Kinetics of microbial growth and substrate consumption

Abstract

A theoretical treatment of the heterogeneous reactions between microorganisms and substrate has been developed, taking into account the self-multiplying nature of enzyme systems. This treatment has been confirmed by experiments on batch cultures of baker's and alcohol yeasts and Escherichia coli. Substrate consumption is related to the quantity of microorganisms x and of substrate s as − ds dt = − ∂s ∂x · dx dt − ∂s ∂p · dp dt = κ.S = κ m.S · x s 1 K + x s where ϰ m and ϰ are the substrate consumption rate constant and the specific substrate consumption rate respectively, K a constant and p the primary product. When substrate is converted into cell material at rate y, the formula for microbial growth is dx dt = −y ds dt = μ · x = μ m · x · s x K + s x where μ m and μ are the growth rate constant and the specific growth rate respectively. When y = 0 or μ m = 0, substrate is catalytically consumed, forming enzyme whose quantity is proportional to the population density. The results here presented generalize the results of several previous workers.