Bridging protein rigidity theory and normal modes using kino‐geometric analysis with hierarchical constraint relaxation

Abstract

AbstractElastic‐Network Models (ENM) and pebble game based rigidity analysis are two distinct coarse‐grained approaches that have provided tremendous insight into conformational flexibility of proteins. However, the topological nature of the pebble game, and thereby the absence of motion modes have limited its applicability and a detailed comparison to ENM. Here, we present an alternative approach to rigidity analysis which eliminates these drawbacks through detailed kinematic analysis of dihedral degrees of freedom and non‐covalent hydrogen bond constraints, collected in the constraint Jacobian matrix J. Our new procedure reveals a spatial hierarchy of protein motions intrinsic to the hydrogen bonding network, ranked by the singular values of J. This spectrum of J yields a striking, fold‐specific signature, differentiating stiffer α‐helical from more collective β‐sheet proteins, which often goes undetected in similarly coarse‐grained methods. Overall, our results agree with experimental data and more detailed simulations, indicating that hydrogen bond networks have evolved with different protein folds to modulate structural dynamics and molecular mechanisms, with broad implications for protein and drug design.