Generalizing the Gaussian Network Model: Spanning-Tree Thermodynamics Shows Entropy-Driven KRAS Activation

Abstract The GTPase KRAS executes a conformational switch between a GTP-bound active state and a GDP-bound inactive state, a process central to oncogenic signalling. However, the structural basis of this switching at the level of residue-contact organization remains incompletely characterized by traditional binary structural models. Here, we present a statistical-mechanical generalization of the Gaussian Network Model (GNM) by constructing spanning-tree partition functions for residue-contact graphs using the weighted Kirchhoff Laplacian in conjunction with the Matrix-Tree Theorem. Within this framework, the standard GNM is recovered in the high-temperature limit, whereas the present formulation enables a continuous Boltzmann-weighted ensemble analysis. We compute the network free energy F , mean contact energy Ē , heat capacity C v , and thermodynamic entropy S across an effective temperature sweep that maps the combinatorial diversity of the contact network, thereby probing the topological landscape rather than structural melting. Differential analysis reveals that KRAS activation reflects a systematic entropy-enthalpy compensation mechanism: the active state incurs a systematic energetic penalty (Δ Ē > 0) that is offset by a marked gain in conformational entropy (Δ S > 0), with a free-energy crossover occurring at kT ≈ 2.41 Å. Edge marginal inclusion probabilities, obtained via effective-resistance theory, identify Switch I (residues 25-40) as the primary allosteric locus of nucleotide-driven network reorganization. This approach provides a thermodynamically grounded perspective on KRAS allostery, quantitatively demonstrating how network architecture enables functional versatility through entropy-driven conformational flexibility. Entropy-driven KRAS activation revealed by spanning-tree thermodynamics Spanning-tree partition functions built from weighted residue-contact graphs show that KRAS activation involves entropy-enthalpy compensation. The GDP-bound network (left) is dominated by a small number of low-energy spanning trees, whereas the GTP-bound network (right) accesses a larger ensemble with greater topological diversity. The active state pays an energetic cost (Δ Ē > 0) offset by a conformational entropy gain (Δ S > 0), with Switch I (residues 25-40, dashed box) emerging as the primary site of nucleotide-driven network reorganisation.