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

Abstract

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.

Sequence Determines Degree of Knottedness in a Coarse-Grained Protein Model

“…Together, these requirements pose a considerable challenge on the computational procedure and, thus, a similar systematic study has not been carried out for any type of protein model so far. Even for the very simplified HP model, estimating the ground-state of a specific HP sequence has only been possible up to around 100 monomers with state of the art techniques and computational power [31][32][33].…”

Versatile Approach to Access the Low Temperature Thermodynamics of Lattice Polymers and Proteins

“…Despite their formal simplicity and minimalistic framework, lattice models represent a challenging testing ground for computational methods because of their complex energy landscapes, conformational constraints and dense packings. The HP model has become a standard for assessing the efficiency of folding algorithms, and numerous -some very tailored -conformational ground state search strategies have been proposed, see e. g. [5][6][7][8] and references therein. More revealing than algorithms that merely search for low energy states, however, are methods which target the sampling of the entire conformation and energy space.…”

Mathematical Programming in Computational Biology: an Annotated Bibliography

“…The ILP fails to find optimal folds for proteins longer than 30 aminoacids. The most successful approaches for HP folding are based on constraint programming, a technique that allows the optimal solution for instances of up to 200 aminoacids [42].…”