Onset of autocatalysis of information-coding polymers

TL;DR

This paper presents a theoretical and numerical analysis of how autocatalysis can spontaneously emerge in information-coding polymers, revealing a phase transition and conditions for heritable information transmission.

Contribution

It introduces a simple, tractable model predicting autocatalysis onset and chain length distribution, highlighting the emergence of heritable information in polymer systems.

Findings

Existence of a first order transition between free monomers and self-sustaining chains

Prediction of chain length distribution based on monomer concentration and rate constants

Emergence of an optimal overlap length enabling heritable information transmission

Abstract

Self-replicating systems based on information-coding polymers are of crucial importance in biology. They also recently emerged as a paradigm in material design on nano- and micro-scales. We present a general theoretical and numerical analysis of the problem of spontaneous emergence of autocatalysis for heteropolymers capable of template-assisted ligation driven by cyclic changes in the environment. Our central result is the existence of the first order transition between the regime dominated by free monomers and that with a self-sustaining population of sufficiently long chains. We provide a simple, mathematically tractable model supported by numerical simulations, which predicts the distribution of chain lengths and the onset of autocatalysis in terms of the overall monomer concentration and two fundamental rate constants. Another key result of our study is the emergence of the kinetically-limited optimal overlap length between a template and each of its two substrates. The template-assisted ligation allows for heritable transmission of the information encoded in chain sequences thus opening up the possibility of long-term memory and evolvability in such systems.