Tubes near the edge of compactness and folded protein structures

The protein folding problem has remained unsolved despite many decades of effort. Motivated by many of the puzzles in this field, we have carried out studies of the zero-temperature geometry of a short tube of non-zero thickness subjected to attractive interactions promoting its compaction. Here we present a review of our recent research on this subject. On varying a parameter, the ratio of the tube thickness to the 'range of attractive interactions, we find a 'transition' between two highly degenerate phases. The transition region in between is characterized by a marked decrease in the degeneracy-the ground state structures are 'marginally compact' and-there is efficient space filling of the core region by the tube. Several classes of structures, especially helices and sheets, emerge as the chosen ground state conformations, many of which are building blocks of biomolecules. We also present results for the temperature-thickness phase diagram of longer tubes. We benchmark our results against experimental observations of proteins