A Universal Method for Analysing Copolymer Growth

TL;DR

This paper introduces a universal analytical method for studying copolymer growth processes, enabling analysis of complex, non-equilibrium, and reversible models without simulation, and deriving thermodynamic, kinetic, and statistical properties.

Contribution

The paper presents a novel, general analytical approach for analyzing complex copolymerization models, including non-equilibrium and reversible processes, without relying on simulation.

Findings

Able to analyze models with arbitrary sub-step networks

Can incorporate dependencies on neighboring sites

Derives thermodynamic, kinetic, and statistical quantities

Abstract

Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in which monomers are added or removed from the growing tip of a long copolymer. To date, the analysis of the most general models of this class has necessitated simulation. We present a general method for analysing such processes without resorting to simulation. Our method can be applied to models with an arbitrary network of sub-steps prior to addition or removal of a monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the approach allows for a dependency of addition and removal reactions on the neighbouring site in the copolymer, and thermodynamically self-consistent models in which all steps are assumed to be microscopically reversible. Using our approach, thermodynamic quantities such as chemical work; kinetic quantities such as time taken to grow; and statistical quantities such as the distribution of monomer types in the growing copolymer can be derived either analytically or numerically directly from the model definition.