Activity-mediated accumulation of potassium induces a switch in firing pattern and neuronal excitability type

During normal neuronal activity, ionic concentration gradients across a neuron’s membrane are often assumed to be stable. Prolonged spiking activity, however, can reduce transmembrane gradients and affect voltage dynamics. Based on mathematical modeling, we investigated the impact of neuronal activity on ionic concentrations and, consequently, the dynamics of action potential generation. We find that intense spiking activity on the order of a second suffices to induce changes in ionic reversal potentials and to consistently induce a switch from a regular to an intermittent firing mode. This transition is caused by a qualitative alteration in the system’s voltage dynamics, mathematically corresponding to a co-dimension-two bifurcation from a saddle-node on invariant cycle (SNIC) to a homoclinic orbit bifurcation (HOM). Our electrophysiological recordings in mouse cortical pyramidal neurons confirm the changes in action potential dynamics predicted by the models: (i) activity-dependent increases in intracellular sodium concentration directly reduce action potential amplitudes, an effect typically attributed solely to sodium channel inactivation; (ii) extracellular potassium accumulation switches action potential generation from tonic firing to intermittently interrupted output. Thus, individual neurons may respond very differently to the same input stimuli, depending on their recent patterns of activity and/or the current brain-state.     

Cell volume regulation in liver

The maintenance of liver cell volume in isotonic extracellular fluid requires the continuous supply of energy: sodium is extruded in exchange for potassium by the sodium/potassium ATPase, conductive potassium efflux creates a cell-negative membrane potential, which expelles chloride through conductive pathways. Thus, the various organic substances accumulated within the cell are osmotically counterbalanced in large part by the large difference of chloride concentration across the cell membrane. Impairment of energy supply leads to dissipation of ion gradients, depolarization and cell swelling. However, even in the presence of ouabain the liver cell can extrude ions by furosemide-sensitive transport in intracellular vesicles and subsequent exocytosis. In isotonic extracellular fluid cell swelling may follow an increase in extracellular potassium concentration, which impairs potassium efflux and depolarizes the cell membrane leading to chloride accumulation. Replacement of extracellular chloride with impermeable anions leads to cell shrinkage. During excessive sodium-coupled entry of amino acids and subsequent stimulation of sodium/potassium-ATPase by increase in intracellular sodium activity, an increase in cell volume is blunted by activation of potassium channels, which maintain cell membrane potential and allow for loss of cellular potassium. Cell swelling induced by exposure of liver cells to hypotonic extracellular fluid is followed by regulatory volume decrease (RVD), cell shrinkage induced by reexposure to isotonic perfusate is followed by regulatory volume increase (RVI). Available evidence suggests that RVD is accomplished by activation of potassium channels, hyperpolarization and subsequent extrusion of chloride along with potassium, and that RVI depends on the activation of sodium hydrogen ion exchange with subsequent activation of sodium/potassium-ATPase leading to the respective accumulation of potassium and bicarbonate. In addition, exposure of liver to anisotonic perfusates alters glycogen degradation, glycolysis and probably urea formation, which are enhanced by exposure to hypertonic perfusates and depressed by hypotonic perfusates.     

Effect of the sodium/potassium ratio on glyceraldehyde 3-phosphate dehydrogenase interaction with red cell vesicles.

Binding of glyceraldehyde 3-phosphate to glyceraldehyde-3-phosphate dehydrogenase, the membrane protein known as Band 6, causes shifts in the 31P nuclear magnetic resonance spectrum of the substrate (Fossel, E.T. and Solomon, A.K (1977) Biochim. Biophys. Acta 464, 82--92). We have studied the resonance shifts produced by varying the sodium/potassium ratio, at constant ionic strength, in order to examine the relationship between the cation transport system and glyceraldehyde-3-phosphate dehydrogenase. Alteration of the potassium concentration at the extracellular face of the vesicle affects the conformation of glyceraldehyde-3-phosphate dehydrogenase at the cytoplasmic face, thus showing that a conformation changed induced by a change in extracellular potassium can be transmitted across the membrane. Alterations of the sodium concentration at the cytoplasmic face also affect the enzyme conformation, whereas sodium changes at the extracellular face are without effect. In contrast, there is no sidedness difference in the effect of potassium concentrations. The half-values for these effects are like those for activation of the red cell (Na4 + K+)-ATPase. We have also produced ionic concentration gradients across the vesicle similar to those Glynn and Lew (1970) J. Physiol. London 207, 393--402) found to be effective in running the cation pump backwards to produce adenosine triphosphate in the human red cell. The sodium/potassium concentration dependence of this process in red cells is mimicked by 31P resonance shifts in the (glyceraldehyde 3-phosphate/glyceraldehyde-3-phosphate dehydrogenase/inside out vesicle) system. These experiments provide strong support for the existence of a functional linkage between the membrane (Na+ + K+)-ATPase and the glyceraldehyde-3-phosphate dehydrogenase at the cytoplasmic face.     

Computer simulation for teaching membrane potential fundamentals

A computer simulation of membrane potential generation is presented. It allows the user to vary the intra and extracellular concentrations of sodium, potassium and chloride ions (Na⁺, K⁺ and Cl⁻), and determine the membrane potential and the equilibrium potential for each ion. The permeability coefficients for the ionic species considered, and the temperature may also be changed at will. Concentration-potential curves may be obtained at any time. The user may also select a voltage clamp option, which allows him to impose a certain membrane potential value, and study the resulting driving force for each ion. The use of the program in general physiology courses has shown it to be a useful aid for teaching the principles of membrane potential generation.     

Effect of the sodium/potassium ratio on glyceraldehyde-3-phosphate dehydrogenase interaction with red cell vesicles

Binding of glyceraldehyde 3-phosphate to glyceraldehyde-3-phosphate dehydrogenase, the membrane protein known as Band 6, causes shifts in the ³¹P nuclear magnetic resonance spectrum of the substrate (Fossel, E.T. and Solomon, A.K. (1977) Biochim. Biophys. Acta 464, 82–92). We have studied the resonance shifts produced by varying the sodium/potassium ratio, at constant ionic strength, in order to examine the relationship between the cation transport system and glyceraldehyde-3-phosphate dehydrogenase. Alteration of the potassium concentration at the extracellular face of the vesicle affects the conformation of glyceraldehyde-3-phosphate dehydrogenase at the cytoplasmic face, thus showing that a conformation change induced by a change in extracellular potassium can be transmitted across the membrane. Alterations of the sodium concentration at the cytoplasmic face also affect the enzyme conformation, whereas sodium changes at the extracellular face are without effect. In contrast, there is no sidedness difference in the effect of potassium concentrations. The half-values for these effects are like those for activation of the red cell (Na⁺ + K⁺)-ATPase. We have also produced ionic concentration gradients across the vesicle similar to those Glynn and Lew ((1970) J. Physiol. London 207, 393–402) found to be effective in running the cation pump backwards to produce adenosine triphosphate in the human red cell. The sodium/potassium concentration dependence of this process in red cells is mimicked by ³¹P resonance shifts in the (glyceraldehyde 3-phosphate/glyceraldehyde-3-phosphate dehydrogenase/inside out vesicle) system. These experiments provide strong support for the existence of a functional linkage between the membrane (Na⁺ + K⁺)-ATPase and the glyceraldehyde-3-phosphate dehydrogenase at the cytoplasmic face.     

Ionic mechanism for the generation of horizontal cell potentials in isolated axolotl retina

The ionic mechanism of horizontal cell potentials was investigated in the isolated retina of the axolotl Ambystoma mexicanum. The membrane potentials of both receptors and horizontal cells were recorded intracellularly while the ionic composition of the medium flowing over the receptor side of the retina was changed. The membrane potential of the horizontal cell is highly depender side of the retina was changed. The membrane potential of the horizontal cell is highly dependent on the extracellular concentration of sodium. When the external ion concentration of either chloride or potassium was changed independently of the other, there were shifts in the membrane potential of the horizontal cell which could not be explained by changes in the equilibrium potential of these ions. If the external concentrations of both potassium and chloride ions were varied so that the product of their external concentrations did not change, the shift in the membrane potential of the horizontal cell was in the direction predicted by the Nernst equation. The results are consistent with the suggestion that in the dark the receptors release a synaptic transmitter which increases primarily the sodium conductance of the horizontal cell postsynaptic membrane.     

Electrophysiology of differentiating mouse spermatozoa.

The morphological aspects of spermatogenesis are well described in many mammalian species, but functional changes are not completely understood. Electrophysiological parameters were investigated in primary spermatocytes and early and late spermatids isolated from the seminiferous tubules of the mouse. Substantial changes were not detected in membrane potential between different developmental stages. Membrane potential was dependent on both potassium and sodium ion concentration gradients, but not on chloride gradients. The ratio of the permeabilities PNa/Pk varied according to the extracellular concentrations of sodium and potassium. Ouabain, a specific inhibitor of Na+, K+-activated ATPase, produced a maximal reduction in membrane potential of 20%. Comparisons were drawn between differentiating germ cells and previously determined properties of mature spermatozoa.     

Ion fluxes in giant excised cardiac membrane patches detected and quantified with ion-selective microelectrodes

We have used ion-selective electrodes (ISEs) to quantify ion fluxes across giant membrane patches by measuring and simulating ion gradients on both membrane sides. Experimental conditions are selected with low concentrations of the ions detected on the membrane side being monitored. For detection from the cytoplasmic (bath) side, the patch pipette is oscillated laterally in front of an ISE. For detection on the extracellular (pipette) side, ISEs are fabricated from flexible quartz capillary tubing (tip diameters, 2-3 microns), and an ISE is positioned carefully within the patch pipette with the tip at a controlled distance from the mouth of the patch pipette. Transport activity is then manipulated by solution changes on the cytoplasmic side. Ion fluxes can be quantified by simulating the ion gradients with appropriate diffusion models. For extracellular (intrapatch pipette) recordings, ion diffusion coefficients can be determined from the time courses of concentration changes. The sensitivity and utility of the methods are demonstrated with cardiac membrane patches by measuring (a) potassium fluxes via ion channels, valinomycin, and Na/K pumps; (b) calcium fluxes mediated by Na/Ca exchangers; (c) sodium fluxes mediated by gramicidin and Na/K pumps; and (d) proton fluxes mediated by an unknown electrogenic mechanism. The potassium flux-to-current ratio for the Na/K pump is approximately twice that determined for potassium channels and valinomycin, as expected for a 3Na/2K pump stoichiometery (i.e., 2K/charge moved). For valinomycin-mediated potassium currents and gramicidin-mediated sodium currents, the ion fluxes calculated from diffusion models are typically 10-15% smaller than expected from the membrane currents. As presently implemented, the ISE methods allow reliable detection of calcium and proton fluxes equivalent to monovalent cation currents <1 pA in magnitude, and they allow detection of sodium and potassium fluxes equivalent to <5 pA currents. The capability to monitor ion fluxes, independent of membrane currents, should facilitate studies of both electrogenic and electroneutral ion-coupled transporters in giant patches.     

A model for axonal propagation incorporating both radial and axial ionic transport.

We present an axonal model that explicitly includes ionic diffusion in the intracellular, periaxonal, and extracellular spaces and that incorporates a Hodgkin-Huxley membrane, extended with potassium channel inactivation and active ion transport. Although ionic concentration changes may not be significant in the time course of one action potential, they are important when considering the long-term behavior (seconds to minutes) of an axon. We demonstrate this point with simulations of transected axons where ions are moving between the intra- and extracellular spaces through an opening that is sealing with time. The model predicts that sealing must occur within a critical time interval after the initial injury to prevent the entire axon from becoming permanently depolarized. This critical time interval becomes considerably shorter when active ion transport is disabled. Furthermore, the model can be used to study the effects of sodium and potassium channel inactivation; e.g., sodium inactivation must be almost complete (within 0.02%) to obtain simulation results that are realistic.     

Potassium uniport and ATP synthesis in Halobacterium halobium.

Light-driven potassium ion uptake in Halobacterium halobium is mediated by bacteriorhodopsin. This uptake is charge-balanced by sodium ions and not by proton release. Light-induced shifts in concentrations of divalent cations were found to be negligible. The transient changes in extracellular pH (alkaline overshoot) can be understood by the concomitant processes of ATP synthesis, proton/sodium exchange and potassium uptake. The driving force of potassium ion uptake is the membrane potential, no ATP-dependent potassium transport process is found. Fluorescence measurements indicate a high permeability of the membrane to potassium ions compared to sodium ions. Therefore the potassium ion diffusion potential contributes to the membrane potential (about 30 mV/decade) and thereby influences the ATP level. Sudden enhancement of the diffusion potential by the potassium ionophore monactin leads to the expected transient increase in cellular ATP level. Due to the large size (up to 100-fold) of the potassium ion gradient and its high capacity (intracellular concentration up to 3 M) the potassium ion gradient can well serve the cell as a long term storage form of energy.     

Temporal relationship between neurotransmitter release and ion flux during spreading depression and anoxia

Brain ion homeostasis is severely perturbed during spreading depression of Leao and during anoxia. The ionic composition of the extracellular space changes abruptly and approaches the intracellular concentrations owing to an increase in cell permeability. In spreading depression, synchronous transmitter efflux caused by a depolarization of the presynaptic terminals has been implicated as a possible mechanism that would explain the concomitant movement of ions. Anoxia, having many features in common with spreading depression, may follow the same mechanism. We have measured the concentrations of extracellular potassium with ion-selective microelectrodes and dopamine by in vivo voltammetry with carbon fiber microelectrodes during spreading depression and anoxia to compare the temporal relationship between the release of dopamine and ion movements in the striatum. There is a pronounced release of dopamine during both spreading depression and anoxia. In spreading depression, the sharp increase of potassium concentration that follows an initial smaller and slower increase of potassium is accompanied by the release of dopamine. In anoxia, the dopamine release clearly precedes the fast rise of extracellular potassium concentration. We conclude that in striatum, there is a pronounced dopamine release during spreading depression and anoxia, but that the relationships between ionic changes and transmitter release for these two phenomena are different and probably reflect different mechanisms.     

Extracellular charge adsorption influences intracellular electrochemical homeostasis in amphibian skeletal muscle

The membrane potential measured by intracellular electrodes, E_m, is the sum of the transmembrane potential difference (E₁) between inner and outer cell membrane surfaces and a smaller potential difference (E₂) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space. This study investigates the influence of E₂ upon transmembrane ion fluxes, and hence cellular electrochemical homeostasis, using an integrative approach that combines computational and experimental methods. First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations. Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume. Second, the novel analytic glycocalyx formulation was incorporated into the charge-difference cellular model of Fraser and Huang to simulate the influence of extracellular fixed charges upon intracellular ionic homeostasis. Experimental measurements of E_m supported the resulting predictions that an increased magnitude of extracellular fixed charge increases net transmembrane ionic leak currents, resulting in either a compensatory increase in Na⁺/K⁺-ATPase activity, or, in cells with reduced Na⁺/K⁺-ATPase activity, a partial dissipation of transmembrane ionic gradients and depolarization of E_m.     

A model of active transport of ions in hepatocytes

A mathematical model of the transport of basic ions (K⁺, Na⁺, Cl⁻) across the hepatocyte membrane has been created using the previously constructed models of active ion transport in biomembranes. The dependence of the resting potential on extracellular ion concentration has been established. Using the model, it is possible to independently calculate the resting potential at the biomembrane and the concentrations of sodium, potassium, and chlorine ions in the cell. The calculated internal concentrations of the ions are in good agreement with the corresponding experimental values.     

A mathematical model of ion movements in grey matter during a stroke

The development of cytotoxic oedema during a stroke consists in cell swelling and shrinking of the extracellular space. This phenomenon is triggered by ion movements through voltage-gated channels, exchangers and pumps. During ischaemia, sodium, calcium and chloride enter the neurons whereas potassium and glutamate are expelled out of the cells. A mathematical model is proposed to represent the long-term dynamics of membrane potentials, cell volumes and ionic concentrations in intracellular and extracellular spaces during a stroke and to study the influence of each ionic current on cell swelling. The model relies on electrophysiological mechanisms and takes into account the behaviour of two types of cells: neurons and also astrocytes known to play a key role in the excitotoxic process in grey matter. The results obtained when a severe or a moderate ischaemia is simulated are consistent with those observed in the in vitro and in vivo experiments. As this model appears to be robust, it is used to perform illustrative simulations aimed at studying the effect of some channel blockers on cell swelling. This approach may help to explore new therapeutic strategies in order to reduce stroke damage.     

Refractoriness of cation transport in turkey erythrocytes to stimulation by cyclic adenosine 3':5'-monophosphate.

In turkey erythrocytes bidirectional fluxes of sodium and potassium develop a time-dependent refractoriness to stimulation by endogenous cyclic adenosine 3':5'-monophosphate (cyclic AMP). The refractoriness of potassium influx and potassium outflux (both of which require extracellular sodium and potassium for stimulation by cyclic AMP) depends on the extracellular concentrations of sodium and potassium. In contrast, the refractoriness developed by sodium outflux (which does not require extracellular sodium or potassium for stimulation by cyclic AMP) does not depend on the extracellular concentrations of sodium or potassium. The refractoriness of these fluxes to cellular cyclic AMP reflects a decrease in the amount by which they can be maximally stimulated and appears to be proportional to the extent to which the transport system is utilized during the course of the incubation. Ouabain significantly reduces the rate at which cation transport in turkey erythrocytes becomes refractory to endogenous cyclic AMP. This effect of the glycoside is independent of the extracellular concentrations of sodium or potassium and does not correlate with how it alters the initial response of the transport systems to cyclic AMP.     

THE SIGNIFICANCE OF IONIC CONCENTRATIONS IN THE INTERNAL MEDIA OF ANIMALS

1. The electrical and ionic gradients across a cell membrane depend on its permeability properties, on the concentration and net valency of the organic constituents of the cytoplasm and on the critical energy barrier to the extrusion of sodium. Such considerations do not, however, explain the small extent to which the concentration of potassium varies in myoplasm which may, instead, be related to the effects of potassium on particular enzymes. 2. The fact that the apparent optimum level of potassium cannot usually be maintained in animals in which the extracellular level of sodium is below about 140 mM may explain why so many non-marine animals have internal media of about that concentration, for more concentrated body fluids would require more work for their regulation. 3. In axoplasm, the concentration of potassium is more nearly proportional to the concentration of sodium in the internal medium and this may partly explain the general correlation between the extracellular levels of sodium and potassium. 4. The relation between pH and temperature in poikilothermic vertebrates is such as to suggest that the prime function of acid-base regulation is to control the ionization of imidazole groups. 5. High tensions of carbon dioxide cannot be maintained in water-breathing animals because of the high solubility of this gas in water as compared with oxygen. Bicarbonate levels are correspondingly low to give a suitable pH. Higher tensions are possible in air-breathing animals, and also necessary if water and heat are to be conserved, but an uncertain upper limit is set by the need for oxygen. The associated higher levels of bicarbonate confer the advantage of better buffering. 6. Calcium and bicarbonate levels are not obviously limited by the solubility of calcium carbonate and a more general limitation on the composition of body fluids seems to arise from the low solubilities of calcium phosphates. 7. The pattern of ionic balance in vertebrate plasma, reflected in a nearly constant value to the molar ratio ([Ca] + 5 × 10^--⁴)/([K] +0.034 [Na]), may be explained in terms of the maintenance of a constant electrical gradient across certain areas of cell membrane, between the inner and outer double layers. 8. The patterns of cation balance in the haemolymphs of molluscs, crustacea and insects are also reviewed, with emphasis on the correlations existing between the concentrations of different cations. An attempt is made to relate the correlations in the mollusca to the concentrations of cations at the surfaces of cells.     

Amazon fish bacterial communities show structural convergence along widespread hydrochemical gradients

The world's richest freshwater fish community thrives in gradients of contrasting environments in Amazonia, ranging from ion‐poor acidic black waters, to ion‐rich circumneutral white waters. These hydrochemical gradients structure Amazonian fish assemblages via ecological speciation events. Fish bacterial communities contain an important genetic heritage essential for their hosts' survival and are also involved in adaptive divergence via niche adaptation processes, but the extent to which they evolve in response to hydrochemical gradients in Amazonia is unknown. Here we investigated bacterial communities (gut and skin mucus) of two ecologically and phylogenetically divergent host species (Mesonauta festivus and Serrasalmus rhombeus) distributed throughout these hydrochemical gradients. The goal was to characterize intra‐ and interspecific Amazonian fish microbiome variations across multiple scales. Using a 16S metabarcoding approach, we investigated the microbiota of 43 wild M. festivus, 32 S. rhombeus and seven water samples, collected at seven sampling sites encompassing both water colours. Taxonomical structures of bacterial communities from both host species were significantly correlated to the environmental continua of magnesium, sodium, dissolved organic carbon, calcium, dissolved O₂, pH, potassium, hardness and chloride. Analysis of discriminating features in community structures across multiple scales demonstrated intra‐ and interspecific structural parallelisms in the response to the hydrochemical gradients. Together, these parallelisms suggest the action of selection on bacterial community structures along Amazonian hydrochemical gradients. Functional approaches along with reciprocal transplant experiments will provide further insights on the potential contribution of Amazonian fish microbiomes in host adaptation and ecological speciation events.     

Effect of ovulation on the ionic and water content of rabbit oviduct

The water content, extracellular space, intracellular water, potassium, sodium and chloride content of oviduct and uterus removed from rabbits in estrus and 24 and 72 h following hCG injection have been determined. Following ovulation, there was an increase in water content of the region of the oviduct corresponding to the ampullary -isthmic junction which, at 24 h, is probably due to increased intracellular water. In the ampullary-isthmic junction, ovulation decreases the potassium content and, at 24 h in the isthmic region of the oviduct, chloride is reduced. The water and ionic content of mucosa and smooth muscle cells has been calculated and mucosa cells have greater intracellular water and chloride and sodium content and less potassium and extracellular space than the smooth muscle cells of the oviduct. The significance of the changes in ionic and water content is discussed.