## Abstract

A robust statistical approach for discrimination of competing microbial growth kinetics models was applied. The phenomenological modeling approach based on unstructured and non-segregated kinetic models was formulated to describe PHB synthesis by Cupriavidus necator that experimentally was carried out in batch system for the given temperatures of 30; 32.5; 35 and 37.5 °C. Further, PHB synthesis was assumed to be non-growth-associated under nitrogen limitation conditions. The stoichiometry of the microbial growth and PHB synthesis was successfully used in kinetics studies combining the knowledge with the deterministic models in ordinary differential equation system. The parameters of the models identification procedure was based on the Genetic Algorithms which were coded in Maple^{®}15 software. Analysis of the normalized least square function, as well as the correlation coefficient, has shown that all competing kinetic models fitted well the experimental data in all studied temperatures. A sequence of statistical tests was used to evaluate the quality of the chosen competing kinetic models and their ability to fit to the experimental data, and more particularly to ensure the reliability of the best model predictions. Hence, as a result was ensured that the mathematical modeling based on Andrews (1968) model was the one that best described the experimental data under the given operational conditions and more particularly obtained at 32.5 °C. The evaluated values of parameters indicated that the specific growth rate (SGR) of active biomass most likely was limited since the nutrient nitrogen concentration was S_{N} ≤3.35 g L^{−1}, and the specific production rate (SPR) of PHB was maximum when the organic substrate concentration reached S_{C} =10 g L^{−1}. Moreover, the experimental tests have shown that the highest biomass (0.361 gcell L^{−1} h^{−1}) and PHB (0.50 gPHB L^{−1} h^{−1}) productivity were attained at 32.5 °C. Andrews (1968) model provide interesting findings for the given oxygen mass-transfer conditions from the gas to the liquid phase and the microbial respiration during the cultivation at 32.5 °C. The cell respiration parameters estimated by GA were 0.89 gcell gO_{2}^{−1} in the growth phase and 0.31 gcell gO_{2}^{−1} in the PHB synthesis phase. These values agreed with those ones found from the stoichiometry of microbial growth and PHB synthesis demonstrated in this study. Thus, application of statistical test analysis can be considered as a powerful tool for discrimination of kinetic hypothesis about the dynamics of the cell growth and product synthesis.

Original language | English |
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Pages (from-to) | 20-33 |

Number of pages | 14 |

Journal | Chemical Engineering Science |

Volume | 160 |

DOIs | |

Publication status | Published - 16 Mar 2017 |

## Keywords

- Competing kinetic models
- Cupriavidus necator
- Genetic algorithms
- PHB
- Statistical tests
- Stoichiometry of the bioprocess