Kinetics and thermodynamics of first-order Markov chain copolymerization

TL;DR

This paper presents an exact theoretical analysis of the kinetics and thermodynamics of first-order Markov chain copolymerization and depolymerization, linking growth dynamics with entropy production and sequence disorder.

Contribution

It provides exact solutions for kinetic equations, identifies equilibrium conditions, and derives entropy production expressions for Markov chain copolymerization processes.

Findings

Exact solutions for steady-state kinetic equations.

Thermodynamic equilibrium characterized by zero growth velocity and detailed balance.

Analytical expression for entropy production in terms of sequence disorder.

Abstract

We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.