Traditional molecular evolution tracks allele frequencies in populations; CAS links this with molecular-level dynamics of RNA--protein complexes. Replicator--mutator equations, extended with ecological coupling, provide a means to simulate how coding rules and protein stability coevolve under selective pressures.
4. Bridging micro- and macro-evolution.
CAS situates molecular processes within a hierarchy: molecular interactions (codon stability, dipeptide motifs) organismal fitness (robustness under thermal stress) population trajectories. This multi-scale approach provides a mechanistic bridge between molecular evolution and larger evolutionary patterns such as punctuated equilibria or Red Queen cycles. In this integration, molecular evolution is not displaced but extended: CAS provides the mathematics to capture interdependent, co-adaptive processes that classical frameworks treat only descriptively. RNA--protein coevolution thus emerges not as a paradox but as a natural consequence of complex adaptive dynamics.
IV. Mathematical Framework
A. Genotype--phenotype mapping (RNA motifs protein domains)
A central challenge in modeling RNA--protein coevolution lies in formalizing the mapping between genotypes (nucleotide sequences and codon assignments) and phenotypes (protein structures and functional domains). Unlike simple one-to-one mappings, this relationship is characterized by nonlinearity, degeneracy, and interdependence. A CAS framework provides a way to capture these complexities.
1. Representation of genotypes.
RNA sequences are modeled as strings G=(g1,g2,...,gn)G = (g_1, g_2, ..., g_n)G=(g1,g2,...,gn), where each gig_igi is a codon drawn from the set of 64 possible triplets. Mutations act at the level of substitution, insertion, or deletion, generating a mutational neighborhood N(G)\mathcal{N}(G)N(G).
2. Representation of phenotypes.
Proteins are modeled as structured sequences of amino acids P=(p1,p2,...,pm)P = (p_1, p_2, ..., p_m)P=(p1,p2,...,pm), where pjp_jpj corresponds to codon translation via a genetic code mapping :gipj\phi: g_i \mapsto p_j:gipj. Phenotypic traits are extracted from sequence and structure, such as thermostability T(P)T(P)T(P), folding energy E(P)E(P)E(P), and domain functionality F(P)F(P)F(P).
3. Nonlinear mapping.
