Predicting template-based catalysis rates in a simple catalytic reaction model

TL;DR

This paper establishes a mathematical link between two versions of a catalytic reaction model, enabling prediction of catalysis levels and autocatalytic set emergence, which advances understanding in origin-of-life research.

Contribution

It derives an analytical method to predict catalysis requirements across different model variants, connecting random and template-based catalysis models in origin-of-life studies.

Findings

Derived an analytical calculation linking the two models

Predicted catalysis levels for autocatalytic set emergence

Established invariance between model versions

Abstract

We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical invariance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular, we derive an analytical calculation that allows us to accurately predict the (observed) required level of catalysis in one version of the model from that in the other version, for a given probability of having self-sustaining autocatalytic sets exist in instances of both model versions. This provides a tractable connection between two models that have been investigated in theoretical origin-of-life studies.