Global optimization of proteins using a dynamical lattice model: Ground states and energy landscapes

A simple approach is proposed to investigate the protein structure. Using a low complexity model, a simple pairwise interaction and the concept of global optimization, we are able to calculate ground states of proteins, which are in agreement with experimental data. All possible model structures of small proteins are available below a certain energy threshold. The exact low­ energy landscapes for the trp cage protein (1L2Y) is presented showing the connectivity of all states and energy barriers. The most challenging problem in quan­ titative biology today would be the resp­ onse to the question, just how the spati­ al structure of a protein is encoded in its sequence of amino acids. The huge number of degrees of freedom per ami­ no acid with respect to its spatial struc­ ture is reflected in the high computatio­ nal complexity in continuous space protein models. Their variants with space discretization are called high coordination lattice models [1]. Alterna­ tively, simple lattice models are widely investigated, based on the assumption that the positions of amino acids are re­ presented by vertices of a regular lattice (see e.g. [2]). In these cases, there are only z­1 possibilities for the position of the next amino acid in a chain, where the coordination number z is 4 for the square lattice and varies between 6 and 12 for the standard 3d lattices. Using simple lattice models, one may study the qualititative behaviour of protein folding and dynamics. However, these models restrict the finding of the real three­dimensional structure because of rigidity in the underlying crystalline (predefined) lattice. We propose a dyna­ mical lattice model (DLM), which belongs to another class of low­coordi­ nation number models: the so­called re­ duced (ϕ−ψ) or (α­τ) models. Its intro­ duction is motivated by the request to combine low computational complexity with the possibility of an adequate de­ scription of the spatial structure. Other investigations on the basis of such redu­ ced discrete state models are done by Park and Levitt [3] without considerati­