Prebiotic Resource Constraints and the Origin of Life: A Linear Logic Framework

Abstract

The origin of life is a complex scientific problem demanding interdisciplinary approaches. We propose a Linear Logic (LL)-based computational framework to formally evaluate the feasibility of early biochemical pathways across competing abiogenesis scenarios. Unlike classical logic, LL explicitly tracks resource consumption and transformation. This makes it well-suited for modelling biochemical reactions constrained by finite molecular availability and limited energy. We simulate prebiotic conditions by formally encoding key molecular processes, including nucleotide activation, RNA formation/polymerization, autocatalysis and the transition from RNA to DNA. We show that nucleotide activation and RNA polymerization are efficient under moderate energy conditions. Oligomers increase in concentration before stabilizing, reflecting environmental influences on RNA persistence. Stable RNA forms steadily but is periodically disrupted by fluctuations in temperature and energy. Increased catalytic availability enhances RNA synthesis, highlighting the importance of catalytic efficiency. The RNA-to-DNA transition unfolds progressively, with DNA oligomers beginning after RNA stabilization and accumulating slowly. Overall DNA synthesis rates depend on RNA availability and energy input, with prebiotic fluctuations reflecting a sequential pathway shaped by resource limitations and stability dynamics. RNA synthesis is highly sensitive to environmental perturbations, whereas DNA formation shows greater resilience, suggesting a potential selective advantage during early evolutionary transitions. Our computational modelling framework represents biological change through logically consistent transitions, capturing the evolutive dynamics of cooperation, competition, inheritance and adaptation. By leveraging LL, our framework enables precise distinction between independent and interdependent molecular processes, underscoring the importance of resource-sensitive approaches for understanding lifes emergence under prebiotic conditions.