The Exact Distribution of the Anderson-Kannemann Statistic

The Anderson-Kannemann test is a rank test for treatment effects in a randomized block design with K treatments and N blocks. In this paper, an algorithm for computing the exact distribution of the Anderson-Kannemann test statistic under the null hypothesis is deduced. Then, the exact distribution is compared with the asymptotic χ²-distribution, and it is shown that the exact distribution is approximated fairly well by the asymptotic distribution. Tables of the exact distribution are given for K = 3, N = 3(1)15; K = 4, N = 3(1)11; K = 5, N = 3(1)7; and K = 6, N = 3(1)5.     

Cytosolic calcium regulates a potassium current in corn (Zea mays) protoplasts

Summary The voltage- and time-dependent K⁺ current,I _K ⁺ _out , elicited by depolarization of corn protoplasts, was inhibited by the addition of calcium channel antagonists (nitrendipine, nifedipine, verapamil, methoxyverapamil, bepridil, but not La³⁺) to the extracellular medium. These results suggested that the influx of external Ca²⁺ was necessary for K⁺ current activation. The IC₅₀, concentration of inhibitor that caused 50% reduction of the current, for nitrendipine was 1 m at a test potential of +60 mV following a 20-min incubation period.In order to test whether intracellular Ca²⁺ actuated the K⁺ current, we altered either the Ca²⁺ buffering capacity or the free Ca²⁺ concentration of the intracellular medium (pipette filling solution). By these means,I _K ⁺ _out could be varied over a 10-fold range. Increasing the free Ca²⁺ concentration from 40 to 400nm also shifted the activation of the K⁺ current toward more negative potentials. Maintaining cytoplasmic Ca²⁺ at 500nm with 40nm EGTA resulted in a more rapid activation of the K⁺ current. Thus the normal rate of activation of this current may reflect changes in cytoplasmic Ca²⁺ on depolarization. Increasing intracellular Ca²⁺ to 500nm or 1 m also led to inactivation of the K⁺ current within a few minutes. It is concluded thatI _K ⁺ _out is regulated by cytosolic Ca²⁺, which is in turn controlled by Ca²⁺ influx through dihydropyridine-, and phenylalkylamine-sensitive channels.     

A unique allosteric insulin receptor monoclonal antibody that prevents hypoglycemia in the SUR-1−/− mouse model of KATP hyperinsulinism

Loss-of-function mutations of the ß-cell ATP-sensitive potassium channels (K_ATP) cause the most common and severe form of congenital hyperinsulinism (K_ATPHI), a disorder of ß-cell function characterized by severe hypoglycemia. Children with K_ATPHI are typically unresponsive to medical therapy and require pancreatectomy for intractable hypoglycemia. We tested the hypothesis that inhibition of insulin receptor signaling may prevent hypoglycemia in K_ATPHI. To test this hypothesis, we examined the effect of an antibody allosteric inhibitor of the insulin receptor, XMetD, on fasting plasma glucose in a mouse model of K_ATPHI (SUR-1^{? / ?} mice). SUR-1^{? / ?} and wild-type mice received twice weekly intraperitoneal injections of either XMetD or control antibody for 8 wks. Treatment with XMetD significantly decreased insulin sensitivity, and increased hepatic glucose output and fasting plasma glucose. These findings support the potential use of insulin receptor antagonists as a therapeutic approach to control the hypoglycemia in congenital hyperinsulinism.     

Auxin augments conductance of K+ inward rectifier in maize coleoptile protoplasts

Potassium is taken up by maize (Zea mays L.) coleoptile cells via a typical plant inward rectifier (K _ir ). Sufficient conductance of this channel is essential in order to maintain auxin-stimulated cell elongation. It was therefore investigated whether the activity of this channel is subject to direct or indirect control by this growth hormone. Patch-clamp measurements of whole coleoptile protoplasts revealed no appreciable effect of externally applied 10 μM or 100 μM α-naphthaleneacetic acid (NAA) on the activity of K _ir over test periods of ≥ 18 or ≥ 8 min, respectively. When, however, K _ir was recorded in the cell-attached configiuration and 10 μM NAA administered to the bath medium, the conductance of K _ir increased significantly in 13 out of 18 protoplasts over the control. This rise occurred at a fixed protoplast voltage after a lag period of less than 10 min and exhibited no voltage dependency. The absence of response to NAA of protoplasts in the whole-cell configuration indicates that auxin perception and channel control is linked via a soluble cytoplasmic factor and that this mediator is washed out or modified upon perfusion of the cytoplasm with pipette solution. To search for this expected diffusible factor the K _ir current was recorded before and after elevation of Ca²⁺ and H⁺ in the cytoplasm. In the whole-cell configuration the increase in Ca²⁺ from a nanomolar value to >1 μM by means of Ca²⁺-release from the caged precursor Na₂-DM-nitrophen left K _ir unaffected. The whole-cell K _ir conductance was also not affected upon addition of 10 mM Na⁺-acetate to the bath medium, an operation used to lower the cytoplasmic pH. This excludes a primary role for the known auxin-evoked rise in cytoplasmic Ca²⁺ and H⁺ in K _ir activity. We postulate that another, as yet unknown, mechanism mediates the auxin-evoked stimulation of the number of active K _ir channels in the plasma membrane. Received: 13 May 1998 / Accepted: 9 November 1998     

Transport of neutral, cationic and anionic amino acids by systems B, b, XAG, and ASC in swine small intestine

Amino acid influx across the brush border membrane of the intact pig ileal epithelium was studied. It was examine whether in addition to system B, systems ASC and b^o,+ were involved in transport of bipolar amino acids. The kinetics of interactions between lysine and leucine demonstrates that system b^o,+ is present and accessible also to -glutamine. -aspartate (K_1/2 0.3 mM) and -glutamate (K_i 0.5 mM) share a high affinity transporter with a maximum rate of 1.3 μmol cm⁻² h⁻¹, while only -glutamate with a K_1/2 of 14.4 mM uses a low affinity transporter with a maximum rate of 2.7 μmol cm⁻² h⁻¹, system ASC, against which serine has a K_i of 1.6 mM. In the presence of 100 mM lysine, -glutamine (A), leucine (B), and methionine (C) fulfilled the criteria of the ABC test for transport by one and the same transporter. However, serine inhibits not only transport of -glutamate but also of glutamine (K_i 0.5 mM), and -glutamate inhibits part of the transport of glutamine. The test does, therefore, only indicate that the three bipolar amino acids have similar affinities for transport by systems B and ASC. Further study of the function of system B must be carried out under full inhibition by lysine and glutamate.     

Effect of intracellular potassium upon the electrogenic pump of frog retinal pigment epithelium

Summary We have studied the hyperpolarizing, electrogenic pump located on the apical membrane of the retinal pigment epithelium (RPE) in anin vitro preparation of bullfrog RPE-choroid. Changes in RPE [K⁺] _i alter the current produced by this pump. Increasing [K⁺] _o in the solution perfusing thebasal membrane increases RPE [K⁺] _i (measured with a K⁺-specific microelectrode), and also depolarizes theapical membrane. This depolarization is due to a decrease in electrogenic pump current flowing across the apical membrane resistance, since it is abolished when the pump is inhibited by apical ouabain, by cooling the tissue, or by 0mm [K⁺] _o outside the apical membrane. Removal of Cl^– from the solution perfusing the basal membrane abolishes the K⁺-evoked apical depolarization by preventing the entry of K⁺ (as KCl) into the cell. We conclude that the increase in [K⁺] _i causes the decrease in pump current. This result is consistent with the finding that [K⁺] _i is a competitive inhibitor of the Na⁺–K⁺ pump in red blood cells.It is possible that the light-evoked changes in [K⁺] _o in the distal retina could alter RPE [K⁺] _i , and thus could affect the pump from both sides of the apical membrane. Any change in pump current is likely to influence retinal function, since this pump helps to determine the composition of the photoreceptor extracellular space.     

Membrane responses to changes in the extracellular potassium concentration in isolated hippocampal pyramidal neurons

The responses of freshly isolated hippocampal pyramidal neurons to rapid, elevations of the external potassium concentration ([K⁺] _out ) were investigated using the whole-cell variation of a patch-clamp technique. An elevation of [K⁺] _out induced a two-phase inward current at the membrane potentials more negative than the reversal potential for K ions. This current consisted of a leakage, current and a time-dependent current (τ=40–50 msec at 21°C), the latter designated below asI _ΔK. It displayed first-order activation kinetics that showed neither voltage, nor concentration dependence. The amplitude of this current was determined by the external K⁺ concentration and increased with hyperpolarization. Voltage dependence ofI _ΔK measured within the range from −20 to −120 mV was similar to that for inward rectifier. Activation ofI _ΔK was utterly dependent on Na⁺; substitution of extracellular Na⁺ with choline chloride almost completely depressedI _ΔK.I _ΔK was absent in the cells freshly dissociated from the nodosal and dorsal root ganglia. This suggests that this earlier unrecognized current is instrumental in preserving densely packed hippocampal pyramidal neurons from sudden increases in [K⁺] _out and following spontaneous over-excitation. It prevents the neurons from responding to K⁺-induced depolarizations by slowing down potassium influx.     

Ca2+-activated K+ conductance of the human red cell membrane: Voltage-dependent Na+ block of outward-going currents

Summary Human red cells were prepared with various cellular Na⁺ and K⁺ concentrations at a constant sum of 156mm. At maximal activation of the K⁺ conductance,g _K(Ca), the net efflux of K⁺ was determined as a function of the cellular Na⁺ and K⁺ concentrations and the membrane potential,V _m , at a fixed [K⁺]_ex of 3.5mm.V _m was only varied from (V _m –E _K)25 mV and upwards, that is, outside the range of potentials with a steep inward rectifying voltage dependence (Stampe & Vestergaard-Bogind, 1988).g _K(Ca) as a function of cellular Na⁺ and K⁺ concentrations atV _m =–40, 0 and 40 mV indicated a competitive, voltage-dependent block of the outward current conductance by cellular Na⁺. Since the present Ca²⁺-activated K⁺ channels have been shown to be of the multi-ion type, the experimental data from each set of Na⁺ and K⁺ concentrations were fitted separately to a Boltzmann-type equation, assuming that the outward current conductance in the absence of cellular Na⁺ is independent of voltage. The equivalent valence determined in this way was a function of the cellular Na⁺ concentration increasing from 0.5 to 1.5 as this concentration increased from 11 to 101mm. Data from a previous study of voltage dependence as a function of the degree of Ca²⁺ activation of the channel could be accounted for in this way as well. It is therefore suggested that the voltage dependence ofg _K(Ca) for outward currents at (V _m –E _K)>25 25 mV reflects a voltage-dependent Na⁺ block of the Ca²⁺-activated K⁺ channels.     

Sodium-dependent Potassium Channels in Leech P Neurons

In leech P neurons the inhibition of the Na⁺-K⁺ pump by ouabain or omission of bath K⁺ leaves the membrane potential unaffected for a prolonged period or even induces a marked membrane hyperpolarization, although the concentration gradients for K⁺ and Na⁺ are attenuated substantially. As shown previously, this stabilization of the membrane potential is caused by an increase in the K⁺ conductance of the plasma membrane, which compensates for the reduction of the K⁺ gradient. The data presented here strongly suggest that the increased K⁺ conductance is due to Na⁺-activated K⁺ (K_Na) channels. Specifically, an increase in the cytosolic Na⁺ concentration ([Na⁺]_i) was paralleled by a membrane hyperpolarization, a decrease in the input resistance (R_in) of the cells, and by the occurrence of an outwardly directed membrane current. The relationship between R_in and [Na⁺]_i followed a simple model in which the R_in decrease was attributed to K⁺ channels that are activated by the binding of three Na⁺ ions, with half-maximal activation at [Na⁺]_i between 45 and 70 mM. At maximum channel activation, R_in was reduced by more than 90%, suggesting a significant contribution of the K_Na channels to the physiological functioning of the cells, although evidence for such a contribution is still lacking. Injection experiments showed that the K_Na channels in leech P neurons are also activated by Li⁺.     

K<Superscript>+</Superscript> Channels of Squid Giant Axons Open by an Osmotic Stress in Hypertonic Solutions Containing Nonelectrolytes

In hypertonic solutions made by adding nonelectrolytes, K⁺ channels of squid giant axons opened at usual asymmetrical K⁺ concentrations in two different time courses; an initial instantaneous activation (I _IN) and a sigmoidal activation typical of a delayed rectifier K⁺ channel (I _D). The current–voltage relation curve for I _IN was fitted well with Goldman equation described with a periaxonal K⁺ concentration at the membrane potential above −10 mV. Using the activation–voltage curve obtained from tail currents, K⁺ channels for I _IN are confirmed to activate at the membrane potential that is lower by 50 mV than those for I _D. Both I _IN and I _D closed similarly at the holding potential below −100 mV. The logarithm of I _IN/I _D was linearly related with the osmolarity for various nonelectrolytes. Solute inaccessible volumes obtained from the slope increased with the nonelectrolyte size from 15 to 85 water molecules. K⁺ channels representing I _D were blocked by open channel blocker tetra-butyl ammonium (TBA) more efficiently than in the absence of I _IN, which was explained by the mechanism that K⁺ channels for I _D were first converted to those for I _IN by the osmotic pressure and then blocked. So K⁺ channels for I _IN were suggested to be derived from the delayed rectifier K⁺ channels. Therefore, the osmotic pressure is suggested to exert delayed-rectifier K⁺ channels to open in shrinking rather hydrophilic flexible parts outside the pore than the pore itself, which is compatible with the recent structure of open K⁺ channel pore.     

The dual effect of rubidium ions on potassium efflux in depolarized frog skeletal muscle

Summary The effects of external Rb⁺ on the efflux of⁴²K⁺ from whole frog sartorius muscles loaded with 305mm K⁺ and 120mm Cl^– were studied. K⁺ efflux is activated by [Rb⁺] _o less than about 40mm according to a sigmoid relation similar to that for activation by [K⁺] _o . At [Rb⁺]_o greater than 40mm, K⁺ efflux declines, although at [Rb⁺] _o =300mm it is still greater than at [Rb⁺] _o =0mm. For low concentrations, the increment in K⁺ efflux over that in K⁺- and Rb⁺-free solution, k, is described by the relation k=a[X⁺] _o ⁿ , for both K⁺ and Rb⁺. The value ofa is larger for Rb⁺ than for K⁺, while the values ofn are similar; the activation produced by a given [Rb⁺] _o is larger than that by an equal [K⁺] _o for concentrations less than about 40mm. Adding a small amount of Rb⁺ to a K⁺-containing solution has effects on K⁺ efflux which depend on [K⁺] _o . At low [K⁺] _o , adding Rb⁺ increases K⁺ efflux, the effect being greatest near [K⁺] _o =30mm and declining at higher [K⁺] _o ; at [K⁺] _o above 40mm, addition of Rb⁺ decreases K⁺ efflux. At [K⁺] _o above 75mm, where K⁺ efflux is largely activated, Rb⁺ reduces K⁺ efflux by a factorb, described by the relationb=1/(1+c[Rb⁺] _o ). Activation is discussed in terms of binding to at least two sites in the membrane, and the reduction in K⁺ efflux by Rb⁺ at high [K⁺] _o in terms of association with an additional inhibitory site.     

The effects of weak acids on potassium uptake by Escherichia coli K-12. Inhibition by low cytoplasmic pH

The activity of the Escherichia coli K⁺ transport system TrkA was measured as a function of the cytoplasmic pH of the cell. For this purpose, pH_in was decreased by the addition of the weak acids acetic acid, benzoic acid or salicylic acid to K⁺-depleted cells. Under these conditions, the initial rate of K⁺ uptake decreased strongly with pH_in, and was almost independent of the acid used. This inhibition was due to a strong decrease in the V_max for K⁺ uptake, which indicates that low cytoplasmic pH inactivates the TrkA K⁺ uptake system. The relevance of this inhibition for growth and metabolism at low pH_in is discussed.     

Chloride Currents in Skeletal Muscles of Bufo arenarum

Cl⁻ currents (I _Cl) were measured in short fibers (1–2 mm) from the lumbricalis muscle of toads (Bufo arenarum) with two microelectrodes (15°C). Initially the fibers were equilibrated in a high K⁺-containing solution: (mm) K₂SO₄ 68; Na₂SO₄ 20; KCl 60; CaSO₄ 8; MgSO₄ 1; HEPES 2.5. Constant pulses were applied when all the external K⁺ was replaced by Cs⁺: Cs₂SO₄ 68; Na₂SO₄ 20; CsCl 60; CaSO₄ 8; HEPES 2.5 (pH 7.5). Under these conditions about 80–90% of the current is carried by Cl⁻. The current-voltage relation is almost linear implying constant conductance and hence voltage-independent permeability. The voltage dependence of the net Cl⁻ current could be fitted by constant field equation with a P _Cl of 3.3 × 10⁻⁶ cm/sec. In a separate group of experiments a two-pulse technique was used to estimate the availability and the inactivation of the initial I _Cl during a test pulse. After returning the potential to the holding potential for various times, test pulses of the same amplitude and duration of the prepulses were applied. The initial current during the test pulse was 70% of the initial current during the prepulse and the recovery was complete in less than 300 msec with a linear relationship between the current during the test pulse and the amplitude of the preceding prepulse. When the test pulses were preceded by a positive prepulse, the initial current for any given test pulse was larger than with a negative prepulse. If we assumed that the initial current during the test pulse is a measure of the number of channels open at the end of the prepulse, these results suggest that hyperpolarizing pulses inactivate and depolarizing prepulses activate the I _Cl. Received: 31 March 1995/Revised: 27 October 1995     

Kinetics of NH4+ and K+ uptake by ectomycorrhizal fungi. Effect of NH4+ on K+ uptake

NH₄⁺ and K⁺ uptake experiments have been conducted with 3 ectomycorrhizal fungi, originating from Douglas fir (Pseudotsuga menziesii (Mirb.] Franco) stands. At concentrations up to 250 μM, uptake of both NH₄⁺ and K⁺ follow Michaelis-Menten kinetics. Laccaria bicolor (Maire) P. D. Orton, Lactarius rufus (Scop.) Fr. and Lactarius hepaticus Plowr. ap. Boud. exhibit K_m values for NH₄⁺ uptake of 6, 35, and 55 μM, respectively, and K_m values for K⁺ uptake of 24, 18, and 96 μM, respectively. Addition of 100 μM NH₄⁺ raises the K_m of K⁺ uptake by L. bicolor to 35 μM, while the V_max remains unchanged. It is argued that the increase of K_m is possibly caused by depolarization of the plasma membrane. It is not due to a competitive inhibition of K⁺ by NH₄⁺ since the apparent inhibitor constant is much higher than the K_m, for NH₄⁺ uptake. The possibility that NH₄⁺ and K⁺ are taken up by the same carrier can be excluded. The K_m, values for K⁺ uptake in the two other fungi are not significantly affected by 100 μM NH₄⁺. Except for a direct effect of NH₄⁺ on influx of K⁺ into the cells, there may also be an indirect effect after prolonged incubation of the cells in the presence of 100 μM NH₄⁺.     

Regulation of the basolateral potassium conductance of theNecturus proximal tubule

Summary Two methods, the measurement of the response of the basolateral membrane potential (V _bl) of proximal tubule cells ofNecturus to step changes in basolateral K⁺ concentration, and cellular cable analysis, were used to assess the changes in basolateral potassium conductance (G _K) caused by a variety of maneuvers. The effects of some of these maneuvers on intracellular K⁺ activity (a _K ⁱ ) were also evaluated using double-barreled ion-selective electrodes. Perfusion with 0mm K⁺ basolateral solution for 15 min followed by 45 min of 1mm K⁺ solution resulted in a fall in basolateral potassium (apparent) transference number (t _K),V _bl anda _K ⁱ . Results of cable analysis showed that total basolateral resistance,R _b , rose. The electrophysiological effects of additional manipulations, known to inhibit net sodium reabsorption across the proximal tubular epithelium ofNecturus, were also investigated. Ouabain caused a fall int _K accompanied by large decreases ina _K ⁱ andV _bl. Lowering luminal sodium caused a fall int _K and a small reduction inV _bl. Selective reduction of peritubular sodium, a maneuver that has been shown to block sodium transport from lumen to peritubular fluid, also resulted in a significant decrease int _K. These results suggest thatG _K varies directly with rate of transport of the sodium pump, irrespective of the mechanism of change in pump turnover.Part of this material has been presented at the 10th International Conference on Biological Membranes (Cohen & Giebisch, 1984).     

Characterisation of soil potassium supply as derived from sorption–desorption experiments

PlantK uptake depends on soil K supply and this can be modelled using the K concentration in the soil solution (C _K), the soil K buffer power (S _K) and the effective K diffusion coefficient. With the appropriate sorption–desorption curve, the parameters C _K and S _K can be estimated from the equilibrium K concentration (C _K,0) and from the slope of the curve at C _K,0 (S _K,0). However, buffer power is frequently estimated by the ratio of the soil exchangeable K content (E _K) to C _K. Up to now, S _K,0 had not been compared with this ratio, nor had C _K,0 been compared with any C _K estimate from soil solution extract measurements. To address this question, we collected 45 soil samples from 15 K fertilisation trials in France. The soils differed widely in their physicochemical characteristics, soil solution K concentration and buffer power. For each soil sample, a sorption–desorption curve was established from 16-h experiments performed at the estimated Ca concentration of the soil solution. The C _K,0 estimates were compared with the K concentrations measured in the soil solution obtained either by direct centrifugation (^C C _K) or by centrifugation with 1,1,2-trichlorotrifluoroethane (^TFE C _K). On average, ^C C _K values were 16% higher than ^TFE C _K values, whereas C _K,0 values were intermediate between the two. The K buffer power increased when CEC increased and when C _K decreased. Multiple linear regressions using either CEC at the soil pH and ^TFE C _K ^–1 or E _K and ^TFE C _K ^–1 as independent variables accounted for more than 98 or 95% of the variability of S _K,0. The buffer power estimated by the ratio of E _K to ^TFE C _K overestimated by 100% the S _K,0 value obtained from the sorption–desorption curves.     

Boundaries of the universal K3 region and plateau region of the dynamic structure factor for DNA

A sufficiently long semiflexible filamentous macromolecule is theroretically expected to exhibit three different domains of behavior of its apparent diffusion coefficient D_app(K) as a function of scattering vector K: (1) the small wave vector limit, where D_app(K) = D₀ is the translational diffusion coefficient of the center-of-mass; (2) the universal K³ region, where D_app(K) = (k_BT/6πη)K is a universal function of K independent of any property of the molecule itself; (c) the plateau region at large K², where D_app(K) approaches either a plateau, or gradually sloping quasiplateau, characteristic of local (elastic) rigid-body motions of the filament. The existence of each of these different domains has now been established experimentally for at least some polymers. The boundaries of the universal K³ region and the plateau region are determined theoretically here using precise quantitative criteria for universal or plateau behavior of D_app(K) for a Rouse-Zimm model containing N + 1 subchains with rms subchain extension b. Allowing a maximum of 13% nonuniversal behavior, the domain of the universal K³ region is given by K²R²_G = K²Nb²/6 ≥ 7 and K²b² ? 0.54. Allowing as much as 10% nonplateau behavior, the boundary for onset of plateau behavior is K²b² = 18.3. D_app(K) is at least 50% nonuniversal when K²b²/6 = 6 ln 3. Extension of these results to DNA is examined theoretically, and good agreement of the pertinent predictions with published experimental data is demonstrated. It is concluded that no truly universal K³ region exists for DNA with M_r ? 10⁷ and persistence length a ≥ 450 Å, although marginally (?17% nonuniversal) universal behavior, is exhibited in a very narrow domain 0.64 × 10¹⁰ ? K² ? 0.84 × 10¹⁰ cm^?2 for ?29 DNA (M_r = 11.5 × 10⁶). More than 50% of D_app(K) is governed by local (elastic) rigid-body motions when K² = 5.23 × 10¹⁰ cm^?2. The existence of a very wide region of nonuniversal apparent K³ behavior extending up to very large K², far into the plateau region, is demonstrated in a plot of D_app(K)/K vs K² for the Rouse-Zimm model. This is shown to stem in part from visual artifacts of plotting D_app(K)/K vs K², even for rigid species.     

Divalent cations and the phosphatase activity of the (Na + K)-dependent ATPase

Phosphatase activity of a kidney (Na + K)-ATPase preparation was optimally active with Mg²⁺ plus K⁺. Mn²⁺ was less effective and Ca²⁺ could not substitute for Mg²⁺. However, adding Ca²⁺ with Mg²⁺ or substituting Mn²⁺ for Mg²⁺ activated it appreciably in the absence of added K⁺, and all three divalent cations decreased apparent affinity for K⁺. Inhibition by Na⁺ decreased with higher Mg²⁺ concentrations, when Ca²⁺ was added, and when Mn²⁺ was substituted for Mg²⁺. Dimethyl sulfoxide, which favorsE ₂ conformations of the enzyme, increased apparent affinity for K⁺, whereas oligomycin, which favorsE ₁ conformations, decreased it. These observations are interpretable in terms of activation through two classes of cation sites. (i) At divalent cation sites, Mg²⁺ and Mn²⁺, favoring (under these conditions)E ₂ conformations, are effective, whereas Ca²⁺, favoringE ₁, is not, and monovalent cations complete. (ii) At monovalent cation sites divalent cations compete with K⁺, and although Ca²⁺ and Mn²⁺ are fairly effective, Mg²⁺ is a poor substitute for K⁺, while Na⁺ at these sites favorsE ₁ conformations. K⁺ increases theK _m for substrate, but both Ca²⁺ and Mn²⁺ decrease it, perhaps by competing with K⁺. On the other hand, phosphatase activity in the presence of Na⁺ plus K⁺ is stimulated by dimethyl sulfoxide, by higher concentrations of Mg²⁺ and Mn²⁺, but not by adding Ca²⁺; this is consistent with stimulation occurring through facilitation of an E₁ to E₂ transition, perhaps an E₁-P to E₂-P step like that in the (Na + K)-ATPase reaction sequence. However, oligomycin stimulates phosphatase activity with Mg²⁺ plus Na⁺ alone or Mg²⁺ plus Na⁺ plus low K⁺: this effect of oligomycin may reflect acceleration, in the absence of adequate K⁺, of an alternative E₂-P to E₁ pathway bypassing the monovalent cation-activated steps in the hydrolytic sequence.     

Microelectrode characterization of the basolateral membrane of rabbit S3 proximal tubule

Summary The purpose of this study was to characterize the basolateral membrane of the S3 segment of the rabbit proximal tubule using conventional and ion-selective microelectrodes. When compared with results from S1 and S2 segments, S3 cells under control conditions have a more negative basolateral membrane potential (V _bl=–69 mV), a higher relative potassium conductance (t _K=0.6), lower intracellular Na⁺ activity (A _Na=18.4mm), and higher intracellular K⁺ activity (A _K=67.8mm). No evidence for a conductive sodium-dependent or sodium-independent HCO ₃ ^– pathway could be demonstrated. The basolateral Na–K pump is inhibited by 10^–4 m ouabain and bath perfusion with a potassium-free (0-K) solution. 0-K perfusion results inA _Na=64.8mm,A _K=18.5mm, andV _bl=–28 mV. Basolateral potassium channels are blocked by barium and by acidification of the bathing medium. The relative K⁺ conductance, as evaluated by increasing bath K⁺ to 17mm, is dependent upon the restingV _bl in both S2 and S3 cells. In summary, the basolateral membrane of S3 cells contains a pump-leak system with similar properties to S1 and S2 proximal tubule cells. The absence of conductive bicarbonate pathways results in a hyperpolarized cell and larger Na⁺ and K⁺ gradients across the cell borders, which will influence the transport properties and intracellular ion activities in this tubule segment.     

Asymptotic Efficiency of the Chi-Square Test for Heterogeneity of Proportions in Some Sparse-Data Cases

We consider the problem of testing for heterogeneity of K proportions when K is not small and the binomial sample sizes may not be large. We assume that the binomial proportions are normally distributed with variance σ². The asymptotic relative efficiency (ARE) of the usual chi-square test is found relative to the likelihood-based tests for σ²=0. The chi-square test is found to have ARE = 1 when the binomial sample sizes are all equal and high relative efficiency for other cases. The efficiency is low only in cases where there is insufficient data to use the chi-square test.