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== Theory ==
The Anisotropic Network Model was introduced in 2000 (Atilgan et al., 2001; Doruker et al., 2000), inspired by the pioneering work of Tirion (1996), succeeded by the development of the [[Gaussian network model]] (GNM) (Bahar et al., 1997; Haliloglu et al., 1997), and by the work of Hinsen (1998) who first demonstrated the validity of performing EN NMA at residue level. <br />It represents the biological macromolecule as an elastic mass-and-spring network, to explain the internal motions of a protein subject to a harmonic potential. In the network each node is the Cα atom of the residue and the springs represent the interactions between the nodes. The overall potential is the sum of harmonic potentials between interacting nodes. To describe the internal motions of the spring connecting the two atoms, there is only one [[degree of freedom]]. Qualitatively, this corresponds to the compression and expansion of the spring in a direction given by the locations of the two atoms. In other words, ANM is an extension of the Gaussian Network Model to three coordinates per atom, thus accounting for directionality.
The network includes all interactions within a cutoff distance, which is the only predetermined parameter in the model. Information about the orientation of each interaction with respect to the global coordinates system is considered within the force constant matrix (''H'') and allows prediction of anisotropic motions. Consider a sub-system consisting of nodes ''i'' and ''j'', let ''r''<sub>''i''</sub> = (''x''<sub>''i''</sub> ''y''<sub>''i''</sub> ''z''<sub>''i''</sub>) and let ''r''<sub>''j''</sub> = (''x''<sub>''j''</sub> ''y''<sub>''j''</sub> ''z''<sub>''j''</sub>) be the instantaneous positions of atoms ''i'' and ''j''. The equilibrium distance between the atoms is represented by ''s''<sub>''ij''</sub><sup>O</sup> and the instantaneous distance is given by ''s''<sub>''ij''</sub>. For the spring between ''i'' and ''j'', the harmonic potential in terms of the unknown spring constant ''γ'', is given by:
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: <math>{\partial^2 V_{ij}\over\partial x_i \, \partial y_j} = {-\gamma\over s_{ij}^2} {(x_j - x_i)}{(y_j-y_i)} </math>
The above is a direct outcome of one of the key underlying assumptions of ANM – that a given crystal structure is an energetic minimum and does not require energy minimization.
The force constant of the system can be described by the [[Hessian matrix]] – (second partial derivative of potential ''V''):
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- [[Rhodopsin]], by Rader et al., 2004.<br />
- [[Nicotinic acetylcholine receptor]], by Hung et al., 2005; Taly et al., 2005.<br />
- [[Auxiliary Activity
== ANM web servers ==
The ANM web server developed by Eyal E, Yang LW, Bahar I. in 2006, presents a web-based interface for performing ANM calculations, the main strengths of which are the rapid computing ability and the user-friendly graphical capabilities for analyzing and interpreting the outputs.
* Anisotropic Network Model web server. [http://ignmtest.ccbb.pitt.edu/cgi-bin/anm/anm1.cgi]
* ANM server. [https://web.archive.org/web/20070624170153/http://gor.bb.iastate.edu/anm/anm.htm]
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# Hinsen, K. (1998) "Analysis of ___domain motions by approximate normal mode calculations", ''Proteins'', 33, 417–429. {{PMID|11159421}}
# Bahar,I. et al. (1997) "Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential". ''Fold Des'', 2, 173–181
# Chennubhotla,C. et al. (2005) "Elastic network models for understanding biomolecular machinery: from enzymes to supramolecular assemblies". ''Phys Biol'', 2, pp.
# Cui,Q. and Bahar,I. (2006) ''Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems''. Chapman & Hall/CRC, Boca Raton, FL.
# Arora et al. (2019) "Structural dynamics of lytic polysaccharide monoxygenases reveals a highly flexible substrate binding region". J ''Mol Graph Model'', 88, 1–10. [https://www.sciencedirect.com/science/article/pii/S1093326318306776?via%3Dihub]
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