A Constraint-Based Approach to Fast and Exact Structure Prediction in Three-Dimensional Protein Models

Simplified protein models are used for investigating general properties of proteins and principles of protein folding. Furthermore, they are suited for hierarchical approaches to protein structure prediction. A well known protein model is the HP-model of Lau and Dill Lau, K. F., & Dill, K. A. (1989)]. A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules, 22, 3986–3997) which models the important aspect of hydrophobicity. One can define the HP-model for various lattices, among them two-dimensional and three-dimensional ones. Here, we investigate the three-dimensional case. The main motivation for studying simplified protein models is to be able to predict model structures much more quickly and more accurately than is possible for real proteins. However, up to now there was a dilemma: the algorithmically tractable, simple protein models can not model real protein structures with good quality and introduce strong artifacts. We present a constraint-based method that largely improves this situation. It outperforms all existing approaches for lattice protein folding in HP-models. This approach is the first one that can be applied to two three-dimensional lattices, namely the cubic lattice and the face-centered-cubic (FCC) lattice. Moreover, it is the only exact method for the FCC lattice. The ability to use the FCC lattice is a significant improvement over the cubic lattice. The key to our approach is the ability to compute maximally compact sets of points (used as hydrophobic cores), which we accomplish for the first time for the FCC lattice.