Figure 1.

How to compute the genus. A biomolecule (schematically shown in the left, with residues represented by black dots, and bonds by blue and red segments) can be represented by a chord diagram shown as the second item. A chord diagram consists of b backbones (horizontal segments) and n chords (arcs). Thickening all backbones and chords (and replacing each stack of parallel chords by a single chord or ribbon) gives rise to a ribbon diagram (the third item), which has r boundary components (shown in yellow). Such a ribbon diagram can be drawn smoothly on a surface (shown on the right) of genus g (the number of ‘holes’) given by the Euler formula b − n = 2 − 2g − r. The ribbon diagram in this figure has b = 1, n = 2, and r = 1 (there is one yellow boundary), so that we find g = 1.