Evolutionary Codes as Complex Adaptive Systems: A Mathematical Framework for RNA--Protein Coevolution
Abstract
The long-standing debate over whether RNA or proteins emerged first has often been framed as a linear sequence of evolutionary innovations. Recent studies, such as the analysis of dipeptide motifs and thermostability in proteomes, suggest that the genetic code and proteins coevolved in a mutually dependent manner. Yet these findings remain largely descriptive and lack a unifying formalism. Here we introduce a Complex Adaptive Systems (CAS) mathematical framework to model the simultaneous coevolution of genetic codes and protein structures. By coupling replicator--mutator dynamics, genotype--phenotype mappings, and fitness functions with interdependent RNA--protein interactions, we demonstrate that stable co-adapted complexes arise naturally as emergent attractors, rather than as linear sequences of innovations. Analytical results reveal conditions for stability and bifurcation, while simulations highlight synchronization, Red Queen-like cycles, and co-selection patterns. This framework provides testable predictions for comparative genomics and experimental directed evolution, reframing the origin of molecular codes as a problem of self-organizing complexity.
Highlights
CAS model formalizes RNA--protein coevolution as feedback-driven dynamics
Bifurcation analysis reveals collapse, Red Queen cycles, and stable attractors
Simulations align with proteomic dipeptide correlations and thermostability data
Reframes RNA-world vs protein-first as synchronization, not linear precedence
Provides scalable theory linking molecular, ecological, and systems evolution
Background
The origin of the genetic code and its relationship to protein evolution remains one of the most enduring puzzles in molecular biology. Competing hypotheses---such as the RNA World, Protein World, and coevolution models---attempt to explain how informational molecules and catalytic structures emerged.
