Effect of a catatoxic steroid pregnenolone-16alpha-carbonitrile, on rat liver microsomal subfractions

Pregnenolone-16α-carbonitrile (PCN), a potent catatoic steroid without known classical hormonal effects, was administered per os to female rats. Its effects were studied on mixed function oxygenases and on various phosphatases in liver microsomal subfractions: rough microsomes, smooth I, and smooth II microsomes. For comparison, phenobarbital (PB) and 3-methylcholanthrene (MC) were also administered. The inducers increased the protein content in total, rough and smooth I microsomes in the following order: PB, PCN, and MC, whereas the protein amount in smooth II microsomal fraction remained unchanged. The content of cytochrome P-450 was about doubled in all subfractions except the smooth II membranes, following treatment with any of the inducers.PCN differed in inducing specificity from PB in increasing benzo(α)pyrene hydroxylase and from MC in stimulating aminopyrine demethylase in total microsomes. PCN also differed from PB in enhancing the capacity not only for rough and smooth I microsomes, but also for smooth II microsomes to demethylase aminopyrine. No major difference in magnitude of effects among the inducers was noted between rough and smooth I microsomes.In contrast to the altered substrate specificities produced in the monooxygenase system by different inducers, a more uniform pattern of specificities was seen in microsomal phosphatases. PCN, MC and PB all increased the activities of nucleoside diphosphatase (IDPase), whereas G6Pase and ATPase activities were little affected. Cycloheximide was partially effective in depressing the increase of both the monooxygenase system (cytochrome P-450 and benzo(α)pyrene hydroxylase) and nucleoside diphosphatase activity. We conclude that (1) treatment with PCN results in different substrate specificity when compared to PB and MC; that (2) PCN is the most potent inducer of the three in stimulating drug hydroxylation in smooth II microsomes, that (3) various smooth microsomal membranes of liver cells are affected differently by inducers of drug metabolism, and finally (4) that drugs also alter some microsomal phosphatase activities but not all.     

Chemical and enzymatic characteristics of cytoplasmic membranes of poliovirus-infected HeLa cells

The density distribution of cytoplasmic membranes separated by centrifugation to equilibrium in discontinuous sucrose gradients is progressively altered after infection of HeLa cells with poliovirus. The most striking changes are a decrease in quantity and an increase in density of rough microsomes and a large increase in quantity of the smooth microsomal membranes with which viral RNA synthesis is associated.     

Age-dependent changes in rat liver microsomal membrane structure and functions under benzene treatment

The influence of benzene on 3 and 24 months old rat liver microsomes was studied. Some structural and functional changes occur under benzene treatment in the cytochrome P-450 system which are more pronounced in 3 months old rat microsomes than in the 24 months ones. Glucose-6-phosphatase and glucose dehydrogenase activities indicate that 3 months old rat microsomal vesicles are more stable against benzene injury than those, of 24 months old ones. In vitro benzene hydroxylation activation by NADPH addition decreased disruptive xenobiotic's effect on 3 but not on 24 months old rat liver microsomal vesicles. This fact suggests that the rate of benzene hydroxylation is important for its membrane damaging action effect. Thus, age-related differences in xenobiotic action on liver microsomes could be related to the decrease of benzene metabolism rate with senescence.     

Changes in ascorbate-induced lipid peroxidation of hepatic rough and smooth microsomes during postnatal development and ageing of rats

In female Wistar rats, sensitivity to ascorbate-induced lipid peroxidation in rough and smooth microsomes increases with age, reaching a maximum in 1-year-old rats and decreases during ageing. Time course of lipid peroxidation, and lipid peroxidation with optimum concentrations of ascorbic acid, Fe2+ and protein in rough microsomes show that 1-year-old rats are the most susceptible followed by 75-day-old, 15-day-old, 2-year-old and 1-day-old rats. However, smooth microsomes show a slightly different trend with maximum sensitivity in 1-year-old rats followed by 15-day-old, 75-day-old, 2-year-old and 1-day-old rats. Smooth microsomes are more susceptible to lipid peroxidation than the rough in all age groups except 75-day-old rats. Smooth microsomes are also more sensitive to inhibitors of lipid peroxidation. Microsomal content of phospholipid increases during postnatal development and decreases during ageing, whereas that of ascorbic acid and alpha-tocopherol do not show any particular trend.     

Age-dependent alterations in the physicochemical properties of rat liver microsomes

Aging results in a significant decline in liver drug metabolism which is largely attributable to changes in the microsomal mixed function oxidase system. For example, the mixed function oxidase system in the livers of senescent rats is characterized by: (1) a reduced cytochrome P-450 content; (2) a decline in the specific activity of NADPH-cytochrome c (P-450) reductase; and (3) a slower rate of ethylmorphine N-demethylation in comparison to young adult animals. Since several factors intrinsic to the microsomes may influence the efficacy of the mixed function oxidase system, e.g. the phospholipid and cholesterol contents, the saturation index of the fatty acids and the fluidity of the membranes, we conducted a physicochemical analysis of liver microsomes isolated from young adult (3-4 months), mature (12-16 months) and senescent (25-27 months) male Fischer rats. Although the microsomal cholesterol content did not change appreciably between maturity and senescence, there was a marked decline in the total phospholipid content. This resulted in a significant increase in the cholesterol/phospholipid ratio, 0.49 to 0.65 between 16 and 27 months of age. The age-related changes in the total phospholipid content were largely reflected in each of the major fractions, i.e. phosphatidylcholine, phosphatidylinositol and phosphatidylethanolamine + phosphatidylserine. Small increases in the relative percentages of highly unsaturated fatty acid species were offset by similar decreases in the more frequent and more saturated species as a function of increased age. As a result, the net change in the fatty acid saturation index was probably minimal. However, the increase in the cholesterol/phospholipid ratio most likely contributes to the significant decline in the order parameter of microsomes isolated from old rats which, in turn, may impair the functional capacity of the hepatic mixed function oxidase system.     

Transitions in membrane composition during postnatal development of rabbit fast muscle

Summary Early postnatal changes (4–5 days to 15 days after birth) in the biochemical composition of microsomes were investigated in rabbit skeletal muscles destined to become fast-twitch muscles. During this period, a steady decrease in the microsomal content of cholesterol and of ouabain-sensitive Na⁺/K⁺-ATPase activity, as well as a decrease in protein electrophoretic components in the 80 000–70 000 molecular weight range, were observed. These changes are probably due to a diminishing yield of microsomal membranes derived from T-tubules, as the age of the animals increases, and are indicated from a knowledge of the mixed composition of muscle microsomes and previous biochemical data on isolated T-tubules. The content of cytochromeb ₅, which was found to be high in muscle microsomes of new born animals, decreased strikingly as the amount of membrane-bound Ca²⁺-ATPase protein increased, with a crossing-over point at about 7–10 days after birth. These changes, possibly corresponding to a transition from precursor sarcoplasmic reticulum (SR) to mature SR, were found to be temporally correlated with changes in [³H]-tocopherol binding ability of the microsomes and in the mitochondrial content of glycerol phosphate dehydrogenase. At the same critical periods, coincident with the onset of motile activity, the immunological cross-reactivity of the Ca²⁺-ATPase protein of microsomal vesicles, with antibody specific for the Ca²⁺-ATPase of adult fast SR, was found to increase markedly, as tested by competitive enzyme-linked immunosorbent assay (ELISA). The immunological data are consistent with data in the literature demonstrating an increase in the concentration of Ca²⁺-ATPase molecules in the SR membranes during ontogenic development. Both these data and catalytic data, however, suggest that the Ca²⁺-ATPase protein is present in the same form in the SR of immature and of adult fast muscle and, in an antigenically different form, in slow muscle SR.     

Effects of starvation on liver microsomal P450 activity in juvenile Pleuronectes americanus.

Recent work has produced evidence to support the existence of a cytochrome P450 CYP2E1-like isoform in the marine fish, Pleuronectes americanus (winter flounder) (Wall K, Crivello JF. Toxicol Appl Pharmacol 1998;151:98-104). Starvation has been previously demonstrated to induce CYP2E1 activity (assayed as chlorzozazone-6-hydroxylase activity) in mammals and this study was undertaken to determine the effects of starvation on liver chlorzozaxone-6-hydroxylase and ethoxy-resorufin-O-deethylase activity (a CYP1A1 activity) in juvenile winter flounder liver microsomes. A 2-week starvation period resulted in a statistically significant increase in liver microsomal protein, and a decrease in liver lipid and liver glycogen. Ethoxy-resorufin-O-deethylase activity (pmol/min/mg microsomal protein) was reduced with starvation, chlorzoxazone 6-hydroxylase activity (pmol/min per mg microsomal protein) initially decreased but then increased over controls. When these activities were expressed per gm/liver (to account for the starvation-induced changes in liver microsomal protein), chlorzoxazone 6-hydroxylase activity doubled over control during starvation but ethoxy-resorufin-O-deethylase was not significantly changed. The effects of starvation on liver microsomal chlorzoxazone 6-hydroxylase and ethoxy-resorufin-O-deethylase activities are discussed in the context of the impact of physiological states on the ability of fish to detoxify marine xenobiotics.     

Liver microsomal drug-metabolizing enzyme activity: enhancement by blockade of degradative processes in promethazine-treated rats.

Daily injection of promethazine over 4 days significantly increased the liver cytochrome P-450 content and ethyl morphine N-demethylase activity. These increases were evident after the first dose and were prevented by puromycin or actinomycin D administration. Repeated administration of promethazine does not increase the liver''s ability to incorporate [14]C DL-leucine in microsomes but slows down the decay of radioactivity in microsomes previously labelled with ([14C]-guanidino) arginine. Repeated treatment with promethazine leads to a marked proliferation of the rough endoplasmic reticulum (RER) and a slight increase in the smooth endoplasmic reticulum (SER). Our findings suggest that the enhancement of P-450 and EM-ase activity result from the decelerating effect of promethazine on protein degradation.     

Metabolic activation of aflatoxin B1 by liver tissue from male fischer F344 rats of various ages

The effect of aging on the ability of the liver to activate chemical procarcinogens was studied using 12-, 18-, and 27-month-old male Fischer F344 rats. The cytochrome P-450 content of the S9 and microsomal fractions of the liver decreased approximately 30% between 12 and 18 months of age. The structural conformation of cytochrome P-450 in microsomes from 12-, 18-, and 27-month-old rats was studied using electron-spin resonance spectroscopy. An age-related decrease in the amount of cytochrome P-450 ferric iron in the liver microsomes was observed. The conversion of the chemical procarcinogen aflatoxin B1 to mutagenic compounds by the S9 and microsomal fractions of liver was measured using the Salmonella typhimurium bioassay. A 40-50% decrease in the metabolic activation of aflatoxin B1 was observed between 12 and 18 months of age. However, the activation of aflatoxin B1 did not change after 18 months of age. The age-related decrease in the activation of aflatoxin B1 by liver appears to be due to a decrease in the metabolic activity of the mixed-function oxidase system.     

Aldehydic products of lipid peroxidation inactivate cytochrome P-450.

The effects of aldehydic products of lipid peroxidation, malondialdehyde (MDA) and 4-hydroxynonenal (HNE), on the structure of rat liver microsomal membrane and cytochrome P-450 was studied. MDA (15-30 microM) similarly to p-chlormercuribenzoate decreased the cytochrome P-450 content by 50 % and lowered microviscosity of lipid surrounding of the spin label OTMB bound to SH-groups of membrane proteins. OTMB was effectively reduced by K3Fe(CN)6 in microsomes preincubated with MDA (20 (M), but not in native microsomes. HNE (10 microM) decreased the cytochrome P-450 content by 90 %. Reduced glutathione and cysteine (5 mM) prevented the decrease of cytochrome P-450 under influence of both MDA or HNE, whereas cytochrome P-420 formation remains unchanged. MDA and HNE decreased activities of NADPH oxidase and NADPH cytochrome c reductase. HNE increased microviscosity of the OTMB lipid environment. The further increase of HNE concentration did not affect this parameter. Both MDA and HNE increased the absorbance at 420 nm, which indicated inactivation of cytochrome P-450 by changes in hydrophobicity of lipid surrounding. We suggest that HNE and aliphatic aldehydes at low concentrations can enter into hydrophobic environment of cytochrome P-450 binding to its SH-groups, which led to inactivation of cytochrome P-450. At the same time, the modification of membrane surface layer and subsequent decrease of hydrophobicity of cytochrome P-450 environment preceded the binding of MDA to SH-groups of cytochrome P-450 to develop its inactivating effect.     

Role of dietary corn oil in the function of hepatic drug and carcinogen metabolizing enzymes of starved-refed rats: response to the mixed function oxidase inducer, 3-methylcholanthrene

Hepatic microsomes from rats starved 48 hours and refed diets containing zero, 3 or 20% corn oil metabolized benzo(a)pyrene, aniline and N-nitrosodimethylamine in proportion to the quantity of corn oil in the diet. No diet-related changes in apparent Km for these reactions were evident. The content of microsomal cytochrome P-450 was also clearly dependent upon the content of corn oil in the refed diets. When metabolism of these three substrates is expressed as product formed per unit of cytochrome P-450, the activities are least in microsomes from rats fed the 20% corn oil diet, suggesting that P-450 species responsible for metabolizing substrates other than these are enhanced preferentially. Cytosolic glutathione S-transferase activities are also increased with increasing corn oil in the diet. The administration of 3-MC increased cytochrome P-448 content of microsomes from all rats, regardless of diet, however highest content was present in microsomes from rats fed the 20% corn oil diet. Induction of benzo(a)pyrene hydroxylase was not influenced by dietary corn oil and, as anticipated, 3-MC caused significant repression of DMN N-demethylase in microsomes from rats fed the 20% corn oil diet. In like manner, 3-MC induced glutathione S-transferase only in cytosol from rats fed the fat-free diet.     

Hepatic microsomal cytochrome P450 system during experimental hookworm infection

Experimental infection of golden hamsters with the hookworm, Ancylostoma ceylanicum, caused a profound decline in the hepatic microsomal cytochrome P450 content. Concomitant decrease was also noticed in aminopyrine N-demethylase and benzo[a]pyrene hydroxylase activities. However, aniline hydroxylase activity was only marginally elevated during the infection. Microsomal markers, viz., cytochrome b5, NADH-cytochrome-c reductase, and glucose-6-phosphatase, were not significantly altered. Hepatic tissue exhibited an accumulation of lipids, especially phospholipids, triglycerides, and cholesterol, resulting in fatty necrosis around the central vein region. Isolated hepatic microsomes showed a decrease in phosphatidylcholine content. Impairment in hepatic mixed function oxidase (MFO) activities was further confirmed by prolongation in hexobarbital sleeping time and zoxazolamine-induced paralysis. The hepatic MFO system of A. ceylanicum-infected hamsters responded qualitatively and quantitatively in a manner similar to that of control hamsters, upon stimulation with selective chemical inducers like phenobarbitone and 3-methylcholanthrene. Kinetic and in vitro substrate binding studies revealed that for aminopyrine the substrate affinity and the maximum enzyme activity (Vmax) were decreased, while for aniline the binding affinity was decreased and the binding capacity was enhanced. Results indicate specific/selective impairment of the hepatic microsomal cytochrome P450 system during hookworm infection and may have many practical implications in toxicology and pharmacology.     

Carbon tetrachloride-induced liver injury in the rabbit.

CCl4 administration to rabbits leads to early destruction of liver microsomal cytochrome P-450, to depression of glucose 6 phosphatase, to ultrastructurally revealable alterations and to an intense necrosis and fat accumulation in liver. Despite the known resistance of rabbit liver microsomes to lipid peroxidation, CCl4 administration to rabbits promoted lipid peroxidation of their liver microsomal lipids as revealable by the diene hyperconjugation technique, at periods of time from 1 to 12 h. Nevertheless, the intensity of this process is not equivalent to that occurring in rat liver microsomes, since the arachidonic acid content of rabbit liver microsomal lipids does not decrease at either 6 or 24 h after CCl4 administration. Rabbit liver is able to activate CCl4 to reactive metabolites that bind covalently to lipids. Relevance of covalent binding of CCl4 reactive metabolites and CCl4-promoted lipid peroxidation to CCl4-induced rabbit liver injury is analysed.     

Effect of prostacyclin on the mixed function microsomal oxigenase system in the rat liver

The microsomal fraction of the liver was studied for protein and cytochrome P450 contents as well as for aminopyrine-N-demethylase and aniline-hydroxylase activity and for its BIC spectrum under the effect of PG-I2 treatment. A significant increase was found in the cytochrome P450 content after short term treatment, while continuation of PG-I2 administration caused a significant and long lasting decrease of cytochrome P450. After prolonged application of PG-I2 the aniline-hydroxylase content decreased significantly, while the aminopyrine-N-demethylase enzyme showed no change. The BIC spectrum after 80 days PG-I2 treatment significantly decreased in the 431-432 nm region, corresponding to the decrease of cytochrome P450. Long term PG-I2 application caused no detectable ultrastructural changes in the liver.     

Decreased microsomal membrane fluidity in the development of cholesterol-induced atherosclerosis in the rabbit

The hypothesis was examined that arterial microsomal membrane fluidity is decreased in atherosclerosis. To investigate this hypothesis, the fluorescence anisotropy (r) of 1,6-diphenylhexa-1,3,5-triene was measured in aortic microsomes isolated from normal and atherosclerotic rabbits. A decrease in membrane fluidity, as indicated by a significant increase in r, was observed in microsomes from atherosclerotic rabbits. Notably, the increase in r occurred prior to macroscopic lesion development. The data support the hypothesis that membrane fluidity is decreased in atherosclerosis and indicate that this decrease occurs early in the atherogenic process. The hypothesis that decreased microsomal membrane fluidity contributes to the increased activity of acyl-CoA:cholesterol acyltransferase (ACAT) in atherosclerosis was also investigated. The hypothesis was rejected on the basis that enrichment of microsomes from normal rabbits with exogenous cholesterol to achieve r values equal to that of microsomes from atherosclerotic rabbits did not result in comparable ACAT activity.     

Lipid composition, physical state, and lipid peroxidation of tumor membranes

Studies were carried out on microsomes isolated from the highly differentiated (slow-growing) Morris hepatoma 9618A, on microsomes and plasma membranes from the poorly differentiated (fast-growing) Morris hepatoma 3924A, and rat liver used as control. The lipid composition (phospholipid and cholesterol content, degree of fatty acid unsaturation) and peroxidation of such membranes has been correlated with the order and fluidity of the membrane bilayer. The results indicate that substrate availability is the rate-limiting step in microsomal and plasma membrane lipid peroxidation of hepatoma 3924A. From diphenylhexatriene fluorescence depolarization measurements it appears that the changes in lipid composition cause an increase in the order of the lipid bilayer on going from the control to hepatoma 9618A and 3924A microsomes, while fluidity is virtually unchanged. Conversely, for similar chemical changes, in plasma membranes from hepatoma 3924A the order is nearly the same and there is a decrease in fluidity. The changes in the above parameters of tumor membranes might be partly related to the loss of protective enzymes against oxygen radicals. This is supported by the observation that inhibition of liver superoxide dismutase and glutathione reductase, by treatment of rats with diethyldithiocarbamate and chloroethyl nitrosourea, respectively, renders the microsomal membranes more resistant to lipid peroxidation in vitro.     

Hepatic microsomal alterations during chronic trypanosomiasis in the field vole, Microtus montanus

The field vole, Microtus montanus, was used as a model system to evaluate the chronic effects of infection by Trypanosoma brucei gambiense on hepatic mixed-function oxidase activity. At day 28 post inoculation there was a 97% increase in liver wet weight per g body weight. A portion of the increase (21%) was accounted for by tissue edema which occurred after day 14 of infection. Total hepatic cytochrome P-450 content and related total tissue mixed-function oxidase activities were decreased to about 60% of control levels at day 28 post inoculation. The decrease in total tissue mixed-function oxidase activity was partly due to a small decrease in microsomal protein per cell, and partly to a large decrease in cytochrome P-450 concentration in the endoplasmic reticulum. Although the decrease in total liver monooxygenase activity in several substrates roughly paralleled the loss in cytochrome P-450 content, several other microsomal enzyme markers not related to cytochrome P-450 monooxygenation were elevated in proportion to total liver microsomal protein content. The results suggest that in M. montanus during trypanosomiasis, there is proliferation of hepatic cells with normal content of endoplasmic reticulum. Furthermore, there appears to be selective toxicity for hepatic cytochrome P-450 and related monooxygenase activities. This may compromise the animals' ability to metabolize and dispose of other drugs to which the animal may be exposed in the course of infection.     

D-galactosamine hepatotoxicity. 3. Normoactive smooth endoplasmic reticulum and modification by phenobarbital

The administration of a single dose of d-galactosamine-HCL (375 mg/kg ip) to female rats produces severe hepatocellular necrosis. Ultrastructural studies disclose a variety of nuclear and cytoplasmic changes including focal and diffuse hyperplasia of the smooth endoplasmic reticulum. The functional capacity of the hyperplastic smooth endoplasmic reticulum was investigated by several criteria. Pentobarbital sleeping time determined 6, 16, and 24 hr after d-galactosamine injection was similar to that observed in saline-treated control animals. Hepatic microsomal protein concentration, cytochrome P-450 content, and NADPH cytochrome c-reductase activity measured at 20 hr were similar in d-galactosamine-treated and control animals. Thus, using these modalities, the hyperplastic smooth endoplasmic reticulum induced by d-galactosamine was not associated with an altered microsomal drug metabolizing activity.When phenobarbital was administered in a dose of 80 mg/kg for 4 days prior to d-galactosamine, the histological evidence of hepatocellular injury and lipid accumulation was less severe than in animals receiving d-galactosamine alone. The mechanism of the modification of hepatotoxicity and fatty liver by phenobarbital remains to be determined.     

The effects of age on the pharmacokinetics and biotransformation of theophylline in vivo and in vitro in the Mongolian gerbil (Meriones unguiculatus).

The effect of post maturational aging on the in vivo disposition of theophylline was examined in the Mongolian gerbils (Meriones unguiculatus) aged 30-39 (old), 12-18 (middle-aged) and 3 (young) months following a 20 mg/kg i.p. dose. Biotransformation of theophylline was also examined in liver microsomes from non-induced and 3-methylcholanthrene induced gerbils. Analysis of theophylline plasma kinetics showed decreased clearance, increased half-life and increased volume of distribution in old vs. young animals. Clearance to the 1,3-dimethyluric acid metabolite was similar for all age groups, while clearance to the 1-methyluric acid metabolite was significantly lower in the middle-aged group compared to that of young and old gerbils. Urinary recovery of 1-methylurate was increased in old vs. young and middle-aged animals while recovery of theophylline was decreased. 3-Methylcholanthrene induction resulted in decreased recovery of theophylline and increased recovery of 1,3-dimethylurate and 1-methylurate in young and middle-aged gerbils compared to non-induced controls. Decreased microsomal protein content was observed in old vs. young and middle-aged gerbils and an age-related decrease in cytochrome P-450 content (nmol P-450/g liver) was also observed. The rate of dimethylurate formation was decreased 37% in microsomes from old vs. young and middle-aged gerbils. 3-Methylcholanthrene administration resulted in a 2- and 1.5-fold increase in the rate of 1,3-dimethylurate formation in young and middle-aged gerbils, respectively. The results of these experiments indicate that the Mongolian gerbil may be useful for the study of the biochemical mechanisms underlying age-related changes in the biotransformation and kinetics of theophylline.     

Effect of acute and repeated chlordimeform treatment on rat hepatic microsomal drug metabolizing enzymes

The effect of chlordimeform treatment on the hepatic microsomal drug metabolizing enzymes was examined in male and female rats following either acute or repeated treatment. After acute administration of chlordimeform (100 mg/kg, ip one hr prior to sacrifice) differential effects were observed in various parameters of the hepatic microsomal mixed function oxidase system with significant decreases in ethylmorphine metabolism, cytochrome P-450 content, NADPH cytochrome c reductase, and in the spectral binding of hexobarbital and aniline while no changes were found in the metabolism of aniline or p-nitroanisole. Durations of zoxazolamine-induced paralysis and pentobarbital-induced hypnosis were increased significantly after acute chlordimeform administration. Following repeated administration of chlordimeform (75 mg/kg ip for four days) to adult male rats, a decrease was observed in zoxazolamine-induced paralysis time while pentobarbital-induced hypnosis was not altered. Metabolism studies using isolated hepatic microsomal fractions showed a decrease rate of biotransformation of ethylmorphine and aniline while the activity of p-nitroanisole O-demethylase was not changed. No differences were found in cytochrome P-450 levels whereas microsomal spectral binding of hexobarbital was reduced while that of aniline was not affected. Following acute or repeated administration of chlordimeform to adult female rats, decreases in the hepatic microsomal metabolism of aniline, but not ethylmorphine or p-nitroanisole, were observed. Addition of chlordimeform to microsomal suspensions yielded a Type I spectral binding curve.