Elastic Network Model

Delarue, M. Sanejouand, Y.H., Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases the elastic network model, J. Mol. Biol. 2002, 320, 1011-1024... 

Figure 7.4 Illustration of the Elastic Network Model for thymidylate kinase (cut-off = 8 Angstroms).

Zheng, W., and Doniach, S. (2003). A comparative study of motor-protein motions by using a simple elastic-network model. Proc. Natl. Acad. Sci. USA 100, 13253-13258. 

Atilgan AR, Durell SR, Jernigan RL et al (2001) Anisotropy of fluctuation dynamics of proteins with an elastic network model. Biophys J 80(1) 505-515... 

Chennubhotla, C., Reader, A.J., Yang, L.-W., and Bahar, I. "Elastic network model for understanding biomolecular machinery from enzymes to supramolecular assemblies". Phys. Biol. 2, S173-S180 (2005). 

The simplest of these approaches includes Gaussian Network Models (GNM) or Elastic Network Models (ENM) which assume that the native state represents the minimum energy configuration. A structure is represented as a network of beads connected by harmonic springs.12,13 One bead represents one residue and is usually centered on the position of the Ca carbon. Single parameter harmonic interactions are assigned to bead pairs which fall within a certain cutoff distance Rc. In case of proteins, Rc is usually around 8-10 A. The representation of the molecule in the... 

Wang Y, Rader AJ, Bahar I, Jernigan RL (2004) Global ribosome motions revealed with elastic network model. J. Struct. Biol. 147 302-314... 

Kurkcuoglu O, Jernigan RL, Doruker P (2004) Mixed levels of coarse-graining of large proteins using elastic network model succeeds in extracting the slowest motions. Polymer 45 649-657... 

Fishing for Functional Motions with Elastic Network Models... 

Sen, T.Z., Feng, Y, Garcia, J.V, Kloczkowski, A., Jernigan, V.L. The extent of cooperativity of protein motions observed with elastic network models is similar for atomic and coarser-grained models, J. Chem. Theory Comput. 2006, 2, 696. 

Jeong, J.I., Jang, Y, Kim, M.K. A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information, J. Mol. Graph. Model. 2006,24,296. 

Song, G., Jernigan, R.L. An enhanced elastic network model to represent the motions of domain-swapped proteins. Proteins 2006, 63,197. 

Ming, D., Bruschweiler, R. Reorientational contact-weighted elastic network model for the prediction of protein dynamics comparison with NMR relaxation, Biophys. J. 2006, 90,3382. 

Kurkcuoglu, O., Jemigan, R. L., and Doruker, R, Collective dynamics of large proteins from mixed coarse-grained elastic network model, QSAR Combinatorial Sci., 24, 443 (2005). 

Lyman, E., Pfaendtner, J., and Voth, G. A., Systematic multiscale parameterization of heterogeneous elastic network models of proteins, Biophys. J., 95, 4183 (2008). 

Fig. 4 The elastic network model approach. A folded protein (left) is reduced to a minimal set of beads representative of its amino acid sequence (centre), Beads are connected to each other (right) through a model pair-potential with global minimum at each pair s distance in the native structure.

Despite their simplicity, elastic network models are based on very solid and intuitive mathematical-physical concepts (like polynomial expansion of the potential energy function from the global minimum), and this has constituted one of the reasons for their success in the literature in the past years. Nonetheless, at the same time, their simplicity restricts their applicability to a relatively small set of studies. 

In particular, elastic network models reproduce the local shape of the folding free energy landscape of a protein by an artificial effective potential that does not contain any information on the physical means by which such shape is obtained. Moreover, they intrinsically bias the global minimum to a selected conformation, and thus they are not capable to capture the protein conformational changes and exploration of multiple structural minima that may be required for exploitation of the protein function (for example, in motor proteins, transporters etc.). Finally, these models do not contain any information on the external potential of the proteins therefore, they cannot be in principle used to explore in detail interactions of proteins with the environment [i.e., with membranes, other proteins or ligands). 

Establishment of CG protocols for proteins having broader applicability than elastic network models requires the definition of potential energy functions containing terms that are based on more general assumptions. The Holy Grail of the present research would be the definition of a universal form for such terms that would guarantee transferability over multiple systems keeping reasonable levels of reliability over several properties of interest. 

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