Voronoï Tessellation Reveals the Condensed Matter Character of Folded Proteins

Soyer, Alain; Chomilier, Jacques; Mornon, Jean‐Paul; Jullien, R.; Sadoc, Jean‐François

doi:10.1103/physrevlett.85.3532

Cited by 59 publications

(65 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proteins can be seen as a close packing of more or less spherical units: the amino-acids [12].These units tend to form tetrahedral packings whose paradigm is the {3, 3, 5} polytope. Nevertheless an important secondary structure in protein is the α-helix which does not appears in the {3, 3, 5} polytope.…”

Section: Discussionmentioning

confidence: 99%

“…Some interesting new polytopes and structures in S 3 are presented emphasising on their description in terms of packing of helices in order to model molecular structures. But the aim of this study is to have structures whose local order can mimic the local order of folded proteins, which could be considered as dense packing of amino-acids [12]. a e-mail: sadoc@lps.u-psud.fr b associé au CNRS 2 Geometry of the {3, 3, 5}-polytope in S 3…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Helices and helix packings derived from the {3, 3, 5} polytope

Sadoc

2001

The European Physical Journal E

View full text Add to dashboard Cite

The {3, 3, 5}-polytope is described and used as template for dense structures. Then larger structures are derived from this polytope, using disclinations. That needs a study of symmetries in this polytope. A discretised version of the Hopf fibration is presented and used in order to generate a family of new polytopes. It is possible to gathered vertices of these structures on several helices and then to consider geometrical relation between these helices. This study is govern by biological consideration of helix building molecules, but the final purpose is to have a geometrical tool to study geometrical relationship occurring between different helices or strands. This can occur for instance in protein folding studies.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Helices and helix packings derived from the {3, 3, 5} polytope

Sadoc

2001

The European Physical Journal E

View full text Add to dashboard Cite

show abstract

“…Since Voronoi tessellations boil up to being optimal partitionings of the space resulting from a set of generating points, they define a natural discrete mathematical measure, and have long been considered for applications in several research areas, such as telecommunications [5], biology [6], astronomy [7], forestry [8], atomic physics [9], metallurgy [10], polymer science [11], materials science [12,13], and biophysics [14]. In condensed matter physics, the Voronoi cell of the lattice point of a crystal is known as the Wigner-Seitz cell, whereas the Voronoi cell of the reciprocal lattice point is the Brillouin zone [15,16].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Break in Voronoi Tessellations

Lucarini

2009

Symmetry

View full text Add to dashboard Cite

Abstract:We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the OPEN ACCESSSymmetry 2009, 1 22 perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomal...

show abstract

“…Contact potentials are statistical potentials that are calculated from experimentally known 3D structures of proteins which calculate the frequencies of occurrences of all possible contacts and convert them into energy values so that frequently occurring contacts have favorable contact scores. This method is an approximation to actual physico-chemical potentials but they have been shown to work as target energy functions on the protein folding problem [7,8,12,13].…”

Section: Methodsmentioning

confidence: 99%

“…A Delaunay tessellated graph includes the neighborhood (contact) information of these Delaunay simplices. In this work, we used Qhull program to derive the Delaunay tessellated graph of our proteins using the alpha carbon atoms as simplices [8,21].…”

Section: Methodsmentioning

confidence: 99%

Discrimination of Native Folds Using Network Properties of Protein Structures

Küçükural¹,

Sezerman²,

Erçil³

2007

Proceedings of the 6th Asia-Pacific Bioinformatics Conference

View full text Add to dashboard Cite

Graph theoretic properties of proteins can be used to perceive the differences between correctly folded proteins and well designed decoy sets. 3D protein structures of proteins are represented with graphs. We used two different graph representations: Delaunay tessellations of proteins and contact map graphs. Graph theoretic properties for both graph types showed high classification accuracy for protein discrimination. Fisher, linear, quadratic, neural network, and support vector classifiers were used for the classification of the protein structures. The best classifier accuracy was over 98%. Results showed that characteristic features of graph theoretic properties can be used in the detection of native folds.

show abstract

Voronoï Tessellation Reveals the Condensed Matter Character of Folded Proteins

Cited by 59 publications

References 27 publications

Helices and helix packings derived from the {3, 3, 5} polytope

Helices and helix packings derived from the {3, 3, 5} polytope

Symmetry-Break in Voronoi Tessellations

Discrimination of Native Folds Using Network Properties of Protein Structures

Contact Info

Product

Resources

About