Elastic Network Model - Modes + Flexible Fitting

What it is

Elastic Network Model (ANM) normal-mode analysis and iMODFIT-style normal-mode-biased flexible fitting for protein flexibility and cryo-EM-style morphing. Treats a protein as one bead per residue (Ca) joined by identical springs within a cutoff, builds the 3N x 3N Anisotropic Network Model Hessian (Atilgan 2001 / Tirion 1996), diagonalises it (cyclic Jacobi - the same modal eigen-primitive as the seismic plugin), and reports the low-frequency collective modes (hinge / domain motions), the per-residue mobility / theoretical B-factor profile, and each mode collectivity. Flexible fitting then morphs an initial model toward a target the way iMODFIT does (Lopez-Blanco & Chacon, J. Struct. Biol. 2013): a Monte-Carlo search in normal-mode space that picks low-frequency modes (biased toward lower-frequency, higher-amplitude ones), deforms, and accepts on an improved score - staying in the smooth low-frequency subspace so it avoids the heavy distortions of unrestrained fitting. A built-in synthetic two-lobe structure (with a known hinge motion) validates the method: the fit recovers a deformation of known size. Honest scope: Cartesian ANM (not iMod internal-coordinate NMA), fitting to a target conformation / simulated density (not a real cryo-EM MRC map), larger proteins via a deflated Lanczos low-mode solver (validated to match Jacobi), sub-second on CPU at N~500 so no GPU is needed. Deterministic, in-browser, no AI / network / key; GeoNum trust on the eigensolve conditioning.

Honest scope

Authorities cited

• Lopez-Blanco, J.R.; Chacon, P. "iMODFIT: efficient and robust flexible fitting based on vibrational analysis in internal coordinates." J. Struct. Biol. 2013, 184(2), 261-270. doi:10.1016/j.jsb.2013.08.010. The normal-mode-biased Monte-Carlo flexible-fitting method this plugin reproduces (Cartesian-ANM analog of its internal-coordinate NMA).
• Lopez-Blanco, J.R.; Garzon, J.I.; Chacon, P. "iMod: multipurpose normal mode analysis in internal coordinates." Bioinformatics 2011, 27(20), 2843-2850. doi:10.1093/bioinformatics/btr497. The internal-coordinate NMA (iMod) that iMODFIT uses to avoid structural distortions - the refinement over the Cartesian ANM here.
• Atilgan, A.R.; Durell, S.R.; Jernigan, R.L.; Demirel, M.C.; Keskin, O.; Bahar, I. "Anisotropic network model: systematic study of vibrational modes and cross-correlations." Biophys. J. 2001, 80(1), 505-515. The 3N x 3N ANM Hessian, the low-frequency collective modes, and the theoretical B-factors implemented here.
• Tirion, M.M. "Large amplitude elastic motions in proteins from a single-parameter, atomic analysis." Phys. Rev. Lett. 1996, 77(9), 1905-1908. The single-spring-constant elastic network potential that underlies all ENM/ANM work.
• Bruschweiler, R. "Collective protein dynamics and nuclear spin relaxation." J. Chem. Phys. 1995, 102, 3396-3403. The mode-collectivity measure (participation-based) reported per mode.