Assembly of heteropolymers via a network of reaction coordinates

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.