Anisotropic Network Model

It is essentially an Elastic Network Model for the Cα atoms with a step function for the dependence of the force constants on the inter-particle distance.

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.

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.

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 ri = (xi yi zi) and let rj = (xj yj zj) be the instantaneous positions of atoms i and j.

For the spring between i and j, the harmonic potential in terms of the unknown spring constant γ, is given by: The second derivatives of the potential, Vij with respect to the components of ri are evaluated at the equilibrium position, i.e. sijO = sij, are 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 higher performance of GNM can be attributed to its underlying potential, which takes account of orientational deformations, in addition to distance changes.

ANM has been evaluated on a large set of proteins to establish the optimal model parameters that achieve the highest correlation with experimental data and its limits of accuracy and applicability.

Recent notable applications of ANM where it has proved to be a promising tool for describing the collective dynamics of the bio-molecular system, include the studies of: - Hemoglobin, by Chunyan et al., 2003.