Lasso type classification

In AlphaLasso database, the piercing information (described in LassoProt database) obtained for each closed loop in a chain enables us to establish lasso type classification. The loop is closed based on the distance of 3 Å between the sulfur atom, which can form a cysteine bond. In general protein lasso has a loop and two tails (N-tail and C-tail). Rarely, when a cysteine bond is created by the first or last residue there is only one tail. Each tail can pierce a loop, even more then once. We distinguish two sides of the loop and we mark them as + and - side, therefore every tail can be described by a sequence of + and - which describe from which side tail is pinning the loop. Most tails which pierce a loop many times do this in an alternating way forming a +-+-+- or -+-+-+ pattern (order is aligned with residue numbering). However, some of them after piercing wind around a loop and pierce a loop again from the same side, therefore in their pattern are two neighboring pluses or minuses. Such lassos we call supercoiled lassos.

Herein, we take into account the following lasso type as described below: piercings by one tail (supercoiled or not) and two-sided (supercoiled from both sides, from one side, or not supercoiled). Then each type can be divided into sub-categories depending on the number of piercings. In the case of protein predicted based on AlphaFold the complexity of the lasso is much greater than that of the known structures deposited in LassoProt.

• L0 - Trivial non-pierced lasso.
• L _iN (L _iC) - One sided lasso. A N-tail (C-tail) goes through the loop i times in an alternating way (every piercing is from a different side than the previous one). The other tail does not pierce the loop.
• LS _iN (LS _iC) - One sided supercoiled lasso. Same as above, but at least one piercing is from the same side as the previous one.
• LL _i,j - Two sided lasso. Both tails go through the loop in alternating ways: A N-tail goes through the loop i times, C-tail goes through the loop j times.
• LSL _i,j - Two sided lasso, N-supercoiled. Same as above, but supercoiled from N-side and regular from C-side.
• LLS _i,j - Two sided lasso, C-supercoiled. Same as above, but regular from N-side and supercoiled from C-side.
• LSLS _i,j - Two sided lasso, supercoiled from both N- and C-side.

Type can be specified further with added piercing pattern e.g. LLS3+,4-++-, which means that from N-tail pierces in an alternating way starting from +, and C-tail pierces from - side, then two times from + side (supercoiling) and again from - side.

1. Lasso

In the case when a covalent loop is pierced by one tail, we identified the following topological types: L₁–L₂₆, L28, and L30. Note that in this case at least one structure with a given topology has been verified by us. This does not mean that all structures of a given class are correct.

• L1 - single lasso, a covalent loop is pierced once by a tail.
• L2 - double lasso, a covalent loop is pierced twice by the same tail (after piercing the loop once the tail winds back and pierces it the second time from the opposite direction).
• L_i - i lasso, a covalent loop is pierced i times by the same tail (similarly as in the L2 case but winding back one more time).

Figure 1. Schematic representation of a regular one-sided lasso, examples of lasso types: L0, L1, L2, and L3 (top panel). Bottom panel, cartoon representations of the protein structures with their AlphaFold IDs.

2. Two-sided lasso

LL1,1, LL1,2, LL1,3, LL1,4, LL1,5, LL1,6, LL1,7, LL1,8, LL1,9, LL1,11, LL1,12, LL2,1, LL2,2, LL2,3, LL2,4, LL2,5, LL2,6, LL2,7, LL2,8, LL2,9, LL2,11, LL2,15, LL3,1, LL3,2, LL3,3, LL3,4, LL3,5, LL3,6, LL3,7, LL4,1, LL4,2, LL4,3, LL4,4, LL4,5, LL4,6, LL4,9, LL5,1, LL5,2, LL5,3, LL5,4, LL5,5, LL5,6, LL5,7, LL5,9, LL6,1, LL6,2, LL6,3, LL6,4, LL6,5, LL6,8, LL7,1, LL7,2, LL7,5, LL8,2, LL8,5, LL9,1, LL15,1, and LL28,1.

• LL_i,j - two-sided lasso, a covalent loop is pierced by two tails, i times by one tail and j times by another tail; sometimes we do not specify the numbers i and j and simply denote two-sided lassos as LL.

Figure 2. Schematic representation of LL1,1 two-sided lasso (left), and LL1,1 protein structure (right) with its respective AlphaFold ID.

Supercoiling lasso

LS₂–LS21, LS24, LS26, LS27, LS35, and LS37.

• LS - supercoiling, one tail pierces the covalent loop, then winds around the protein chain comprising the loop, and pierces it again (the covalent loop is pierced twice, each time from the same direction).

Figure 3. Schematic representation of LS2 supercoiled lasso (left), and LS2 protein structure (right) with its respective AlphaFold ID.

Disulfide bridge, S-S

Disulfide bridges, also known as S-S bridges, are strong covalent linkages formed between two cysteine amino acids within a protein, Figure 4. These linkages occur when the side chains of two cysteines, containing thiol groups (SH), react with each other to form a disulfide bond (S-S). Disulfide bridges significantly contribute to protein stability by creating a cross-link between different parts of the protein chain, thereby maintaining its three-dimensional structure.

Figure 4. Cysteine (Disulfide) bridge, S-S, in carton (left panel) and stick (right panel) representation. Left panel, cartoon representation of AlphaFold ID A0A067QHV7 protein, lasso type L1, with the minimal surface in dark gray and the cysteine bridge in yellow. The zoom region highlighted the atoms forming the S-S bridge. Right panel, stick representation, the cysteines are separated by orange arcs. Dashed lines denote the remaining part of the protein chain.

Two different file extensions are accepted to compute the lasso properties, CIF and PDB. In a CIF file disulfide bridges can be found in the “struct_conn” category. Record describes disulfide bridge if the value of “conn_type_id” is equal to “disulf”. PDB files utilize three different records to identify S-S bridge: (i) "CONECT” - these lines show which non-backbone atoms are connected within the protein structure; (ii) “SSBOND" or (iii) "LINK" to explicitly define S-S bridges.

Unfortunately AlphaFold doesn't identify disulfide bridges, therefore records mentioned above are empty. However, AlphaLasso doesn't need those records to identify disulfide bridges! We identify bridges by finding pairs of cysteine sulfurs which are no further than 3 Å.