Statistical Evaluation of the Mathematical Modelling on the Molybdenum Reduction Kinetics of a Molybdenum-reducing Bacterium

Abstract

Molybdenum is a global pollutant that has been increasingly found to be toxic to
spermatogenesis in several animal model studies. Thus its removal and the studies of its reduction kinetics for removal are very important. In a previous study (1), three kinetic models; i.e. Haldane, Luong and Monod were evaluated to study the reduction kinetics of the molybdenum-reducing bacterium Bacillus sp. strain A.rzi. We revisited the model used in this bacterium and extend the study by incorporating more reduction kinetics models such as Hans- Levenspiel, Yano, Aiba, Webb, Hinshelwood and Teissier. We then evaluated the accuracy of the fitted model using statistical analysis. The best model was Han Levenspiel instead of Luong as proposed previously with the majority of the statistical evaluation such as the lowest values for RMSE, the highest adjusted R2 values and with Bias Factor and Accuracy Factor nearest to unity (1.0) indicated that the model was the best. The calculated values for the Han-Levenspiel constants qmax (the maximum specific substrate reduction rate (h−1), Sm (the critical inhibitor concentration (mM) above which reactions stops), Ks (concentration of substrate giving half maximal reduction rate (mM) and the empirical constants m and n (both dimensionless) were 3.832, 106.16, 48.19, -1.271 and 1.001, respectively. The true qmax value where the gradient for
the slope is zero was 1.107 h-1 at 38 mM molybdate as a substrate. The results indicate that the exhaustive use of mathematical models provides new understanding of the way molybdenum inhibits production into molybdenum blue in bacterium. This can provide new knowledge on ways to predict progress of molybdenum reduction in the laboratory and during bioremediation works.