Flexibility Drives Information Flow in Proteins: Fluctuation Potential Gradients Dictate Directional Entropy Transfer

Allosteric communication in biomacromolecules is fundamentally governed by thermal fluctuation gradients, yet standard Gaussian Network Models (GNMs) treat atomic contacts as uniform, binary couplings without differentiating core constraints from solvent-exposed surface flexibility. Here, we present an analytical matrix framework that incorporates continuous distance-dependent weighting into the Kirchhoff matrix L. This formulation captures the steep steric constraints of hydrophobic core packing versus peripheral surface loops while strictly recovering the classic unweighted GNM as a high-temperature limit (T [->]{infty}). Using Schur complements of partitioned joint covariance matrices, we show that conditional fluctuation variances and higher-order entropy-transfer terms reduce analytically to exact ratios of submatrix determinants (covariance minors), eliminating the need for fitting parameters or molecular dynamics trajectories. Applied to KRAS (PDB: 6GOD), this framework constructs an integrated directional entropy-transfer asymmetry map. Order-1 minors (h(i) = Kii) establish a single-node fluctuation potential gradient, while order-2 minors (Rij) define pairwise channel bandwidths. Higher-order minors show multi-body spatial coupling: order-4 minors identify rigid core residues such as Phe156 as strategic interlobe relay hubs linking Lobe 1 and Lobe 2, and an order-3 triad cooperation index demonstrates that signal transmission from Switch II (Gln61) to Gly60 and Phe156 converges on a single, mechanically integrated allosteric sector. By deriving directional information flow directly from experimental atomic displacement parameters, this approach establishes a rigorous, computationally efficient framework for mapping allosteric networks across structural ensembles.