A cooperative transition theory applied to the kinetics of ionic exchanges in cells

Manifestations of a cooperative interaction between ion-adsorbing sites in cells include steep, sigmoidal equilibrium adsorption isotherms of K+ and Na+, critical temperature transitions of net exchanges of Na+ for K+, and the allosteric nature of the effects of ligands on cellular K+ and Na+. Cooperative ionic adsorption is described by a one-dimensional Ising model. The experimentally-determined equilibrium parameters permit prediction of the kinetics of exchange of K+ for Na+ (the approach to equilibrium) by stochastic or hydrodynamic solutions of a time-dependent Ising model. Studies of the rates of self-exchange of adsorbed ions reveal properties of the cooperatively interacting adsorption sites and their dependence on temperature and chemical potential. High rates of isotopic exchanges of K+ and Na+ occur near the transition point. This is explained by the hypothesis of an increase in susceptibility of the ensemble to slight variations of microK or microNA near the phase transition, which leads to an increase in microscopic fluctuations within the ensemble. It is suggested that the isotopic ion exchange experiment may be a means to explore the microscopic states of the ensemble and their transition probabilities.     

A cooperative transition theory applied to the kinetics of ionic exchanges in cells

Manifestations of a cooperative interaction between ion-adsorbing sites in cells include steep, sigmoidal equilibrium adsorption isotherms of K⁺ and Na⁺, critical temperature transitions of net exchanges of Na⁺ for K⁺, and the allosteric nature of the effects of ligands on cellular K⁺ and Na⁺. Cooperative ionic adsorption is described by a onedimensional Ising model. The experimentally-determined equilibrium parameters permit prediction of the kinetics of exchange of K⁺ for Na⁺ (the approach to equilibrium) by stochastic or hydrodynamic solutions of a time-dependent Ising model. Studies of the rates of self-exchange of adsorbed ions reveal properties of the cooperatively interacting adsorption sites and their dependence on temperature and chemical potential. High rates of isotopic exchanges of K⁺ and Na⁺ occur near the transition point. This is explained by the hypothesis of an increase in susceptibility of the ensemble to slight variations of {ie93-1} or {ie93-2} near the phase transition, which leads to an increase in microscopic fluctuations within the ensemble. It is suggested that the isotopic ionic exchange experiment may be a means to explore the microscopic states of the ensemble and their transition probabilities.     

Steady-state current-voltage relationship of the Na/K pump in guinea pig ventricular myocytes

Whole-cell currents were recorded in guinea pig ventricular myocytes at approximately 36 degrees C before, during, and after exposure to maximally effective concentrations of strophanthidin, a cardiotonic steroid and specific inhibitor of the Na/K pump. Wide-tipped pipettes, in combination with a device for exchanging the solution inside the pipette, afforded reasonable control of the ionic composition of the intracellular solution and of the membrane potential. Internal and external solutions were designed to minimize channel currents and Na/Ca exchange current while sustaining vigorous forward Na/K transport, monitored as strophanthidin-sensitive current. 100-ms voltage pulses from the -40 mV holding potential were used to determine steady-state levels of membrane current between -140 and +60 mV. Control experiments demonstrated that if the Na/K pump cycle were first arrested, e.g., by withdrawal of external K, or of both internal and external Na, then neither strophanthidin nor its vehicle, dimethylsulfoxide, had any discernible effect on steady-state membrane current. Further controls showed that, with the Na/K pump inhibited by strophanthidin, membrane current was insensitive to changes of external [K] between 5.4 and 0 mM and was little altered by changing the pipette [Na] from 0 to 50 mM. Strophanthidin-sensitive current therefore closely approximated Na/K pump current, and was virtually free of contamination by current components altered by the changes in extracellular [K] and intracellular [Na] expected to accompany pump inhibition. The steady-state Na/K pump current-voltage (I-V) relationship, with the pump strongly activated by 5.4 mM external K and 50 mM internal Na (and 10 mM ATP), was sigmoid in shape with a steep positive slope between about 0 and -100 mV, a less steep slope at more negative potentials, and an extremely shallow slope at positive potentials; no region of negative slope was found. That shape of I-V relationship can be generated by a two-state cycle with one pair of voltage-sensitive rate constants and one pair of voltage-insensitive rate constants: such a two-state scheme is a valid steady-state representation of a multi-state cycle that includes only a single voltage-sensitive step.     

Temperature-dependence of ATP level, organic phosphate production and Na,K-ATPase in human lymphocytes

It was previously shown that human lymphocytes maintain a normal accumulation of K+ and exclusion of Na+ between 37 degrees and 10 degrees C., and a significant net accumulation of K+ and exclusion of Na+ at even lower temperatures. The studies reported here show that the level of ATP is near-normal for at least 24 hours between 37 degrees and 10 degrees C., but that ATP synthesis and utilization are progressively and markedly decreased with decreasing temperatures below 37 degrees C. The activities of the membrane Na+- and K+-activated ATPases have typical marked temperature-dependences. Therefore, the normal accumulation of K+ and exclusion of Na+ between 37 degrees and 10 degrees C., and the normal rate of Na+ efflux at these temperatures, do not correlate with properties of the Na+,K+-ATPase or with rates of synthesis and utilization of ATP.     

Anion transport in embryonic and adult chicken red blood cells

The rates of Cl and SO₄ transport at 0° and 37°C, respectively, have been measured under exchange conditions for red blood cells of embryonic and adult chickens. It was found that the rate of self-exchange of SO₄ in embryonic red cells decreases as the embryo matures, and that the SO₄ transport rate was lower in adult compared to embryonic red cells. In contrast, no difference in the rate of Cl self-exchange was found between adult and embryonic red cells.     

Age-related changes in [3H] ouabain binding to synaptic plasma membranes isolated from mouse brains.

Age-related changes in ouabain binding to synaptic plasma membranes isolated from cerebral cortices of C57BL/6 mice were investigated to examine whether the density of Na+, K(+)-ATPase decreases with advancing age. Specific binding of [3H]ouabain did not change until around 20 months of age, but a 22% decrease in binding was found in the late senescent stage (29 months). Scatchard analysis of the binding revealed that the maximum number of binding sites (Bmax) was lower in aged mice, while the binding affinity (Kd) for ouabain receptor remained unchanged with aging. These results indicate that the density of Na+,K(+)-ATPase enzyme sites in the plasma membranes of brain synapses decreases in aged mice. Since the activity of Na+,K(+)-ATPase has been found to start declining at a much earlier stage [Tanaka, Y. & Ando, S. (1990) Brain Res. 506, 46-52; Ando, S. & Tanaka, Y. (1990) Gerontology 36, 10-14] than that at which the decrease of Bmax is manifested, at least two mechanisms may underlie the age-related decrease of the enzyme activity. We speculate that the lipid microenvironment which regulates the enzyme activity starts to change at the early stage of senescence, followed by the decrease in the enzyme content in the later stage, that is, both changes cooperatively diminish the Na+,K(+)-ATPase activity in senescence.     

Effect of the phorbol ester 12-O-tetradecanoylphorbol-13-acetate (TTPA) upon membrane ionic exchanges in sea urchin eggs

The effect of TPA (12-O-tetradecanoylphorbol-13-acetate) upon ionic exchanges was investigated in eggs of the sea urchin Arbacia lixula. Ouabain-sensitive 86Rb uptake and amiloride-sensitive 24Na influx were dramatically stimulated after TPA addition, indicating an enhancement of total ionic permeabilities. Stimulation by TPA of both Na+/H+ and Na+/K+ exchanges was canceled by amiloride, suggesting that activation of protein kinase C elicits, via Na+/H+ activity, stimulation of the sodium pump. However, TPA did not stimulate sodium pump activity and Na+/H+ exchange at the same rate as fertilization, probably because of an absence of calcium-dependent events. Further fertilization of TPA-pretreated eggs triggered an enhancement of sodium pump activity when the TPA treatment duration did not exceed 10 min. It is suggested that TPA activates preexisting transporting mechanisms in plasma membranes of unfertilized eggs (Na+ pump, Na+/H+ exchange) without eliciting corresponding regulatory mechanisms (Na+ stat, pH stat).     

The permeability of human lymphocytes to chloride

The normal amount of Cl in human lymphocytes is 82 mmoles/kg wet weight. Half of this undergoes rapid self-exchange with a half-time of 3 minutes, while the remainder exchanges slowly with a half-time of 180 minutes. The fast fraction of self-exchange of Cl also undergoes a rapid net loss into medium with a low concentration of Cl. Thus, exchange of Cl in lymphocytes has properties like that of K and Na with permeability constants on the order of 10(-6) cm/sec. The results are compatible with a simple model in which the fast fractions are dissolved within ordered cellular water at concentrations less than in the external medium and the slow fractions are adsorbed onto intracellular macromolecules.     

Ouabain binding and coupled sodium, potassium, and chloride transport in isolated transverse tubules of skeletal muscle

The affinity and number of binding sites of [3H]ouabain to isolated transverse (T) tubules were determined in the absence and presence of deoxycholate. In both conditions the KD was approximately 53 nM while deoxycholate increased the number of binding sites from 3.5 to 37 pmol/mg protein. We concluded that the ouabain binding sites were located primarily on the inside of the isolated vesicle and that the vesicles were impermeable to ouabain. ATP induced a highly active Na+ accumulation by the T tubules which increased Na+ in the T tubular lumen by almost 200 nmol/mg protein. The accumulation had an initial fast phase lasting 2-3 min and a subsequent slow phase which continued for at least 40 min. The rate of the initial fast phase indicated a turnover number of 20 Na+/s. The Na+ accumulation was prevented by monensin but was unaffected by valinomycin. Ouabain did not influence Na+ uptake, but digitoxin inhibited it. At low K+ the accumulation of Na+ was reduced 3.7-fold below the value at 50 mM K+. 86Rb, employed as a tracer to detect K+, showed a first phase of K+ release while Na+ was accumulated. After 2-3 min, K+ was reaccumulated while Na+ continued to increase in the lumen. T tubules accumulated Cl- on addition of ATP. This suggested that ATP initiated an exchange of Na+ for K+ followed by uptake of Na+ and K+ accompanied by Cl-.     

Sodium and potassium fluxes and membrane potential of human neutrophils: evidence for an electrogenic sodium pump

Sodium and potassium ion contents and fluxes of isolated resting human peripheral polymorphonuclear leukocytes were measured. In cells kept at 37 degrees C, [Na]i was 25 mM and [K]i was 120 mM; both ions were completely exchangeable with extracellular isotopes. One-way Na and K fluxes, measured with 22Na and 42K, were all approximately 0.9 meq/liter cell water . min. Ouabain had no effect on Na influx or K efflux, but inhibited 95 +/- 7% of Na efflux and 63% of K influx. Cells kept at 0 degree C gained sodium in exchange for potassium ([Na]i nearly tripled in 3 h); upon rewarming, ouabain-sensitive K influx into such cells was strongly enhanced. External K stimulated Na efflux (Km approximately 1.5 mM in 140-mM Na medium). The PNa/PK permeability ratio, estimated from ouabain insensitive fluxes, was 0.10. Valinomycin (1 microM) approximately doubled PK. Membrane potential (Vm) was estimated using the potentiometric indicator diS-C3(5); calibration was based on the assumption of constant-field behavior. External K, but not Cl, affected Vm. Ouabain caused a depolarization whose magnitude dependent on [Na]i. Sodium-depleted cells became hyperpolarized when exposed to the neutral exchange carrier monensin; this hyperpolarization was abolished by ouabain. We conclude that the sodium pump of human peripheral neutrophils is electrogenic, and that the size of the pump-induced hyperpolarization is consistent with the membrane conductance (3.7-4.0 microseconds/cm2) computed from the individual K and Na conductances.     

Self-exchange of sodium in human lymphocytes.

Self-exchanges of Na and K in human lymphocytes were measured by isotopic efflux techniques. In washed cells, K exchanged in a single slow exponential fraction, but the Na exchange had a marked curvature. It was shown that the curvature was not caused by simple bulk-phase diffusion, and it was resolved into three major fractions: fast (F) (half-time, t1/2 = 2-4 min), intermediate (I) (t1/2 = 12 min), and slow (S) (t1/2 = 125 min). Each of these appeared to follow an exponential function. The I fraction contained approximately 10 mmol Na/kg cells (25-30% of normal cellular Na), was not affected by manipulations that cause lymphocytes to gain Na, and had little or no temperature dependence. The S fraction of Na in normal cells (S1) contained approximately 10 mmol Na/kg cells, had only a slight temperature dependence, and the amount and rate of S1 were independent of external K concentration (Kex). Another slow fraction (S2) appeared when the cells underwent a net gain of Na in exchange for K, and was characterized by a steep temperature dependence and a peak rate around the transition point (the point at which half of cellular K is replaced by Na) at 0.4 mM Kex. The results are discussed within context of a theory that assigns the exchange of the major part of K in its slow exponential fraction and the Na exchange in S2 to interactions of these ions with fixed anionic sites, on intracellular macromolecules, which have been shown previously to interact cooperatively in their association with K and Na.     

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.     

Use of low temperature and high K+ incubation media for in vitro tissue preparation for X-ray microanalysis

Incubation of tissue slices in physiological buffers gives rise to significant changes in the intracellular ion concentrations, which may disturb subsequent X-ray microanalysis. In the present study it was attempted to design incubation conditions that retain the in vivo conditions better. The following variables were investigated: (1) exchange of Na⁺ in the incubation medium for K⁺, and exchange of Cl^–for the less permeable gluconate anion; (2) incubation at 4°C rather than at 37°C; and (3) addition of dextran to the incubation medium. Brief exposure (a few seconds) of liver slices to a buffer causes changes in the intracellular Na, Cl and K concentrations, depending on the ionic composition of the buffer. Incubation in a normal physiological (high NaCl) buffer at 37°C results in a further increase of Na and Cl and a further decrease in K in liver cells. The changes reach a maximum at 30 min and the concentrations then remain stable throughout a 2-h incubation. Incubation in sodium gluconate medium or addition of dextran to the physiological buffer somewhat reduces the changes in the intracellular ion composition (compared to the standard physiological incubation medium). Incubation in potassium gluconate medium results in a decrease in cellular Na and an increase in K. Quantitative morphological studies show that tissue oedema is observed to the same extent in hepatocytes incubated in sodium gluconate, potassium gluconate and physiological buffer containing 10% dextran. However, these buffers cause significantly less cell oedema than the physiological (high NaCl) buffer. Incubation of liver, cerebral cortex or submandibular gland slices in physiological (high NaCl) solutions at 4°C for 4 h caused a more extensive increase in Na⁺ and decrease in K⁺ than incubation at 37°C for 2 h. This suggests inhibition of the Na⁺, K⁺-ATPase under these conditions. As compared to incubation at 37°C for 2 h, tissues incubated in potassium gluconate buffer at 4°C for 4 h have a cellular K concentration closer to the in situ value. Cholinergic stimulation of tissue slices from cerebral cortex and submandibular gland at room temperature for 1 min shows the best physiological response in tissue slices preincubated at 4°C for 4 h in high KCl, potassium gluconate and high NaCl, in this order. The response can, however, only be seen, when cholinergic stimulation is carried out in a standard physiological buffer with a high NaCl concentration. It is concluded that in vitro storage of tissue for X-ray microanalysis is best carried out at 4°C in a solution with a high K⁺ concentration.     

Some further observations on the stimulation by monensin of the sodium efflux in barnacle muscle fibers.

Internal application of 20 μg/ml monensin causes a large rise in the Na efflux into Na-free Li-substituted artificial sea water (ASW). A comparable effect is observed in fibers pretreated with ouabain. External acidification fails to significantly augment the response to monensin of the ouabain-insensitive Na efflux into Li-ASW. Fibers cooled to 0°C fail to respond to monensin, when the pH of Li-ASW is adjusted from 7.8 to 6.0. These results are in keeping with the view that the ion exchange induced by momensin does not necessarily involve Na for Na. The cooling experiments establish that momensin can be stopped from acting when the environmental temperature is 0°C, presumably as the result of membrane conformational changes.     

Ca2+ transport by intact synaptosomes: the voltage-dependent Ca2+ channel and a re-evaluation of the role of sodium/calcium exchange

The verapamil-sensitive Ca2+ channel in the synaptosomal plasma membrane is investigated. Verapamil is without effect on Ca2+ uptake or steady-state content in synaptosomes with a polarized plasma membrane, but completely inhibits the additional Ca2+ uptake following plasma-membrane depolarization by high [K+], by veratridine plus ouabain or by high concentrations of the permeant cation tetraphenylphosphonium. Verapamil-insensitive Ca2+ influx and steady-state content are identical in polarized and depolarized synaptosomes, even though the Na+ electrochemical potential is greatly decreased in the latter, indicating that Na+/Ca2+ exchange is not a significant mechanism for Ca2+ efflux under these conditions. A transient Na+-dependent Ca2+ efflux can only be observed on addition of Na+ to Na+-depleted depolarized synaptosomes. While 0.2 mM verapamil decreases the ate of 86Rb+ efflux and 22Na+ entry during depolarization induced by veratridine plus ouabain, the final steady-state Na+ accumulation is not inhibited. Ca2+ efflux from synaptosomes following mitochondrial depolarization does not occur by a verapamil-sensitive pathway.     

Characterization of gill (Na+ + K+)-ATPase in the sea bass (Dicentrarchus labrax L.)

Bass gill microsomal preparations contain both a Na+, K+ and Mg2+-dependent ATPase, which is completely inhibited by 10(-3)M ouabain and 10(-2)M Ca2+, and also a ouabain insensitive ATP-ase activity in the presence of both Mg2+ and Na+. Under the optimal conditions of pH 6.5, 100 mM Na+, 20 mM K+, 5 mM ATP and 5 mM Mg2+, (Na+ + K+)-ATPase activity at 30 degrees C is 15.6 mumole Pi hr/mg protein. Bass gill (Na+ + K+)-ATPase is similar to other (Na+ + K+)-ATPases with respect to the sensitivity to ionic strength, Ca2+ and ouabain and to both Na+/K+ and Mg2+/ATP optimal ratios, while pH optimum is lower than poikilotherm data. The enzyme requires Na+, whereas K+ can be replaced efficiently by NH+4 and poorly by Li+. Both Km and Vm values decrease in the series NH+4 greater than K+ greater than Li+. The break of Arrhenius plot at 17.7 degrees C is close to the adaptation temperature. Activation energies are scarcely different from each other and both lower than those generally reported. The Km for Na+ poorly decreases as the assay temperature lowers. The comparison with literature data aims at distinguishing between distinctive and common features of bass gill (Na+ + K+)-ATPase.     

Kinetics of the sodium pump in red cells of different temperature sensitivity

Ouabain-sensitive K influx into ground squirrel and guinea pig red cells was measured at 5 and 37 degrees C as a function of external K and internal Na. In both species the external K affinity increases on cooling, being three- and fivefold higher in guinea pig and ground squirrel, respectively, at 5 than at 37 degrees C. Internal Na affinity also increased on cooling, by about the same extent. The effect of internal Na on ouabain-sensitive K influx in guinea pig cells fits a cubic Michaelis-Menten-type equation, but in ground squirrel cells this was true only at high [Na]i. There was still significant ouabain-sensitive K influx at low [Na]i. Ouabain-binding experiments indicated around 800 sites/cell for guinea pig and Columbian ground squirrel erythrocytes, and 280 sites/cell for thirteen-lined ground squirrel cells. There was no significant difference in ouabain bound per cell at 37 and 5 degrees C. Calculated turnover numbers for Columbian and thirteen-lined ground squirrel and guinea pig red cell sodium pumps at 37 degrees C were about equal, being 77-100 and 100-129 s-1, respectively. At 5 degrees C red cells from ground squirrels performed significantly better, the turnover numbers being 1.0-2.3 s-1 compared with 0.42-0.47 s-1 for erythrocytes of guinea pig. The results do not accord with a hypothesis that cold-sensitive Na pumps are blocked in one predominant form.     

Effect of temperature and ionic environment on the specific binding of 3H(—)sulpiride to membranes from different rat brain regions

Sulpiride is an antipsychotic drug endowed with the properties of a dopamine antagonist. The failure of sulpiride to inhibit neostriatal dopamine stimulated adenylate cyclase activity indicated that this drug is a selective D₂ receptor antagonist. In this study we used a novel synthesized ²H(—)sulpiride with very high specific activity (72 Ci/mol) and characterized the temperature sensitivity of the binding sites labeled by this compound. Kinetic analysis of ³H(—)sulpiride binding in rat striatum showed unstable behavior when incubation was performed at 37 or 30°C. However when experiments were carried out at 15 or 10°C, binding reached a stable steady-state within 10 min. Scatchard analysis of binding isotherms obtained at 10°C showed a 5-fold increase in the maximum number of binding sites and a decrease in K_d values to one-third those obtained at 37°C. Pharmacological characterization of the binding sites labeled by ³H(—)sulpiride at 10°C showed a greater affinity for antagonists but not for agonists than 37°C. Under both experimental condition, ³H(—)sulpiride binding sites were Na⁺ and GTP-sensitive. The temperature sensitive binding phenomenon appeared to be area specific. ³H(—)sulpiride binding sites in tissues other than from striatum were influenced less or not at all by changes in incubation temperature.     

Transport of sodium and potassium in intestinal epithelial cells

Transport properties of rabbit small intestinal mucosa were investigated $\text{in vitro}$ to characterize the process by which epithelial cells maintain normal Na and K gradients across the cell membrane. Active transport of Na from the cell proceeded at a faster rate in the presence of K; and active transport of K into the cell was stimulated by the presence of Na. Following preincubation at 0°C to reduce tissue K content, a greater transmural electrical potential difference (PD) and short-circuit current (I_sc) developed as the temperature was raised to 37°C if K was present in the bathing solution. The PD and I_sc, which generally reflect the rate of active Na transport in ileum under control conditions, increased immediately upon raising the K concentration in the serosal solution from 0 to 10 nM.The results present the first direct indication in mammalian intestine of an interdependence of the Na and K active transport processes which regulate the intracellular content of these cations.     

Effect of inhibition of Na+/K(+)-ATPase on the vasopressin-induced increase in intracellular Na+ concentration in vascular smooth muscle cells.

The effect of inhibition of Na+/K(+)-ATPase by ouabain on the arginine vasopressin (AVP)-induced increase in intracellular Na+ concentration [( Na+]i) was examined in cultured rat vascular smooth muscle cells (VSMC) by the direct measurement of [Na+]i using a fluorescent indicator dye. AVP at a concentration of 1 x 10(-9) M or higher increased [Na+]i in a dose-dependent manner in cultured rat VSMC. The preincubation of cells with 1 x 10(-4) M ouabain for 1 hr at 37 degrees C did not affect the basal [Na+]i but enhanced the 1 x 10(-6) M AVP-induced increase in [Na+]i. The preincubation was not necessary because similar results were obtained after the simultaneous administration of AVP and ouabain. The treatment with ouabain did not affect the intracellular pH changes induced by AVP. These results therefore indicate that the inhibition of Na+/K(+)-ATPase enhances the AVP-induced increase in [Na+]i by decreasing cellular Na+ efflux in cultured rat VSMC.