Such "perturbed" structures can for instance be used as templates for crystal structure determination, using molecular replacement approaches, when standard ones fail, as a consequence of some large conformational change. This approach has noteworthy been implemented in the PHASER package.

Modes can be calculated like in ELNEMO with the bash script enm_modes.sh (v1.12, 2017), which uses the latest versions of PDBMAT and DIAGRTB.

Perturbed structures can be generated like in ELNEMO with the bash script dq_modes.sh (v1.9, 2017) and the corresponding fortran program.

References:

Suhre, K., & Sanejouand, Y.H. (2004): "ElNemo: a normal mode server for protein movement analysis and the generation of templates for molecular replacement", Nucl. Ac. Res. vol.32 (Web server issue), pW610-W614.

Suhre, K., & Sanejouand, Y.H. (2004): "On the potential of normal mode analysis for solving difficult molecular replacement problems", Acta Cryst. D vol.60, p796-799.

McCoy, A.J., Grosse-Kunstleve, R.W., Adams, P.D., Winn, M.D., Storoni, L.C. & Read, R.J. (2007): "Phaser crystallographic software" J. Appl. Cryst. vol.40, p658-674.

Mahajan, S. & Sanejouand, Y.H. (2017): "Jumping between protein conformers" J. Comput. Chem. to be published.

Requirements: a file with the coordinates of the system, in PDB (Protein Data Bank) or "x y z mass" format.

Output: the hessian (the mass-weighted second derivatives of energy matrix), in the "i j non-zero-ij-matrix-element" format.

diagstd, a fortran program with a standard diagonalization routine, can next be used in order to obtain the corresponding normal modes of the system. If the system is large, the RTB approximation can prove usefull (see below).

The 2004 version of the code is the one used by Elnemo.

References:

Tirion, M. (1996): "Large amplitude elastic motions in proteins from a single-parameter, atomic analysis", Phys. Rev. letters vol.77 (9), p1905-1908.

Tama, F., & Sanejouand, Y.H. (2001): " Conformational change of proteins arising from normal mode calculations ", Protein Engineering vol.14, p1-6.

Delarue, M., & Sanejouand, Y.H. (2002): " Simplified normal mode analysis of conformational transitions in DNA-dependant polymerases: the Elastic Network Model", J. Mol. Biol. vol.320, p1011-1024.

Nicolay, S., & Sanejouand, Y.H. (2006): "Functional modes of proteins are among the most robust", Phys. Rev. letters vol.96, p078104.

If the matrix was obtained, for instance, with the PDBMAT program, these eigenvectors correspond to the low-frequency normal modes (i.e., mostly those with a collective character) of the system. Note that in the case of proteins, low-frequency normal modes thus obtained are found to be very close to those obtained with standard, much more realistic (e.g., all atoms with empirical force fields), models.

The method used rests upon the RTB approximation (standing for Rotations-Translations-of-Blocks). Within the frame of this approximation, blocks of n (n=1,2,...) consecutive monomers (amino-acid residues) are assumed to behave like rigid bodies.

Requirements: a matrix in the "i j non-zero-ij-matrix-element" format. A file with the coordinates of the system, in the PDB or "x y z mass block-number" format.

The 2004 version of the code is the one used by Elnemo.

A more efficient and more general version of RTB, called BNM, used to be available in the CHARMM package (first, in version 32).

References:

Durand, P., Trinquier, G., & Sanejouand, Y.H. (1994): " A new approach for determining low-frequency normal modes in macromolecules", Biopolymers, vol.34, p759 (scanned: 7 Mo).

Tama, F., Gadea, F.X., Marques, O., & Sanejouand, Y.H. (2000): " Building-block approach for determining low-frequency normal modes of macromolecules", Proteins: Structure, Function and Genetics vol.41(1), p1-7.

Li, G., & Cui, Q (2002): " A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase", Biophys. J. vol.83, p2457-2474.

Last modification: May 3th, 2017, by Yves Henri Sanejouand. You may see the list of my other works there.