Mathematical Modeling of Molybdenum Blue Production from Bacillus amyloliquefaciens strain KIK-12

Abstract

Molybdenum reduction to molybdenum blue is a detoxification process, and production of Mo-blue is growth associated. Mathematical modelling of the reduction process can reveal important parameters such as specific reduction rate, theoretical maximum reduction and whether reduction at high molybdenum concentration affected the lag period of reduction. The used of linearization method through the use of natural logarithm transformation, although popular, is inaccurate and can only give an approximate value for the sole parameter measured; the specific growth rate. In this work, a variety of models for such as logistic, Gompertz, Richards, Schnute, Baranyi-Roberts, Von Bertalanffy, Buchanan three-phase and more recently Huang were utilized to obtain values for the above parameters or constants from Bacillus amyloliquefaciens strain KIK-12. The Mo-blue production from this bacterium was sigmoidal in shape with a lag phase of about 15 hours and reaching maximum Mo-blue production at approximately 50 hours of static incubation. The resultant fitting shows visually acceptable fitting. The best performance was modified Gompertz model based on statistical tests such as root-mean-square error (RMSE), adjusted coefficient of determination (R2), bias factor (BF), accuracy factor (AF) and corrected AICc (Akaike Information Criterion). The modified Gompertz model was then utilized to model the Mo-blue production curves to obtain reduction coefficients. The parameter constants successfully developed from this work will be very useful for the development of further secondary models.