Lattice protein models are well-studied abstractions of globular proteins. By discretizing the structure space and simplifying the energy model over regular proteins, they enable detailed studies of protein structure formation and evolution. However, even in the simplest lattice protein models, the prediction of optimal structures is computationally difficult. Therefore, often, heuristic approaches are applied to find such conformations. Commonly, heuristic methods find only locally optimal solutions. Nevertheless, there exist methods that guarantee to predict globally optimal structures. Currently, only one such exact approach is publicly available, namely the constraint-based protein structure prediction method and variants. Here, we review exact approaches and derived methods. We discuss fundamental concepts like hydrophobic core construction and their use in optimal structure prediction, as well as possible applications like combinations of different energy models.
A high coordination lattice discretization of protein conformational space is described. The model allows discrete representation of polypeptide chains of globular proteins and small macromolecular assemblies with an accuracy comparable to the accuracy of crystallographic structures. Knowledge based force Held, that consists of sequence specific short range interactions, cooperative model of hydrogen bond network and tertiary one body, two body and multibody interactions, is outlined and discussed. A model of stochastic dynamics for these protein models is also described. The proposed method enables moderate resolution tertiary structure prediction of simple and small globular proteins. Its applicability in structure prediction increases significantly when evolutionary information is exploited or/and when sparse experimental data are available. The model responds correctly to sequence mutations and could be used at early stages of a computer aided protein design and protein redesign. Computational speed, associated with the discrete structure of the model, enables studies of the long time dynamics of polypeptides and proteins and quite detailed theoretical studies of thermodynamics of nontrivial protein models.
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