3-Dimensional Protein Reconstruction from Contact Maps: Complexity and Experimental Results

Abstract

The prediction of the protein tertiary structure from solely its residue sequence is one of the most challenging problems in structural bioinformatics. Predicting the tertiary structure of a protein directly from its primary structure is a complex problem. A typical alternative approach is to identify a set of sub-problems, such as prediction of residue contacts and try to reconstruct the three-dimensional structure from this partial information. The general problem of recovering a set of three-dimensional coordinates consistent with some given contact map is known as unit disk graph realization problem and it’s recently proven to be NP-hard. The specific protein reconstruction problem poses further constraints to the general realization problem. In particular, proteins always presents a typical ordered substructure which is called backbone. In the first part of this thesis we investigate the computational complexity of the protein reconstruction problem and prove that the 2-dimensional realization problem remains NP-hard even with the backbone constraint. In the second part of the thesis we present COMAR, an heuristic algorithm for the reconstruction of protein 3D-structure from contact map. Such algorithm has been tested on a non redundant data set consisting of 1760 proteins. and it was always able to produce three-dimensional coordinates consistent with the initial contact map for the whole data set. Performance analysis of the algorithm shows that there exist native contact maps for which there are numerous different possible structures consistent with them. We proceed further to evaluate the fault tolerance of COMAR introducing three different class of random errors. The analysis shows that