The topological study of biological polymers has led to important insights into their structural properties and evolution. From a topological point of view polymers can be naturally modeled as sequences of 3D points, i.e. open polygonal paths. Their closure generates classical objects in topology called knots. The simplest knot is the trefoil knot, illustrated in Figure 1A. The characterization of knotted proteins, due to their close structurefunction relationship and reproducible entangled folding, is a subject of increasing interest in both experimental and computational biology. Knots investigation was initially fostered by the discovery of knotted circular single-stranded DNA and has been followed by the study of the underlying enzymatic mechanisms and more recently by the description of the topological organization and packing dynamics of bacteriophage P4 genome. Despite those great advances in knotted DNA studies, we are only beginning to go deeper into protein knots characterization and the understanding of their biological role. After the pioneering work of Mansfield and the definition of topological descriptors for the analysis of protein symmetries and proteins classification, the detection of knots in proteins was boosted by Taylor��s work. The exponential growth of the total number of structures deposited into the Protein Data Bank requires dedicated computational highthroughput methods able to deal with a large amount of data. These methods combine a structure reduction scheme of a protein backbone model with the computation of a knot invariant, the Alexander polynomial. Hereinafter with the term reduction we refer to a stepwise deletion of a certain number of points from the original structure that preserves its ambient isotopy class. The most affirmed reduction algorithm is the KMT reduction scheme. KMT owes its name to the different algorithms proposed by Koniaris and Muthukumar and Taylor. Since the use of this acronym has engendered a little confusion on which algorithm is precisely being used in literature we will explicitly refer to them by authors�� names. Ifetroban sodium Globally, these methods are based on the concept of elementary deformation, which consists in the replacement of two sides of a triangle with the third provided that the triangle is empty. In particular while Koniaris and Muthukumar��s algorithm essentially reproduces the ideas of Alexander-Briggs and Reidemeister, in the Taylor��s algorithm the elementary deformation is done in steps that progressively smooth the chain at the cost of introducing points not Atropine belonging to the protein backbone; the edge replacement depends on some selected conditions chosen to prevent numerical problems.