Elastic-network analysis of any structure.
Drop in a PDB and the browser builds the Anisotropic Network Model, diagonalises the Hessian, and returns the slowest collective modes, a dynamic cross-correlation matrix, a steered-response field, and betweenness scores — all client-side, nothing uploaded.
The lowest non-trivial eigenmodes of the Hessian describe the collective, low-frequency motions of the protein — the directions in which the structure is softest. In well-studied enzymes these often correspond to functional motions: domain hinging, loop gating, flap opening. Mode 1 is typically the largest-amplitude, most collective motion.
A normalised entropy measure (Brüschweiler 1995) of how many residues participate in a mode. Values near 1 describe delocalised, global motions (usually the slowest). Values near 0 describe localised flapping of a small region.
Cij = ⟨Δri·Δrj⟩ / √(⟨Δri²⟩⟨Δrj²⟩), summed over all positive modes. Gold regions are pairs moving together (rigid bodies or tightly coupled substructures); terra regions move in opposite directions (hinges).
Residues with high BC sit on many shortest paths through the dynamically weighted contact graph. They are the wiring of the protein — hubs through which mechanical perturbations must pass. Cross-reference with the catalytic residues: a residue far from the active site with high BC is a candidate allosteric site or cryptic target.
The implementation follows Atilgan et al. 2001 (Biophys J 80:505) for the ANM Hessian construction, Brüschweiler 1995 (J Chem Phys 102:3396) for mode collectivity, and Brandes 2001 (J Math Sociol 25:163) for weighted-graph betweenness. The steered response uses the pseudo-inverse of the Hessian projected onto non-trivial modes; the dynamic pathway is Dijkstra with edge weights 1/(ε + |Cij|) over contact neighbours. Hessian construction is O(N²), eigendecomposition O(N³).
For structures larger than ~1200 residues or systems needing explicit solvent dynamics, use a dedicated MD package (OpenMM, GROMACS, NAMD). This workbench is designed for rapid, interactive, hypothesis-generating analysis — not production-quality MD.