Modeling of the enzymatic kinetic synthesis of cephalexin--influence of substrate concentration and temperature

During enzymatic kinetic synthesis of cephalexin, an activated phenylglycine derivative (phenylglycine amide or phenylglycine methyl ester) is coupled to the nucleus 7-aminodeacetoxycephalosporanic acid (7-ADCA). Simultaneously, hydrolysis of phenylglycine amide and hydrolysis of cephalexin take place. This results in a temporary high-product concentration that is subsequently consumed by the enzyme. To optimize productivity, it is necessary to develop models that predict the course of the reaction. Such models are known from literature but these are only applicable for a limited range of experimental conditions. In this article a model is presented that is valid for a wide range of substrate concentrations (0-490 mM for phenylglycine amide and 0-300 mM for 7-ADCA) and temperatures (273-298 K). The model was built in a systematic way with parameters that were, for an important part, calculated from independent experiments. With the constants used in the model not only the synthesis reaction but also phenylglycine amide hydrolysis and cephalexin hydrolysis could be described accurately. In contrast to the models described in literature, only a limited number (five) of constants was required to describe the reaction at a certain temperature. For the temperature dependency of the constants, the Arrhenius equation was applied, with the constants at 293 K as references. Again, independent experiments were used, which resulted in a model with high statistic reliability for the entire temperature range. Low temperatures were found beneficial for the process because more cephalexin and less phenylglycine is formed. The model was used to optimize the reaction conditions using criteria such as the yield on 7-ADCA or on activated phenylglycine. Depending on the weight of the criteria, either a high initial phenylglycine amide concentration (yield on 7-ADCA) or a high initial 7-ADCA concentration (yield on phenylglycine amide) is beneficial.