Studies on the lipolytic enzyme action: IV. Example of mathematical treatment of an enzymatic process consisting of consecutive reactions

Abstract

The kinetics od the hydrolisis of tripropionyl glycerol by liver esterase—a reaction which according to previously published inverstigations proceeds via I,2-dipropionyl and 2-monopropionyl glycerol—have been made the subject of a closer examination. 1. 1. the experimental findings justify the assumption that the transformation in each of the reactions tripropiionyl glycerol to I,2-dipropionyl glycerol + propionic acid, I,2-dipropionyl glycerol to 2-monopropionyl glycerol + propionic acid and 2-monopropionyl glycerol to glycerol and propionic acid is explained by a reaction scheme which is a closed sequence consisting of two partial reactions. On the basis of experiments in which the initial substrate concentration is varied the following k-values are calculated for one and the same enzyme concentration ( E = 1): k 1 = 0.0718 min −1mmol −1 k −1 = 0.01455 in −1mmol −1, k 2 = 0.1772 min −1, k 3 = 0.004056 min −1mmol −1, k −3 = 0.002245 min −1mmol −1, k 4 = 0.02146 min −1, k 5 = 0.000286 min −mmol −1, k 6 = 0.1167 in −1. 2. 2. A conceivable reaction scheme is putforward for the complete hydrolysis of tripropionyl glycerol by liver esterase, cf. p. 81. One and the same enzyme is supposed to catalyze the degrdation of tripropionyl glycerol and the intermediate glycerides. Each of the three consecutive reactions is assumed to consist of two partial reactions which are in a stationary state. On the assumption that k −1/ k 2 = k −3 = k −5/ k 6 or that the ratios are of the same order of magnitude equations are derived which using log 10 a a−x as a parameter are able to render the experimental data quite satisfactorily. 3. 3. The mathematical treatment of the kinetic problem investigated may be of interest in connection with other enzymatic consecutive reactions.