Mathematical Modeling of the Molybdenum Blue Production from Serratia sp. strain DRY5

Abstract

The reduction of molybdenum to molybdenum blue is a detoxification process and the development of Mo-blue is associated with growth. Significant parameters such as precise reduction rate, theoretical maximum reduction and whether reduction at high molybdenum concentration influenced the lag time of reduction can be discovered by mathematical modeling of the reduction phase. While common, the use of the linearization method by the use of natural logarithm transformation is inaccurate and can only provide an approximate value for the calculated single parameter, the real 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. The Huang model was the best model in modelling the Mo-blue production curve of the Serratia sp. strain DRY5 based on statistical tests such as root-mean-square error (RMSE) (0.043), adjusted coefficient of determination (R2) (0.994), bias factor (BF) (1.00), accuracy factor (AF) (1.03) and corrected AICc (Akaike Information Criterion) (-67.02). Parameters obtained from the fitting exercise were maximum Mo-blue production rate (m), lag time () and maximal Mo-blue production (Ymax). We make use of primary growth models for modeling Mo-blue output in this work. This is an emerging method of identifying constants of parameters that control the reduction of molybdenum. For the creation of further secondary models, the constants calculated from this work will be utilized for such purpose. The use of these primary models can also be broadened to processes involving the detoxification of other heavy metals.