Visible Volume: a Robust Measure for Protein Structure Characterization

We propose a new characterization of protein structure based on the natural tetrahedral geometry of the β carbon and a new geometric measure of structural similarity, called visible volume. In our model, the side-chains are replaced by an ideal tetrahedron, the orientation of which is fixed with respect to the backbone and corresponds to the preferred rotamer directions. Visible volume is a measure of the non-occluded empty space surrounding each residue position after the side-chains have been removed. It is a robust, parameter-free, locally-computed quantity that accounts for many of the spatial constraints that are of relevance to the corresponding position in the native structure. When computing visible volume, we ignore the nature of both the residue observed at each site and the ones surrounding it. We focus instead on the space that, together, these residues could occupy. By doing so, we are able to quantify a new kind of invariance beyond the apparent variations in protein families, namely, the conservation of the physical space available at structurally equivalent positions for side-chain packing. Corresponding positions in native structures are likely to be of interest in protein structure prediction, protein design, and homology modeling. Visible volume is related to the degree of exposure of a residue position and to the actual rotamers in native proteins. In this article, we discuss the properties of this new measure, namely, its robustness with respect to both crystallographic uncertainties and naturally occurring variations in atomic coordinates, and the remarkable fact that it is essentially independent of the choice of the parameters used in calculating it. We also show how visible volume can be used to align protein structures, to identify structurally equivalent positions that are conserved in a family of proteins, and to single out positions in a protein that are likely to be of biological interest. These properties qualify visible volume as a powerful tool in a variety of applications, from the detailed analysis of protein structure to homology modeling, protein structural alignment, and the definition of better scoring functions for threading purposes.National Library of Medicine (LM05205-13

Sub-Subgiants in the Old Open Cluster M67?

We report the discovery of two spectroscopic binaries in the field of the old open cluster M67 -- S1063 and S1113 -- whose positions in the color-magnitude diagram place them approximately 1 mag below the subgiant branch. A ROSAT study of M67 independently discovered these stars to be X-ray sources. Both have proper-motion membership probabilities greater than 97%; precise center-of-mass velocities are consistent with the cluster mean radial velocity. S1063 is also projected within one core radius of the cluster center. S1063 is a single-lined binary with a period of 18.396 days and an orbital eccentricity of 0.206. S1113 is a double-lined system with a circular orbit having a period of 2.823094 days. The primary stars of both binaries are subgiants. The secondary of S1113 is likely a 0.9 Mo main-sequence star, which implies a 1.3 Mo primary star. We have been unable to explain securely the low apparent luminosities of the primary stars; neither binary contain stars presently limited in radius by their Roche lobes. We speculate that S1063 and S1113 may be the products of close stellar encounters involving binaries in the cluster environment, and may define alternative stellar evolutionary tracks associated with mass-transfer episodes, mergers, and/or dynamical stellar exchanges

Identifying networks with common organizational principles

Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.Comment: 26 pages, 7 figure