeability coefficients were calculated from the rate constants measured, using the Goldman flux equation, with and without making allowance for surface potentials. Only when allowance was made for surface potentials and the associated differences beween ion concentrations in the bulk solutions and at the membrane surface, the permeability coefficient remained constant. Best agreement between experimental data and theoretically calculated values was obtained when an interior surface potential of – 110 mV was assumed.When the surface charge of erythrocytes is reduced by neuraminidase, the rate constants for Rb⁺ efflux decreased, indicating a significant influence of surface potential.     

Inward Rectifying K Channels in the Plasma Membrane of Arabidopsis thaliana

Ion channels in the plasma membrane of protoplasts isolated from cultured cells of Arabidopsis thaliana were studied by means of the patch-clamp technique applied in the whole-cell configuration. In some protoplasts, depolarizing pulses and, in other protoplasts, hyperpolarizing pulses elicited time-dependent currents; both kinds of current were only rarely observed in the same protoplast. The hyperpolarization-activated inward rectifying currents, the focus of this paper, appeared to be due to the relatively slow opening of channels (activation time constant = 150 to 300 milliseconds), which closed at positive potentials. The reversal potential of this current, measured in the presence of different ion concentrations (symmetrical or asymmetrical K⁺ and Cl⁻ or gluconate), was always close to the electrochemical equilibrium potential of K⁺. The currents were inhibited by 10 millimolar tetraethylammonium, a K⁺ channel blocker. These data show that the hyperpolarization-activated currents flow through K⁺ channels, which can provide a pathway for the passive diffusion of K⁺ down its electrochemical gradient.     

Effect of Salinity upon Cell Membrane Potential in the Marine Halophyte, Salicornia bigelovii Torr

The electrophysiology of root cells of the marine halophyte, Salicornia bigelovii Torr., has been investigated. Cellular concentrations of K⁺, Cl⁻, and Na⁺ and resulting cell membrane potentials were determined as functions of time and exposure to dilutions of artificial seawater. Treatment of these data by the Nernst criterion suggests that Cl⁻ is actively transported into these root cells, but that active transport need not be invoked to explain the accumulation of Na⁺ at all salinities investigated nor for K⁺ at moderate to high salinities. In low environmental salinity, the cell electropotential of Salicornia root cells was found to respond to inhibitors in a fashion similar to that observed in glycophytes; in high environmental salinity, root cell membrane potential appears to be insensitive to bathing salinity and m-chlorocarbonylcyanide phenylhydrazone induces membrane hyperpolarization, in contrast to the response of glycophytes to such treatments. The fact that measured membrane potentials exceed diffusion potentials for Na⁺, K⁺, and Cl⁻ and the observation of a rapid depolarization by CO in the dark suggests an electrogenic component in Salicornia root cell membrane potentials.     

Membrane potential genesis in<Emphasis Type="Italic"> Nitella</Emphasis> cells,mitochondria, and thylakoids

The resting membrane potential of Nitella cells shifts in parallel with the change in H⁺ equilibrium potential, but is not equal to the H⁺ equilibrium potential. The deviation of the membrane potential from the H⁺ equilibrium potential depends on the extrusion rate of H⁺ by the electrogenic H⁺-pump. The activity of the electrogenic H⁺-pump was formulated in terms of the change in the free energy of ATP hydrolysis. The deviation of membrane potential from the H⁺ equilibrium potential induces a passive H⁺ flow. The passive inward H⁺ current may be coupled with Cl^– uptake. The coupling rate of H⁺,Cl^– co-transport was discussed. The membrane potential of mitochondria was electrochemically formulated in terms of oxidation–reduction H₂/H⁺ half-cells spontaneously formed at the inner and outer boundaries of each trans-membrane electron-conducting pathway. The membrane potential formed by a pair of H₂/H⁺ redox cells is pH-sensitive in its nature, but deviates from the H⁺ equilibrium potential to an extent that depends on the logarithm of the ratio of H₂ concentrations at the inner and outer boundaries. The membrane potential of thylakoids is considered to be primarily due to the electromotive force of photocells embedded in the thylakoid membrane, as far as the anode and cathode of each photocell are in contact with the inner and outer solutions, respectively. The light-induced electronic current yields oxygen at the inner boundary and causes an increase in the H₂ pool at the outer boundary of the electron-conducting pathway, which has no shunting plastoquinone chain between these two boundaries.