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

Abstract

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.

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids

“…As an alternative to this cutoff model, Xia et al (2014) proposed to use all edges of the Delaunay triangulation of the selected atoms as an alternate elastic network. We believe that the use of Delaunay triangulation to define the ENM extends the range of applicability of NMA to the realm of less globular proteins.…”

“…The elastic constants can also be adjusted to have the fluctuations of the atoms of the molecule computed from the equations of motions given by Equation (7) to match the atomic fluctuations captured experimentally and usually reported as B-factors. Many methods have been developed for that purpose (see for example Xia et al, 2013, 2014 and references therein). Among those methods, the one proposed by Erman (2006) is worth discussing.…”

“…With these features we depart from the original Elastic Network Model (Tirion, 1996), but keep most of its salient features, as the construction of the original Tirion Elastic Model remains available. We found for example that the Elastic Network coming from a Delaunay tessellation correctly handles PDB models with isolated domains and/or dangling ends (Xia et al, 2014). In addition, the performance of the calculation of Normal Modes has been improved to a point where it can deal with 100,000 atoms routinely, making it possible, for instance, to deal with entire virus capsids without having to resort to a symmetry-specific implementation (Simonson and Perahia, 1992; van Vlijmen and Karplus, 2005; Peeters and Taormina, 2009).…”

A new algorithm for construction of coarse-grained sites of large biomolecules

“…In the multiscale simulations of proteins, a coarse‐grained (CG) map should be predefined, which transforms the high‐resolution configuration based on a fine‐grained (FG) model to a low‐resolution configuration. The FG model of a protein could be an elastic network model (ENM), such as the anisotropic network model (ANM) that could be based on the all‐atom or Cα‐atom representations. In ANM, the secondary structure of protein is normally represented by the sequential Cα atoms of backbone.…”

Dissecting the roles of local packing density and longer-range effects in protein sequence evolution

“…Such structural partitioning has a long history in the analysis of protein structures 42,43 . In particular, the Voronoi tessellation and its dual graph, the Delaunay triangulation, have been used in several studies analyzing the internal structure of proteins and/or developing empirical potentials [44][45][46] . The Voronoi tessellation divides the Euclidean space into regions, called cells, and each belonging to exactly one centroid point (seed), such that the cell corresponding to each centroid point consists of every region in space whose distance is less than or equal to its distance to any other centroid point ( Figure 2).…”