Analysis of the inhibition of N-nitroso-dimethylamine activation in the liver by N-nitro-dimethylamine using a new non-linear statistical method

Eva Frei3, Frank Gilberg1,2, Manuela Schröder, Andrea Breuer, Lutz Edler1 and Manfred Wiessler

Division of Molecular Toxicology, C0300 and
1 Department of Biostatistics, German Cancer Research Centre, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany


    Abstract
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
N-nitro-dimethylamine (NTDMA) is carcinogenic to rats: it induces nasal cavity tumours. It can be demethylated to N-nitromethylamine and formaldehyde and reduced to N-nitroso-dimethylamine (NDMA): a potent liver carcinogen and also of the nasal cavity if activation in the liver is blocked. To explain the mechanism of NTDMA carcinogenicity we compared its demethylation with that of NDMA in liver microsomes from female and male rats, untreated, fasted or treated with ethanol to induce cytochrome P450 2E1 (CYP2E1). Kinetic parameters were analysed by non-linear statistical methods, which yielded unbiased parameter estimates for the calculated Km and Vmax values. Km for both compounds was very similar in females (24–47 µM) whereas Vmax for NTDMA was consistently higher than for NDMA as substrate: 1.07–4.70 nmol formaldehyde/mg microsomal protein x min and 0.52–2.76 nmol, respectively. In liver microsomes from induced male rats NTDMA was found to be a much more effective inhibitor of NDMA activation (KEI 39.6–73.6 µM) than NDMA of NTDMA demethylation (KEI 224–286 µM). Nasal microsomes can demethylate both NDMA and NTDMA but the kinetics are vastly different. NTDMA is demethylated at a linear rate and ~10-fold more effectively than NDMA. The mechanism of carcinogenicity of ingested NTDMA, we propose, is a partial reduction to NDMA in the liver and inhibition of NDMA activation in the liver by residual NTDMA, which enables NDMA to reach the nasal mucosa where it is activated to DNA-alkylating species and the observed tumours are formed.

Abbreviations: CYP2E1, cytochrome P450 2E1; NDMA, N-nitroso-dimethylamine; NTDMA, N-nitro-dimethylamine; OLS, ordinary least squares; TBS, transform both sides; WLS, weighted least squares.


    Introduction
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
N-nitroso-dimethylamine (NDMA) is a potent hepatocarcinogen in all animal species tested. High oral doses lead to tumours of the kidney and nasal cavity, which is also the target after inhalation of NDMA (1). N-nitro-dimethylamine (NTDMA) is also carcinogenic, albeit at much higher concentrations than NDMA, and leads to tumours of the nasal cavity if administered by gavage (2). If the compound is given continuously in drinking water, liver and kidneys are additional targets (reviewed in ref. 2). Both compounds are hydroxylated, NDMA to formaldehyde and the ultimate carcinogen methyldiazonium ion, and NTDMA is oxidized to HCHO and N-nitromethylamine (3) (Figure 1Go). The latter compound, on further activation, probably reduction (4), leads to tumours of the spinal cord (2). NDMA is metabolized by CYP2E1, an enzyme that is inducible by ethanol, which stabilizes the protein, and by fasting, which increases CYP2E1 mRNA levels (5). Because NTDMA is structurally so similar to NDMA our working hypothesis is that both compounds are hydroxylated by the same enzyme. Since the product of NTDMA hydroxylation, N-nitromethylamine, is not an ultimate carcinogen and the tumour site is different for the two compounds, we postulated a reduction of NTDMA to NDMA as the first step in NTDMA activation to the ultimate carcinogen.



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Fig. 1. Activation mechanism for NDMA by CYP2E1 to N-nitroso hydroxymethyl methylamine, which decomposes to methyldiazonium ion, the ultimate carcinogen, and formaldehyde. NTDMA can be oxidized, probably also by CYP2E1, to N-nitro-hydroxymethyl methylamine, a stable compound that is in equilibrium with N-nitromethylamine, itself a carcinogen after metabolic activation, and formaldehyde. NTDMA can also be reduced to NDMA.

 
We found NDMA in blood (6) and urine of rats treated with NTDMA and analysed NADH- and/or NADPH-dependent cytosolic reductase in liver (4). The NDMA formed by this pathway in the liver would have to be further activated to cause liver tumours, which we did not observe after NTDMA gavage; only nasal cavity tumours occurred. A near complete shift in tumour incidence from liver to nasal cavity was observed if hepatic activation of NDMA was inhibited by disulfiram (7). We therefore postulate that NTDMA still present in the liver will inhibit NDMA activation, so that reductively formed NDMA can leave the liver and reach other organs, namely the nose.

To prove this hypothesis we investigated the metabolism in liver microsomes of radioactively labelled NDMA to [14C]HCHO in the presence of NTDMA, and vice versa, of [14C]NTDMA in the presence of NDMA to elucidate the kinetics of inhibition. We compared microsomes obtained from starved rats with those from ethanol-treated rats. We also compared NDMA activation and NTDMA demethylation in nasal mucosa microsomes from untreated rats.

To analyse the data obtained from these reactions in a statistically valid form, mathematical models were developed and used to estimate the Michaelis–Menten constants. We not only present the results of our analyses but also the procedure used to fit the data and the criteria for the choice of the models used for the analyses.


    Materials and methods
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Animals and treatments
Male and female Sprague–Dawley rats were purchased from Charles-River WIGA (Sulzfeld, Germany) and kept on a 12 h light:dark cycle. They were fed Altromin standard diet (Lage, Germany), water ad libitum and acclimatized for 1 week before pre-treatment. To induce CYP2E1, male rats weighing 80–100 g or female rats were either fasted for 24 h or treated with 15% (v/v) ethanol in tap water for 3 days. Each rat drank 20–35 ml per day. In the experiments that used untreated males, these weighed 170 g. All the females weighed 130–160 g. The rats were killed by asphyxia in CO2, livers were perfused in situ with ice-cold 0.15 M KCl and microsomes isolated as described elsewhere (8). Nasal microsomes were isolated in the same way from the whole nasal mucosa, mainly the olfactory and respiratory epithelia isolated from the noses of 50 untreated rats killed for other purposes.

Chemicals
[14C]HCHO (sp. act. 0.37 Gbq/mmol) and [14C]NDMA (sp. act. 1.8 Gbq/mmol) were purchased from NEN (Boston, MA). [14C]NDMA was diluted with inactive NDMA to a specific activity of 0.11 GBq/mmol. [14C]NTDMA was synthesized according to Braun et al. (9), with a specific activity of 1.9 GBq/mmol and diluted with inactive NTDMA to 0.17 Gbq/mmol for substrate concentrations from 0.17 to 1.7 mM or diluted to 0.4 Gbq/mmol for substrate concentrations from 0.004 to 0.06 mM. The purity and specific activity of the stock solutions was checked by ion pair HPLC on an RP18 5 µm column, 250x4.6 mm; solvent: 3 mM tetrabutylammonium phosphate, pH 7.0, at a flow of 1 ml/min; retention times of NTDMA = 7.5 min and NDMA = 5.8 min; detected at 232 nm. Glucose-6-phosphate, NADP and glucose-6-phosphate dehydrogenase were purchased from Boehringer Mannheim (Mannheim, Germany), tetrabutylammonium hydroxide 40% in water from Riedel-de-Haen (Seelze, Germany) and Ready Safe scintillation cocktail from Beckmann (Munich, Germany). All other chemicals were of the highest purity available and purchased from Merck (Darmstadt, Germany).

Incubations
[14C]HCHO generated from [14C]NDMA or [14C]NTDMA was analysed by the method of Hutton et al. (10) as modified by Yoo et al. (11). [14C]HCHO is derivatized with dimedon and formaldimedon extracted into hexane. Hexane extractions of 1 mM [14C]NDMA gave no detectable radioactivity in the hexane, whereas 0.3% of 1 mM [14C]NTDMA was extracted into hexane under the assay conditions used. For each substrate concentration, therefore, a control without microsomes was run to account for the background. Generated [14C]HCHO was read from a calibration curve performed with [14C]HCHO. Incubations were performed in triplicate in 4 ml screw-cap tubes at 37°C for 15 min, in 500 µl containing an NADPH-regenerating system with 2 mM glucose-6-phosphate, 0.08 mM NADP and 0.08 IU glucose-6-phosphate dehydrogenase, 2 mM MgCl2, 0.3 mg microsomal protein, and 14C-labelled substrate with or without inhibitor at the concentrations indicated in the Results section, in 0.06 M phosphate buffer, pH 7.4, containing 0.07 M KCl. NDMA or NTDMA used as inhibitors were diluted in water, stored at –20°C and their content determined by HPLC. Aliquots of each dilution (at least four) were added to the incubations as indicated in Table IIGo.


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Table II. Estimated values for kinetic parameters and variance parameters of NDMA and NTDMA demethylation by different microsomes using the transform both sides (TBS) model
 
Kinetic modelling and statistical analyses
For the statistical evaluation of the experiments comparing NDMA and NTDMA metabolism in liver microsomes from female rats treated with different induction protocols and from untreated males we characterized the enzymatic reaction with simple hyperbolic saturation kinetics. The functional relationship between the velocity of the reaction and the concentration of substrate is characterized by the Michaelis–Menten equation:



where y is the reaction velocity, Vmax the maximum velocity of the reaction, x the concentration of substrate and Km the half-saturation constant.

Linearizing transformations of this non-linear function (e.g. Lineweaver and Burk, Eadie, Scatchard) have been shown to yield suboptimal estimates of the parameters Vmax and Km, because each one makes different assumptions about the underlying experimental error (12). Since, normally, the error structure of the data is not known, a statistical method should be applied that is able to identify the unknown error structure from the data themselves.

Such a flexible model was introduced by Ruppert et al. (13). It integrates into the model possible error structures that are determined by additional parameters that can be estimated from the data. This approach is the so-called weighted transform both sides (TBS) model.



with i = 1,..., n where n represents the number of different substrate concentrations for each experiment, f(x, ß) is the regression function, as for example the function in equation [1] above, and g(x, {theta}) is a variance weighting function. ({lambda}, ß, {theta}) are the unknown parameters and {varepsilon} the statistical error. In this model, the same transformation, denoted by superscript ({lambda}), is applied to both sides of the model equation because then, in the absence of any experimental error, the functional relationship between independent and dependent variable remains. The Box–Cox power transformation (14) is defined by



It has been shown to be flexible enough for most experimental data and is able to remove a possibly skewed error distribution. The weighting function g(x, {theta}) has the task to force the errors towards constant variances across all observations. Under these model conditions the errors {varepsilon}i, i = 1,... n, are assumed to be approximately normal with mean 0 and variance {sigma}2, and {lambda} and {theta} are parameters describing the possible error structures of the data. The Michaelis–Menten model (equation [1]) in this non-linear weighted TBS approach is defined by



if the variance weighting function is chosen as a power function g(x, {theta}) = x{theta}. This allows the standard deviation of the transformed response y{lambda} to depend on the substrate concentration x, therefore an influence of the substrate concentration on the variability of the observed reaction velocity is accounted for. Notice, that by fixing the parameters {lambda} and/or {theta} one obtains the linearized statistical models as special cases of this wider model class (13). For example, choosing {lambda} = 1 and {theta} = 0 yields the pure non-linear model of equation [1], which can be fitted with the ordinary least squares (OLS) method, and choosing {lambda} = –1 and {theta} = 0 yields the Lineweaver–Burk model. By only fixing {theta} = 0 one obtains the pure TBS model, and if no transformation is performed a weighted least squares fit (WLS). The advantage of model I [3] is its flexibility, which establishes the superiority of this weighted TBS approach over less flexible statistical model fit procedures.

To verify whether the underlying kinetic model is at least approximately fulfilled, we examined the data sets graphically by residual plots and calculated the adjusted coefficient of determination R2 to determine the goodness-of-fit. For some of the experiments the observations were only measured at low substrate concentrations, which is in the linear part of the kinetic of this process only. For an overall comparability of the results, however, we used the same statistical models for all analysed experiments, taking into account a possible lack of saturation in the case of linear kinetics.

In the case of a competitive enzyme inhibition, the Michaelis–Menten equation [1] generalizes to



where I is the inhibitor concentration and KEI the inhibition constant.

It is useful biochemically to estimate one value for Km and to incorporate the inhibition constant KEI into the statistical model as in equation [4]. In this case the concentration of the inhibitor is a second statistical co-variable and the inhibition constant KEI can be estimated directly from all observed data points. For our statistical analyses it is assumed that the error structure for each inhibition experiment is the same, and that parameter estimation is feasible by pooling the observations.

A combination of the weighted TBS model I equation [3] and equation [4] leads to



The fit of this model to the data from the inhibition experiments was carried out in two steps. At first we fitted the data with model II [5] and estimated all parameters in this weighted TBS model (full model) simultaneously. After inspection of the estimated error structure of each data set, we checked whether it was possible to reduce the complexity of the statistical model by omitting one variance parameter for a new fit of the data either by a pure TBS model or by a WLS model (reduced model). This procedure was necessary because in some cases when model II [5] was used the estimated standard errors of the estimated parameters could be affected in an undesirable manner if the model was overparameterized.

All statistical calculations were performed using the SAS NLIN procedure (SAS Institute, Cary, NC).


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For the statistical analyses, the OLS fits of all gender/treatment/substrate concentration groups were compared with a TBS fit and a WLS fit. Table IGo shows the resulting estimates for NDMA demethylation in microsomes from control and ethanol-treated females as a typical example of this analysis. In all groups except the male/control/NTDMA group the standard errors of both the Vmax and Km values were lowest when the TBS model was applied, and the difference in the case of male/control/NTDMA was <5%. In a second step, we restricted the reported analysis results to the application of the TBS model, exclusively. These results are shown in Table IIGo. Two experiments for each substrate and treatment group were performed in triplicate and analysed. [14C]NDMA substrate concentrations were between 6 and 90 µM and those of [14C]NTDMA between 10 and 76 µM. The turnover of NTDMA in all groups is higher by almost 2-fold than that of NDMA. For both substrates ethanol is the best inducer. Microsomes from uninduced male rats have a higher turnover rate than from uninduced females. For a further comparison of the individual experiments with respect to the Km values we calculated 95% confidence limits by using the estimated standard errors of the estimated parameters of the TBS fit in Table IIGo. These results are shown in Figure 2Go.


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Table I. Estimated values for kinetic parameters and variance parameters for NDMA demethylation by microsomes from untreated and ethanol-treated females using the three different methods: ordinary least squares (OLS), transform both sides (TBS) and weighted least squares (WLS)
 


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Fig. 2. Km values in liver microsomes from different groups calculated with the TBS model in Table IIGo. The error bars are the 95% confidence intervals calculated from the standard errors for both substrates and for differently treated rats.

 
Except in microsomes from untreated females, NDMA and NTDMA showed Km values that were very similar. As expected, the different treatment protocols of female rats did not significantly change the Km values of hepatic microsomal metabolism of either compound. No difference was observed between males and induced or control females.

In nasal microsomes, the concentrations of both NTDMA and NDMA used did not result in Michaelis–Menten type saturation kinetics, so that Vmax and Km values could not be calculated with the models described herein. The graphs in Figure 3Go show that the turnover of NTDMA demethylation is again much higher than the activation of NDMA. Both reactions are nearly linear. NTDMA demethylation was determined up to 1.7 mM and remained linear (for clarity only data up to 0.17 mM are shown).



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Fig. 3. Demethylation of NDMA or NTDMA by nasal microsomes from untreated rats. The left y-axis shows the turnover of NTDMA in nmol HCHO/mg microsomal proteinxmin, while the right y-axis shows the turnover of NDMA.

 
The treatment of male rats with ethanol lead to a lower Km value (0.0751 mM) for NDMA demethylation than fasting (0.1612 mM), whereas the turnover in microsomes from fasted rats was higher (Table IIIGo). The low Km of 40–50 µM reported by Yoo et al. (11) for NDMA activation was only observed after ethanol induction and in untreated males (Table IIGo). Again, as in the case of microsomes from female rats, ethanol was the best inducer of NTDMA demethylation. The Km determined for NTDMA demethylation in microsomes from ethanol and fasted rats was very similar, but higher than for untreated males (Table IIGo).


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Table III. Estimated values of kinetic parameters and variance parameters for inhibition kinetics of [14C]NDMA activation by NTDMA as inhibitor or [14C]NTDMA demethylation by NDMA as inhibitor using the transform both sides (TBS) model (reduced model)
 
With microsomes from induced male rats, the inhibition of [14C]NDMA demethylation by NTDMA and vice versa, that of [14C]NTDMA demethylation by NDMA, was studied (Table IIIGo). [14C]NDMA demethylation was inhibited by NTDMA with a KEI of 0.0736 mM in microsomes from ethanol-treated rats. For a representation of the experiments, we produced a graph of the data points transformed according to a Lineweaver–Burk plot but we used the parameter estimates of Table IIIGo. These are shown in Figure 4aGo with the means of triplicate experimental data points. An even lower KEI of 0.0396 mM NTDMA for inhibition of NDMA activation was determined in microsomes from fasted rats.




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Fig. 4. Double reciprocal plots of [14C]NDMA demethylation in the presence of 0–0.05 mM NTDMA (a) or [14C]NTDMA demethylation in the presence of 0–1.4 mM NDMA (b). Lines are drawn with the parameter estimates calculated in Table IIIGo, and the symbols are the means of triplicate experimental data used in the calculations, see text for details.

 
In microsomes from fasted rats, the KEI of inhibition by NDMA of [14C]NTDMA demethylation was 0.2855 mM. Figure 4bGo shows the parameter estimates from Table IIIGo in a Lineweaver–Burk transformation with the means of triplicate data points. In ethanol-induced microsomes a similar KEI value of 0.2237 mM NDMA for the inhibition of [14C]NTDMA demethylation was calculated.


    Discussion
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NDMA and NTDMA metabolism data were analysed by model I in a two-step procedure. To estimate the enzyme kinetic parameters Vmax and Km for NDMA or NTDMA as substrate, we chose as a first-step three different statistical fitting methods (OLS, TBS and WLS; Table IGo). We performed no analysis with the weighted TBS model, because the determination of two additional variance parameters was not feasible in this case.

The results for NDMA showed slightly higher estimates with the OLS fit for both kinetic parameters than the TBS or WLS models. The two models with flexible treatment of the error structure yielded similar estimates for Vmax and Km, and also the calculated variance parameters {lambda} and {theta} were nearly the same across all experiments. The transformation parameter {lambda} ranged from –0.16 to 0.08, and {theta} ranged from 0.49 to 0.74. This result is an indication of the equality of the experimental conditions in all incubations.

The results for NTDMA showed only marginal differences between the estimates of the kinetic parameters obtained with the three model fits; the values calculated for the ethanol-treated females were a little higher with the TBS and WLS fits than the OLS fit. Here the estimated values of the variance parameters ranged from –0.40 to 0.68 for {lambda} and from 0.16 to 0.75 for {theta}. Therefore, the experimental conditions were not as consistent as in the experiments with NDMA as substrate. In all analyses a calculated adjusted coefficient of determination R2 >0.95 indicated a sufficient goodness-of-fit.

Our results indicate that NDMA and NTDMA are demethylated by the same enzyme in liver microsomes from female rats and uninduced male rats: presumably CYP2E1. The Km values obtained correspond well to the value for NDMA demethylation of 40–50 µM reported by Yoo et al. (11). NTDMA is demethylated more rapidly than NDMA to consistently yield more formaldehyde.

In male rats, the Km values differed with different treatment protocols and only in control microsomes was the low Km of CYP2E1 measurable. In microsomes from fasted male rats with NDMA as substrate, a higher Km of 0.1612 was found and a similar value for NTDMA as substrate in microsomes from pre-treated rats. Therefore, in these experiments another enzyme might be responsible for NDMA activation and NTDMA demethylation, which has been described by others (15). The low Km form observed in control males did not seem to contribute to the demethylation reaction in these microsomes. The analysis of residuals and the calculated R2 indicate that the assumptions of the underlying non-linear model are fulfilled and the goodness-of-fit is sufficient (R2 > 0.95).

In nasal microsomes, the kinetics for both substrates are vastly different, with NDMA showing slight saturation at very low substrate concentrations whereas NTDMA is demethylated very effectively at a linear rate up to 1.7 mM, probably by another enzyme specifically expressed in rat nasal mucosa, such as a CYP2A species, which was found by Thornton-Manning et al. (16) to cross-react with rabbit anti-CYP2A10 and CYP2A11 antibodies. These two enzymes are abundant in nasal mucosa of rabbits, therefore we assume that such a P450 enzyme in rat nasal mucosa is responsible for NTDMA demethylation. Another member of the CYP2A family, probably CYP2A3 with coumarin-7-hydroxylase activity, is solely expressed in rat nose, not in liver, as Béréziat et al. (17) showed with anti-CYP2a5 antibody raised against mouse liver coumarin hydroxylase. The antibody inhibits N-nitroso-diethylamine activation by 80–90%, so that nitrosamines and maybe also nitramines are substrates for enzymes of the CYP2A family. Activation of NDMA by nasal mucosa microsomes was also shown by Hong et al. (18), who showed that CYP2E1 was only responsible for part of the activity. The data in Figure 3Go, with a partial saturation of NDMA demethylation at 0.12 mM and a linear increase at higher substrate concentrations, point to at least two enzymes involved in NDMA activation in nasal mucosa.

For NTDMA, however, demethylation is not an activation mechanism leading to an ultimate carcinogen, as it is for NDMA, but results in HCHO and N-nitromethylamine. HCHO could be considered a direct carcinogen, since it reacts with DNA and forms DNA–protein crosslinks (19). But HCHO is also a normal metabolite of many physiological processes and is very effectively detoxified by binding to glutathione and is oxidized by aldehyde dehydrogenases, which occur in nasal mucosa (20). Glutathione concentrations in nasal mucosa homogenates are 30–35 pmol/mg protein (19), therefore probably sufficiently high to bind HCHO generated from NTDMA. The tumours observed after NTDMA administration were esthesioneuroepithelioma (2), not squamous cell carcinoma, which is the tumour type induced by HCHO (19). Unclear of course is the effect of HCHO in a setting where alkylating species generated from activated NDMA are also present and where HCHO might enhance DNA damage.

N-nitromethylamine is only carcinogenic after further activation, probably reduction to methyldiazonium ion, and it induces tumours of the spinal cord (2). NDMA on demethylation also decomposes to methyldiazonium ion, which, if it reacts with DNA, leads to mutations. Methyldiazonium ions also react with nucleophiles in proteins, probably also with the active site of cytochrome P450 (21). Nevertheless, NTDMA is a much more effective inhibitor of NDMA activation than NDMA of NTDMA demethylation, with KEI of 0.0396–0.0736 mM for NTDMA as inhibitor as opposed to 0.2237–0.2855 mM for NDMA as inhibitor.

Again, similar to above, the estimates of the parameters Vmax, Km and KEI were only marginally different when using the more parsimonious reduced WLS or TBS model compared with the full model. The estimated error structure represented by {lambda} and {theta} of the full model (weighted TBS) were used to decide if it was possible to fix one variance parameter and use a reduced model (TBS or WLS). This was the case in the experiments with NDMA as substrate, where the TBS model yielded lower standard errors, and also with NTDMA as substrate in microsomes from ethanol-treated rats. For NTDMA demethylation in microsomes from fasted rats, the application of the full model gave parameter estimates of higher accuracy than the WLS or TBS fits. The differences were, however, small. Given these results we decided to report the results of the reduced model with the resulting estimates of the error structure parameters {lambda} and {theta} (Table IIIGo). Again the goodness-of-fit was sufficient because of a calculated adjusted coefficient of determination of R2 >0.95 in all analyses. By applying this model hierarchy to our data we were able to achieve good protection against biased estimates of the kinetic parameters.

The experimental data presented herein strongly support the mechanism postulated in the Introduction for the activation of NTDMA to an ultimate carcinogen. We have previously shown that NTDMA is reduced to NDMA by cytoplasmic enzyme(s) in the liver (4). Both compounds are substrates for the same demethylase in liver microsomes, and NTDMA is a very effective inhibitor of NDMA activation in the liver. Due to this inhibition, NDMA can leave the liver and is activated in the nasal mucosa to a directly alkylating species, which may be the cause of the observed nasal tumours after NTDMA administered by gavage.


    Notes
 
2 Present address: Department of Statistics, University of Dortmund, 44221 Dortmund, Germany Back

3 To whom correspondence should be addressed Email: e.frei{at}dkfz-heidelberg.de Back


    References
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 

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Received June 10, 1998; revised September 22, 1998; accepted October 23, 1998.