Excitable Delaunay triangulations

In an excitable Delaunay triangulation every node takes three states (resting, excited and refractory) and updates its state in discrete time depending on a ratio of excited neighbours. All nodes update their states in parallel. By varying excitability of nodes we produce a range of phenomena, including reflection of excitation wave from edge of triangulation, backfire of excitation, branching clusters of excitation and localized excitation domains. Our findings contribute to studies of propagating perturbations and waves in non-crystalline substrates

VLDP web server: a powerful geometric tool for analysing protein structures in their environment.

International audienceProtein structures are an ensemble of atoms determined experimentally mostly by X-ray crystallography or Nuclear Magnetic Resonance. Studying 3D protein structures is a key point for better understanding protein function at a molecular level. We propose a set of accurate tools, for analysing protein structures, based on the reliable method of Voronoi-Laguerre tessellations. The Voronoi Laguerre Delaunay Protein web server (VLDPws) computes the Laguerre tessellation on a whole given system first embedded in solvent. Through this fine description, VLDPws gives the following data: (i) Amino acid volumes evaluated with high precision, as confirmed by good correlations with experimental data. (ii) A novel definition of inter-residue contacts within the given protein. (iii) A measure of the residue exposure to solvent that significantly improves the standard notion of accessibility in some cases. At present, no equivalent web server is available. VLDPws provides output in two complementary forms: direct visualization of the Laguerre tessellation, mostly its polygonal molecular surfaces; files of volumes; and areas, contacts and similar data for each residue and each atom. These files are available for download for further analysis. VLDPws can be accessed at http://www.dsimb.inserm.fr/dsimb_tools/vldp

Recognition of Interaction Interface Residues in Low-Resolution Structures of Protein Assemblies Solely from the Positions of Cα Atoms

Background: The number of available structures of large multi-protein assemblies is quite small. Such structures provide phenomenal insights on the organization, mechanism of formation and functional properties of the assembly. Hence detailed analysis of such structures is highly rewarding. However, the common problem in such analyses is the low resolution of these structures. In the recent times a number of attempts that combine low resolution cryo-EM data with higher resolution structures determined using X-ray analysis or NMR or generated using comparative modeling have been reported. Even in such attempts the best result one arrives at is the very course idea about the assembly structure in terms of trace of the C alpha atoms which are modeled with modest accuracy. Methodology/Principal Findings: In this paper first we present an objective approach to identify potentially solvent exposed and buried residues solely from the position of C alpha atoms and amino acid sequence using residue type-dependent thresholds for accessible surface areas of C alpha. We extend the method further to recognize potential protein-protein interface residues. Conclusion/Significance: Our approach to identify buried and exposed residues solely from the positions of C alpha atoms resulted in an accuracy of 84%, sensitivity of 83-89% and specificity of 67-94% while recognition of interfacial residues corresponded to an accuracy of 94%, sensitivity of 70-96% and specificity of 58-94%. Interestingly, detailed analysis of cases of mismatch between recognition of interface residues from C alpha positions and all-atom models suggested that, recognition of interfacial residues using C alpha atoms only correspond better with intuitive notion of what is an interfacial residue. Our method should be useful in the objective analysis of structures of protein assemblies when positions of only C alpha positions are available as, for example, in the cases of integration of cryo-EM data and high resolution structures of the components of the assembly

Discrimination of thermophilic and mesophilic proteins

<p>Abstract</p> <p>Background</p> <p> There is a considerable literature on the source of the thermostability of proteins from thermophilic organisms. Understanding the mechanisms for this thermostability would provide insights into proteins generally and permit the design of synthetic hyperstable biocatalysts.</p> <p>Results</p> <p> We have systematically tested a large number of sequence and structure derived quantities for their ability to discriminate thermostable proteins from their non-thermostable orthologs using sets of mesophile-thermophile ortholog pairs. Most of the quantities tested correspond to properties previously reported to be associated with thermostability. Many of the structure related properties were derived from the Delaunay tessellation of protein structures.</p> <p>Conclusions</p> <p> Carefully selected sequence based indices discriminate better than purely structure based indices. Combined sequence and structure based indices improve performance somewhat further. Based on our analysis, the strongest contributors to thermostability are an increase in ion pairs on the protein surface and a more strongly hydrophobic interior.</p

Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction

General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be subjected to a geometric hardcore interaction, forcing the cells not to be too large, too small, or too flat. This setting, natural for applications, introduces some theoretical difficulties since the interaction is not necessarily hereditary. Mathematical results available for studying these models are reviewed and further outcomes are provided. They concern the existence, the simulation and the estimation of such tessellations. Based on these results, tools to handle these objects in practice are presented: how to simulate them, estimate their parameters and validate the fitted model. Some examples of simulated tessellations are studied in details

Cavities and Atomic Packing in Protein Structures and Interfaces

A comparative analysis of cavities enclosed in a tertiary structure of proteins and interfaces formed by the interaction of two protein subunits in obligate and non-obligate categories (represented by homodimeric molecules and heterocomplexes, respectively) is presented. The total volume of cavities increases with the size of the protein (or the interface), though the exact relationship may vary in different cases. Likewise, for individual cavities also there is quantitative dependence of the volume on the number of atoms (or residues) lining the cavity. The larger cavities tend to be less spherical, solvated, and the interfaces are enriched in these. On average 15 Å3 of cavity volume is found to accommodate single water, with another 40–45 Å3 needed for each additional solvent molecule. Polar atoms/residues have a higher propensity to line solvated cavities. Relative to the frequency of occurrence in the whole structure (or interface), residues in β-strands are found more often lining the cavities, and those in turn and loop the least. Any depression in one chain not complemented by a protrusion in the other results in a cavity in the protein–protein interface. Through the use of the Voronoi volume, the packing of residues involved in protein–protein interaction has been compared to that in the protein interior. For a comparable number of atoms the interface has about twice the number of cavities relative to the tertiary structure

Characterization of 3D Voronoi Tessellation Nearest Neighbor Lipid Shells Provides Atomistic Lipid Disruption Profile of Protein Containing Lipid Membranes

Quantifying protein-induced lipid disruptions at the atomistic level is a challenging problem in membrane biophysics. Here we propose a novel 3D Voronoi tessellation nearest-atom-neighbor shell method to classify and characterize lipid domains into discrete concentric lipid shells surrounding membrane proteins in structurally heterogeneous lipid membranes. This method needs only the coordinates of the system and is independent of force fields and simulation conditions. As a proof-of-principle, we use this multiple lipid shell method to analyze the lipid disruption profiles of three simulated membrane systems: phosphatidylcholine, phosphatidylcholine/cholesterol, and beta-amyloid/phosphatidylcholine/cholesterol. We observed different atomic volume disruption mechanisms due to cholesterol and beta-amyloid. Additionally, several lipid fractional groups and lipid-interfacial water did not converge to their control values with increasing distance or shell order from the protein. This volume divergent behavior was confirmed by bilayer thickness and chain orientational order calculations. Our method can also be used to analyze high-resolution structural experimental data