Fig. 1: The protein universe is topologically rich.

The 214M AlphaFold2 protein structures, organised by species and plotted as a tree of life (A). Their topological analysis (sketched in the purple box, B) reveals intricacy and variety of topological features and a remarkable complexity across the evolutionary tree, which we represent using a circle packing plot. The area of each circle is proportional to the number of proteins grouped in it (C). Circles saturation represents average topological richness, which is also shown numerically for domains, kingdoms, phyla, and selected species of interest. The average richness is approximated here by normalising by group-averaged protein size. The colour scale has the upper bound set by the 95% quantile to ignore outliers and emphasise differences, and has domain averages indicated by black lines (D). Boundaries of circles are coloured by topological variance (E). Zooming into humans, each protein is shown as a dot, with colour saturation proportional to its topological richness. Haemoglobin (G) is plotted showing its most persistent one-dimensional (left, a loop) and two-dimensional (right, a void) topological features (H), and below with amino-acids coloured by their topological influence score (I), with a white-blue-purple scale (F).