Detecting the Information Flow in Proteins by Hodge Decomposition

Allosteric communication in proteins is commonly quantified as a directed or undirected coupling between residues, but such descriptors mix distinct modes of signalling into a single pattern. Here we treat the net transfer entropy flux from a dynamic Gaussian network(dGNM) model as an edge flow on the residue contact graph and apply the combinatorial Hodge decomposition, which dissects the flow orthogonally into a gradient (global source-to-sink hierarchy), a curl (local three-clique circulation) and a harmonic (cavity-scale circulation) component. Applied to the wild-type KRAS and ten oncogenic KRAS variants spanning the principal GTPase-cycle mechanism classes, partial-hydrolysis position-12 (G12D, G12C, G12S), GAP-occluding position-12 (G12V, G12R), catalytic switch II (Q61R, Q61H), fast-cycling (G13D, A146T) and a combined steric and catalytic double mutant (G12D/Q61H), on a side-chain-centroid contact network, the decomposition shows that the transfer entropy flux is overwhelmingly hierarchical: the gradient term carries 97.5-98.4% of the flux in every variant (permutation p = 0.002), and the recovered scalar potential is strongly anti-correlated with each residues net outgoing transfer entropy (Spearman {rho} {approx} -0.92 to -0.95). The hierarchy is conserved in magnitude but relocated by mutations: the dominant information sources move from the C-terminal 5/hypervariable region in wild type into the nucleotide-processing core, the switch I/II machinery and the 4/distal lobe in a way that tracks the GTPase-cycle mechanism of the substitution, while the sinks remain fixed. The method provides a parameter-free, residue-level readout of how mutations of different mechanism reposition the source of allosteric signalling in KRAS.