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.     

The Protein Structure Prediction Problem: A Constraint Optimization Approach using a New Lower Bound

The protein structure prediction problem is one of the most (if not the most) important problem in computational biology. This problem consists of finding the conformation of a protein with minimal energy. Because of the complexity of this problem, simplified models like Dill's HP-lattice model [15], [16] have become a major tool for investigating general properties of protein folding. Even for this simplified model, the structure prediction problem has been shown to be NP-complete [5], [7]. We describe a constraint formulation of the HP-model structure prediction problem, and present the basic constraints and search strategy. Of course, the simple formulation would not lead to an efficient algorithm. We therefore describe redundant constraints to prune the search tree. Furthermore, we need bounding function for the energy of an HP-protein. We introduce a new lower bound based on partial knowledge about the final conformation (namely the distribution of H-monomers to layers).