Enzyme kinetic modelling as a tool to analyse the behaviour of cytochrome P450 catalysed reactions: application to amitriptyline N-demethylation

1. To determine kinetic parameters (Vmax, K(m)) for cytochrome P450 (CYP) mediated metabolic pathways, nonlinear least squares regression is commonly used to fit a model equation (e.g., Michaelis Menten [MM]) to sets of data points (reaction velocity vs substrate concentration). This method can also be utilized to determine the parameters for more complex mechanisms involving allosteric or multi-enzyme systems. Akaike's Information Criterion (AIC), or an estimation of improvement of fit as successive parameters are introduced in the model (F-test), can be used to determine whether application of more complex models is helpful. To evaluate these approaches, we have examined the complex enzyme kinetics of amitriptyline (AMI) N-demethylation in vitro by human liver microsomes. 2. For a 15-point nortriptyline (NT) formation rate vs substrate (AMI) concentration curve, a two enzyme model, consisting of one enzyme with MM kinetics (Vmax = 1.2 nmol min-1 mg-1, K(m) = 24 microM) together with a sigmoidal component (described by an equation equivalent to the Hill equation for cooperative substrate binding; Vmax = 2.1 nmol min-1 mg-1, K' = 70 microM; Hill exponent n = 2.34), was favoured according to AIC and the F-test. 3. Data generated by incubating AMI under the same conditions but in the presence of 10 microM ketoconazole (KET), a CYP3A3/4 inhibitor, were consistent with a single enzyme model with substrate inhibition (Vmax = 0.74 nmol min-1 mg-1, K(m) = 186 microM, K1 = 0.0028 microM-1). 4. Sulphaphenazole (SPA), a CYP2C9 inhibitor, decreased the rate of NT formation in a concentration dependent manner, whereas a polyclonal rat liver CYP2C11 antibody, inhibitory for S-mephenytoin 4'-hydroxylation in humans, had no important effect on this reaction. 5. Incubation of AMI with 50 microM SPA resulted in a curve consistent with a two enzyme model, one with MM kinetics (Vmax = 0.72 nmol min-1 mg-1, K(m) = 54 microM) the other with 'Hill-kinetics' (Vmax = 2.1 nmol min-1 mg-1, K' = 195 microM; n = 2.38). 6. A fourth data-set was generated by incubating AMI with 10 microM KET and 50 microM SPA. The proposed model of best fit describes two activities, one obeying MM-kinetics (Vmax = 0.048 nmol min-1 mg-1, K(m) = 7 microM) and the other obeying MM kinetics but with substrate inhibition (Vmax = 0.8 nmol min-1 mg-1, K(m) = 443 microM, K1 = 0.0041 microM-1). 7. The combination of kinetic modelling tools and biological data has permitted the discrimination of at least three CYP enzymes involved in AMI N-demethylation. Two are identified as CYP3A3/4 and CYP2C9, although further work in several more livers is required to confirm the participation of the latter.