Transitions between graphs can be interpreted as micro-state bifurcations, where slight variations in environmental conditions or sequence mutations lead to drastically different folding routes---mirroring the sensitivity to initial conditions characteristic of CAS.
To simulate folding trajectories:
We employ graph morphing algorithms guided by energy minimization,
Use probabilistic rewiring rules to account for stochasticity in molecular dynamics,
Quantify stability using graph entropy and network resilience measures.
This allows folding to be modeled not as a single deterministic path, but as a probability-weighted ensemble of topological evolutions, consistent with the ruggedness of protein energy landscapes.
2. Mutation Networks as Evolutionary Graphs
Mutation processes---whether random, induced, or directed---can be naturally represented as mutation networks, where:
Nodes denote sequence variants or folding graphs,
Edges represent single or multiple mutations,
Transition probabilities are assigned based on empirical mutation rates, codon biases, or thermodynamic feasibility.
