The effects of calcitonin on calcium uptake and respiration in rat-liver mitochondria

The action of calcitonin on both the transport of calcium across the mitochondrial membrane and cellular respiration has been studied in the presence and absence of added phosphate. In the presence of phosphate, both the rate of calcium entry and the amount of calcium accumulated was stimulated by calcitonin, above a threshold concentration, in a saturable manner. In the absence of phosphate, calcitonin enhanced the rate of calcium entry, but had no appreciable effect on the levels of total calcium accumulated. The minimum concentration of calcitonin necessary to produce these effects was in all cases dependent on the external calcium concentration. Mitochondrial respiration was inhibited only at calcitonin levels much higher than those affecting calcium uptake. These results are consistent with the idea that the action of calcitonin is directly related to the mechanism of calcium uptake, and not to the respiratory process.     

Regulation of cellular calcium metabolism and calcium transport by calcitonin.

Calcitonin was studied in isolated kidney cells and in isolated mitochondria. A concentration of 10 ng/ml of synthetic calcitonin increases the cellular accumulation of 45Ca and the total cell calcium. The mitochondrial pool is increased several-fold. Kinetic analysis of the data shows that although the total cellular exchangeable calcium pool is enlarged, calcium influx and efflux are significantly depressed by calcitonin. The absence of phosphate or the presence of inhibitors of mitochondrial calcium transport completely abolish the effects of the hormone. In isolated mitochondria, the hormone stimulates the active calcium uptake and depresses the extramitochondrial calcium activity. Calcitonin counteracts the effects of cyclic AMP which stimulates the release of calcium from mitochondria and increases the extramitochondrial calcium activity. These data indicate that cellular calcium homeostasis is controlled by the mitochondrial calcium turnover. They suggest that calcitomin regulates the cell calcium metabolism and inhibits the transcellular calcium transport by stimulating the rate of calcium uptake by mitochondria which depresses cytoplasmic calcium activity.     

Regulation of calcium transport in bovine spermatozoa

Calcium uptake into bovine epididymal spermatozoa is enhanced by introducing phosphate in the suspending medium (Babcock et al. (1975) J. Biol. Chem. 250, 6488-6495). This effect of phosphate is found even at a low extracellular Ca2+ concentrations (i.e., 5 microM) suggesting that phosphate is involved in calcium transport via the plasma membrane. Bicarbonate (2 mM) cannot substitute for phosphate, and a relatively high bicarbonate concentration (20 mM) causes partial inhibition of calcium uptake in absence of Pi. In the presence of 1-2 mM phosphate, 20 mM bicarbonate enhances Ca2+ uptake. The data indicate that the plasma membrane of bovine spermatozoa contains two carriers for Ca2+ transport: a phosphate-independent Ca2+ carrier that is stimulated by bicarbonate and a phosphate-dependent Ca2+ carrier that is inhibited by bicarbonate. Higher phosphate concentrations (i.e., 10 mM) inhibit Ca2+ uptake into intact cells (compared to 1.0 mM phosphate) and this inhibition can be relieved partially by 20 mM bicarbonate. This effect of bicarbonate is inhibited by mersalyl. Calcium uptake into the cells is enhanced by adding exogenous substrates to the medium. There is no correlation between ATP levels in the cells and Ca2+ transport into the cell. ATP levels are high even without added exogenous substrate and this ATP level is almost completely reduced by oligomycin, suggesting that ATP can be synthesized in the mitochondria in the absence of exogenous substrate. Calcium transport into the sperm mitochondria (washed filipin-treated cells) is absolutely dependent upon the presence of phosphate and mitochondrial substrate. Bicarbonate cannot support Ca2+ transport into sperm mitochondria. There is good correlation between Ca2+ uptake into intact epididymal sperm and into sperm mitochondria with the various substrates used. This indicates that the rate of calcium transport into the cells is determined by the rate of mitochondrial Ca2+ uptake and respiration with the various substrates.     

Acute responsiveness to calcitonin in chronic renal failure.

The acute effect of porcine calcitonin was tested in 17 patients undergoing chronic haemodialysis. In normal adults calcitonin has no effect on plasma calcium or phosphate levels, but in nine patients both concentrations were substantially reduced after calcitonin. This hypocalcaemic and hypophosphataemic effect was a function of the initial plasma phosphate level but was unrelated to the initial plasma calcium level. Plasma hydroxyproline levels were not significantly different in the two groups an were unaffected by calcitonin. In 11 patients fasting plasma calcitonin levels were undetectable with an assay sensitive to 0-1 mug/1. Calcitonin seems to have an acute effect in chronic renal failure which may not operate by arresting bone resorption but is dependent on the plasma phosphate concentration.     

Transport mechanism for calcium and phosphate in ram spermatozoa

Calcium uptake into ejaculated ram spermatozoa is highly enhanced by the addition of extracellular phosphate. Under identical conditions, extracellular calcium stimulates the uptake of phosphate by the cells. Both calcium and phosphate uptake are comparably inhibited by the sulfhydryl reagent mersalyl. The I50 was found to be 6.36 and 10.14 nmol mersalyl per mg protein for phosphate and calcium uptake, respectively. Calcium uptake is inhibited by mersalyl whether phosphate is present or not. Extracellular fructose causes a 5-fold increase in calcium uptake. When fructose and phosphate are present in the cell's medium, there is an additive effect, which indicates that two independent systems are involved in calcium transport into the cell. Ruthenium red, which blocks Ca2+ transport into the mitochondria, causes 70% and 95% inhibition of calcium uptake in the absence or in the presence of fructose, respectively. Ruthenium red does not affect phosphate uptake unless calcium was present in the incubation medium. The stimulatory effect of fructose upon calcium uptake can be mimicked by L-lactate and can be inhibited by the glycolytic inhibitor 2-deoxyglucose. Fructose and L-lactate stimulate mitochondrial respiration in a comparable way. Oligomycin, which inhibits mitochondrial ATP synthesis, does not inhibit Ca2+ uptake. This indicates that ATP is not involved in the mechanism by which mitochondrial respiration stimulates Ca2+ uptake. The calcium channel blocker, verapamil, inhibits Ca2+ uptake in the presence or absence of extracellular phosphate. The phosphate-dependent calcium transport mechanism is more sensitive to verapamil than is the phosphate-independent transporter. In summary, the data indicate that the plasma membrane of mammalian spermatozoa contains a calcium/phosphate symporter, a phosphate-independent calcium carrier and a calcium-independent phosphate carrier.     

Mechanism of action of ryanodine on cardiac sarcoplasmic reticulum

Ryanodine was found to initially inhibit calcium uptake by cardiac sarcoplasmic reticulum. This initial depression was followed by a later marked stimulation of calcium uptake. These effects were noted when calcium uptake was measured in the presence or absence of oxalate. The requirement for preincubation with ryanodine was highly dependent on ryanodine concentration and temperature. The mechanism of action of ryanodine clearly was not an effect on oxalate entry or calcium oxalate precipitation because the effects were also observed in the absence of oxalate. Ryanodine also had no effect on passive calcium efflux from actively loaded vesicles. Because ryanodine had no effect on Ca2+-ATPase activity under defined conditions of an ATP-regenerating system and no calcium gradient, we suggest ryanodine does not change the stoichiometry of the pump. Our results are consistent with the hypothesis that ryanodine closes a calcium channel in a subpopulation of the vesicles.     

Effect of theophylline and theobromine on cell respiration and calcium transport in isolated rat liver mitochondria

The influence of theophylline and theobromine on cellular respiration and on membrane transport of calcium has been studied in isolated rat liver mitochondria, using oxygen and Ca2+ selective electrodes. A linear decrease in respiratory coefficients, in the total amount and rate of "extra" oxygen consumption induced by ADP is observed with drug concentration. Theobromine does not show any appreciable effect on these respiratory parameters, but this result is similar to that observed with theophylline for the same concentration range. Calcium uptake coupled to respiration is inhibited by both drugs depending on their concentrations. Theobromine is more effective than theophylline. Calcium saturation of the mitochondria takes place in all cases after 36 +/- 2 s but only a 20% of the maximum calcium uptake observed in the absence of the drugs is determined in the presence of 15 mM theophylline or only 1.8 mM theobromine. Comparative studies show direct correlation between the pharmacological activities as stimulants of caffeine, theophylline and theobromine and their behaviour as inhibitors of calcium uptake coupled to respiration by mitochondria.     

Embryonic chick intestine in organ culture: hydrocortisone and vitamin D-mediated processes.

The effects of the glucocorticoid, hydrocortisone (HC), on vitamin D-mediated responses were examined in the organ-cultured, embryonic chick duodenum. In this system tissue responses to vitamin D-steroids in the culture medium include increased cAMP concentration, de novo synthesis of a specific calcium-binding protein (CaBP), enhanced uptake and transmucosal transport of calcium, and increased alkaline phosphatase activity. HC at levels ≥ 27.5 nm increased vitamin D-induced CaBP concentration: This apparently represents the first report of an interaction of HC with another steroid, vitamin D, in the regulation of the concentration of a specific protein. High levels of HC (≥27.5 μm) in the culture medium reduced duodenal calcium uptake and transmucosal transport regardless of the presence of vitamin D. However, at lower concentrations of HC (≤2.75 μm), only vitamin D-independent calcium uptake (basal calcium uptake) was reduced. Actinomycin D had no effect on HC reduction of basal calcium uptake suggesting that new protein synthesis is not involved in this action. In other experiments either HC or vitamin D stimulated phosphate and glucose uptake, and this uptake was potentiated by the presence of both steroids. HC also stimulated alanine uptake. Either HC or vitamin D increased both alkaline phosphatase activity (APA) and cAMP concentration, but together their activities were only additive. The data accumulated thus far indicate that HC directly influences calcium (and other nutrient) uptake by the duodenum and increases the concentration of the vitamin D-induced CaBP. Other vitamin D-mediated responses (APA and cAMP) were influenced by HC but there was no readily discernible relationship to nutrient uptake.     

The effects of fasting and refeeding on serum parathormone and calcitonin concentrations in young and old male rats.

Although fasting and refeeding reveal the existence of age-related changes in carbohydrate and lipid metabolism, the effects of aging on mineral metabolism in refed animals are unknown. We therefore investigated hormonal regulation of calcium metabolism in young (4 months) and old (26 months) male rats fasted for 48 hours and then refed for 4 or 24 hours. Serum concentrations of total and ionized calcium and parathormone were similar in control young and old rats. Serum calcitonin level was higher, and the concentrations of albumin and inorganic phosphate and alkaline phosphatase activity were lower in fed old rats. In young fasted rats, the serum ionized and total calcium was decreased, and phosphate concentration was increased. In old rats, fasting resulted in the increase of serum parathormone level. Fasting reduced serum alkaline phosphatase activity to a similar extent in both age groups. In young rats, refeeding for 24h normalized serum calcium and phosphate levels and alkaline phosphatase activity, and decreased serum concentrations of PTH and calcitonin. In old refed rats, serum calcitonin concentration was raised by 77% compared to fed or fasted animals, whereas parathormone levels were normalized. Our results indicate that old fasted or refed rats maintain normal serum calcium concentration in a different way than young animals, possibly through the increase in serum levels of parathormone and/or calcitonin. Thus, dietary manipulations such as fasting and refeeding constitute an interesting model for the investigation of the effects of aging on the hormonal regulation of serum calcium level.     

The effect of acetylcholine on inositol lipid metabolism and intracellular calcium concentrations in bovine anterior pituitary cells

Acetylcholine (ACh) increased the intracellular calcium concentration in bovine anterior pituitary cells. In the presence of the calcium channel antagonists verapamil (20 microM) or nitrendepine (1 microM) the increase in calcium was partially inhibited but showed both transient and sustained components. In the presence of EGTA (2.5 mM) only the transient component was observed. ACh also decreased inositol radioactivity in phosphatidylinositides and increased it in inositol phosphates. It is concluded that the increase in calcium caused by acetylcholine requires both the entry of external calcium and mobilisation of internal calcium. Replacement of external sodium by N-methyl-D-glucamine inhibited the rises in calcium and inositol phosphate labelling in response to ACh. Tetrodotoxin (3 microM) or ouabain (50 microM) did not affect either response to ACh. Verapamil did not affect the calcium rise induced by ACh in the absence of external sodium. The phorbol ester PMA (10 nM) caused a transient rise in calcium and inhibited the calcium rise caused by acetylcholine: it did not modify the effect of acetylcholine on inositol phosphates. The dependence of the stimulation of external calcium entry and inositol phosphate production on external sodium ions and protein kinase C is discussed.     

Ionic control of renal gluconeogenesis IV. Effect of extracellular phosphate concentration

Isolated rat renal tubules from glucose from pyruvate, malate, glycerol and α-ketoglutarate. The rate of glucose formation from all but glycerol is enhanced by an increase in Ca²⁺ concentration. Because changes in inorganic phosphate concentrations influence the uptake and retention of calcium by isolated cells, the effect of changes in phosphate concentration upon renal gluconeogenesis was examined. It was found that changing phosphate concentration altered the metabolism of isolated rat renal tubules in three ways which dependend upon the Ca²⁺ concentration. In the absence of Ca²⁺, increasing phosphate concentration from 0.07 to 1.2 mM led to a stimulation of the decarboxylation of [U-¹⁴C]malate, [1-14C]pyruvate, [2-¹⁴C]-pyruvate, α-keto[5-¹⁴C]glutarate and [1,3-¹⁴C₂]glycerol, and to an increase in ATP concentration but had no effect upon the rate of glucose formation from malate, pyruvate, α-ketoglutarate but a slight stimulation of glucose production from glycerol. A further increase in phosphate above 1.2 mM had no effect on any of these parameters. In the presence of either low (0.2 mM) or high (2.0 mM) Ca²⁺, changing phosphate concentration had no effect upon the decarboxylation of any of these substrates except glycerol whose decarboxylation was stimulated by increasing medium phosphate concentration. In the presence of calcium, increasing phosphate concentration led to an inhibition of glucose formation from malate, pyruvate and α-ketoglutarate but not from glycerol. Also in the presence of calcium both parathyroid hormone and cyclic AMP stimulated glucose formation, and under these conditions increasing phosphate concentration led to an inhibition of glucose formation. In tubules treated with parathyroid hormone an increase in phosphate concentration from 0.07 to 6.0 mM led to a significant increase in cyclic AMP concentration even though the rate of glucose formation decreased.Analysis of metabolite concentrations and rates of substrates decarboxylations, under a variety of conditions, revealed that P_i altered renal gluconeogenesis at a site different from those controlled by changes in Ca²⁺ concentration. The P_i-control site was tentatively identified as the glyceraldehyde phosphate dehydrogenase-glycerate kinase reaction sequence. However, the effect of changing P_i concentration upon parathyroid hormone-induced alterations in cyclic AMP concentration could not be explained by this action of P_i, and was probably due to an effect of P_i upon cellular calcium distribution. Thus, changes in P_i concentration appear to have two cellular effects, only one of which is related to a change in cellular calcium metabolism.     

Phosphate Uptake in an Obligately Marine Fungus II. Role of Culture Conditions, Energy Sources, and Inhibitors

Phosphate uptake in the obligately marine fungus, Thraustochytrium roseum, is maximal at pH 7.5 to 7.8, is dependent on temperature, and varies with phosphate concentration. Pyruvate and succinate stimulate phosphate uptake, although they do not increase respiration. The uncoupling agents, 2,4-dinitrophenol and dicoumerol, inhibit phosphate uptake but stimulate oxygen consumption only in the presence of NaCl. Oligomycin inhibits both processes. Among the inhibitors of protein synthesis, chloramphenicol reduces phosphate uptake without affecting respiration. Puromycin is unique in that it greatly enhances phosphate uptake and abolished the lag period associated with this phenomenon. It does not affect respiration.     

pH gradient as an additional driving force in the renal re-absorption of phosphate.

The effects of the Na+ gradient and pH on phosphate uptake were studied in brush-border membrane vesicles isolated from rat kidney cortex. The initial rates of Na(+)-dependent phosphate uptake were measured at pH 6.5, 7.5 and 8.5 in the presence of sodium gluconate. At a constant total phosphate concentration, the transport values at pH 7.5 and 8.5 were similar, but at pH 6.5 the influx was 31% of that at pH 7.5. However, when the concentration of bivalent phosphate was kept constant at all three pH values, the effect of pH was less pronounced; at pH 6.5, phosphate influx was 73% of that measured at pH 7.5. The Na(+)-dependent phosphate uptake was also influenced by a transmembrane pH difference; an outwardly directed H+ gradient stimulated the uptake by 48%, whereas an inwardly directed H+ gradient inhibited the uptake by 15%. Phosphate on the trans (intravesicular) side stimulated the Na(+)-gradient-dependent phosphate transport by 59%, 93% and 49%, and the Na(+)-gradient-independent phosphate transport by 240%, 280% and 244%, at pH 6.5, 7.5 and 8.5 respectively. However, in both cases, at pH 6.5 the maximal stimulation was seen only when the concentration of bivalent trans phosphate was the same as at pH 7.5. In the absence of a Na+ gradient, but in the presence of Na+, an outwardly directed H+ gradient provided the driving force for the transient hyperaccumulation of phosphate. The rate of uptake was dependent on the magnitude of the H+ gradient. These results indicate that: (1) the bivalent form of phosphate is the form of phosphate recognized by the carrier on both sides of the membrane; (2) protons are both activators and allosteric modulators of the phosphate carrier; (3) the combined action of both the Na+ (out/in) and H+ (in/out) gradients on the phosphate carrier contribute to regulate efficiently the re-absorption of phosphate.     

Regulation of calcium fluxes in rat pancreatic islets: Quinine mimics the dual effect of glucose on calcium movements

The effects of quinine and 9-aminoacridine, two blockers of potassium conductance in islet cells, on ⁴⁵Ca efflux and insulin release from perifused islets were investigated in order to elucidate the mechanisms by which glucose initially reduces ⁴⁵Ca efflux and later stimulates calcium inflow in islet cells. In the absence of glucose, 100 μM quinine stimulated ⁴⁵Ca net uptake, ⁴⁵Ca outflow rate and insulin release. Quinine also dramatically enhanced the cationic and the secretory response to intermediate concentrations of glucose, but had little effect on ⁴⁵Ca net uptake, ⁴⁵Ca fractional outflow rate and insulin release at a high glucose concentration (16.7 mM). The ability of quinine to stimulate ⁴⁵Ca efflux depended on the presence of extracellular calcium, suggesting that it reflects a stimulation of calcium entry in the islet cells. In the absence of extracellular calcium, quinine provoked a sustained decrease in ⁴⁵Ca efflux. Such an inhibitory effect was not additive to that of glucose, and was reduced at low extracellular Na⁺ concentration. At a low concentration (5 μM), quinine, although reducing ⁸⁶Rb efflux from the islets to the same extent as a non-insulinotropic glucose concentration (4.4 mM), failed to inhibit ⁴⁵Ca efflux. In the presence of extracellular calcium, 9-aminoacridine produced an important but transient increase in ⁴⁵Ca outflow rate and insulin release from islets perifused in the absence of glucose. In the absence of extracellular calcium, 9-aminoacridine, however, failed to reduced ⁴⁵Ca efflux from perifused islets. It is concluded that quinine, by reducing K⁺ conductance, reproduces the effect of glucose to activate voltage-sensitive calcium channels and to stimulate the entry of calcium into the B-cell. However, the glucose-induced inhibition of calcium outflow rate, which may also participate in the intracellular accumulation of calcium, does not appear to be mediated by changes in K⁺ conductance.     

Morphological and functional studies during aging at mitochondrial level. Action of drugs

1. Mitochondria show morphological changes on aging: the volume density decreases and the total surface area or volume increase. 2. Biochemical studies indicated a decrease in the rate of oxygen consumption and ATP levels for increasing age. Measurements of calcium transport across the mitochondrial membrane revealed a decrease in accumulated calcium and an alteration in the uptake kinetics of the ion in older animals. 3. Theophylline and calcitonin action were also studied. In both age groups (young and old) theophylline shows an inhibitory effect on all the parameters studied (both morphological and biochemical). 4. Calcitonin showed no effect on morphological and respiratory parameters, although it increased calcium uptake into the mitochondrion to a lesser extent in the 24 month old animals.     

Effects of ATP and Taurine on Calcium Uptake by Membrane Preparations of the Rat Retina

Abstract: The effects of ATP and taurine on the kinetics of calcium uptake in rat retinal membrane preparations were determined. ATP increased calcium uptake at low calcium ion concentrations. Addition of ATP plus taurine further increased calcium uptake. Cooperative relationships were observed for calcium uptake in the absence of ATP and taurine. In the presence of phosphate ions reciprocal plots demonstrated upward deflections from linear ty, while in the absence of phosphate ions downward deflections were noted. Addition of ATP plus taurine to the incubation system appeared to obliterate the cooperativity. Two uptake systems for calcium were observed.     

Studies on the energy-linked Ca2+ accumulation in pig heart mitochondria - role of Mg2'ons

Comparative intracellular distribution of Ca2+, Mg2+ and adenine nucleotides has been studied in pig heart by differential centrifugation or fractional extraction and has shown that Mg2+ and ATP are associated mainly with soluble fractions whereas Ca2+ and ADP are more tightly bound to subcellular structures. Ca2+ accumulation and Ca2+ stimulated respiration were studied in pig heart mitochondria under different energetic conditions in the absence or presence of phosphate. Ca2+ concentrations of about 1200 nmoles/mg protein inhibit Ca2+ accumulation, site I substrate oxidation and induce an efflux of mitochondrial Mg2+. These deleterious effects of Ca2+ on respiration occur even in the absence of phosphate or oxidizable substrate; they are completely prevented by ruthenium red only, and partially prevented by the addition of M2+ to the medium. The kinetics of Ca2+ uptake become of the sigmoidal type when Mg2+ is present. This cation strongly inhibits the rate of Ca2+ uptake in the presence of added phosphate and decreases the affinity of Ca2+ for its transport system. In the absence of phosphate, Mg2+ has no effect on Ca2+ uptake. The possible physiological implications of these findings are discussed     

The existence of an optimal range of cytosolic free calcium for insulin-stimulated glucose transport in rat adipocytes

We have examined the effects of extracellular and intracellular Ca2+ concentrations upon basal and insulin-stimulated 2-deoxyglucose uptake in isolated rat adipocytes. In the absence of extracellular Ca2+, both basal and insulin-stimulated glucose uptake were significantly reduced. Insulin-stimulated glucose transport was optimal at 1 and 2 mM Ca2+. Further increases in extracellular Ca2+ concentration (3 mM) significantly diminished insulin-stimulated glucose uptake. When intracellular Ca2+ concentrations were augmented by ionomycin (1 microM), insulin-stimulated glucose uptake was significantly reduced at extracellular Ca2+ concentrations of 2 and 3 mM. The levels of intracellular free Ca2+ concentrations were then measured with Ca2+ indicator fura-2. The correlation between the levels of intracellular free Ca2+ and the magnitude of insulin-stimulated glucose uptake revealed that the optimal effect of insulin is observed at Ca2+ levels between 140 and 370 nM. At both extremes outside of this window, both low and high levels of intracellular Ca2+ result in diminished cellular responsiveness to insulin. These data suggest that intracellular calcium concentrations may exert a dual role in the regulation of cellular sensitivity to insulin. First, there must exist a minimal concentration of intracellular calcium to promote insulin action. Second, increased levels of intracellular calcium may provide a critical signal for diminution of insulin action.     

Study of the mitochondrial phosphate carrier in the course of calcium phosphate accumulation: A requirement for Mg2+ and ADP of its sensitivity to thiol reagents

1. The accumulation of calcium phosphate driven by succinate oxidation is ADP-dependent. In its absence the accumulation stops after a short incubation time and the oxygen uptake is permanently stimulated. This uncoupled oxygen uptake is insensitive to the inhibitors of phosphate transport, like mersalyl and N-ethylmaleimide. When ADP plus Mg²⁺ are added to the medium, or when ADP is added in the initial presence of magnesium, the inhibitory action of the thiol reagents on oxygen uptake is re-established. ADP alone or Mg²⁺ alone are without any effect.2. Phosphate/phosphate exchange has been studied, in the absence of ADP, when calcium phosphate accumulation had stopped and oxygen uptake is uncoupled. Under these conditions the exchange process becomes insensitive to thiol reagents. Sensitivity is recovered solely in the presence of ADP plus Mg²⁺.3. When mitochondrial swelling is studied according to the method of Chappell, it also appears that the phosphate carrier loses it sensitivity to mersalyl in the absence of ADP, which confirms the data obtained with phosphate/phosphate exchange experiments. When ADP plus Mg²⁺ are added (or present), together with mersalyl, the action of the thiol inhibitor is recovered. ADP and magnesium are inactive separately. EGTA plus Mg²⁺ (but not EGTA plus ADP) may substitute for ADP plus Mg²⁺ in this process.4. A possible interaction between the magnesium binding site and the phosphate carrier is considered and discussed.