First order phase transition and hysteresis in a cell’s maintenance of the membrane potential—An essential role for the inward potassium rectifiers

Hysteretic behavior is found experimentally in the transmembrane potential at low extracellular potassium in mouse lumbrical muscle cells. Adding isoprenaline to the external medium eliminates the bistable, hysteretic region. The system can be modeled mathematically and understood analytically with and without isoprenaline. Inward rectifying potassium channels appear to be essential for the bistability. Relations are derived to express the dimensions of the bistable area in terms of system parameters. The selective advantage and evolutionary origin of inward rectifying channels and hysteretic behavior is discussed.     

Purinergically induced membrane fluidization in ciliary cells: characterization and control by calcium and membrane potential.

To examine the role of membrane dynamics in transmembrane signal transduction, we studied changes in membrane fluidity in mucociliary tissues from frog palate and esophagus epithelia stimulated by extracellular ATP. Micromolar concentrations of ATP induced strong changes in fluorescence polarization, possibly indicating membrane fluidization. This effect was dosage dependent, reaching a maximum at 10-microM ATP. It was dependent on the presence of extracellular Ca2+ (or Mg2+), though it was insensitive to inhibitors of voltage-gated calcium channels. It was inhibited by thapsigargin and by ionomycin (at low extracellular Ca2+ concentration), both of which deplete Ca2+ stores. It was inhibited by the calcium-activated potassium channel inhibitors quinidine, charybdotoxin, and apamine and was reduced considerably by replacement of extracellular Na+ with K+. Hyperpolarization, or depolarization, of the mucociliary membrane induced membrane fluidization. The degree of membrane fluidization depended on the degree of hyperpolarization or depolarization of the ciliary membrane potential and was considerably lower than the effect induced by extracellular ATP. These results indicate that appreciable membrane fluidization induced by extracellular ATP depends both on an increase in intracellular Ca2+, mainly from its internal stores, and on hyperpolarization of the membrane. Calcium-dependent potassium channels couple the two effects. In light of recent results on the enhancement of ciliary beat frequency, it would appear that extracellular ATP-induced changes both in ciliary beat frequency and in membrane fluidity are triggered by similar signal transduction pathways.     

[K+] dependence of open-channel conductance in cloned inward rectifier potassium channels (IRK1, Kir2.1).

Potassium conduction through unblocked inwardly rectifying (IRK1, Kir2.1) potassium channels was measured in inside-out-patches from Xenopus oocytes, after removal of polyamine-induced strong inward rectification. Unblocked IRK1 channel current-voltage (I-V) relations show very mild inward rectification in symmetrical solutions, are linearized in nonsymmetrical solutions that bring the K+ reversal potential to extreme negative values, and follow Goldman-Hodgkin-Katz constant field equation at extreme positive E alpha. When intracellular K+ concentration (KIN) was varied, at constant extracellular K+ concentration (KOUT) the conductance at the reversal potential (GREV) followed closely the predictions of the Goldman-Hodgkin-Katz constant field equation at low concentrations and saturated sharply at concentrations of > 150 mM. Similarly, when KOUT was varied, at constant KIN, GREV saturated at concentrations of > 150 mM. A square-root dependence of conductance on KOUT is a well-known property of inward rectifier potassium channels and is a property of the open channel. A nonsymmetrical two-site three-barrier model can qualitatively explain both the I-V relations and the [K+] dependence of conductance of open IRK1 (Kir2.1) channels.     

Nigericin-induced charge transfer across membranes.

The electric properties of the bilayer lecithin membranes have been studied in the presence of the antibiotic nigericin. When the antibiotic concentration is about 10(-7) ohm-1 cm-2. The potassium ion concentration gradient gives rise to a transmembrane potential of the order of 40 mV per 10-fold concentration gradient with the side of the higher potassium concentration negative. The transmembrane potential produced by the hydrogen ion concentration gradient is a function of the potassium ion concentration which is equal on both sides of the membrane. For low potassium ion concentrations the hydrogen potential has the expected polarity with the solution having higher concentration of protons negative. For potassium ion concentrations exceeding 0.03 M the hydrogen potential has the reverse polarity. This unexpected result cannot be accounted for in terms of the available simple hypotheses about the charge transport mechanism for nigericin in BLM. In order to account for the experimental results obtained, a theoretical approach has been developed based on the assumption that charge is transported across the membrane by nigericin dimers. The theoretical predicitons are in satisfactory agreement with the experimental results. The model also yields some predictions which may be verified in future experiments.     

The ionic basis of electrical activity in embryonic cardiac muscle

The intracellular sodium concentration reported for young, embryonic chick hearts is extremely high and decreases progressively throughout the embryonic period, reaching a value of 43 mM immediately before hatching. This observation suggested that the ionic basis for excitation in embryonic chick heart may differ from that responsible for electrical activity of the adult organ. This hypothesis was tested by recording transmembrane resting and action potentials on hearts isolated from 6-day and 19-day chick embryos and varying the extracellular sodium and potassium concentrations. The results show that for both young and old embryonic cardiac cells the resting potential depends primarily on the extracellular potassium concentration and the amplitude and rate of rise of the action potential depend primarily on the extracellular sodium concentration.     

Measurements of Electrical Potential Differences on Single Nephrons of the Perfused Necturus Kidney

Stable electrical potential differences can be measured by means of conventional glass microelectrodes across the cell membrane of renal tubule cells and across the epithelial wall of single tubules in the doubly perfused kidney of Necturus. These measurements have been carried out with amphibian Ringer's solution, and with solutions of altered ionic composition. The proximal tubule cell has been found to be electrically asymmetrical inasmuch as a smaller potential difference is maintained across the luminal cell membrane than across the peritubular cell boundary. The tubule lumen is always electrically negative with respect to the peritubular extracellular medium. Observations on the effectiveness of potassium ions in depolarizing single tubule cells indicate that the transmembrane potential is essentially an inverse function of the logarithm of the external potassium concentration. The behavior of the peritubular transmembrane potential resembles more closely an ideal potassium electrode than that of the luminal transmembrane potential. From these results, and the effects of various ionic substitutions on the electrical profile of the renal tubular epithelium, a thesis concerning the origin of the observed potential differences is presented. A sodium extrusion mechanism is considered to be located at the peritubular cell boundary, and reasons are given for the hypothesis that the electrical asymmetry across the proximal renal tubule cell could arise as a consequence of differences in the relative sodium and potassium permeability at the luminal and peritubular cell boundaries.     

Effect of potassium on cell volume regulation in renal straight proximal tubules

Summary The present study was designed to assess for the influence of extracellular potassium and of inhibitors of potassium transport on cell volume regulatory decrease in isolated perfused straight proximal tubules of the mouse kidney. Volume regulatory decrease is virtually unaffected when bath potassium concentration is elevated from 5 to 20 mmol/liter, and still persists, albeit significantly retarded, in the presence of the potassium channel blocker barium on both sides of the epithelium and during virtually complete dissipation of the transmembrane potassium gradient by increasing extracellular potassium concentration to 40 mmol/liter. As evident from electrophysiologic observations, barium blocks the potassium conductance of the basolateral cell membrane. Reduction of bicarbonate concentration and increase of H⁺ concentration in the bath solution cannot compensate for enhanced potassium concentration and cell volume regulatory decrease is not affected in the presence of the K/H exchange inhibitor omeprazole. Similarly cell volume regulatory decrease is not affected by ouabain. In conclusion, potassium movements through potassium channels in the basolateral cell membrane are important determinants of cell volume and may participate in cell volume regulatory decrease. However, a powerful component of cell volume regulatory decrease in straight proximal tubules of the mouse kidney is apparently independent of potassium conductive pathways, K/H exchange and Na⁺/K⁺-ATPase.     

Two types of single inward rectifying potassium channels in rat myocardial cells

The patch-clamp method was used to examine inward rectifying potassium channels in the membrane of rat ventricular myocytes. Two types of inward rectifying channels strongly selective for K+ ions and with different conductance and kinetics coexist in rat myocardial cells. When the concentration of K+ was 140 mmol/l on the extracellular side of the patch, the conductance was 38.9 pS for type I channels and 25.7 pS for the type II. The type II channels had a detectable conductance (4 pS) at potentials positive than the potassium equilibrium potential. The mean open time was 18 ms at -60 mV patch membrane potential and 12 ms at -100 mV for type I channels, and 1.3 s at -60 mV and 0.94 s at -105 mV for type II channels, respectively. The opening probability of type II channels decreased with hyperpolarization. The type II channels can adopt several (about 10 or more) conductance states, which can occur either within one opening or as individual events.     

Low pH inhibits compensatory endocytosis at a step between depolarization and calcium influx

Cell function can be modulated by the insertion and removal of ion channels from the cell surface. The mechanism used to keep channels quiescent prior to delivery to the cell surface is not known. In eggs, cortical vesicle exocytosis inserts voltage-gated calcium channels into the cell surface. Calcium influx through these channels triggers compensatory endocytosis. Secretory vesicles contain high concentrations of calcium and hydrogen ions. We propose that lumenal hydrogen ions inhibit vesicular calcium channel gating prior to exocytosis, discharge of lumenal protons upon vesicle-plasma membrane fusion enables calcium channel gating. Consistent with this hypothesis we find that cortical vesicle lumens are acidic, and exocytosis releases lumenal hydrogen ions. Acidic extracellular pH reversibly blocks endocytosis, and the windows of opportunity for inhibition with a calcium-channel blocker or hydrogen ions are indistinguishable. Calcium ionophore treatment circumvents the low pH block, suggesting that calcium influx, or an upstream step, is obstructed. Inhibition of calcium influx by preventing membrane depolarization is unlikely, as elevation of the extracellular potassium concentration failed to overcome the pH block, and low extracellular pH was found to depolarize the membrane potential. We conclude that low pH inhibits endocytosis at a step between membrane depolarization and calcium influx .     

The effect of altered transmembrane ion gradients on membrane potential and aggregation of human platelets in blood plasma

The resting membrane potential of platelets suspended in blood plasma buffer mixture measured using tritiated triphenylmethylphosphonium was 48 ± 13 mV. Increases in extracellular potassium concentration caused depolarization of the platelet membrane. Ouabain (1.0 μM) produced a depolarization of 13 ± 5 mV. Depolarization with elevated extracellular potassium or ouabain potentiated the aggregating effects of adenosine diphosphate even in the presence of methysergide suggesting that the effects are not mediated through ion linked serotonin transport. These observations are consistent with the suggestion that transmembrane ion gradients and membrane potential can regulate platelet sensitivity to the aggregating agent adenosine diphosphate.     

The coupling between extra- and intracellular electric potentials in Bidens pilosa L.

The extracellular electrical potential in Bidens pilosa has been compared with the transmembrane potential in hypocotyl cells. We found that variations in the extracellular electrical potential, induced by different KCI concentrations, were identical to the variations of the transmembrane potential. In order to explain the strong correlation between the extracellular potential and the transmembrane potential, an interpretative model based on the electrical diagram of the plant was tested. From our data, we found that: (1) the symplast behaves as a low resistance pathway compared with the apoplast; and (2) the cell wall contributes weakly (20% at the most) to the transmembrane potential. It is concluded that each hypocotyl cell is strongly coupled electrically with its neighbour. This property, together with the high apoplast resistance, accounts for the similarity in the extracellular and transmembrane potential measurements. These properties, which are characteristic of excitable organs, support the existence of action potentials in Bidens.     

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.     

Nigericin-induced charge transfer across membranes

Summary The electric properties of the bilayer lecithin membranes have been studied in the presence of the antibiotic nigericin. When the antibiotic concentration is about 10^–6 m the conductivity of the BLM is increased up to 10^–7 ohm^–1 cm^–2. The potassium ion concentration gradient gives rise to a transmembrane potential of the order of 40 mV per 10-fold concentration gradient with the side of the higher potassium concentration negative. The transmembrane potential produced by the hydrogen ion concentration gradient is a function of the potassium ion concentration which is equal on both sides of the membrane. For low potassium ion concentrations the hydrogen potential has the expected polarity with the solution having higher concentration of protons negative. For potassium ion concentrations exceeding 0.03m the hydrogen potential has the reverse polarity. This unexpected result cannot be accounted for in terms of the available simple hypotheses about the charge transport mechanism for nigericin in BLM. In order to account for the experimental results obtained, a theoretical approach has been developed based on the assumption that charge is transported across the membrane by nigericin dimers. The theoretical predictions are in satisfactory agreement with the experimental results. The model also yields some predictions which may be verified in future experiments.     

Constitutive activity of TRPML2 and TRPML3 channels versus activation by low extracellular sodium and small molecules

The transient receptor potential channels TRPML2 and TRPML3 (MCOLN2 and MCOLN3) are nonselective cation channels. They are widely expressed in mammals. However, little is known about their physiological function(s) and activation mechanism(s). TRPML3 can be activated or rather de-inhibited by exposing it first to sodium-free extracellular solution and subsequently to high extracellular sodium. TRPML3 can also be activated by a variety of small chemical compounds identified in a high throughput screen and is inhibited by low pH. Furthermore, it was found that TRPML3 is constitutively active in low or no sodium-containing extracellular solution. This constitutive activity is independent of the intracellular presence of sodium, and whole-cell current densities are similar with pipette solutions containing cesium, potassium, or sodium. Here, we present mutagenesis data generated based on the hypothesis that negatively charged amino acids in the extracellular loops of TRPML3 may interfere with the observed sodium inhibition. We systematically mutated negatively charged amino acids in the first and second extracellular loops and found that mutating Glu-361 in the second loop has a significant impact on the sodium-mediated block of TRPML3. We further demonstrate that the TRPML3-related cation channel TRPML2 is also activated by lowering the extracellular sodium concentration as well as by a subset of small chemical compounds that were previously identified as activators of TRPML3, thus confirming the functional activity of TRPML2 at the plasma membrane and suggesting similar gating mechanisms for both TRPML channels.     

Ionic channels of the vacuolar membrane of higher plants

The vacuole is the major storing compartment of the plant cell. There are two different H(+)-translocating pumps generating transmembrane pH gradients and several types of calcium, anion and potassium channels. The fast-activating vacuolar (FV) current dominates at the physiological level of cytoplasmic Ca2+. An increase in the cytoplasmic Ca2+ concentration causes a decrease in the activity of FV channels and a shift of the membrane potential to more negative values. In this case voltage-dependent Ca2+ channels capable of mediating the vacuolar Ca2+ release can be activated. Moreover, an increase in the cytoplasmic Ca2+ concentration activated vacuolar K+ channels described in the vacuolar membrane of stomatal guard cells. A role of slow-activating channels in the Ca(2+)-induced Ca2+ release is rather improbable.     

External K+ modulates the activity of the Arabidopsis potassium channel SKOR via an unusual mechanism

Plant outward-rectifying K+ channels mediate K+ efflux from guard cells during stomatal closure and from root cells into the xylem for root-shoot allocation of potassium (K). Intriguingly, the gating of these channels depends on the extracellular K+ concentration, although the ions carrying the current are derived from inside the cell. This K+ dependence confers a sensitivity to the extracellular K+ concentration ([K+]) that ensures that the channels mediate K+ efflux only, regardless of the [K+] prevailing outside. We investigated the mechanism of K+-dependent gating of the K+ channel SKOR of Arabidopsis by site-directed mutagenesis. Mutations affecting the intrinsic K+ dependence of gating were found to cluster in the pore and within the sixth transmembrane helix (S6), identifying an 'S6 gating domain' deep within the membrane. Mapping the SKOR sequence to the crystal structure of the voltage-dependent K+ channel KvAP from Aeropyrum pernix suggested interaction between the S6 gating domain and the base of the pore helix, a prediction supported by mutations at this site. These results offer a unique insight into the molecular basis for a physiologically important K+-sensory process in plants.     

Localization of the extracellular end of the voltage sensor S4 in a potassium channel

The opening and closing of the pore of voltage-gated ion channels is the basis for the nervous impulse. These conformational changes are triggered by the movement of an intrinsic voltage sensor, the fourth transmembrane segment, S4. The central problem of how the movement of S4 is coupled to channel opening and where S4 is located in relation to the pore is still unsolved. Here, we estimate the position of the extracellular end of S4 in the Shaker potassium channel by analyzing the electrostatic effect of introduced charges in the pore-forming motif (S5-S6). We also present a three-dimensional model for all transmembrane segments. Knowledge of this structure is essential for the attempts to understand how voltage opens these channels.     

Topology of the Shaker Potassium Channel Probed with Hydrophilic Epitope Insertions

The structure of the Shaker potassium channel has been modeled as passing through the cellular membrane eight times with both the NH₂ and COOH termini on the cytoplasmic side (Durrell, S.R., and H.R. Guy. 1992. Biophys. J. 62:238–250). To test the validity of this model, we have inserted an epitope consisting of eight hydrophilic amino acids (DYKDDDDK) in predicted extracellular and intracellular loops throughout the channel. The channels containing the synthetic epitope were expressed in Xenopus oocytes, and function was examined by two-electrode voltage clamping. All of the mutants containing insertions in putative extracellular regions and the NH₂ and COOH termini expressed functional channels, and most of their electrophysiological properties were similar to those of the wild-type channel. Immunofluorescent staining with a monoclonal antibody against the epitope was used to determine the membrane localization of the insert in the channels. The data confirm and constrain the model for the transmembrane topology of the voltage-gated potassium channel.     

Position and role of the BK channel alpha subunit S0 helix inferred from disulfide crosslinking

The position and role of the unique N-terminal transmembrane (TM) helix, S0, in large-conductance, voltage- and calcium-activated potassium (BK) channels are undetermined. From the extents of intra-subunit, endogenous disulfide bond formation between cysteines substituted for the residues just outside the membrane domain, we infer that the extracellular flank of S0 is surrounded on three sides by the extracellular flanks of TM helices S1 and S2 and the four-residue extracellular loop between S3 and S4. Eight different double cysteine-substituted alphas, each with one cysteine in the S0 flank and one in the S3-S4 loop, were at least 90% disulfide cross-linked. Two of these alphas formed channels in which 90% cross-linking had no effect on the V(50) or on the activation and deactivation rate constants. This implies that the extracellular ends of S0, S3, and S4 are close in the resting state and move in concert during voltage sensor activation. The association of S0 with the gating charge bearing S3 and S4 could contribute to the considerably larger electrostatic energy required to activate the BK channel compared with typical voltage-gated potassium channels with six TM helices.     

A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations. Received: 9 December 1998 / Revised version: 30 August 1999 / Accepted: 15 October 1999