Kinetic values for mechanism-based enzyme inhibition: Assessing the bias introduced by the conventional experimental protocol

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Abstract

The in vitro characterisation of a mechanism-based enzyme inactivator (MBEI) includes determination of the maximum inactivation rate constant (kinact), the inactivator concentration that produces half-maximal rate of inactivation (KI), and the partition ratio (r). Conventional experimental protocols (CEPs) assume insignificant metabolism of the MBEI during the “pre-incubation” stage and negligible inactivation of enzyme during the “incubation” stage. The aim of this study was to evaluate the bias in the estimation of kinetic values as a consequence of these assumptions. Ranges of values of kinact, KI, and r for reported MBEIs were collated and data for 27 virtual compounds were generated by combining the median, high and low values of each parameter. The kinetics of the virtual compounds and of four reported MBEIs were simulated under CEP, but taking account of enzyme inactivation, metabolism of the MBEI and the probe substrate, and their interaction at relevant stages. The differences between the estimated and starting kinetic values reflect the bias introduced by the CEP in the absence of experimental error. Despite simulating a stringent experimental procedure, 19% of the estimated kinetic values of the 27 virtual MBEIs had greater than 100% bias. Simulations relating to two of the actual MBEIs indicated no bias in kinact and 8–33% bias in KI. However, the bias in KI values of the two other compounds exceeded 98% and corresponding bias in kinact was greater than 300%. Thus, CEP may introduce substantial bias in estimated kinetic values for mechanism-based inhibition, and the validity of some of the reported kinetic parameters may be questionable.

Introduction

An increasing number of drugs are reported to cause mechanism-based inhibition (MBI) of cytochrome P450 enzymes (CYPs). All types of enzyme inhibition have a mechanism, but the term MBI is applied conventionally to cases where a compound causes irreversible or quasi-irreversible enzyme inhibition, requiring synthesis of new enzyme for recovery of activity. A specific type of MBI refers to the case where a mechanism-based enzyme inactivator (MBEI) first binds to and is then catalytically activated by a target enzyme to a reactive intermediate that covalently binds to a moiety in the enzyme active site, resulting in an irreversible loss of enzymatic activity (Silverman, 1988). This may affect the clearance of the MBEI itself, as well as that of other compounds metabolized by the same enzyme.

The effect of an MBEI in vivo will be a composite function of its ability to inactivate the enzyme and the synthesis rate of enzyme (Mayhew et al., 2000). Therefore, to assess the potential impact of MBI in vivo, it is necessary to determine the inactivation parameters of the MBEI in vitro. An MBEI is characterised by three parameters: kinact, the maximum rate of inactivation; KI, the concentration of inhibitor that produces half-maximal inactivation, and the partition ratio; (r), a measure of the efficiency of inactivation relative to metabolism. The partition ratio can be viewed as the number of inactivator molecules metabolized per molecule of enzyme inactivated. Its value can vary from zero, when the rate of metabolite formation is negligible, to infinity, when the rate of enzyme inactivation is negligible.

Silverman, 1988, Silverman, 1995 described an experimental procedure to determine the kinetic parameters of an MBEI, which is followed by most investigators. We shall refer to this as the conventional experimental protocol (CEP). The approach consists of a “pre-incubation” stage followed by an “incubation” stage. During the first stage, enzyme and cofactors are incubated with the MBEI at several concentrations and over a range of times to determine the decrease in active enzyme over time. The incubates are then diluted in order to “quench” inactivation, and the remaining enzyme activity is measured with a probe substrate at a saturating concentration in the second stage of the procedure. Two important assumptions are made, namely that there is negligible metabolism of the MBEI during the “pre-incubation” stage, and that negligible enzyme inactivation occurs during the “incubation” stage. The impact of these assumptions on the estimation of kinetic values has not been evaluated rigorously.

We recently evaluated the experimental protocols used to characterise MBEIs of human CYPs in vitro (Ghanbari et al., in preparation). Of these studies, 97% reported both kinact and KI values, and 19% reported partition ratios. A wide variability in the timing of the first sample during the “pre-incubation” stage, the dilution factor, and the incubation time for measurement of remaining enzyme activity was apparent in the studies. The aim of the present study was to evaluate the performance of the CEP by in silico simulation.

Section snippets

Theoretical background

A schematic of enzyme kinetics involving MBI (Walsh et al., 1978, Waley, 1980) is shown in Fig. 1.

At given concentrations of inactivator and enzyme, the reactions indicated in Fig. 1 are governed by the first-order rate constants k1, k−1, k2, k3, and k4. The rate of enzyme inactivation can be represented by Eq. (1) (Kitz and Wilson, 1962, Jung and Metcalf, 1975):d[E]tdt=kinact[I]KI+[I][E]twhere [E]t is the active enzyme concentration at time t, [I] the inactivator concentration, kinact the

Simulations based on virtual MBEIs

The differences between the estimated and starting kinetic values reflect the bias introduced by the CEP. The results showed that the CEP was associated with significant bias in estimating parameter values even in the absence of experimental errors (Fig. 3). In most cases, there was an overestimation of the starting values of the kinetic constants. The CEP failed to provide accurate estimates of the partition ratio for MBEIs with low r values (e.g. r = 2). When the Kitz–Wilson plot was applied to

Discussion

The simulated CEP for 27 virtual MBEIs followed a stringent design with regard to a short initial sampling time during the “pre-incubation” stage (2 min, i.e. kobs was determined from the 0- to 2-min data), a relatively high dilution factor (20-fold), a high concentration of probe substrate (10Km,S), and a short “incubation” time (3 min). Nevertheless, considerable bias was observed in the recovery of starting kinetic parameters, even in absence of experimental error (Fig. 3). This bias arises

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