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 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 , mean contact energy , heat capacity , and thermodynamic entropy 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 that is offset by a marked gain in conformational entropy , with a free‐energy crossover occurring at . 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.