Single Mathematical Parameter for Evaluation of the Microorganisms' Growth as the Objective Function in the Optimization by the DOE Techniques.

The cultivation of bacteria sets a ground for studying biological processes in many scientific disciplines. The development of the bacterial population is commonly described with three factors that can be used to evaluate culture conditions. However, selecting only one of them for the optimization protocol is rather problematic and may lead to unintended errors. Therefore, we proposed a novel mathematical approach to obtain a single factor that could be used as the objective function to evaluate the whole growth dynamic and support the optimization of the biomass production process. The sigmoidal-shape curve, which is the commonly used function to plot the amount of biomass versus time, was the base for the mathematical analysis. The key process parameters, such as maximal specific growth rate and lag-phase duration were established with the use of mathematical coefficients of the model curve and combined to create the single growth parameter. Moreover, this parameter was used for the exemplary optimization of the cultivation conditions of Klebsiella pneumoniae that was cultured to be further used in the production of lytic bacteriophages. The proposed growth parameter was successfully validated and used to calculate the optimal process temperature of the selected bacterial strain. The obtained results indicated that the proposed mathematical approach could be effortlessly adapted for a precise evaluation of growth curves.