Impact of enzyme turnover on the dynamics of the Michaelis-Menten model

Enzymatic (metabolic rate) processes are traditionally modelled by means of Michaelis-Menten type reactions. The experimental setup is usually performed in vitro also denoted as a 'closed system'. In this paper we explore the impact of enzyme turnover on the classical Michaelis-Menten model by modifying it to include enzyme turnover, specifically through zeroth-order synthesis and first-order degeneration of the enzyme. It is shown how enzyme turnover significantly alters the dynamics of substrate, free- and bound enzyme, and impacts the rate with which substrate is converted to a metabolite P. Qualitative and quantitative estimates are derived for the effect of the parameters k_syn, k_deg and k_cat on the dynamics of substrate, and free- and bound enzyme. The model integrates four distinct processes, each characterised with its own parameter(s): (i) substrate-enzyme binding, characterised by k_on and k_off; (ii) the catalytic process, characterised by k_cat; (iii) simultaneous re-generation of free enzyme; and (iv) turnover of free enzyme, characterised by k_deg. The properties of the open Michaelis-Menten model have a direct bearing on the drug discovery process, the translation of data to the human situation and on explaining deviating clinical metabolic observations.