Raptor: Optimal Protein Threading by Linear Programming

Abstract

This paper presents a novel linear programming approach to do protein 3-dimensional (3D) structure prediction via threading. Based on the contact map graph of the protein 3D structure template, the protein threading problem is formulated as a large scale integer programming (IP) problem. The IP formulation is then relaxed to a linear programming (LP) problem, and then solved by the canonical branch-and-bound method. The final solution is globally optimal with respect to energy functions. In particular, our energy function includes pairwise interaction preferences and allowing variable gaps which are two key factors in making the protein threading problem NP-hard. A surprising result is that, most of the time, the relaxed linear programs generate integral solutions directly. Our algorithm has been implemented as a software package RAPTOR-RApid Protein Threading by Operation Research technique. Large scale benchmark test for fold recognition shows that RAPTOR significantly outperforms other programs at the fold similarity level. The CAFASP3 evaluation, a blind and public test by the protein structure prediction community, ranks RAPTOR as top 1, among individual prediction servers, in terms of the recognition capability and alignment accuracy for Fold Recognition (FR) family targets. RAPTOR also performs very well in recognizing the hard Homology Modeling (HM) targets. RAPTOR was implemented at the University of Waterloo and it can be accessed at http://www.cs.uwaterloo.ca/~j3xu/RAPTOR_form.htm.

Recent Advances in Solving the Protein Threading Problem

“…Our definition is very close to the one given in [9,34]. It follows a few basic assumptions widely adopted by the protein threading community [11,35,9,34,12,17]. Consequently, the algorithms presented in the next sections can be easily plugged in most of the existing fold recognition methods based on threading.…”

“…It significantly outperforms the MIP model used in the RAPTOR package [12] for all large instances (see [11] for more details). Both models (MYZ and RAPTOR) are solved using a linear programming relaxation (LP).…”

“…Until recently, it was the main obstacle to the development of efficient threading methods. During the last few years, much progress has been accomplished toward a solution of this problem for most real life instances [9,10,11,12,13,14].…”

“…Two protein threading packages are currently available that implement exact methods based on the latter approach: RAPTOR 5 [12] and FROST 6 [7]. In section 3 we will describe in more details the FROST implementation of the MIP models.…”

“…3(b)). Different definitions for residues in contact in the core can be used, for instance in [12] they assume that two amino acids interact if the distance between their C β atoms is within pÅ and they are at least q positions apart along the template sequence (with p = 7 and q = 4). There is an interaction between two segments, i and j, if there is at least one pairwise interaction between amino acids belonging to i and amino acids belonging to j.…”