Exact methods for lattice protein models

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.

THE STRUCTURE OF THE FREE ENERGY SURFACE OF COARSE-GRAINED OFF-LATTICE PROTEIN MODELS

We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with a simple effective, coarse-grained off-lattice model to study the structure and the topology of the energy surface. The multicanonical method samples the whole rugged energy landscape, in particular the low-energy part, and enables one to better understand the critical behaviors and visualize the folding pathways of the considered protein model.

STUDIES OF FINDING LOW ENERGY CONFIGURATIONS IN OFF-LATTICE PROTEIN MODELS

We studied two three-dimensional off-lattice protein models with two species of monomers, hydrophobic and hydrophilic. Low energy configurations in both models were optimized using the energy landscape paving (ELP) method and subsequent gradient descent. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. For all sequences with lengths 13 ≤ n ≤ 55, the algorithm finds states with lower energy than previously proposed putative ground states.