Algoritmo genético na estimação dos parâmetros da produção de poli(3-hidroxibutirato) por Cupriavidus necator

Abstract

Biopolymers, especially Poly(3-hydroxybutyrate) (PHB), have been receiving big attention in order to minimize environmental damage caused by plastics from petrochemical industries. In this context, the aim of this paper was to formulate a mathematical model to describe the PHB production by Cupriavidus necator, from a detailed theoretical study. To this end, 6 models were evaluated, being 5 for cell growth and 1 for product formation, all from the literature. The ordinary differential equations system was solved numerically by Rosenbrock method. To the parameters estimation, an algorithm based on the Genetic Algorithms was developed and implemented in the software Maple®. To validate the models, experimental data at 30, 32,5, 35 and 37,5 °C were obtained from the literature. From the data analysis, it was observed that the best temperature, for both cell growth and product formation was 32,5 °C, and that the PHB production in partially associated with cell growth. To the parameters estimation, the ordinary differential equations system, obtained from the phenomenological modelling of non-structured and non-segregated models, was evaluated together with the models from the literature. The results for the objective function and correlation coefficient indicated that all the studied models adjusted well to the experimental data at all temperatures. Thus, some statistical tests were applied in order to better evaluate the models fitting, and the results indicated the Andrews’s (1968) model as the one that best represents the data from 32,5 °C, and Heinzle e Lafferty’s (1980) model for 35 °C. For the data at 30 and 37,5 °C there was no statistically valid models found. In conclusion, the statistical methodology applied for the models discrimination and fitting evaluation made it possible to say which model best represents data at each temperature.