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

The GTPase KRAS executes a conformational switch between a GTP-bound active state and a GDP-bound inactive state, a process central to oncogenic signaling. 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 $\overline{E}$ , 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 $\left(\Delta \overline{E}>0\right)$ that is offset by a marked gain in conformational entropy $\left(\Delta S>0\right)$ , with a free-energy crossover occurring at $\mathrm{kT}\approx 2.41\AA$ . 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.