An error estimation of Michaelis-Menten (Monod)-type kinetics

Abstract

Due to research on biochemistry and genetic engineering, mathematical models of microbial growth have become more complicated but Michaelis-Menten or Monod type expressions have still been used for conversion rates, uptake rates, etc. It is worth examining the error that can be caused by these quasi-steady-state hypotheses. This paper presents a simple but very effective rationale function that describes the error of the quasisteady-state hypothesis in enzyme kinetics. A simplified fermentation kinetic model was used for comparison of microbial growth but no analytical error function has been found for batch cultivation. In the case of continuous fermentation the error can be given in an analytical form. Many simulations, based on real SCP experiments, show a significant effect of the quasi-steady-state hypothesis. Since the rate constants of intracellular events are not really known, we have to be very careful when taking into account Michaelis-Menten type expressions in the building of complicated models.

Monte Carlo Analysis of Michaelis—Menten Type Kinetics

“…However, the more precise investigations of enzyme systems pose the question of assessing the quality of information obtained using Michaelis -Menten kinetic approach. This is the aim of many 59 publications dedicated to error estimation ( 1,2,3,4,5,6), influence of the violation of steady-state assumptions (9), analysis of the informative value of the equations (15), sensitivity of the integration procedures (8) etc. (7,10,11,12,13,14,(16)(17)(18)(19)(20)(21)(22).…”