Figure 1.

Proteins that represent various classes of entangled structures identified by KnotProt 2.0 (top row, structures with PDB codes, from left to right: 2EFV, 2RH3, 1AOC, 2P4Z, 2ML7) and their schematic representation (bottom row). Probabilistic knots are identified based on the protein backbone chain; the dashed line denotes a possible chain closure. All the structures with probabilistic knots are subjected to the knotoid analysis. Knotoids provide a refined characterization and classification of open chains, which depends, however, on the choice of the projection plane. Deterministic knots are detected based on all possible combinations of covalent bonds or interactions via ions with the protein’s backbone. In the case of probabilistic covalent and ion-based knots, the chain is closed based on the methods established previously for knotted proteins. The green bead in the schematic depiction denotes the ion, while the orange stripes denote the covalent connections (e.g. disulfide bonds). For structures with covalent bridges, consecutive parts of the chain constituting the knot are colored red to blue. The parts of the chain not building the knot are marked with light grey. The rightmost structure is a cysteine knot, which in fact is not a mathematical knot (for more details see Figure 11); in this example, the loop (blue) is closed by two disulfide bridges (orange) and pierced by the third disulfide bond (red).