Modelagem matemática para sínteses enzimáticas de biossurfactantes catalisadas por lipases imobilizadas

Abstract

Enzymatic reactions of esterification of fatty acids with carbohydrates generate biosurfactants, products with high capacity to reduce surface and interfacial tensions, applicable mainly in the food, pharmaceutical and cosmetic industries. Mathematical modeling, in turn, can be a useful tool, in its different approaches, for the simulation and optimization of enzymatic processes. Thus, this work was carried out in three distinct steps and aimed at the mathematical modeling of enzymatic processes to produce biosurfactants, making use of the application of phenomenological (semi-mechanistic), neural and fuzzy approaches. The phenomenological kinetic model of Ping Pong Bi Bi was fitted to experimental data. For this, kinetic data of the production of biosurfactants by esterification of oleic and lauric acids with fructose and lactose, using immobilized lipase B from Candida antarctica (CALB-IM-T2-350) and lipase from Pseudomonas fluorescens (PFL) immobilized on octyl-silica (silanized with octyltriethoxysilane), provided by LabEnz-UFSCar, were used. The classic Levenberg-Marquardt parameter fitting method was applied, resulting in a good correspondence between the proposed model and the experimental data. For validation of the semi-mechanistic model, a new set of experimental data was used, showing excellent predictive capacity of the model. Then, neural kinetic models were built using experimental data of enzymatic esterification of xylose with oleic and/or lauric acids, performed using the biocatalyst CALB-IM-T2-350 and CALB derivatives immobilized on Silica Magnetic Microparticles (SMMPs) with octyl groups (CALB-SMMP-octyl) or with octyl groups plus glutaraldehyde (CALB-SMMP-octyl-glu). Using Matlab Neural Network Toolbox, five artificial neural networks (ANNs) were trained, one for each type of biocatalyst and acid, obtaining R-squared values greater than 0.97. As a last effort in neural modeling, two ANNs were fitted (for two of the biocatalysts), each one of them already incorporating, in its inputs, an option referring to the type of acid. The R-squared values, above 0.98, also showed good predictability. Finally, modeling by fuzzy inference systems was studied, using the Neuro Fuzzy Designer tool from ANFIS (Adaptive Network-Based Fuzzy Inference System) of Matlab. Fuzzy models were built for each of the three biocatalysts under study (CALB-IM-T2-350, CALB-SMMP-octyl and CALB-SMMP-octyl-glu), considering as input linguistic variables the type of acid, temperature, reaction time and substrate molar ratio to predict the conversion of the esterification process. Gaussian membership functions and linear output functions were used, in a Takagi- Sugeno’s fuzzy approach. The parameters were fitted by a hybrid parametric optimization method. The results showed that the fuzzy model outputs were very close to the targets, with RMSE values below 0.006. To demonstrate the potential of fuzzy modeling to optimize processes, response surfaces were built for the conversion of xylose as a function of different operating conditions. The fuzzy surfaces indicated that higher values of conversion are reached after 45h of reaction, at temperatures above 50°C and at RMS of 1:0.2 (acid:sugar). Thus, the present work explored, in a broad way, all the capability of mathematical modeling, under different approaches, in the study of enzymatic production of biosurfactants.