APPLICATIONS OF DELAUNAY TESSELLATION TO THE ANALYSIS OF PROTEIN STRUCTURES

 

Authors:

Dr. Todd J. Taylor,  NIST Postdoc, MSID Division (Division 826)

Prof. Iosif I. Vaisman, Bioinformatics and Computational Biology, George Mason University

 

Contact:

Todd  J. Taylor   (Sigma Xi application pending, I think)

Bldg 220, Room A349

Mailstop 8263

Phone: 301-975-4322

Email: todd.taylor@nist.gov

Mentor: Dr. Ram Sriram

Most appropriate categories: Biology, Mathematics

 

 

 

 

 

Abstract:

 

Delaunay tessellation, a technique from computational geometry for decomposing a point set into non-overlapping tetrahedral subsets, has proven extremely versatile in the analysis of protein structures. This work details a few results from the study of protein structures under such a partitioning.

 

We relate a definition of secondary structure that, unlike existing methods,  uses only patterns of carbon alpha Delaunay contacts and has no explicit dependence on angles, lengths, or areas. It uses structural descriptors called t-numbers and agrees very well with more conventional definitions.

 

We relate a method of protein structural domain decomposition based on the Potts model from statistical physics. Each residue in a tessellated protein is considered a site in an irregular lattice where lattice neighbors are joined by Delaunay edges. We assign initial integer value 'spins' to each residue/site, and let them interact via a simple Ising/Potts ferromagnetic-like energy function. Clusters of like spins emerge like magnetic domains and it turns out the clusters correspond closely to expert assigned protein structural domains.

 

Large sets of real and simple model protein structures were subjected to Delaunay tessellation and statistical differences in the geometry and contact patterns between real proteins and models were characterized. Some applications of the results include protein structure prediction through fold recognition as well as discrimination of  hyper-thermostable proteins from their non-thermostable analogs and perhaps ultimately design of thermostable proteins.