1. Level of Interaction (L)
This variable captures the scale and complexity of node interactions, corresponding to amino acid residues, structural domains, or mutation sites. Interaction levels are categorized as:
Level 2 (pairwise residue interactions), Level 3 (triplet configurations such as beta-turns or triads), and Level 4+ (domain-wide or network-level interactions).
In evolutionary terms, higher-order interactions often account for epistasis and allosteric regulation, both critical for emergent functions such as substrate specificity or thermostability. CAS modeling treats these levels as dynamically adaptive: mutations can shift interactions from local to global regimes.
2. Pattern of Interaction (P)
Interactions between protein elements can be structured as: Combinatorial, where any subset of residues may influence the system function independently, Permutational, where ordering and directionality matter (e.g., N-terminal to C-terminal folding paths).
This distinction is essential in modeling folding kinetics, where path dependence leads to kinetic traps or alternative stable configurations. CAS frameworks formalize these patterns through directed graphs or tensors, enabling simulation of evolutionary trajectories that preserve function under structural reordering.
3. Probabilistic Affinity (Pr)
Each interaction is assigned a probability distribution reflecting its likelihood under given environmental or mutational contexts. These probabilities can be derived from:
Thermodynamic potentials (e.g., G of binding or folding), Evolutionary frequency matrices (e.g., BLOSUM, PAM), Machine learning-derived likelihoods from historical sequence databases.
In CAS, this probabilistic modeling acknowledges the non-determinism inherent in evolution while enabling predictive capacity through statistical constraints and boundary conditions.
