Non-Markovian polymer reaction kinetics

TL;DR

This paper introduces an analytical method to accurately calculate the reaction times of polymer reactions considering their non-Markovian dynamics, revealing that reactive conformations are more extended and lead to faster reactions than classical models predict.

Contribution

The paper presents the first exact analytical approach for transport-limited polymer reaction kinetics that accounts for non-Markovian chain dynamics.

Findings

Reactive conformations are more extended than equilibrium states.

Reaction times are significantly shorter than classical Markovian predictions.

Provides new insights into the reaction path and conformational statistics.

Abstract

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.