Protein KnotsThe knot server allows the user to check pdb entries or uploaded structures for
knots and to visualize them. The size of a knot is determined by deleting amino
acids from both ends. This procedure is, however, not perfect and the resulting
size should only be treated as a guideline.
List of known knots
How we define knots
Mathematically, knots are
only well defined in closed (circular) loops. However, both the N- and
C-termini of open proteins are typically located close to the surface of the
protein and can be connected unambiguously: We reduce the protein to its
backbone and draw two lines outward starting at the termini in the direction of
the connection line between the centre of mass of the backbone and the
respective ends. The two lines are joined by a big loop, and the structure is
topologically classified by the determination of its Alexander polynomial. To
determine an estimate for the size of the knotted core, we successively delete
amino acids from the N-terminus until the protein becomes unknotted. The
procedure is repeated at the C-terminus starting with the last N-terminal
deletion structure that contained the original knot. For each deletion, the
outward-pointing line through the new termini is parallel to the respective
lines computed for the full structure. Unfortunately, the size of a knot is not
always precisely determined by this procedure, so reported sizes should
therefore only be treated as approximate.
To speed up calculations, the KMT reduction scheme is used. This algorithm
successively deletes amino acids that are not essential to the topological
structure of the protein. It is also employed to create a reduced
representation of the knot. In the course of our investigations we came up
with a number of stringent criteria that a structure should satisfy to be
classified as knotted:
- The Alexander polynomial should yield a knot.
- There should not be any gaps in the polypeptide backbone. (See below.)
- The knot should persist if two amino acids are removed from each end. (This prevents knots formed by just a few residues at the end of the chain passing through the loop - "shallow knots" and knots which only appear due to our specific loop closure procedure.)
Unfortunately, there are some structures containing regions of the backbone
that were not resolved and for which coordinates are not reported in PDB (a gap
in the structure). Mobile loops may not be resolved by X-ray crystallography
unless they are stabilized by a ligand or by protein engineering, for example.
If the polypeptide chain contains a gap, the knot is reported if a knot is
present in at least one fragment of the chain and the structure that
results from gaps being bridged with straight lines contains a knot. These
criteria form the basis of our list of known knots. We have also included
knotted structures with gaps if at least one homolog is knotted.
Questions about particular knots? Contact Peter Virnau.