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.     

Further studies on the partial double Donnan. Is isosmotic KCl solution isotonic with cells of respiratory trees of the holothurian Isostichopus badionotus Selenka?

As potassium, chloride and water traverse cell membranes, the cells of stenohaline marine invertebrates should swell if exposed to sea water mixed with an isosmotic KCl solution as they do when exposed to sea water diluted with water. To test this hypothesis respiratory tree fragments of the holothurian Isostichopus badionotus were exposed to five isosmotic media prepared by mixing artificial sodium sea water with isosmotic (611 mmol/l) KCl solution to obtain 100, 83, 71, 60 and 50% sea water, with and without 2 mmol/l ouabain. For comparison, respiratory tree fragments were incubated in sea water diluted to the same concentrations with distilled water, with and without ouabain. Cell water contents and potassium and sodium concentrations were unaffected by KCl-dilution or ouabain in isosmotic KCl-sea water mixtures. In tissues exposed to H(2)O-diluted sea water, cell water increased osmometrically and potassium, sodium and chloride concentrations decreased with dilution; ouabain caused a decrease in potasium and an increase in sodium but no effect on chloride concentrations. The isotonicity of the isosmotic KCl solution cannot be adscribed to impermeability of the cell membrane to KCl as both ions easily traverse the cell membrane. Rather, operationally immobilized extracellular sodium ions, which electrostatically hold back anions and consequently water, together with the lack of a cellward electrochemical gradient for potassium, resulting from membrane depolarization caused by high external potassium concentration, would explain the isotonicity of isosmotic KCl solution. The high external potassium concentration also antagonizes the inhibitory effect of ouabain on the Na(+)/K(+) ATPase responsible for sodium and potassium active transport.     

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.     

Activation of cell membrane potassium conductance by mercury in cultured renal epithelioid (MDCK) cells

To elucidate mechanisms of mercury toxicity, the cell membrane potential has been determined continuously in cultured kidney (MDCK)-cells during reversible application of mercury ions to extracellular perfusate. Exposure of the cells to 1 microM mercury ions is followed by rapid, sustained, and slowly reversible hyperpolarization of the cell membrane, increase of cell membrane potassium selectivity, and decrease of cell membrane resistance. Thus, mercury ions enhance the potassium conductance of the cell membrane. Half maximal hyperpolarizing effect is elicited by approximately 0.2 microM. Higher concentrations of mercury ions (greater than 10 microM) eventually depolarize the cell membrane. At extracellular calcium activity reduced to less than 0.1 microM, 1 microM mercury ions still leads to a sustained hyperpolarization and increase of potassium selectivity of the cell membrane. As evident from fluorescence measurements, 10 microM, but not 1 microM mercury ions leads to a rapid increase of intracellular calcium activity. Pretreatment of the cells with either pertussis toxin or cholera toxin does not blunt the hyperpolarizing effect of mercury ions. In conclusion, mercury ions activate the potassium conductance by a mechanism independent of increase of intracellular calcium activity and of cholera toxin- or pertussis toxin-sensitive G-proteins. This activation of potassium conductance may account for early effects of mercury intoxication, such as kaliuresis.     

Water and ion balance in the tissues of the dehydrated cockroach, Periplaneta americana

Cockroaches dehydrated for 8 days lost nearly 50% of their haemolymph volume and approx 25% of their tissue water. Haemolymph osmolality and sodium, potassium, and chloride concentrations in the haemolymph and tissue water were all regulated within narrow limits. It is confirmed that sodium and potassium ions are sequestered within the fat body during periods of dehydration. The increase in sodium and potassium ions in the fat body is shown to arise from ionic regulation of haemolymph and other tissues. During periods of rehydration, sodium and potassium concentrations decrease in the fat body and haemolymph volume and ionic concentrations return to near original levels. A small proportion of the surplus haemolymph chloride ions is shown to be associated with the cuticle during times of water deprivation.     

Osmoregulation in the Extremely Euryhaline Marine Micro-Alga Chlorella autotrophica

Chlorella autotrophica (Clone 580) grows over the external salinity range of 1 to 400% artificial sea water (ASW), can photosynthesize over the range from 1 to 600% ASW, and survives the complete evaporation of seawater. The alga grown at high salinities shows an increase in cell volume and a small decrease in cell water content. Measurements of ion content were made by neutron activation analysis on cells washed in isoosmotic sorbitol solutions which contained a few millimolar of major ions to prevent ion leakage. Cells grown at various ASW concentrations contain large quantities of sodium, potassium, and chloride ions. Measurements of cations associated with cell wall and intracellular macromolecules were made to determine intracellular concentration of free ions. The proline content of cells increases in response to increases in external salinity. Cells in 300% ASW contain 1500 to 1600 millimolar proline.     

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the “mechanism of adhesion-induced compression of cells,” i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.     

A thermodynamic study of electroneutral K-Cl cotransport in pH- and volume-clamped low K sheep erythrocytes with normal and low internal magnesium

Swelling-induced human erythrocyte K-Cl cotransport is membrane potential independent and capable of uphill transport. However, a complete thermodynamic analysis of basal and stimulated K-Cl cotransport, at constant cell volume, is missing. This study was performed in low K sheep red blood cells before and after reducing cellular free Mg into the nanomolar range with the divalent cation ionophore A23187 and a chelator, an intervention known to stimulate K- Cl cotransport. The anion exchange inhibitor 4,4''diisothiocyanato- 2,2''disulfonic stilbene was used to clamp intracellular pH and Cl or NO3 concentrations. Cell volume was maintained constant as external and internal pH differed by more than two units. K-Cl cotransport was calculated from the K effluxes and Rb (as K congener) influxes measured in Cl and NO3, at constant internal K and external anions, and variable concentrations of extracellular Rb and internal anions, respectively. The external Rb concentration at which net K-Cl cotransport is zero was defined as flux reversal point which changed with internal pH and hence Cl. Plots of the ratio of external Rb concentrations corresponding to the flux reversal points and the internal K concentration versus the ratio of the internal and external Cl concentrations (i.e., the Donnan ratio of the transported ions) yielded slopes near unity for both control and low internal Mg cells. Thus, basal as well as low internal Mg-stimulated net K-Cl cotransport depends on the electrochemical potential gradient of KCl.     

Regulation of ion permeabilities of isolated rat liver cells by external calcium concentration and temperature.

Regulation of ion transport through the plasma membrane was studied on single cell suspensions of hepatocytes, obtained after perfusion of rat liver with collagenase/hyaluronidase solution. Steady-state intracellular K and Na contents were shown to be markedly dependent on external Ca concentration and temperature, the sum of both ion concentrations remaining nearly constant. In contrast, steady-state intracellular chloride content was found to be independent of external Ca concentration, but dependent on temperature. Using the constant field relations, the passive permeabilities PK and PCl for potassium and chloride, respectively, were derived from the experimental data. At temperatures at and above 37 degrees C, with increasing external Ca concentration, PK, exhibits a sharp decrease at about 10(-4)M. In contrast, PCl at 37 degrees C was found to be independent of Ca concentration within experimental error. Earth alkali ions other than Ca, show marked but different effects on PK if compared at equal concentrations. Preincubation of the cells with cholesterol leads to a broadening of the dependence of PK on external Ca concentration. The above results, as well as those on the dependence of PK on external Ca concentration obtained by other authors, could be quantitatively described by a theoretical model of the plasma membrane proposed earlier. This model postulates regulatory binding sites, which cooperatively undergo a cation exchange of divalent cations by K+ ions from the external medium if the cation composition of the latter is altered.     

Membrane potential measurements during rat liver regeneration

Membrane potential was measured in perfused rat liver and was shown to increase from ?33 ± 1.0 mV in livers from normal rats to ?50 ± 1.1 mV in livers from rats 12 hr after partial hepatectomy. The hyperpolarization of the membrane in regenerating liver was no longer evident after perfusion with 1 mM ouabain for 5 min. Ouabain had a small (4 mV) depolarizing effect on membrane potential in normal liver. The potential measured in normal and regenerating liver decreased as a function of the external potassium concentration above 5 mM; however, the potential was more electronegative in regenerating liver compared to normal liver at all values of external potassium concentration, and the differences in potential between the two kinds of cells did not decrease at higher concentrations of external potassium. Thus, a plot of membrane potential vs external potassium concentration resulted in approximately parallel curves for the two different cell types. We conclude that hyperpolarization of the liver cell membrane is an early event during rat liver regeneration and results from an electrogenic Na-K pump.     

Energetics of swelling in isolated hepatocytes: A comprehensive study

Cell swelling is now admitted as being a new principle of metabolic control but little is known about the energetics of cell swelling. We have studied the influence of hypo- or hyperosmolarity on both isolated hepatocytes and isolated rat liver mitochondria. Cytosolic hypoosmolarity on isolated hepatocytes induces an increase in matricial volume and does not affect the myxothiazol sensitive respiratory rate while the absolute value of the overall thermodynamic driving force over the electron transport chain increases. This points to an increase in kinetic control upstream the respiratory chain when cytosolic osmolarity is decreased. On isolated rat liver mitochondria incubated in hypoosmotic potassium chloride media, energetic parameters vary as in cells and oxidative phosphorylation efficiency is not affected. Cytosolic hyperosmolarity induced by sodium co-transported amino acids, per se, does not affect either matrix volume or energetic parameters. This is not the case in isolated rat liver mitochondria incubated in sucrose hyperosmotic medium. Indeed, in this medium, adenine nucleotide carrier is inhibited as the external osmolarity increases, which lowers the state 3 respiration close to state 4 level and consequently leads to a decrease in oxidative phosphorylation efficiency. When isolated rat liver mitochondria are incubated in KCl hyperosmotic medium, state 3 respiratory rate, matrix volume and membrane electrical potential vary as a function of time. Indeed, matrix volume is recovered in hyperosmotic KCl medium and this recovery is dependent on Pi-Kentry. State 3 respiratory rate increases and membrane electrical potential difference decreases during the first minutes of mitochondrial incubation until the attainment of the same value as in isoosmotic medium. This shows that matrix volume, flux and force are regulated as a function of time in KCl hyperosmotic medium. Under steady state, neither matrix volume nor energetic parameters are affected. Moreover, NaCl hyperosmotic medium allows matrix volume recovery but induces a decrease in state 3 respiratory flux. This indicates that potassium is necessary for both matrix volume and flux recovery in isolated mitochondria. We conclude that hypoosmotic medium induces an increase in kinetic control both upstream and on the respiratory chain and changes the oxidative phosphorylation response to forces. At steady state, hyperosmolarity, per se, has no effect on oxidative phosphorylation in either isolated hepatocytes or isolated mitochondria incubated in KCl medium. Therefore, potassium plays a key role in matrix volume, flux and force regulation.     

Relationship between ion distribution and membrane potential during a steady state

Equations were derived showing the relationship between the membrane potential and the quantities which influence it under steady state conditions. Essentially, the membrane potential is caused by the valence and concentration of the non-permeating ions. The permeating ions can modify the membrane potential by altering the relative concentration of the non-permeating ions with respect to the concentration of the permeating ions. For muscle, the sodium cations act as the non-permeating ions in the extracellular environment by the maintenance of some type of active metabolic process and large anions act as the non-permeating ions in the intracellular environment. Both of these non-permeating ions contribute about equally to the maintenance of the resting membrane potential. When the active metabolic process for sodium extrusion breaks down or when acids are added, the membrane potential should decrease. Water should enter the cell when the sodium metabolic process is diminished; water should leave the cell when acids are added. When acid is added, it is expected that the cations potassium and sodium will leave the cell with little or no shift of the chloride ions.     

Effects of external ions on membrane potentials of a lobster giant axon

The effects of varying external concentrations of normally occurring cations on membrane potentials in the lobster giant axon have been studied and compared with data presently available from the squid giant axon. A decrease in the external concentration of sodium ions causes a reversible reduction in the amplitude of the action potential and its rate of rise. No effect on the resting potential was detected. The changes are of the same order of magnitude, but greater than would be predicted for an ideal sodium electrode. Increase in external potassium causes a decrease in resting potential, and a decrease in potassium causes an increase in potential. The data so obtained are similar to those which have been reported for the squid giant axon, and cannot be exactly fitted to the Goldman constant field equation. Lowering external calcium below 25 mM causes a reduction in resting and action potentials, and the occasional occurrence of repetitive activity. The decrease in action potential is not solely attributable to a decrease in resting potential. Increase of external calcium from 25 to 50 mM causes no change in transmembrane potentials. Variations of external magnesium concentration between zero and 50 mM had no measurable effect on membrane potentials. These studies on membrane potentials do not indicate a clear choice between the use of sea water and Cole's perfusion solution as the better external medium for studies on lobster nerve.     

Effects of lead chloride on human erythrocyte membranes and on kinetic anion sulphate and glutathione concentrations

Our study concerns the effects of exposure to lead chloride on the morphology, K⁺ efflux, SO₄ ^? influx and GSH levels of the human erythrocyte. Blood was collected in heparinized tubes and washed three times. The cells were suspended at 3% hematocrit and incubated for 1 h at 25°C in a medium containing increasing concentrations of lead chloride (0, 0.3, 0.5 and 1 ??M). After incubation, the suspensions were centrifuged and the erythrocyte pellets were divided into three aliquots for testing. The results show: an increase in the permeability of erythrocytes treated with lead chloride with consequent damage and cellular death, especially in the presence of high concentrations; an increase in potassium ion efflux; alterations in the morphology and membrane structure of the red blood cells; and a decrease in sulphate uptake, due either to the oxidative effect of this compound on the band 3 protein, which loses its biological valence as a carrier of sulphate ions, or to a decrease in the ATP erythrocyte concentration. In conclusion, the exposure of erythrocytes to Pb²⁺ ions leads to a reduction in the average lifetime of the erythrocytes and the subsequent development of anemia. These data are discussed in terms of the possible effect of lead on the reduction-oxidation systems of the cell. Oxidant agents, such as lead, are known to cross-link integral membrane proteins, leading to K/Cl-cotransport. The increased K⁺ efflux affects the altered redox state.     

A network model for biofilm development in Escherichia coli K-12

Proteins in any solution with a pH value that differs from their isoelectric point exert both an electric Donnan effect (DE) and colloid osmotic pressure. While the former alters the distribution of ions, the latter forces water diffusion. In cells with highly Cl^--permeable membranes, the resting potential is more dependent on the cytoplasmic pH value, which alters the Donnan effect of cell proteins, than on the current action of Na/K pumps. Any weak (positive or negative) electric disturbances of their resting potential are quickly corrected by chloride shifts. In many excitable cells, the spreading of action potentials is mediated through fast, voltage-gated sodium channels. Tissue cells share similar concentrations of cytoplasmic proteins and almost the same exposure to the interstitial fluid (IF) chloride concentration. The consequence is that similar intra- and extra-cellular chloride concentrations make these cells share the same Nernst value for Cl^-. Further extrapolation indicates that cells with the same chloride Nernst value and high chloride permeability should have similar resting membrane potentials, more negative than -80 mV. Fast sodium channels require potassium levels >20 times higher inside the cell than around it, while the concentration of Cl^- ions needs to be >20 times higher outside the cell. When osmotic forces, electroneutrality and other ions are all taken into account, the overall osmolarity needs to be near 280 to 300 mosm/L to reach the required resting potential in excitable cells. High plasma protein concentrations keep the IF chloride concentration stable, which is important in keeping the resting membrane potential similar in all chloride-permeable cells. Probable consequences of this concept for neuron excitability, erythrocyte membrane permeability and several features of circulation design are briefly discussed.     

Effects of hyperosmolarity and furosemide on resting membrane potentials and skeletal muscle fiber volume in rats

The changes of the muscle fibres volume and resting membrane potential (RMP) were studied following treatment with hypertonic medium and furosemide. The volume changes in hypertonic medium began with cell shrinkage and later have been followed by the volume increase up to normal level during 30-40 minutes. At the same time the medium hypertonicity caused muscle fibres depolarisation. The hypertonic-induced decrease of the RMP was delayed in the furosemide-treated muscle. Besides, furosemide abolished the muscle fibres volume restorative properties in hypertonic medium. It is suggested that the membrane depolarisation and cell volume restoration in hypertonic medium are the resultant effects of intracellular chloride ions level elevation which, in turn, have been evoked by activation of furosemide-sensitive Cl(-)-influx system.     

Efflux and exchange of glycine by plasma membrane vesicles isolated from glioblastoma cells

The efflux and exchange of glycine were studied in plasma membrane vesicles isolated from cultured glioblastoma cells. The mechanism of glycine translocation has been probed by comparing the ion dependence of net efflux to that of exchange. Dilution-induced efflux requires the simultaneous presence of internal sodium and chloride, while influx is dependent on the presence of these two ions on the outside (Zafra, F. and Giménez, C. (1986) Brain Res. 397, 108-116). Glycine efflux from the membrane vesicles is stimulated by external glycine, this exchange being dependent on external sodium, but not on external chloride. The parallelism observed in influx and efflux processes suggests that glycine is translocated in both directions across the membrane, probably by interacting with the carrier. To account for all the observed effects of external ions, glycine concentrations and membrane potential on glycine influx and efflux, a kinetic model of the Na+/Cl-/glycine cotransport system is discussed.     

Motile activities of Dictyostelium discoideum differ from those in Protista or vertebrate animal cells

Cell movement in the amoebae Dictyostelium discoideum has been examined in media differing in monovalent cation concentration (i.e. Na+ and K+). Under isotonic or even slightly hypertonic conditions, the cells move equally well in solutions in which either potassium or sodium ions dominate. However, in strongly hypertonic solutions the amoebae showed motility in a 2% potassium chloride solution, but remained motionless in a hypertonic 2% sodium chloride solution. This inhibition of D. discoideum amoebae movement in a hypertonic sodium chloride solution was fully reversible. Such behaviour corresponds to that of plant, fungi, and some invertebrate animal cells rather than protozoan or vertebrate cells. These observations suggest that studies using D. discoideum as a model for cell motility in vertebrate animal tissue cells should be considered with caution, and would seem to confirm the classification of cellular slime moulds as related rather to Fungi than to Protista. This also shows that the cell membrane models should consider the asymmetry in sodium/potassium ion concentrations found in vertebrate animal cells as one of various possibilities.     

Involvement of Volume-Activated Chloride Channels in H2O2 Preconditioning Against Oxidant-Induced Injury Through Modulating Cell Volume Regulation Mechanisms and Membrane Permeability in PC12 Cells

The functions of chloride channels in preconditioning-induced cell protection remain unclear. In this report, we show that the volume-activated chloride channels play a key role in hydrogen peroxide (H₂O₂) preconditioning-induced cell protection in pheochromocytoma PC12 cells. The preconditioning with 100 μM H₂O₂ for 90 min protected the cells from injury induced by long period exposure to 300 μM H₂O₂. The protective effect was attenuated by pretreatment with the chloride channel blockers, 5-nitro-2-3-phenylpropylamino benzoic acid (NPPB) and tamoxifen. H₂O₂ preconditioning directly activated a chloride current, which was moderately outward-rectified and sensitive to the chloride channel blockers and hypertonicity-induced cell shrinkage. H₂O₂ preconditioning functionally up-regulated the activities of volume-activated chloride channels and enhanced the regulatory volume decrease when exposure to extracellular hypotonic challenges. In addition, acute application of H₂O₂ showed distinctive actions on cell volume and membrane permeability in H₂O₂ preconditioned cells. In H₂O₂ preconditioned cells, acute application of 300 μM H₂O₂ first promptly induced a decrease of cell volume and enhancement of cell membrane permeability, and then, cell volume was maintained at a relatively stable level and the facilitation of membrane permeability was reduced. Conversely, in control cells, 300 μM H₂O₂ induced a slow but persistent apoptotic volume decrease (AVD) and facilitation of membrane permeability. H₂O₂ preconditioning also significantly up-regulated the expression of ClC-3 protein, the molecular candidate of the volume-activated chloride channel. These results suggest that H₂O₂ preconditioning can enhance the expression and functional activities of volume-activated chloride channels, thereby modulate cell volume and cell membrane permeability, which may contribute to neuroprotection against oxidant-induced injury.     

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.