Chain length distribution and kinetic characteristics of an enzymatically produced polymer

Abstract

Abstract Non-processive enzymatic polymerization leads to a distribution of polymer chain lengths. A polymerization model was developed to investigate the relation between the extent of this distribution on one hand, and the polymerization start conditions and reaction kinetics on the other hand. The model describes changes in concentration of chains of length n as the result of two elongation reactions: elongation by monomer addition to length n-1 and elongation by monomer addition to length n. Polymerization reactions were assumed to be zero order in monomer concentration and to obey Michaelis-Menten kinetics with respect to polymer concentrations. In addition, the amount of enzyme available for each individual reaction (n → n+1) is assumed to be proportional to the concentration of polymer substrate of length n. The development of the shape of the chain length distribution was found to be independent of the value of the overall reaction rate constant; only the rate at which these shapes developed was influenced by the 1st-order rate constant. The value of the Michaelis parameter did affect the form of the chain length distribution curve since it affects the reaction order. An increase in reaction order was found to promote widening of the chain length distribution. Differences in kinetic parameters between the subsequent polymerization reactions, if any, were also found to have a large effect on the development of the chain length distribution. An increase in rate constants with chain length entailed a wider distribution; a more narrow distribution would require a decrease in rate constants with chain length.