Cytotoxic and non-cytotoxic cardiac glycosides isolated from the combined flowers,leaves, and twigs of Streblus asper

A new non-cytotoxic [(+)-17β-hydroxystrebloside (1)] and two known cytotoxic [(+)-3′-de-O-methylkamaloside (2) and (+)-strebloside (3)] cardiac glycosides were isolated and identified from the combined flowers, leaves, and twigs of Streblus asper collected in Vietnam, with the absolute configuration of 1 established from analysis of its ECD and NMR spectroscopic data and confirmed by computational ECD calculations. A new 14,21-epoxycardanolide (3a) was synthesized from 3 that was treated with base. A preliminary structure-activity relationship study indicated that the C-14 hydroxy group and the C-17 lactone unit and the established conformation are important for the mediation of the cytotoxicity of 3. Molecular docking profiles showed that the cytotoxic 3 and its non-cytotoxic analogue 1 bind differentially to Na⁺/K⁺-ATPase. Compound 3 docks deeply in the Na⁺/K⁺-ATPase pocket with a sole pose, and its C-10 formyl and C-5, C-14, and C-4′ hydroxy groups may form hydrogen bonds with the side-chains of Glu111, Glu117, Thr797, and Arg880 of Na⁺/K⁺-ATPase, respectively. However, 1 fits the cation binding sites with at least three different poses, which all depotentiate the binding between 1 and Na⁺/K⁺-ATPase. Thus, 3 was found to inhibit Na⁺/K⁺-ATPase, but 1 did not. In addition, the cytotoxic and Na⁺/K⁺-ATPase inhibitory 3 did not affect glucose uptake in human lung cancer cells, against which it showed potent activity, indicating that this cardiac glycoside mediates its cytotoxicity by targeting Na⁺/K⁺-ATPase but not by interacting with glucose transporters.     

Synthesis and evaluation of panaxatriol derivatives as Na+, K+-ATPase inhibitors

Panaxatriol, a triterpene bearing a steroid-like structure similar to cardiac glycosides, was presumed to share the same bioactivity with cardiac glycosides, and may be a potential Na⁺, K⁺-ATPase inhibitor. In this paper, a series of panaxatriol derivatives were synthesized and evaluated for Na⁺, K⁺-ATPase inhibitory activities. The results of biological tests showed that more than half of the synthesized derivatives presented increased inhibitory activities compared with panaxatriol. Of these compounds, 13a with a 3, 4-seco skeleton showed the most potent inhibitory activity, which was equal to that of the standard drug digoxin. To understand the binding mode of the most active compound, molecular docking study of 13a with Na⁺, K⁺-ATPase was conducted. Therefore, 13a may serve as a new lead compound for the development of novel Na⁺, K⁺-ATPase inhibitors.     

Characterization,quantitation, similarity evaluation and combination with Na+,K+-ATPase of cardiac glycosides from Streblus asper

Streblus asper Lour. (Moraceae) is a medicinal plant in Asian countries including India and Thailand, possessing activities of anti-tumor, anti-allergy, anti-parasitic and anti-bacterial. In this paper, characterization, quantitation and similarity evaluation of cardiac glycosides in different parts of S. asper were investigated by HPLC-Q-TOF-MS and chemometric methods. Then, the inhibition of Na⁺,K⁺-ATPase activity by the compounds isolated from S. asper was measured. Meanwhile, enzyme kinetics and molecular docking were determined to exhibit the combination modes between cardiac glycosides and Na⁺,K⁺-ATPase. As a result, twenty peaks of cardiac glycosides were assigned. Strophanthidin-3-O-α-l-rhamnopyranosyl-(1 → 4)-6-deoxy-β-d-allopyranoside (1), glucostrebloside (2), strebloside (4) and mansonin (8) with a significant activity of inhibiting Na⁺,K⁺-ATPase (IC₅₀ 7.55–13.60 μM) were chosen for the determination of enzyme kinetics, exhibiting anticompetitive inhibitory characteristics towards Na⁺,K⁺-ATPase. Compound 4 could reasonably bind to the active sites of Na⁺,K⁺-ATPase, proved by molecular docking. Furthermore, the contents of the major compounds in four different parts of S. asper were extremely different, analyzed by chemometric methods, similarity analysis and principle compounds analysis. All these findings indicated that the contents of major compounds in different parts of S. asper were extremely different with a significant activity of inhibiting Na⁺,K⁺-ATPase, providing a reference for determination of effective part and administered dosage. The combination modes between cardiac glycosides and Na⁺,K⁺-ATPase were also revealed by enzyme kinetics and molecular docking, which provided a basis for further study of pharmacological activity.     

Hyperkalemia Develops in Some Thyroidectomized Patients Undergoing Thyroid Hormone Withdrawal in Preparation for Radioactive Iodine Ablation for Thyroid Carcinoma

Objective: Hyponatremia is observed in hypothyroidism, but it is not known if hypo- or hyperkalemia is associated with hypothyroidism. To study these questions, we determined serum potassium (K⁺) levels in thyroidectomized patients undergoing levothyroxine withdrawal before radioactive iodine (RAI) therapy for thyroid carcinoma.Methods: We retrospectively studied the records of 108 patients who had undergone total thyroidectomy for thyroid carcinoma followed by levothyroxine withdrawal and then ablation with RAI at Nagasaki University Hospital from 2009–2013. Blood samples were analyzed for serum K⁺ concentrations when patients were euthyroid just before levothyroxine withdrawal and hypothyroid 21 days after levothyroxine withdrawal. We determined the proportion of patients who developed hyperkalemia (K⁺ ≥5 mEq/L) and hypokalemia (K⁺ ≤3.5 mEq/L).Results: Five (4.6%) patients developed hyperkalemia and 2 (1.9%) patients developed hypokalemia after levothyroxine withdrawal. The mean serum K⁺ level after levothyroxine withdrawal was significantly higher than before levothyroxine withdrawal (4.23 ± 0.50 mEq/L vs. 4.09 ± 0.34 mEq/L; P<.001). After levothyroxine withdrawal, serum K⁺ values were significantly correlated with age, serum sodium and creatinine levels, and the estimated glomerular filtration rate but not with serum free thyroxine or thyroid-stimulating hormone concentrations. The finding of an elevated serum K⁺ of >0.5 mEq/L after levothyroxine withdrawal was more prevalent with age >60 years (odds ratio [OR], 4.66; P = .026) and with the use of angiotensin-II receptor blockers or angiotensin-converting enzyme inhibitors (OR, 3.53; P = .033) in a multivariate analysis.Conclusion: Hyperkalemia develops in a small percentage of hypothyroid patients after thyroid hormone withdrawal, especially in patients over 60 years of age who are using antihypertensive agents that inhibit the reninangiotensin- aldosterone system.Abbreviations: ACE-I = angiotensin-converting enzyme inhibitor ARB = angiotensin-II receptor blocker Cr = creatinine eGFR = estimated glomerular filtration rate Eu-K⁺ = serum level of K⁺ in the euthyroid state Hypo-K⁺ = serum level of K⁺ in the hypothyroid state K⁺ = potassium Na⁺ = sodium ?K⁺ = Hypo-K⁺ value minus Eu-K⁺ value RAI = radioactive iodine TSH = thyroid-stimulating hormone     

Activation of Apical K<Superscript>+</Superscript> Conductances by Muscarinic Receptor Stimulation in Rat Distal Colon: Fast and Slow Components

In the epithelium of rat distal colon the acetylcholine analogue carbachol induces a transient increase of short-circuit current (I_sc) via stimulation of cellular K⁺ conductances. Inhibition of the turnover of inositol-1,4,5-trisphosphate (IP₃) by LiCl significantly reduced both the amplitude and the duration of this response. When the apical membrane was permeabilized with nystatin, LiCl nearly abolished the carbachol-induced activation of basolateral K⁺ conductances. In contrast, in epithelia, in which the basolateral membrane was bypassed by a basolateral depolarization, carbachol induced a biphasic increase in the K⁺ current across the apical membrane consisting of an early component carried by charybdotoxin- and tetraethylammonium-sensitive K⁺ channels followed by a sustained plateau carried by channels insensitive against these blockers. Only the latter was sensitive against LiCl or inhibition of protein kinases. In contrast, the stimulation of the early apical K⁺ conductance by carbachol proved to be resistant against inhibition of phospholipase C or protein kinases. However, apical dichlorobenzamil, an inhibitor of Na⁺/Ca²⁺ exchangers, or a Ca²⁺-free mucosal buffer solution significantly reduced the early component of the carbachol-induced apical K⁺ current. The presence of an apically localized Na⁺/Ca²⁺-exchanger was proven immunohistochemically. Taken together these experiments reveal divergent regulatory mechanisms for the stimulation of apical Ca²⁺-dependent K⁺ channels in this secretory epithelium, part of them being activated by an inflow of Ca²⁺ across the apical membrane.

Relation of increased potassium nutrition to photosynthesis and translocation of carbon

Effects of supplying K⁺ at 2 or 10 millimolarity concentration on net carbon exchange and translocation of products of photosynthesis were studied in plants of Beta vulgaris L. (var. Klein E). Transport of K⁺ into and out of leaves was studied with ⁴²K over a 3-day period. Increasing the K⁺ supplied to the roots from 2 millimolarity, a level just sufficient to overcome obvious deficiency symptoms, to 10 millimolarity resulted in a gradual accumulation of K⁺ per unit area and an increased export of K⁺ to sink regions. No significant increase in net carbon exchange was observed in leaves that had accumulated a high level of K⁺ per unit area. Initiation rate, total area, and total fresh weight of leaves of plants with K⁺ supplied at 10 millimolarity was similar to that for leaves from plants at a 2 millimolarity level. Shoot/root ratio and dry weight accumulation, which are indicative of translocation and partitioning over the long term, were independent of K⁺ supply in the 2 to 10 millimolarity range. Accumulation of K⁺ by exporting leaves and its subsequent recirculation to sinks increased when K⁺ supply was increased in this range but did not appear to affect carbon nutrition even after a long period.     

Glucose transport in a model of the rat proximal tubule epithelium

A mathematical model of the rat proximal tubule epithelium has been extended to include terms for glucose-sodium cotransport, as well as the passive permeability properties of urea. Except for a metabolically driven Na⁺-K⁺ exchanger at the cell basolateral membrane, all membrane transport is represented by the relations of linear nonequilibrium thermodynamics. Use of this formalism permits the explicit calculation of the intracellular depolarization immediately following the luminal application of glucose, and shows the magnitude of this potential deflection proportional to the glucose chemical-potential change. The steady-state glucose transport by this model epithelium, like experimental data, is fitted remarkably well by a three-parameter pump-leak model of transport. In view of the nonsaturability of the cotransporter of the model epithelium, the goodness of fit to the three-parameter model is surprising and underscores the uncertainty in extracting individual membrane properties from whole epithelial data. Experiments are simulated in which hypertonic glucose placed in the bath induces cell swelling and K⁺ uptake; a hypertonic impermeant induces cell shrinkage and K⁺ loss. Although this parallels the observations in vivo, the large K⁺ shifts predicted by the model suggest the absence of important volume-regulatory mechanisms from the model scheme.     

tert-Butyl 1,5-bis(4-(benzo[d]isothiazol-3-yl)piperazin-1-yl)-1,5-dioxopentan-2-ylcarbamate urea/thiourea derivatives as potent H+/K+-ATPase inhibitors

Amino acids are known to possess variable efficacy against ulceration. Considering the good antiulcer activity of amino acids, a series of urea/thiourea derivatives of glutamic acid conjugated benzisothiazole analogue 3a–u with various substituents on aryl ring were synthesized, spectroscopically characterized and evaluated for in vitro H⁺/K⁺-ATPase inhibition. Majority of the compounds possessed potency compared to that of omeprazole, a reference drug. In particular, methoxy derivatives 3p–u were the most active compounds possessing a significant 15-fold increase for para substituent thus, contributing positively to gastric H⁺/K⁺-ATPase inhibition.     

The Effect of the Gamma Modulator on Na/K Pump Activity of Intact <Emphasis Type="Italic">Mammalian Cells</Emphasis>

This study concerns the modulatory effects of the gamma modulator of the Na/K pump, in particular whether the effects seen in previous experiments with isolated membranes are relevant to Na/K pump behavior in intact mammalian cells. For this purpose, HeLa cells previously transfected with the rat Na/K catalytic subunit were used. The results show that both variants of the regulator, γa and γb, decrease the apparent affinity of the pump for Na⁺ and cause a modest increase in apparent ATP affinity as seen in measurements of ouabain-sensitive ⁸⁶Rb(K⁺) influx into cells in which ATP was varied using antimycin A and glucose. Equivalent results had been obtained previously in our analyses of Na,K-ATPase activity of membrane fragments, i.e., an increase in K_0.5(Na) at high K⁺ concentration and a decrease in K′_ATP. Comparison of clones of γ-transfected and mock-transfected cells (with similar V_max values) indicated that γ causes a modest ≈30% increase in the steady-state concentration of intracellular Na⁺. Furthermore, for both γa and γb, values of intracellular Na⁺ were similar to those predicted from the kinetic constants, K_0.5(Na) and V_max. Finally, there was a γ-mediated increase in apparent affinity for extracellular K⁺, which had not been detected in assays of permeabilized membranes.

Molecular cloning and expression analysis of a gene encoding KUP/HAK/KT-type potassium uptake transporter from Cryptomeria japonica

Key message

The molecular mechanism of potassium ion transport across membranes in conifers is poorly known. We isolated and analyzed a gene encoding a potassium transporter from the conifer Cryptomeria japonica.

Abstract

Potassium ion (K⁺) is an essential and the most abundant intracellular cation in plants. The roles of K⁺ in various aspects of plant life are closely linked to its transport across biological membranes such as the plasma membrane and the tonoplast, which is mediated by membrane-bound transport proteins known as transporters and channels. Information on the molecular basis of K⁺ membrane transport in trees, especially in conifers, is currently limited. In this study, we isolated one complementary DNA, CjKUP1, which is homologous to known plant K⁺ transporters, from Cryptomeria japonica. Complementation tests using an Escherichia coli mutant, which is deficient in K⁺ uptake activity, was conducted to examine the K⁺ uptake function of the protein encoded by CjKUP1. Transformation of the K⁺-uptake-deficient mutant with CjKUP1 complemented the deficiency of this mutant. This result indicates that CjKUP1 has a function of K⁺ uptake. The expression levels of CjKUP1 in male strobili were markedly higher from late September to early October than in other periods. The expression levels in male and female strobili were higher than those in other organs such as needles, inner bark, differentiating xylem, and roots. These results indicate that CjKUP1 is mainly involved in K⁺ membrane transport in the cells of reproductive organs of C. japonica trees, especially in male strobili during pollen differentiation.     

Thermodynamics and coordination characteristics of the hydronium-uranium(VI)-dicyclohexano-24-crown-8 extraction complex

The extraction equilibrium of the hydronium-uranium(VI)-dicyclohexano-24-crown-8 complex was carried out in the crown ether1,2-dichloroethaneHCl aqueous solution system at different temperatures. The extraction complex has the overall composition (L)₂·(H₃O⁺·χH₂O)₂·UO₂Cl₄²⁻ (L = dicyclohexano-24-crown-8). The values of the extraction equilibrium constants (K_ex) increase steadily with a decrease in temperature: 13.5 (298 K), 7.96 (301 K), 4.20 (303 K) and 2.07 (305 K). A plot of log K_ex against 1/T shows a straight line. The value of the enthalpy change, ΔH°, was calculated from the slope and equals −212 kJ mol⁻¹. The value of the entropy change, ΔS°, was calculated from ΔH° and K_ex and equals −690 J K⁻¹ mol⁻¹, whereas ΔG° = −6.45 kJ mol⁻¹. Comparing these thermodynamic parameters with those of the dicyclohexano-18-crown-6 isomer A [1] (ΔS° = −314 J K⁻¹ mol⁻¹, ΔH° = −101 kJ mol⁻¹ and ΔG° = −8.37 kJ mol⁻¹), it can be seen that ΔH° and ΔS° are more negative for the former than for the latter, and both are enthalpy-stabilized complexes. The molecular structure of the complex has the feature that there are two H₅O₂⁺ ions in it, in contrast to the H₃O⁺ ions in the dicyclohexano-18-crown-6 isomer A complex [1]. Each of the H₅O₂⁺ ions is held in the crown ether cavity by four hydrogen bonds. The H₅O₂⁺ ion has a central bond. The uranium atom forms UO₂Cl₄²⁻ as a counterion away from the crown ether. The formation of this complex is in good agreement with more negative entropy change and less negative free energy change, as mentioned above.     

A reverse method for diversity introduction of benzimidazole to synthesize H(+)/K(+)-ATP enzyme inhibitors

A series of 2-[(2-pyridylmethyl)sulfinyl]benzimidazole derivatives were synthesized via a solution phase synthetic route using a reversal method of diversity introduction. Using this synthetic strategy, we obtained two key intermediates (4-A and 4-B) simultaneously, which allows us to introduce diversity points onto the benzimidazole part of the final product under reliable reaction conditions to identify potent H⁺/K⁺-ATP enzyme inhibitors. Compound 14l (IC₅₀ = 1.6 × 10⁻⁵ M) was comparable with H⁺/K⁺-ATP enzyme inhibitor in vitro.     

Asymmetric incorporation of Na+, K+-ATPase into phospholipid vesicles

Purified lamb kidney Na⁺, K⁺-ATPase, consisting solely of the Mτ = 95,000 catalytic subunit and the M_τ～- 44,000 glycoprotein, was solubilized with Triton X-100 and incorporated into unilamellar phospholipid vesicles. Freeze-fracture electron microscopy of the vesicles showed intramembranous particles of approximately 90–100 Å in diameter, which are similar to those seen in the native Na⁺,K⁺-ATPase fraction. Digestion of the reconstituted proteins with neuraminidase indicated that the glycoprotein moiety of the Na⁺,K⁺-ATPase was asymmetrically oriented in the reconstituted vesicles, with greater than 85% of the total sialic acid directed toward the outside of the vesicles. In contrast, in the native Na⁺,K⁺-ATPase fraction, the glycoprotein was symmetrically distributed. Purified glycoprotein was also asymmetrically incorporated into phospholipid vesicles using Triton X-100 and without detergents as described by R. I. MacDonald and R. L. MacDonald (1975, J. Biol. Chem.250, 9206–9214). The glycoprotein-containing vesicles were 500–1000 Å in diameter, unilamellar, and, in contrast to the vesicles containing the Na⁺,K⁺-ATPase, did not contain the 90- to 100-Å intramembranous particles. These results indicate that the intramembranous particles observed in the native Na⁺,K⁺-ATPase and in the reconstituted Na⁺,K⁺-ATPase are not due to the glycoprotein alone, but represent either the catalytic subunit, or the catalytic plus the glycoprotein subunit.     

Synthesis and SAR studies of potent H+/K+-ATPase inhibitors of quinazolinone-Schiff’s base analogues

A series of quinazolinone derived Schiff base derivatives 7–36 were synthesized and characterized by analytical and spectroscopic techniques. The synthesized analogues were screened for their in vitro H⁺/K⁺-ATPase inhibition. Most of the compounds showed excellent activity, compared to that of omeprazole, a reference drug. In particular, hydroxy and methoxy derivatives 13–24 were the most active compounds possessing a significant increase for different substituents on the benzene ring thus, contributing positively to gastric H⁺/K⁺-ATPase inhibition. Preliminary structure-activity relationship revealed that the compounds 13–24 with electron donating moiety (OH, OCH₃) were found to be excellent activity and compounds 9–12 and 25–36 with electron withdrawing moiety (Cl, F, NO₂ and Br) were found to be least antiulcer agents.     

Sodium and potassium balance of captive meadow voles (Microtus pennsylvanicus) fed laboratory chow and vegetation diets

• 1.1. Mineral balance was studied in meadow voles (Microtus pennsylvanicus) maintained in the laboratory.
• 2.2. Urine and fecal Na⁺ contents of voles on low-Na⁺ diets were comparable to those reported for other herbivore species, but urine and fecal K levels were higher.
• 3.3. Voles approached Na⁺ balance (input = output) on diets with Na⁺ content as low as 56 ppm.
• 4.4. There was not a clearcut hypertrophy of the adrenal-gland zona glomerulosa in voles maintained on low-Na⁺ diets.
• 5.5. Plasma K content and bone water content were higher in voles maintained on high-Na ⁺ vegetation diets, suggesting expansion of extracellular fluid volume.

     

Relationship between intracellular K+ concentrations and K+ fluxes in growing and contact-inhibited cells

The K⁺ content and the K⁺ flux were measured in the cell lines ME₂ and MF₂ isolated from plasmocytoma MOPC 173. Both cell lines were shown to have the same K⁺ content and the same K⁺ steady state flux per unit of surface area.In ME₂ cells, no modification of the exchange movement was observed during contact inhibition. However, contact-inhibited cells exhibited an increased resistance to depletion, characterized by a lower K⁺ net movement.The (Na⁺ + K⁺)-ATPase measured in homogenates is poorly correlated to in vivo cation fluxes both because of the enhancement due, presumably, to the drop of K⁺ concentration on the cytoplasmic face of the membrane and because of losses during preparation which can be conspicuous, especially in contact-inhibited cells.The K⁺ net flux is considerably increased when the intracellular K⁺ level is reduced after preincubation of the cells in a K⁺-free medium. Thus, internal K⁺ seems to regulate the K⁺ influx.     

Potassium fluxes in the rat reticulocyte Ouabain sensitivity and changes during maturation

K⁺ turnover is markedly enhanced in the rat reticulocyte, both influx and efflux rates being increased by factors of approximately 3 over the corresponding rates in adult cells. These accelerated fluxes are observed despite the absence of any appreciable change in intracellular K⁺ concentration during the course of maturation. Qualitative characteristics of the active transport process for K⁺ influx appear to be identical in reticulocytes and mature erythrocytes with regard both to K⁺ sensitivity, and to ouabain sensitivity as a function of external K⁺ concentration. The number of ouabain binding sites per unit volume of cells, however, is increased by a factor of approximately three in the reticulocyte and thus correlates well with the observed degree of enhancement of active K⁺ influx in these cells. Half-maximal rates of ouabain-sensitive K⁺ influx are observed at external K⁺ concentrations well below 1 mM for both reticulocytes and mature erythrocytes. It is concluded that the enhanced rate of K⁺ accumulation in the reticulocyte can be quantitatively attributed to an increased number of pump units which are qualitatively identical to those in the mature cell, and which function at a near-maximal rate at the ambient K⁺ concentration present in normal rat plasma.     

Multi-targeted dihydrazones as potent biotherapeutics

Hydrazone compounds were considered as a useful moiety in drug design development. Therefore, these studies were aimed at the synthesis of new dihydrazones and were screened for their in vitro H⁺/K⁺-ATPase and anti-inflammatory activities. The results revealed that compounds 9 (22 ± 0.62 µg/mL), 10 (26 ± 0.91 µg/mL), 15 (24 ± 0.44 µg/mL), 16 (28 ± 0.63 µg/mL), 17 (12 ± 0.38 µg/mL), 18 (14 ± 0.47 µg/mL), 19 (26 ± 0.54 µg/mL), 20 (16 ± 0.41 µg/mL), 25 (06 ± 0.68 µg/mL) and 26 (08 ± 0.43 µg/mL) showed excellent H⁺/K⁺-ATPase activity and their IC₅₀ value were lower than the standard drug Omerazole (48 ± 0.12 µg/mL). Compounds 5 (28 ± 0.65 µg/mL), 6 (24 ± 0.61 µg/mL), 7 (28 ± 0.64 µg/mL), 8 (26 ± 0.45 µg/mL), 11 (30 ± 0.74 µg/mL), 12 (28 ± 0.40 µg/mL), 13 (32 ± 0.24 µg/mL), 14 (30 ± 0.55 µg/mL) and 21 (08 ± 0.47 µg/mL), 22 (12 ± 0.47 µg/mL), 23 (10 ± 0.51 µg/mL) and 24 (14 ± 0.84 µg/mL) showed better anti-inflammatory activity compared to standard indomethacin (44 ± 0.15 µg/mL). The structure activity relationship (SAR) showed that, electron donating groups (OH, OCH₃) favored the H⁺/K⁺-ATPase and antioxidants activity, whereas, electron withdrawing groups (F, Cl, Br and NO₂) favored the anti-inflammatory activity. Furthermore, molecular docking study was performed to investigate the binding interactions of the most active analogs with the active site of H⁺/K⁺-ATPase enzyme. Compounds 25 (G-score = −9.063) and 26 (G-score = −8.977) showed the highest docking G-scores for H⁺/K⁺-ATPase inhibition activity.     

Mathematical modelling of ATP, K and Na interactions with (Na + K)-ATPase occurring under equilibrium conditions

The controlling effect of ATP, K⁺ and Na⁺ on the rate of (Na⁺ + K⁺)-ATPase inactivation by 7-chloro-4-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl) is used for the mathematical modelling of the interaction of the effectors with the enzyme under equilibrium conditions.

1. 1. Of a series of conceivable interaction models, designed without conceptual restrictions to describe the effector control of inactivation kinetics, only one fits the experimental data described in a preceding paper.

2. 2. The model is characterized by the coexistence of two binding sites for ATP and the coexistence of two separate binding sites for K⁺ and Na⁺ on the enzyme-ATP complex. On the basis of this model, the effector parameters fitting the experimental data most closely are estimated by means of nonlinear least-squares fits.

3. 3. The apparent dissociation constants for ATP of the enzyme-ATP complex or of the enzyme-(ATP)₂ complex are computed to lie near 0.0024 mM and 0.34 mM, respectively, irrespective of whether K⁺ and Na⁺ were absent or K⁺ and K⁺ plus Na⁺, respectively, were present in the experiments.

4. 4. The origin of the high and the low affinity site for binding of ATP to the (Na⁺ + K⁺)-ATPase molecule is traced back to the coexistence of two catalytic centres which, although primarily equivalent as to the reactivity of their thiol groups with NBD-Cl, are induced into anticooperative communication by ATP binding and thus show an induced geometric asymmetry.