Reconstruction of 3D Structures from Protein Contact Maps

Abstract

Proteins are large organic compounds made of amino acids arranged in a linear chain (primary structure). Most proteins fold into unique three-dimensional (3D) structures called interchangeably tertiary, folded, or native structures. Discovering the tertiary structure of a protein (Protein Folding Problem) can provide important clues about how the protein performs its function and it is one of the most important problems in Bioinformatics. A contact map of a given protein P is a binary matrix M such that M _i,j= 1 iff the physical distance between amino acids i and j in the native structure is less than or equal to a pre-assigned threshold t. The contact map of each protein is a distinctive signature of its folded structure. Predicting the tertiary structure of a protein directly from its primary structure is a very complex and still unsolved problem. An alternative and probably more feasible approach is to predict the contact map of a protein from its primary structure and then to compute the tertiary structure starting from the predicted contact map. This last problem has been recently proven to be NP-Hard [6]. In this paper we give a heuristic method that is able to reconstruct in a few seconds a 3D model that exactly matches the target contact map. We wish to emphasize that our method computes an exact model for the protein independently of the contact map threshold. To our knowledge, our method outperforms all other techniques in the literature [5,10,17,19] both for the quality of the provided solutions and for the running times. Our experimental results are obtained on a non-redundant data set consisting of 1760 proteins which is by far the largest benchmark set used so far. Average running times range from 3 to 15 seconds depending on the contact map threshold and on the size of the protein. Repeated applications of our method (starting from randomly chosen distinct initial solutions) show that the same contact map may admit (depending on the threshold) quite different 3D models. Extensive experimental results show that contact map thresholds ranging from 10 to 18 Ångstrom allow to reconstruct 3D models that are very similar to the proteins native structure. Our Heuristic is freely available for testing on the web at the following url: http://vassura.web.cs.unibo.it/cmap23d/