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

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