Exploring protein folding trajectories using geometric spanners.

We describe the 3-D structure of a protein using geometric spanners--geometric graphs with a sparse set of edges where paths approximate the n2 inter-atom distances. The edges in the spanner pick out important proximities in the structure, labeling a small number of atom pairs or backbone region pairs as being of primary interest. Such compact multiresolution views of proximities in the protein can be quite valuable, allowing, for example, easy visualization of the conformation over the entire folding trajectory of a protein and segmentation of the trajectory. These visualizations allow one to easily detect formation of secondary and tertiary structures as the protein folds.