Fiedler Inversion Score (FIS): A Calpha-only Geometric Metric for Classifying Protein Conformational Transitions

We introduce FIS (Fiedler Inversion Score), a parameter-free metric derived solely from Calpha coordinates for classifying protein conformational transitions. By computing Graph Laplacian Fiedler vectors for open and closed protein states, FIS = -cos(theta) between the two Fiedler vectors captures domain topology reorganization. Validated on 25 protein pairs across 12 functional classes (mean |FIS| = 0.8005, permutation p less than 0.0001). Three mechanistically distinct types are identified: Type I Domain Inversion (n=8, 32%), Type II Rigidity Change (n=2, 8%), and Type III Internal Strain (n=12, 48%). Key discovery: EGFR T790M drug resistance is classified as Type II rigidity mutation (lambda2 ratio=4.4x, FIS~0), not a topology change, providing a new geometric explanation for clinical resistance. FIS runs in less than 1 second per pair and is applicable to AlphaFold structures.