Angiotensin II inhibits bTREK-1 K+ channels in adrenocortical cells by separate Ca2+- and ATP hydrolysis-dependent mechanisms

Bovine adrenocortical cells express bTREK-1 K+ channels that set the resting membrane potential (V(m)) and couple angiotensin II (AngII) and adrenocorticotropic hormone (ACTH) receptors to membrane depolarization and corticosteroid secretion. In this study, it was discovered that AngII inhibits bTREK-1 by separate Ca2+- and ATP hydrolysis-dependent signaling pathways. When whole cell patch clamp recordings were made with pipette solutions that support activation of both Ca2+- and ATP-dependent pathways, AngII was significantly more potent and effective at inhibiting bTREK-1 and depolarizing adrenal zona fasciculata cells, than when either pathway is activated separately. External ATP also inhibited bTREK-1 through these two pathways, but ACTH displayed no Ca2+-dependent inhibition. AngII-mediated inhibition of bTREK-1 through the novel Ca2+-dependent pathway was blocked by the AT1 receptor antagonist losartan, or by including guanosine-5'-O-(2-thiodiphosphate) in the pipette solution. The Ca2+-dependent inhibition of bTREK-1 by AngII was blunted in the absence of external Ca2+ or by including the phospholipase C antagonist U73122, the inositol 1,4,5-trisphosphate receptor antagonist 2-amino-ethoxydiphenyl borate, or a calmodulin inhibitory peptide in the pipette solution. The activity of unitary bTREK-1 channels in inside-out patches from adrenal zona fasciculata cells was inhibited by application of Ca2+ (5 or 10 microM) to the cytoplasmic membrane surface. The Ca2+ ionophore ionomycin also inhibited bTREK-1 currents through channels expressed in CHO-K1 cells. These results demonstrate that AngII and selected paracrine factors that act through phospholipase C inhibit bTREK-1 in adrenocortical cells through simultaneous activation of separate Ca2+- and ATP hydrolysis-dependent signaling pathways, providing for efficient membrane depolarization. The novel Ca2+-dependent pathway is distinctive in its lack of ATP dependence, and is clearly different from the calmodulin kinase-dependent mechanism by which AngII modulates T-type Ca2+ channels in these cells.     

The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain

The expressions for the kinetic constants corresponding to the steady state model for hydrolysis of ATP catalyzed by (Na+ + K+)-ATPase proposed recently are analyzed with the object of determining the rate constants. The theoretical background for the necessary procedures is described. The results of this analysis are: (1) A small class (four) of rate constants are determined directly by the previously published values of the kinetic constants. (2) For a somewhat larger class of rate constants upper and lower bounds may be established. For several rate constants the upper and lower bounds differ by less than a factor 1.6 (for the "(Na+ + K+)-enzyme", i.e. the enzyme activity with K+ and millimolar substrate concentration) and 1.2 (for the "Na+-enzyme",i.e. the activity at micromolar substrate concentrations). (3) Experiments on inhibition by K+ of the Na+-enzyme at various Mg2+ concentrations are reported and analyzed. With the additional assumption that the rate constants governing the addition to ATP of Mg2+ is independent of whether or not ATP is bound to an enzyme molecule, a set of consistent values for all the 23 rate constants in the mechanism may be obtained. (4) The values of some rate constants lend further support to the contention discussed in a previous paper that the enzyme hydrolyzes ATP along two kinetically distinct pathways, depending on the presence of K+ and on the concentration of substrate, without the necessity of having more than one active substrate site per enzyme unit at any time. (5) The results show that while the two enzyme forms, the "Na+-enzyme" E1 and the "K+-enzyme" E2K, add substrate with (second order) rate constants of the same order of magnitude (differing only by a factor of four in favor of the former), the rate constants for the reverse processes differ by a factor of 100, being largest for the K+-enzyme. This is the main reason for the large difference in the Michaelis constants for the two forms reported previously. (6) Compatibility of the model with the well-known rapid dephosphorylation of the phosphorylated enzyme in the presence of K+ requires the presence, at non-zero steady state concentration, of an enzyme-potassium-phosphate intermediate, which is acid labile and is therefore not detected as a phosphorylated enzyme using conventional methods.     

Investigations into the mechanism of hormone release by rat adrenocortical cells

Summary Vinblastine treatment blocks corticosterone release from rat adrenal zona fasciculata without impairing hormone synthesis, and induces the formation of acid phosphatase-positive granular clumps at the juxta-sinusoidal pole of the cells. Autoradiography shows that ACTH administration to vinblastine-treated animals mobilizes the 3H-cholesterol stored in the lipid droplets and leads to a noticeable labelling of the granular clumps. The possible significance of these granules is discussed.     

Opening of mitochondrial K+ channels increases ischemic ATP levels by preventing hydrolysis

Mitochondrial ATP-sensitive K⁺ channels (mitoK_ATP) have been proposed to mediate protection against ischemic injury by increasing high-energy intermediate levels. This study was designed to verify if mitochondria are an important factor in the loss of cardiac ATP associated to ischemia, and determine the possible role of mitoK_ATP in the control of ischemic ATP loss. Langendorff-perfused rat hearts subjected to ischemia were found to have significantly higher ATP contents when pretreated with oligomycin or atractyloside, indicating that mitochondrial ATP hydrolysis contributes toward ischemic ATP depletion. MitoK_ATP opening induced by diazoxide promoted a similar protection against ATP loss. Diazoxide also inhibited ATP hydrolysis in isolated, nonrespiring mitochondria, an effect accompanied by a drop in the membrane potential and Ca²⁺ uptake. In hearts subjected to ischemia followed by reperfusion, myocardial injury was prevented by diazoxide, but not atractyloside or oligomycin, which, unlike diazoxide, decreased reperfusion ATP levels. Our results suggest that mitoK_ATP-mediated protection occurs due to selective inhibition of mitochondrial ATP hydrolysis during ischemia, without affecting ATP synthesis after reperfusion.     

The pre-steady-state hydrolysis of ATP by porcine brain (Na+ + K+)-dependent ATPase.

The hydrolysis of [gamma-32P]ATP by porcine brain (Na+ + K+)-stimulated ATP phosphohydrolase (EC 3.6.1.3) has been studied at 28 degree C in a rapid mixing quenched-flow apparatus. An "early burst" in the release of Pi from ATP has been observed when the enzyme is mixed with ATP, Na+ and a relatively high concentration of K+ (10 mM) but the burst is less pronounced with 0.5 mM K+. This "early burst" of Pi release is suppressed when the enzyme is pre-mixed with 10 mM K+ or 20% (v/v) dimethylsulphoxide before mixing with ATP and Na+, and premixing of enzyme with Na+ antagonizes this effect of dimethylsulphoxide. The results have been analysed by a non-linear least squares regression treatment and are consistent with a mechanism involving three steps, one of which may be a relatively slow change in enzyme conformation following release of Pi from its covalent linkage with the enzyme, in addition to formation of the enzyme-substrate complex. Rate constants (and S.E.) for these steps have been calculated and the roles of phospho-enzyme and other intermediates in the reaction mechanism of the transport ATPase are dicussed.     

Angiotensin II inhibits native bTREK-1 K+ channels through a PLC-, kinase C-, and PIP2-independent pathway requiring ATP hydrolysis

Angiotensin II (ANG II) inhibits bTREK-1 (bovine KCNK2) K(+) channels in bovine adrenocortical cells through a Gq-coupled AT(1) receptor by activation of separate Ca(2+)- and ATP hydrolysis-dependent signaling pathways. Whole cell patch-clamp recording from bovine adrenal zona fasciculata (AZF) cells was used to characterize the ATP-dependent signaling mechanism for inhibition of bTREK-1 by ANG II. We discovered that ATP-dependent inhibition of bTREK-1 by ANG II occurred through a novel mechanism that was independent of PLC and its established downstream effectors. The ATP-dependent inhibition of bTREK-1 by ANG II was not reduced by the PLC antagonists edelfosine and U73122, or by the PKC antagonists bisindolylmaleimide I (BIM) or calphostin C. bTREK-1 was partially inhibited ( approximately 25%) by the PKC activator phorbol 12,13 dibutyrate (PDBu) through an ATP-dependent mechanism that was blocked by BIM. Addition of Phosphatidylinositol(4,5) bisphosphate diC8 [DiC(8)PI(4,5)P(2)], a water-soluble derivative of phosphotidyl inositol 4,5 bisphosphate (PIP(2)) to the pipette solution failed to alter inhibition by ANG II. bTREK-1 inhibition by ANG II was also insensitive to antagonists of other protein kinases activated by ANG II in adrenocortical cells but was completely blocked by inorganic polytriphosphate PPPi. DiC(8)PI(4,5)P(2) was a weak activator of bTREK-1 channels, compared with the high-affinity ATP analog N(6)-(2-phenylethyl)adenosine-5'-O-triphosphate (6-PhEt-ATP). These results demonstrate that the modulation of bTREK-1 channels in bovine AZF cells is distinctive with respect to activation by phosphoinositides and nucleotides and inhibition by Gq-coupled receptors. Importantly, ANG II inhibits bTREK-1 channels through a novel pathway that is different from that described for inhibition of native TREK-1 channels in neurons, or cloned channels expressed in cell lines. They also indicate that, under physiological conditions, ANG II inhibits bTREK-1 and depolarizes AZF cells by two, novel, independent pathways that diverge proximal to the activation of PLC.     

The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain. I. Substrate identity

A detailed steady-state kinetic investigation of the hydrolysis of ATP catalyzed by (Na+ + K+)-ATPase is reported. The activity was studied in the presence of (i) Na+ (130 mM), K+ (20 mM) and micromolar ATP concentrations and Na+ (150 mM) the ('Na+-enzyme'). The data obtained lead to the following results: 1. The action of each enzyme may be described by a simple kinetic mechanism with one (Na+-enzyme) or two ((Na+ + K+)-enzyme) dead-end Mg complexes. 2. For both enzymes, both MgATP and free ATP are substrates, with Mg2+, in the latter case, as the second substrate. 3. For each enzyme, the complete set of kinetic constants (seven for the Na+-enzyme, eight for the (Na+ + K+)-enzyme) are determined from the data. 4. For each enzyme it is shown that, in the alternate substrate mechanism obtained, the ratio of net steady-state flux along the 'MgATP pathway' to that of the 'ATP-Mg pathway' increases linearly with the concentration of free Mg2+. The parameters of this function are determined from the data. As a result of this, at high (greater than 3 mM) free Mg2+ concentrations the alternate substrate mechanism degenerates into a 'limiting' kinetic mechanism, with MgATP as the (essentially) sole substrate, and Mg2+ as an uncompetitive (Na+-enzyme) or non-competitive ((Na+ + K+)-enzyme) inhibitor.     

On the mechanism by which dicyclohexylcarbodiimide and quinine inhibit K+ transport in rat liver mitochondria

Passive uptake of potassium acetate into the mitochondrial matrix can be induced by nigericin, a K+/H+ antiporter, or by A23187, a Mg2+/2H+ antiporter. The latter process is thought to reflect operation of the Mg2+-dependent, endogenous K+/H+ antiporter, but there is ambiguity with respect to the mechanism of K+ transport in this assay (Nakashima, R.A., and Garlid, K.D. (1982) J. Biol. Chem. 257, 9252-9254). Kinetic analysis of potassium acetate transport provides verification that Mg2+ depletion 1) unmasks the K+/H+ antiporter, 2) opens up an intrinsic anion uniporter, 3) has no effect on acetic acid transport, and 4) does not induce high K+ uniport conductance. Mg2+-dependent uptake of potassium acetate is thereby shown to be mediated specifically by operation of the endogenous K+/H+ antiporter, as previously proposed. An extension of this analysis confirms that N,N'-dicyclohexylcarbodiimide and quinine block potassium acetate uptake via specific action on the K+/H+ antiporter. These findings support those of a previous study (Martin, W.H., Beavis, A.D., and Garlid, K.D. (1984) J. Biol. Chem. 259, 2062-2065) in which binding of [14C]N,N'-dicyclohexylcarbodiimide to membrane proteins under selective conditions was used to identify an 82,000-dalton band as the protein responsible for K+/H+ antiport in mitochondria.     

The sided action of Na+ and of K+ on reconstituted shark (Na+ + K+)-ATPase engaged in Na+-Na+ exchange accompanied by ATP hydrolysis. I. The ATP activation curve

The ATP hydrolysis dependent Na+-Na+ exchange of reconstituted shark (Na+ + K+)-ATPase is electrogenic with a transport stoichiometry as for the Na+-K+ exchange, suggesting that translocation of extracellular Na+ is taking place via the same route as extracellular K+. The preparation thus offers an opportunity to compare the sided action of Na+ and K+ on the affinity for ATP in a reaction in which the intermediary steps in the overall reaction seems to be the same without and with K+. With Na+ but no K+ on the two sides of the enzyme, the ATP-activation curve is hyperbolic and the affinity for ATP is high. Extracellular K+ in concentrations of 50 microM (the lowest tested) and up gives biphasic ATP activation curves, with both a high- and a low-affinity component for ATP. Cytoplasmic K+ also gives biphasic ATP-activation curves, however, only when the K+ concentration is 50 mM or higher (Na+ + K+ = 130 mM). The different ATP-activation curves are explained from the Albers-Post scheme, in which there is an ATP-dependent and an ATP-independent deocclusion of E2(Na2+) and E2(K2+), respectively, and in which the dephosphorylation of E2-P is rate limiting in the presence of Na+ (but no K+) extracellular, whereas in the presence of extracellular K+ it is the deocclusion of E2(K2+) which is rate limiting.     

K+ channel cAMP activated in guinea pig gallbladder epithelial cells

In guinea pig gallbladder epithelial cells, an increase in intracellular cAMP levels elicits the rise of anion channel activity. We investigated by patch-clamp techniques whether K(+) channels were also activated. In a cell-attached configuration and in the presence of theophylline and forskolin or 8-Br-cAMP in the cellular incubation bath, an increase of the open probability (P(o)) values for Ca(2+)-activated K(+) channels with a single-channel conductance of about 160 pS, for inward current, was observed. The increase in P(o) of these channels was also seen in an inside-out configuration and in the presence of PKA, ATP, and cAMP, but not with cAMP alone; phosphorylation did not influence single-channel conductance. In the inside-out configuration, the opioid loperamide (10(-5) M) was able to reduce P(o) when it was present either in the microelectrode filling solution or on the cytoplasmic side. Detection in the epithelial cells by RT-PCR of the mRNA corresponding to the alpha subunit of large-conductance Ca(2+)-activated K(+) channels (BK(Ca)) indicates that this gallbladder channel could belong to the BK family. Immunohistochemistry experiments confirm that these cells express the BK alpha subunit, which is located on the apical membrane. Other K(+) channels with lower conductance (40 pS) were not activated either by 8-Br-cAMP (cell-attached) or by PKA + ATP + cAMP (inside-out). These channels were insensitive to TEA(+) and loperamide. The data demonstrate that under conditions that induce secretion, phosphorylation activates anion channels as well as Ca(2+)-dependent, loperamide-sensitive K(+) channels present on the apical membrane.     

beta-Adrenergic induced K+ current in Xenopus oocytes: role of cAMP, inhibition by muscarinic agents

The K+ current induced by isoprenaline acting on beta-adrenergic receptors in Xenopus laevis has been studied in oocytes still surrounded by their follicular cells and inner ovarian epithelium. Forskolin, an adenylate cyclase activator, induced a similar K+ current and when used at subliminal concentration it potentiated the current induced by isoprenaline. Inhibition of phosphodiesterase by methylisobutylxanthine also enhanced the response to isoprenaline. 8-Br-cAMP, a permeant analogue of cAMP also produced a K+ current. Acetylcholine produced a long lasting inhibition of the isoprenaline current. This inhibition was not seen in the presence of atropine. It is concluded that the K+ current induced by the activation of beta-adrenergic receptors in the oocyte is mediated by an intracellular rise of cAMP.     

The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain. III. A minimal model

A steady-state kinetic investigation of the effect of K+ on the Na+-enzyme activity of the (Na+ + K+)-ATPase in broken membrane preparations is reported. Analysis of the kinetic patterns obtained, together with the results reported in the first two articles of this series permit the following conclusions. 1. K+ inhibits the Na+-enzyme (the enzyme activity measured at micromolar substrate concentrations in the presence of Na+). The inhibition of non-competitive at low and competitive at higher K+ concentrations and is enhanced by free Mg2+. 2. The results indicate that the Na+-enzyme at steady-state tends to be accumulated in an enzyme-potassium complex when K+ is added. 3. The enzyme-potassium complex, in turn, binds Mg2+ in a dead-end fashion. The dissociation constant for the enzyme-K-Mg complex, estimated from the data, is 7.2 mM. The same value was obtained earlier for the Mg2+ inhibition constant of the substrate-free form of the (Na+ + K+)-enzyme (the enzyme activity measured with Na+ and K+ and at millimolar substrate concentrations) suggesting that the two constants describe the same equilibrium. 4. On the basis of the known (optimal) activity of the (Na+ + K+)-ATPase, relative to that of the Na+-ATPase, a rate constant condition is found which must be met if the Post-Albers kinetic scheme is to satisfy the data. Kinetic data for the phosphoenzyme indicate that this condition is not satisfied. 5. On the basis of the kinetic results a model for the hydrolytic action of (Na+ + K+)-ATPase is proposed. This model encompasses the Post-Albers scheme but contains two distinctive hydrolysis cycles (an 'Na+-enzyme cycle' and a '(Na+ + K+)-enzyme cycle') with widely different affinities for the substrates. Only one of the cycles (the Na+-enzyme cycle) involves acid-stable phosphorylated enzyme intermediates at discernible steady-state concentrations. Which of the two main cycles is predominant in any particular system is determined by the concentration of ligands and substrates. 6. According to this scheme, an enzyme preparation may exhibit both a high (Na+-enzyme) and a low ((Na+ + K+)-enzyme) substrate affinity, without the necessity of assigning more than one substrate site to a particular enzyme unit at any one time.     

Conformational change of sodium- and potassium-dependent adenosine triphosphatase. Conformational evidence for the Post-Albers mechanism in Na+- and K+-dependent hydrolysis of ATP

The addition of ATP with K+ to pig kidney Na+,K+-ATPase (EC 3.6.1.3) modified with a sulfhydryl fluorescent reagent N-[p-(2-benzimidazolyl)phenyl]maleimide induced a transient decrease (t 1/2 = 0.01 s) in the fluorescence in the presence of Mg2+ with 0.64 M Na+, followed by a slow increase (t 1/2 = 0.08 s), to give a higher steady level than that observed without K+. The addition induced a transient increase (t 1/2 less than 0.02 s) in the amount of phosphoenzyme, followed by a slow decrease (t 1/2 = 0.08 s), but the addition without K+ induced a monophasic increase (t 1/2 = 0.02 s). The addition of ATP in the presence of 2 M Na+ with Ca2+ induced a monophasic decrease (t 1/2 = 0.1 s) in the fluorescence along with a much slower increase (t 1/2 = 1.2 s) in the amount of phosphoenzyme. No significant burst of acid-labile phosphate was observed. The data showed clearly the accumulation of the enzyme-ATP complex preceding the phosphoenzyme formation. Fluorescence intensity of these enzyme species and the amount of phosphoenzyme permitted the simulation using the reaction mechanism including enzyme-ATP complex, ADP-sensitive phosphoenzyme, K+-sensitive phosphoenzyme, and K+-bound enzyme. The simulation gave a good fit to the experimental data which showed that ATP is hydrolyzed in sequence through the above intermediates in the presence of both Na+ and K+.     

Chaperonin-facilitated refolding of ribulosebisphosphate carboxylase and ATP hydrolysis by chaperonin 60 (groEL) are K+ dependent

Both the chaperonin- and MgATP-dependent reconstitution of unfolded ribulosebisphosphate carboxylase (Rubisco) and the uncoupled ATPase activity of chaperonin 60 (groEL) require ionic potassium. The spontaneous, chaperonin-independent reconstitution of Rubisco, observed at 15 but not at 25 degrees C, requires no K+ and is actually inhibited by chaperonin 60, with which the unfolded or partly folded Rubisco forms a stable binary complex. The chaperonin-dependent reconstitution of Rubisco involves the formation of a complex between chaperonin 60 and chaperonin 10 (groES). Formation of this complex almost completely inhibits the uncoupled ATPase activity of chaperonin 60. Furthermore, although the formation of the chaperonin 60-chaperonin 10 complex requires the presence of MgATP, hydrolysis of ATP may not be required, since complex formation occurs in the absence of K+. The interaction of chaperonin 60 with unfolded or partly folded Rubisco does not require MgATP, K+, or chaperonin 10. However, discharge of the complex of chaperonin 60-Rubisco, which leads to the formation of active Rubisco dimers, requires chaperonin 10 and a coupled, K(+)-dependent hydrolysis of ATP. We propose that a role of chaperonin 10 is to couple the K(+)-dependent hydrolysis of ATP to the release of the folded monomers of the target protein from chaperonin 60.     

Nonenzymatic glycation of Na,K-ATPase. Effects on ATP hydrolysis and K+ occlusion

Glycation of the Na,K-ATPase in vitro (formation of Schiff base with glucose followed by reduction with NaCNBH3) shows the presence of three classes of reactive amino groups that differentially affect catalysis and cation binding. Reaction in the absence of ATP results in irreversible inhibition of enzyme activity with a t1/2 of 53 min. This is due to modification of one class of amino groups that affect the catalytic domain of the enzyme. In the presence of ATP, glycation first results in a shift in the steady state kinetics of ATP hydrolysis from substrate activation to Michaelis-Menten kinetics accompanied by an increase in the apparent affinity for K+ in the p-nitrophenylphosphatase reaction. This change in kinetic properties occurs with a t1/2 of 9 min and results in the complete loss of K+ occlusion. Incorporation of glucose is into the catalytic subunit, remote from the N-terminal end. Apparent total inhibition of K+ occlusion occurs with a stoichiometry 0.8 mol of glucose incorporated per mol of enzyme. Therefore, there is a rapidly reacting amino group that affects the cation binding domain of the Na,K-ATPase. More slowly, with a t1/2 of 9 h, the ATP hydrolysis kinetics change from Michaelis-Menten to substrate inhibition without recovery of K+ occlusion, showing that, in the E1 conformation, there is a third, slower reacting class of amino groups in the Na,K-ATPase that affects low affinity nucleotide interaction with the catalytic subunit.     

The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain. II. Kinetic characterization of phosphointermediates

(1) The kinetics of the phosphorylated enzymic intermediates of (Na+ + K+)-ATPase from ox brain, which are formed by incubation of the enzyme with 25 microM AT32P, 150 mM Na+ and 1 mM Mg2+, have been studied in dephosphorylation experiments at 1 degree C. The dephosphorylation of the 32P-labelled enzyme was initiated by addition of either 1 mM unlabelled ATP, 2.5 mM ADP or 1 mM unlabelled ATP + ADP in concentrations from 25 to 1000 microM. (2) In the absence of ADP the dephosphorylation curve was linear in a semilogarithmic plot almost from t = 0, whereas by addition of ADP a biphasic behaviour was obtained. The slope of the slow phase of dephosphorylation was virtually independent of the ADP concentration. (3) The results were analysed by the mathematical equation corresponding to the simplest possible model for the interconversion and breakdown of the phosphointermediates: (formula: see text) where alpha, beta, H and G are functions of all the rate constants and H and G furthermore are functions of the initial values for [E1P] and [E2P]. (4) The analysis confirmed the model and enabled the determination of all the rate constants. (5) k-1 was found to be equal to k'-1 + k"-1 . [ADP] indicating an ADP-independent 'spontaneous' dephosphorylation of E1P. The rate constant for this process was close to that for dephosphorylation of E2P, i.e., k'-1 congruent to k3. Also the value of k"-1 was determined. (6) k3 was found to be at least 10 . k-2. The implication of this for the role of the E1P to E2P transition in the Na+ + K+)-stimulated ATP hydrolysis will be discussed in detail in the following paper (Plesner, I.W., Plesner, L., N?rby, J.G. and Klodos, I. (1981) Biochim. Biophys. Acta 643, 483--494). (7) A refinement of the model, accounting for the effect of Na+ on the steady-state ratio between [E1P] and [E2P] is proposed: (formula: see text). At [Na+] = 150 mM as used here, E1P(Na) and E'1P are assumed to be in rapid equilibrium. (8) Comparison of our results with those of others underlines the general validity of the conclusions of the present paper.