Steady states of an enzymatic membrane reactor with product retention for a system of non-cooperating enzymes — model predictions

The aim of this study was to explore the structure of steady state of an enzymatic membrane reactor for a system of two non-cooperating enzymes. Both enzymes show activity towards the substrate of a reaction producing weak acid. The enzymes differ in their activity profile with respect to pH of reaction medium. The influence of catalytic properties of the enzymes, inhibition of enzymatic activity by substrate, retention of reagents, and pK of a product on the reactor performance was investigated. The structure of steady state was presented in bifurcation diagrams X = f(F) and sections of catastrophic sets on a plane (F, pK). The results of the analysis proved that the difference of pHopt of enzymes (δ) is one of the decisive factors influencing on the static behaviour of the reactor. For all investigated cases, a threshold value of the δ parameter was found. The structure of steady state below and above a threshold point differs substantially. The steady states of multiplicities from one to seven are allowed for a system with the uncompetitive inhibition by substrate. The calculations have been performed with the use of a mathematical model of the reactor.