The Gaussian network model as a framework for allosteric analysis: dynamic distance, edge centrality, and entropy...

Allosteric communication in proteins relies on network connectivity patterns that channel conformational signals between distant sites. We introduce a unified mathematical framework based on three complementary measures of network organization derived from a single quantity. The first, the dynamic distanceRij, quantifies the mean-squared relative fluctuation between residue pairs. From this foundation, we derive two further metrics: the edge centrality, which identifies contacts critical for global connectivity by measuring their recurrence across all possible communication pathways, and the entropy sensitivity, which quantifies how perturbations to specific interactions alter system-wide flexibility. The mathematical structure shows that both topological centrality and thermodynamic sensitivity are linear functions of the dynamic distance. This derived unification demonstrates that residue pairs with high dynamic dissimilarity simultaneously function as flexible bottlenecks essential for allosteric communication. Applied to the oncoprotein KRAS, all three measures converge to identify the same residue pairs, corresponding to experimentally known allosteric sites. This convergence provides a unified graph-theoretical explanation for their functional importance. Analysis of the G12D and Q61H mutations and adagrasib binding shows how local perturbations rewire global communication pathways, highlighting specific residue pairs that gain or lose importance as network bottlenecks.