Mathematical modelling of cyclodextrin-glucano-transferase production by immobilised cells of Bacillus circulans ATCC 21783 at batch cultivation

The goal of the present paper is to propose a mathematical model, based on experimental data and suitable for description and prediction of the process of microbial synthesis of CGTase by immobilised bacterial cells.The model consists of a set of ordinary differential equations taking into account the microbial growth, the substrate inhibition, the decay of the microbial culture with time and the product degradation. The possible cell leakage and the resulting growth of a free culture are taken into account. The model is very sensitive towards the yield coefficients of bacterial growth and product formation. The model is suitable for estimation of the specific growth rates and the yield coefficients for free and immobilised cell growth.The model is used to evaluate kinetic constants from experimental data for the microbial production of CGTase by cells of the strain Bacillus circulans ATCC 21783 attached to poly-sulfonate membranes in a fluidized bed bioreactor operating in a batch mode.The attached cells showed higher yield than the free ones and the estimated leakage rates are pretty low. It was concluded therefore that the contribution of the immobilised cells for the CGTase formation in the considered case is dominant.