Mathematical simulation of pseudo-crystallofermentation of hydrocortisone by Arthrobacter simplex

A mathematical model has been developed to simulate the pseudo-crystallofermentation process of hydrocortisone by Arthrobacter simplex. The model describing the process included considerations on the kinetics of microbial growth, the rate of enzyme formation, the rate of substrate dissolution, the rate of solute crystallization, and the kinetics of enzymatic reaction. The system of equations was solved numerically by the Runge-Kutta-Gill method. The good agreement between prediction and experiment indicated the reliability of the established model. The simulation was capable of predicting the time when the crystallization of product occurred, which could be further verified by microscopic observation on the culture medium, as well as cell growth, enzyme synthesis, product formation, and the composition of the final product crystals.