Growth and dissolution of macromolecular Markov chains

TL;DR

This paper analyzes the kinetics and thermodynamics of copolymerization processes where the sequence forms a kth-order Markov chain, providing analytical expressions for growth velocity, entropy production, and sequence disorder in steady growth and depolymerization regimes.

Contribution

It introduces a comprehensive analytical framework for understanding the sequence statistics and thermodynamics of kth-order Markov chain copolymerization and depolymerization processes.

Findings

Mean growth velocity and entropy production are derived analytically.

Entropy production in depolymerization satisfies Landauer's principle.

Sequence disorder is quantitatively characterized in different regimes.

Abstract

The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.