Identification of closed Michaelis‐Menten system by a linear approach

Abstract

Purpose

This paper aims at identifying the closed Michaelis‐Menten (M‐M) system. The system governs many phenomena that are based on “enzyme reactions”.

Design/methodology/approach

A linearization method is used. The system, however is not homogeneous and consequently earlier identification results obtained by the author cannot be applied. The approach is to show that the closed Michaelis‐Mentan system can be approximated by a sequence of open M‐M systems. The M‐M parameters are then obtained by continuity from the Cauchy's problem solution.

Findings

The main results – the identification of a closed M‐M system is described. The linearization of the closed M‐M compartmental system led to a linear nonhomogeneous system. Earlier classical methods could not applied but the “Reasonable Biological Hypothesis” of the author allowed further study.

Research limitations/implications

This study takes a preferred theoretical aspect. A generalization to n, n≥3 is considered to be interesting because we can consider an open compartmental system having n compartments as a closed system with n+1 compartments. Further work on this generalization is contemplated.

Practical implications

This theoretical study will further increase the use compartmental analysis to modelling any phenomena depending only on time.

Originality/value

Provides a methodology for identification of M‐M system using a linear strategy.

Citation

Hebri, B. and Cherruault, Y. (2005), "Identification of closed Michaelis‐Menten system by a linear approach", Kybernetes, Vol. 34 No. 7/8, pp. 1012-1026. https://doi.org/10.1108/03684920510605830