An integer programming model for protein structure prediction using the 3D-HP side chain model

In spite of the fact that many simplified model variants of protein structure prediction have been widely studied in the past years, few attention has been given to discrete models with side chains, for which there is no specific benchmark. In this paper, we propose an integer programming model for the 3D-HP side chain protein structure prediction problem. The model accounts for the energy resulting from all types of interactions, between pairs of backbone elements, hydrophilic side chains and hydrophobic side chains. Three sets of instances, modified from the literature, were used in the experiments, and the maximum number of non-local hydrophobic contact was found using the ILOG CPLEX optimization package. We offer the optimal solution found for several instances of the benchmark. It is expected that the mathematical model allow further studies of the protein structure prediction with side chains and may, for some cases, provide new optimal values or new bounds that would rekindle the interest to this fascinating problem domain.