Protein Side-Chain Packing Problem : solution quality analysis of a simple rotamer library

The three-dimensional structure prediction problem consists in predicting the coordinates in the space for each one of the backbone and side chain atoms in a protein, given the linear sequence of amino acids that compose it. This problem plays an important role in protein design and prediction of biological functions. The importance, from a computational point of view, to infer the three dimensional structure of a protein from its amino acid sequence, is based on the cost relative to the time and effort involved in determining the structure of a protein by experimental techniques such as X-ray crystallography or nuclear magnetic resonance. This paper focuses on the Protein Side-Chain Packing Problem (PSCPP), which is a subproblem of the general structure prediction problem. Specifically, this problem consists in predicting the best conformation of a protein side-chain, given the amino acid sequence and the coordinates of the backbone atoms as input data. It has been shown that proteins side-chains tend to cluster in a limited number of conformations [6], known as rotamers. The rotamers are identified by the frequency of occurrences of the side-chain conformations in databases of protein structures, such as the Protein Data Bank (PDB) [2]. The total energy of a molecule can be expressed as the sum of energies from the pairwise interaction between its atoms and is used to evaluate the quality of rotamers assigned to the backbone of a protein. Then, the PSCPP can be formally defined as a combinatorial optimization problem where the objective is to choose a rotamer for each amino acid so that the total energy of the protein is minimized, this problem belongs to the NP-hard complexity class [1]. This paper proposes an experimental analysis of the highest accuracy that can be achieved with a particular rotamer library [5], in addition to understand how the number of interatomic collisions influences the quality of solutions predicted by an optimization algorithm. To perform the experiment 10 proteins randomly selected from among those proposed in the work of Corona [4] were used. Absolute accuracy is a measure of quality of solutions [5-8], and was used in [4] to present the maximum absolute accuracy achieved by the backbone-independent rotamer library [5]. The average results, over 770 proteins, were as follows: % = 99.6%, % = 93.0%, and % = 90.8%. However, the number of collisions was high. With this upper bound on the absolute accuracy that the backbone-independent rotamer library [5] can reach, it is in the interest of this work to know whether it is possible or not to reduce the number of collisions without strongly affecting the solutions quality. That is, we want to know how the absolute accuracy is affected by minimizing the number of collisions. In order to find the sequence of rotamers which minimizes the number of collisions, we use a variant of the CIS optimization algorithm [3] so as to remove atomic collisions from the conformation that obtained the maximum absolute accuracy of each protein and to which in this paper we call it Best. CIS is basically an optimization algorithm that solves the PSCPP and whose main characteristic is being a clash-detection guided iterative search algorithm. Thus, the experiment consisted in taking the solution of Best as the seed of the CIS algorithm in order to obtain the solution with the minimum number of collisions. As part of this work we also present the results obtained by the two best state-of-theart methods for PSCPP: OPUS-Rota [8] and SCWRL4 [7]. It is worth mentioning here that both methods use more updated rotamer libraries than the one analysed in this work. The following