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

Abstract

1To determine kinetic parameters (V_max, 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.

2For a 15-point nortriptyline (NT) formation rate vs substrate (AMI) concentration curve, a two enzyme model, consisting of one enzyme with MM kinetics (V_max=1.2 nmol min⁻¹ mg⁻¹, K_m=24 μm) together with a sigmoidal component (described by an equation equivalent to the Hill equation for cooperative substrate binding; V_max=2.1 nmol min⁻¹ mg⁻¹, K′=70 μm; Hill exponent n=2.34), was favoured according to AIC and the F-test.

3Data generated by incubating AMI under the same conditions but in the presence of 10 μm ketoconazole (KET), a CYP3A3/4 inhibitor, were consistent with a single enzyme model with substrate inhibition (V_max=0.74 nmol min⁻¹ mg⁻¹, K_m=186 μm, K₁=0.0028 μm⁻¹).

4Sulphaphenazole (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.

5Incubation of AMI with 50 μm SPA resulted in a curve consistent with a two enzyme model, one with MM kinetics (V_max=0.72 nmol min⁻¹ mg⁻¹, K_m=54 μm) the other with ‘Hill-kinetics’ (V_max=2.1 nmol min⁻¹ mg⁻¹, K′=195 μm; n=2.38).

6A fourth data-set was generated by incubating AMI with 10 μm KET and 50 μm SPA. The proposed model of best fit describes two activities, one obeying MM-kinetics (V_max=0.048 nmol min⁻¹ mg⁻¹, K_m=7 μm) and the other obeying MM kinetics but with substrate inhibition (V_max=0.8 nmol min⁻¹ mg⁻¹, K_m=443 μm, K₁=0.0041 μm⁻¹).

7The 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.

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