Identifying essential pairwise interactions in elastic network model using the alpha shape theory

Elastic network models (ENM) are based on the idea that the geometry of a protein structure provides enough information for computing its fluctuations around its equilibrium conformation. This geometry is represented as an elastic network (EN) that is, a network of links between residues. A spring is associated with each of these links. The normal modes of the protein are then identified with the normal modes of the corresponding network of springs. Standard approaches for generating ENs rely on a cutoff distance. There is no consensus on how to choose this cutoff. In this work, we propose instead to filter the set of all residue pairs in a protein using the concept of alpha shapes. The main alpha shape we considered is based on the Delaunay triangulation of the Cα positions; we referred to the corresponding EN as EN(∞). We have shown that heterogeneous anisotropic network models, called αHANMs, that are based on EN(∞) reproduce experimental B-factors very well, with correlation coefficients above 0.99 and root-mean-square deviations below 0.1 Å(2) for a large set of high resolution protein structures. The construction of EN(∞) is simple to implement and may be used automatically for generating ENs for all types of ENMs.