Rate equations for two enzyme-catalyzed Ping Pong bi bi reactions in series: General formulation for two reaction loops joined by a common vertex and deduction of a reaction loop selectivity factor

Interest is increasing in the application of lipases to catalyze sequential hydrolysis or transesterification reactions with diacids. In such systems, there are two Ping Pong bi bi reaction loops, with the free enzyme being the only enzyme form that is common to both loops. The modeling of such systems has not received much attention to date. The current work derives an expression for a reaction loop selectivity factor, denominated L, which is given by the ratio of the specificity constant of the enzyme for the first substrate of the second loop to the specificity constant for the first substrate of the first loop. The value of L is determined for two case studies using literature data. For the hydrolysis of diethyl adipate by Rhizopus arrhizus lipase, L is equal to 0.062, indicating that the specificity of this lipase for hydrolyzing diethyl adipate is much higher than that for hydrolyzing monoethyl adipate. For the CALB-catalyzed transesterification of diethyl azelate with 2-ethylhexan-1-ol, producing ethyl 2-ethylhexyl azelate as an intermediate and bis (2-ethylhexyl) azelate as the final product, L is 0.37, meaning that CALB prefers to transesterify diethyl azelate, rather than the intermediate ethyl 2-ethylhexyl azelate.