Integration of yield factor expression into Haldane's model for substrate inhibition.

Abstract

Haldane equation is a mathematical expression that has been widely used in growth kinetics to give a proper fit to experimental data in case of substrate inhibition during enzymatic processes. It determines the specific growth rate of a microorganism based on the substrate concentration, the half saturation constant, the inhibitory constant and the maximum growth rate achievable. However, for practical and experimental design purposes it is important to describe Haldane equation in terms of the initial concentration of substrate, since this information is required to know the proper amount of initial substrate to be used. For this reason, in the present paper we proposed to integrate the expression of yield factor and the definition of specific growth rate in a batch system into Haldane's equation and to solve analytically the mathematical equations in order to obtain a final expression that correlates the maximum growth rate, the limiting nutrient concentration at which the specific growth is half its maximum value, the inhibitory constant, the initial concentration of substrate and the initial amount of biomass required in time. Accordingly, simulation and numerical studies are presented to analyze and discuss the importance of the obtained model. © 2018 The Authors, published by EDP Sciences.