Is there a Mobius band in closed protein β-sheets?

Protein beta-strands can form beta-barrels and other complicated structures. This paper defines bifurcations and pseudobifurcations of beta-sheets. They are important structural elements for protein folding. This paper also presents a characteristic number that can be used to test whether the surface of a closed beta-sheet is one- or two-sided. Searching the whole Protein Data Bank released in April 1997 with the definition of beta-structures given by the DSSP program, we do not find any one-sided beta-Mobius band. However, there are interesting structures such as beta-bands with odd number of antiparallel ladders and odd number of bifurcations. There are also beta-structures that are closed only at a singular point. Adding a small patch near the singular point in different ways can make it a one- or two-sided surface. The catalytic triad of a GMP synthetase (1GPM) is near the singular point of such a beta-sheet.