Optimal size for emergence of self-replicating polymer system

TL;DR

This paper investigates the stochastic dynamics of autocatalytic polymerization, identifying an optimal volume that minimizes the transition time to a self-sustaining catalytic state, with implications for understanding the origin of life.

Contribution

It introduces a theoretical analysis of the transition dynamics in autocatalytic polymer systems and identifies an optimal volume for emergence, advancing understanding of prebiotic chemistry.

Findings

Identified an optimal volume minimizing transition time

Found the optimal volume relates inversely to catalyst concentration at an unstable fixed point

Discussed implications for the origin of life

Abstract

A biological system consists of a variety of polymers that are synthesized from monomers, by catalysis that exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization. We analyze here the stochastic polymerization reaction dynamics, to investigate the transition time from a state with almost no catalysts to a state with sufficient catalysts. We found an optimal volume that minimizes this transition time, which agrees with the inverse of the catalyst concentration at the unstable fixed point that separates the two states, as is theoretically explained. Relevance to the origin of life is also discussed.