Intrinsic noise suppression in protein allostery: Quantifying pathway redundancy via spanning tree statistics

Allosteric regulation in proteins arises from collective dynamics distributed over networks of residue contacts, but how multiple communication pathways contribute to signal transmission and noise suppression remains unclear. Here we develop a spanning-tree-based framework to quantify allosteric communication as an ensemble of pathways in protein contact networks. We introduce a dynamic distance measure linking local perturbations of residue interactions to global changes in network entropy, establishing a local-to-global scaling between local dynamics and global sensitivity. Using spanning-tree calculus, we derive exact probabilities for all simple paths connecting prespecified functional residue pairs. This enables a comparison between an approximate description based on uniform path usage and a topology-aware description in which path probabilities are determined by the Burton-Pemantle theorem and reflect network dependencies. From these path ensembles, we define corresponding signal-to-noise ratios and quantify how pathway multiplicity and statistical weighting shape noise suppression. Applied to KRAS and to 20 additional allosteric proteins spanning diverse functional classes, the analysis shows large variability in path usage, entropy reduction, and signal-to-noise enhancement, while consistently demonstrating that topology-aware weighting concentrates signal transmission onto dominant short pathways. This suggests that the robustness of allosteric signaling is a fundamental emergent property of protein contact topology. The spanning tree ensemble constitutes a distinct physical model whose partition function is the matrix tree theorem; the Gaussian network model is recovered as its high temperature limit. These results provide a quantitative framework linking protein structure, dynamics, and information flow, and show that robustness in allosteric communication, manifested as noise suppression through pathway redundancy, can be interpreted as an intrinsic noise averaging mechanism arising from network topology.