### Ya-xiang Yuan (Chinese Academy of Sciences, Beijing)

#### Distance geometry problem for protein modeling via geometric buildup

*Friday 7 March 2008 at 14.00, JCMB 5326*

##### Abstract

A well-known problem in protein modeling is the determination of the
structure of a protein with a given set of inter-atomic or inter-residue
distances obtained from either physical experiments or theoretical estimates.
A general form of the problem is known as the distance geometry problem in
mathematics, the graph embedding problem in computer science, and the
multidimensional scaling problem in statistics. The problem has applications
in many other scientific and engineering fields as well such as sensor network
localization, image recognition, and protein classification. We describe the
formulations and complexities of the problem in its various forms, and
introduce a so-called geometric buildup approach to the problem. We present the
general algorithm and discuss related computational issues including control of
numerical errors, determination of rigid vs. unique structures, and tolerance
of distance errors. The theoretical basis of the approach is established based
on the theory of distance geometry. A group of necessary and sufficient
conditions for the determination of a structure with a given set of distances
using a geometric buildup algorithm are justified. The applications of the
algorithm to model protein problems are demonstrated.

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