Constraint Network Analysis of Global and Local Rigidity in Wild-Type EGFR: Apo vs Gefitinib-Bound States

The mechanical rigidity-flexibility architecture of protein kinases play a critical role in regulating conformational stability and inhibitor response, yet remains insufficiently quantified for Epidermal Growth Factor Receptor (EGFR). Here, we apply Constraint Network Analysis (CNA) to systematically characterize the global and local mechanical properties of wild-type EGFR in its apo state and when bound to the ATP-competitive inhibitor gefitinib. Analysis of multiple global rigidity indices reveal a well-defined rigidity percolation transition in apo EGFR at an energy cutoff of approximately -2.0 kcal mol-1, indicative of an intrinsically stable mechanical framework. Gefitinib binding shifts this transition slightly to higher energies and sharpens the percolation behavior, accompanied by enhanced long-range mechanical coupling, increased rigidity order parameters, and reduced configurational entropy. Importantly, residue-level rigidity and percolation profiles remain largely conserved between the two states, demonstrating that ligand binding does not induce large-scale reorganization of the EGFR mechanical network. Instead, inhibition arises from subtle, localized rigidification within functionally relevant regions, consistent with stabilization of an inactive conformational ensemble. Collectively, this work establishes the first CNA-based mechanical reference state for wild-type EGFR and underscores the utility of network rigidity analysis for resolving ligand-induced effects that are structurally subtle yet mechanistically significant. This framework provides a quantitative baseline for future studies of oncogenic mutations and drug-resistant EGFR variants.