The Geometry of Allostery: Quantifying Pathway Organization in Protein Networks

Abstract

Supporting material for the manuscript The Geometry of Allostery: Quantifying Pathway Organization in Protein Networks (Fatma Şengüler Çiftçi and Burak Erman, Koç University). The paper works out what happens when you take Laplacian minors of a protein contact network past the pairwise level. The first minor counts spanning trees, the second gives the usual effective distance, and the third and fourth pick up three- and four-residue path correlations that pairwise metrics cannot see. Bound ligands are folded in exactly with a Schur complement rather than being truncated away. We ran this on the eight PSD95-PDZ3 structures from Raman et al. and found that residue 332 acts as the pivot through which the G330T and H372A mutations rewire the domain. Three files here: The audio file is a 45-minute spoken walkthrough of the paper. The appendices contain the derivations that were too long for the main text: the inner product space behind the effective distances, the law-of-cosines expression for the three-body overlap, the general m-th order case with its [0,1] range proof, and how all of it maps onto elastic network fluctuations. Supplementary Note S1 checks whether the effective-resistance profile survives structural uncertainty. We recomputed it across 25 AlphaFold 3 predictions of 5HED; the ensemble is tight and tracks the experimental profile closely. Code: https://github.com/fatmasenguler/laplacian-minor-hierarchy