Abstract
Most theoretical work on the origin of heredity has focused on how genetic information can be maintained without mutational degradation in the absence of error-proofing systems. A simple and parsimonious solution assumes the first gene sequences evolved inside dividing protocells, which enables selection for functional sets. But this model of information maintenance does not consider how protocells acquired their genetic information in the first place. Clues to this transition are suggested by patterns in the genetic code, which indicate a strong link to autotrophic metabolism, with early translation based on direct physical interactions between amino acids and short RNA polymers, grounded in their hydrophobicity. Here, we develop a mathematical model to investigate how random RNA polymers inside autotrophically growing protocells could evolve better coding sequences for discrete functions. The model tracks a population of protocells that evolve towards two essential functions: CO2 fixation (which drives monomer synthesis and cell growth) and copying (which amplifies replication and translation of sequences inside protocells). The model shows that distinct coding sequences can emerge from random RNA sequences driving increased protocell division. The analysis reveals an important restriction: growth-supporting functions such as CO2 fixation must be more easily attained than informational processes such as RNA copying and translation. This uncovers a fundamental constraint on the emergence of genetic heredity: growth precedes information at the origin of life.