iTreePack: Protein Complex Side-Chain Packing by Dual Decomposition

Protein side-chain packing is a critical component in obtaining the 3D coordinates of a structure and drug discovery. Single-domain protein side-chain packing has been thoroughly studied. For instance, our efficient tree decomposition algorithm TreePack has been re-implemented in SCWRL, the widely-used side-chain packing program, for monomer side-chain packing. A major challenge in generalizing these methods to protein complexes is that they, unlike monomers, often have very large treewidth, and thus algorithms such as TreePack cannot be directly applied. To address this issue, SCWRL4 treats the complex effectively as a monomer, heuristically excluding weak interactions to decrease treewidth; as a result, SCWRL4 generates poor packings on protein interfaces. To date, few side-chain packing methods exist that are specifically designed for protein complexes. In this paper, we introduce a method, iTreePack, which solves the side-chain packing problem for complexes by using a novel combination of dual decomposition and tree decomposition. In particular, iTreePack overcomes the problem of large treewidth by decomposing a protein complex into smaller subgraphs and novelly reformulating the complex side-chain packing problem as a dual relaxation problem; this allows us to solve the side-chain packing of each small subgraph separately using tree-decomposition. A projected subgradient algorithm is applied to enforcing the consistency among the side-chain packings of all the small subgraphs. Computational results demonstrate that our iTreePack program outperforms SCWRL4 on protein complexes. In particular, iTreePack places side-chain atoms much more accurately on very large complexes, which constitute a significant portion of protein-protein interactions. Moreover, the advantage of iTreePack over SCWRL4 increases with respect to the treewidth of a complex. Even for monomeric proteins, iTreePack is much more efficient than SCWRL and slightly more accurate.