Model equations for the kinetics of covalent irreversible enzyme inhibition and spontaneous reactivation: Esterases and organophosphorus compounds

Abstract

Type B carboxylesterases (acetylcholinesterases, neuropathy target esterase, serine peptidases), catalyse the hydrolysis of carboxyl-ester substrates by formation of a covalent acyl-enzyme intermediate and subsequent cleavage and release of the acyl group. Organophosphorus compounds, carbamates, and others exert their mechanism of neurotoxicity by permanent covalent organophosphorylation or carbamylation at the catalytic site of carboxylesterases. Classical kinetic studies converted the exponential kinetic equation to a logarithmic equation for graphic analysis. This process, however, does not allow analysing complex situations. In this paper, kinetic model equations are reviewed and strategies developed for the following cases: (a) single enzyme, with classical linear equation; (b) multi-enzymatic system—discriminating several inhibitor-sensitive and inhibitor-resistant components; (c) ‘ongoing inhibition’—high sensitive enzymes can be significantly inhibited during the substrate reaction time, the model equations need a correction; (d) spontaneous reactivation (de-phosphorylation)—one or several components can be simultaneously inhibited and spontaneously reactivated; (e) spontaneous reactivation from starting time with the enzyme being partly or totally inhibited; (f) aging—single enzyme can be inhibited, spontaneously reactivated and dealkylating reaction (‘aging’) simultaneously occurs; and (g) aging and spontaneous reactivation from starting time with the enzyme being partly or totally inhibited. Analysis of data using the suggested equations allows the deduction of inhibition kinetic constants and the proportions of each of the enzymatic components. Strategies for practical application of the models and for obtaining consistent kinetic parameters, using multi-steps approaches or 3D fitting, are presented.

Keywords::

• Acetylcholinesterase
• aging reaction
• carbamates
• dephosphorylation
• esterases
• inhibition
• kinetic
• model equation
• neuropathy target esterase
• ongoing inhibition
• organophosphorus
• phosphorylation
• reactivation

Acknowledgements

We express our gratitude to the journal’s reviewers and the journal’s Editor, who have given very positive and useful suggestions to improve the manuscript, to Dr L. Sultatos for specific advice and discussion, to Professor H. Bolt for his useful suggestions, and to Dr J. Barril, Dr A. G. García-Pérez, and Dr M. A. Sogorb from our laboratory for their scientific discussions and advice. We recognize those researchers who have made scientific contributions to the field, especially W. N. Aldridge, A. R. Main, E. Reiner, J. M. Chemnitius, M. K. Johnson, R. J. Richardson, J. M. Worek, M. Jokanovic, and their co-workers, who have made significant influence in the concepts developed in this paper. This work has been partly supported by the project ad051/2007/3-14.4 of the Ministry of Environment and with institutional support from the University Miguel Hernández de Elche.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.