Complex lasso: new entangled motifs in proteins

Abstract

We identify new entangled motifs in proteins that we call complex lassos. Lassos arise in proteins with disulfide bridges (or in proteins with amide linkages), when termini of a protein backbone pierce through an auxiliary surface of minimal area, spanned on a covalent loop. We find that as much as 18% of all proteins with disulfide bridges in a non-redundant subset of PDB form complex lassos, and classify them into six distinct geometric classes, one of which resembles supercoiling known from DNA. Based on biological classification of proteins we find that lassos are much more common in viruses, plants and fungi than in other kingdoms of life. We also discuss how changes in the oxidation/reduction potential may affect the function of proteins with lassos. Lassos and associated surfaces of minimal area provide new, interesting and possessing many potential applications geometric characteristics not only of proteins, but also of other biomolecules.

Figure 1. An example of a pierced lasso configuration of L₂ type.

Two cysteines form a disulfide bridge (orange) that closes (B,C) part of the backbone chain into a covalent loop. (A–F) Parts of the backbone chain are called tails. A minimal surface (in gray) spanned on the (B,C) loop is pierced twice by the (C–F) tail, at positions (D,E).

Figure 2

Left panel: cartoon representation of an oxidoreductase protein (PDB code 2oiz). Middle panel: triangulation of a minimal surface for 2oiz protein. The triangulated “soap bubble” surface, spanned on the covalent loop, is crossed twice by a tail, through triangles in blue and green. Two cysteines and a cysteine bond are shown in orange. Right panel: barycentric representation of a minimal triangulated surface for the protein 2oiz. Two cysteines and a disulfide bridge comprise a part of the boundary and are shown in orange. Green and blue triangles are pierced from opposite sides by 127th and 172nd tail segment respectively.

Figure 3. Various types of complex lasso motifs, denoted by: L₁ (single lasso), L₂ (double lasso), L₃ (triple lasso) – top row, left to right; LS (supercoiling) and LL_1,1 (two-sided lasso) – bottom row.

More complex lassos such as L₆ or LL_2,4 have an analogous structure.

Figure 4. Representation of hydrolase protein (PDB code 2ehg).

Left panel: cartoon representation of hydrolase protein (PDB code 2ehg). Middle panel: triangulation of a minimal surface for 2ehg protein. The triangulated “soap bubble” surface, spanned on the covalent loop, is crossed three times, through triangles in blue (once) and green (twice). Two cysteines and a cysteine bond are shown in orange. Right panel: barycentric representation of a minimal triangulated surface for 2ehg protein. Two cysteines and a cysteine bond comprising a part of the boundary and are shown in orange. Green and blue triangles are pierced from opposite sides by 6th, 21st and 36th tail segment.