Stochastic Mechanochemical Description of a Bioinspired Polymerization Process

Abstract

We present a theoretical investigation of a polymerization process catalyzed by an enzyme. A structural model of enzyme, sliding along the polymer chain as a Brownian particle, is proposed, and a stochastic approach is employed to describe the kinetics of the whole process. The key point of this work is the coupling mechanics/chemistry obtained by assuming that (1) some rates of chemical reaction depend on the position of the enzyme with respect to the polymer chain and (2) the potential energy and the friction coefficient in the Langevin equation depend on the chemical state of the polymerizing complex. We describe an algorithm for computing our stochastic model and a methodology to solve the Langevin equation numerically. We predict in particular: (1) the sudden arrest of the polymerization, (2) the decrease in the relative polydispersity with the increase in the length of the polymer chain, (3) the occurrence of four regimes, (4) the manifestation of the coupling mechanics/chemistry for one regime and (5) the possibility to evaluate the mechanical variables through classical chemical analysis. Although essentially devoted to the elongation phase, this work also briefly addresses the problem of phase termination and we propose a new device aimed at reducing the polydispersity of technical origin in actual polymerization processes.

Keywords: Catalysis; Langevin equation; Molecular motor; Polymerization; Stochastic mechanochemistry.