**Title: ****PROPERTIES OF RESIDUE CONTACT NETWORKS OF DELAUNAY
TESSELLATED PROTEIN STRUCTURES**

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__Todd J. Taylor__, NIST Gaithersburg, MD 20899.

Iosif I.Vaisman, George Mason University, Manassas, VA

Delaunay tessellation, a technique from computational geometry for decomposing a point set into non-overlapping tetrahedral subsets of mutual nearest neighbors, has proven extremely versatile in the analysis of protein structures The authors have subjected several sets of real and simplified model protein structures to this procedure. The system of contacts defined by residues joined with simplex edges in the tessellation can be thought of as a graph or network. Properties like the graph distances between residues and clustering coefficients can be computed to investigate the nature of such contact networks [1].

Using metric multi-dimensional scaling, the effective dimensionality d of the space in which such networks live can also be computed from a matrix of all inter-residue graph distances. We find that protein contact networks have small world character, but are not strictly small world networks, as has previously been asserted [2]. And the variation of d with simplex edge length cutoff gives a set of natural distance scales for proteins. These two results are related—d determines how the characteristic path length of the contact graph scales with the number of residues N.

[1] TJ Taylor, II Vaisman, Phys Rev E Stat
Nonlin Soft Matter Phys **73,** 4 Pt 1. (2006)

[2]
TJ Taylor, II Vaisman, Proceedings of the 5^{th} International
Symposium on Voronoi Diagrams in Science and Engineering (2008).

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**CATEGORIES:
Biology, Mathematics **

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**Name: Dr.
Todd J. Taylor (Sigma Xi Member)**

**Division:
826, Laboratory: DPG**

**Room: A349,
Building: 220, Mail stop: 8263**

**Tel:
301-975-4322**

**Fax: --**

**Email:todd.taylor@nist.gov**