A methodology, Excel Solver tool based, to determine the kinetic parameters of enzymatic ping-pong reactions: application to an esterification reaction

Abstract

In this work, a new methodology to calculate the kinetic parameters of enzymatic reactions has been developed. The methodology has been applied to esterification in solvent free conditions, in which the kinetics follow a bisubstrate ping-pong mechanism: the synthesis of laurate of 2-hexyl-1-decanol, a biolubricant additive, in a batch reactor, in the presence of immobilized Novozym® 435 lipase. As an alternative to the traditional differential methods, based on the use of initial reaction rate data, this methodology is based on the integral analysis to solve the reactor model once it has been developed, so that an explicit expression for the reaction time as a function of the substrate conversion can be obtained. Adding this function to the Excel Solver tool and by minimizing the sum of the square differences between the experimental and calculated values of the reaction time, the kinetic parameters have been determined. After using these parameters and the model equation, theoretical values of conversion have been calculated by means of the bisection method implemented in VBA language and compared with the experimental ones. High values of determination coefficients were obtained, which validated both the procedure of parameter determination and the reactor model. In addition, optimal reaction conditions were determined, and it was confirmed that the catalyst could be reused several times without significant variation in its activity.