# Assembly of heteropolymers via a network of reaction coordinates

## TL;DR

This paper introduces a novel theoretical framework for modeling heteropolymer assembly using a continuous reaction coordinate, enabling estimation of error rates and speeds from the Gibbs free energy landscape, including complex error correction mechanisms.

## Contribution

It presents a new approach applying reaction rate theory to heteropolymer assembly, capturing non-equilibrium dynamics and error correction in a unified continuous model.

## Key findings

- The model estimates incorporation speed and error rates from free energy landscapes.
- Application to simple and complex systems demonstrates versatility.
- Incorporates error correction mechanisms like kinetic proofreading.

## Abstract

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate meta-stable states. In this paper, we use ideas from reaction rate theory and describe non-equilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows to estimate the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples, from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms such as kinetic proofreading.