Once the reduction has been accomplished knot type identification can be performed. This can be done either by visual inspection or by computing a polynomial invariant. Being easy to compute the Alexander polynomial represents the current default choice. This is also supported by the evidence that protein knots detected to date are the simplest ones as illustrated in Figure 2. Unfortunately, the Alexander polynomial does not distinguish a knot from its mirror image. Thus, for instance leftand right-handed trefoil knots share the same polynomial. Instead, more powerful invariants are able to determine knots chirality. Whereas to define the handedness of the simplest knot types is straightforward, its extension to more complex knots requires carefulness. However, for the purpose of this article, a knot is chiral if its mirror image and the knot itself belong to two Beclomethasone different ambient isotopy classes and it is achiral otherwise. As far as proteins are concerned, the handedness of protein knots was only partially addressed so far. Taylor points out the existence of both right- and left-handed trefoil knots, with a neat right-handed preference. This hypothesis was supported by the finding that all trefoil knotted proteins belong to the SCOP ba class, where an intrinsic right-handed preference for bab unit connections exists. The only left-handed trefoil knot was detected in the ubiquitin C-terminal hydrolases considered afterwards as an incomplete five crossings knot. However, by considering individual fragments the knot vanishes. A more recent work that removed sequence redundancy, intriguingly highlights a global 5 to 3 balance between right-handed and left-handed knots, not suggesting a bias for one of the two hands. Generally, the skein relation does not preserve the multiplicity of a link. For example if Lz is a knot, L0 will be a two components link. The recursion of the skein relation together with the values of the given polynomial on the unknot allows to reconstruct the polynomial of any given link. Binucleine 2 Therefore, the complexity of the polynomial computation grows exponentially with the number of crossings to be processed. Our algorithm relies on the iteration of the skein relation and explicitly constructs the Conway skein triple associated to a given crossing by a stepwise insertion of auxiliary points. In order to deal with multi-component links and speed up computations, the polynomial computation is preceded by the application of a structure reduction scheme, which we call MSR.