Evaluation of various mathematical models for cell growth and high bioconversion potent protease production of Microbacterium sp. in shake flask fermentations

Proteases, which catalyze the hydrolysis of protein molecules to peptides and amino acids, are being used in various industries and bioconversion processes in the world. Due to the high demand, plenty number of studies are available in the literature about microbial production of protease. However, mathematical modeling of the microbial protease production processes has not been studied enough to bring light to industrial level productions. In this study, twelve nonlinear mathematical models (Gompertz, generalized Gompertz, modified Gompertz, re-modified Gompertz, logistic, generalized logistic, modified logistic, re-modified logistic, Richards, generalized Richards, modified Richards, and re-modified Richards) were applied to fit cellular growth and protease production of Microbacterium sp. in shake flask fermentations. Goodness of fit was measured by calculation of RMSE, MAE, BF, AF, R², and slope. Evaluation of twelve models resulted in that modified Gompertz (RMSE = 7.18, MAE = 4.92, BF = 0.94, AF = 1.11, R² = 1.00, and slope = 0.93) and modified Richards (RMSE = 6.31, MAE = 5.48, BF = 0.69, AF = 1.49, R² = 1.00, and slope = 0.93) were selected as the best models for representation of cellular concentration. Additionally, modified Gompertz and re-modified Gompertz models (RMSE = 11.71, MAE = 9.38, BF = 0.5, AF = 2.13, R² = 0.97, and slope = 0.92) predicted protease activity during the production more successfully compared to others evaluated. Overall, this study demonstrated that modeling of cellular concentration and protease production with Microbacterium sp. provides better understanding of fermentation kinetics and sets the stage for scaleup to industrial production.