Output: a set of evolved protein graphs, each representing a viable fold-function solution.
These graphs can then be reverse-engineered into amino acid sequences via graph-to-sequence translation models (e.g., GNN-informed transformers), bridging theoretical modeling with experimental design.
3.B. Representing Folding Pathways and Mutation Networks as Adaptive Topologies
To fully capture the dynamic behavior of enzyme evolution, we extend the graph-based modeling of residue interactions to encompass entire folding pathways and mutation-driven evolutionary networks. Within a Complex Adaptive Systems (CAS) framework, both processes are best understood as adaptive topologies---dynamic networks that co-evolve in response to internal perturbations and external selection pressures.
1. Folding Pathways as Temporal Topological Transitions
Protein folding is not a static transformation but a trajectory through conformational space, where the system traverses multiple intermediate states en route to a thermodynamically favorable native structure. These intermediate forms can be modeled as a sequence of temporally evolving graphs:
G0G1GnG_0 \rightarrow G_1 \rightarrow \dots \rightarrow G_n
Each graph GiG_i represents a partially folded structure, with:
Edges encoding transient interactions (e.g., hydrogen bonding, hydrophobic contacts),
Node features reflecting local entropy, side-chain accessibility, or conformational freedom,
Edge weights fluctuating over time based on free energy changes and kinetic constraints.
