Aplicabilidade de modelos cinéticos para modelagem matemática de cultivo em batelada de Bacillus firmus (Cepa 37) na produção de ciclomaltodextrina glucanotransferase (CGTase)

Abstract

This work had as objective evaluates the applicability of the classical kinetic models in the production of the enzyme Ciclomaltodextrin-Glucanotransferase (CGTase) produced in a batch process by Bacillus firmus STRAIN 37. The purpose of studying the application of the kinetic models in the production of the enzyme CGTase is to use the mathematical modeling as a tool for optimization of the process of production of the referred enzyme and also allow the simulation of new production situations without involving expenses of and time spent at laboratory. The data used in this work were extracted of the dissertations of master's degree of Marques (2004) and of the work of scientific initiation of Calderaro (2007), that evaluate several experimental conditions of cultivation of Bacillus firmus (STRAIN 37) in the production of CGTase. The work consisted in evaluating the application of kinetic models through an algorithm of resolution of differential equations written in the software MATLAB® that was elaborated to solve a system of three differential equations, being the one that represents the tax of cellular growth, dX/dt, the one that represents the tax of expressed product formation in enzymatic activity, dP/dt (or dA/dt) and the one that represents the tax of substrate consumption, dS/dt. Inside of this differential equations the approached kinetic models were substituted, being used models of Monod (1949), the Aiba et al (1968) and the Andrews (1968). They were then developed four systems of differential equations, the first that it involved the representation of the cellular growth for Monod (1949), of the enzymatic activity for Aiba et al (1968) and of the substrate consumption as the relationship between the cellular growth and the observed enzymatic activity. The second system of differential equations involved the representation of the cellular growth also for Monod (1949), the representation of the enzymatic activity for Andrews (1968) and the substrate consumption as the relationship between the cellular growth and the observed enzymatic activity. In the system three, so much for the cellular growth as for the enzymatic activity it was considered that their behaviors respected the kinetic equation of Aiba et al (1968) and the substrate consumption stayed the relationship between the cellular growth and of the enzymatic activity. In the system four, the cellular growth and enzymatic activity they were considered as respecting the kinetic equation of Andrews (1968) to the substrate consumption stayed the relationship between the cellular growth and the enzymatic activity. Were they also analyzed the behaviors of the curves of specific rate of cellular growth (μX), substrate consumption (μS) and enzymatic activity (μA) in function of the time, with the objective of verify some relationship among the three curves of specific rate and try to classify the production of CGTase by Bacillus firmus STRAIN 37 how production of associated enzyme or not to the cellular growth. Was it observed for some culture means a relationship among the specific rates of substrate consumption (μS) and of enzymatic activity (μA), done characterize by the amylolytic activity of the enzyme CGTase, but could not one affirm that the production of the enzyme is associated to the growth of the Bacillus firmus STRAIN 37 in the studied conditions. Was another accomplished observation the relationship of Luedeking and Piret (1959) among the specific rate of product formation (μA) and the specific rate of cellular growth (μX), through the elaboration of the graphs for each medium, in what the specific rate of enzymatic activity (μA) did it composes the axis "y" and the specific rate of cellular growth (μX) did it composes the axis "x". For the concentrations of starch used in the culture mediums studied (larger of the than 10g/L), was not a lineal relationship observed between the specific rate of enzymatic activity (μA) and of cellular growth (μX), not being possible to apply the relationship of Luedeking and Piret (1959) in the study of the kinetic models. For most studied mediums, the model Aiba et al (1949) didn't present any result, being difficult the resolution of the system of equations in the studied conditions, already the combination Monod-Aiba presented similar results, graphically, that the combination Monod-Andrews, and the model of Andrews (1968) presented good results for practically all of the mediums, none of the studied kinetic equations was enough to adjust the three groups of given simultaneously. For this reason, for the production of CGTase for Bacillus firmus STRAIN 37, in the studied conditions, it's necessary to manipulates the existent kinetic equations or to develop new kinetic equations to allow to represent this fermentative process appropriately.