To assess if move length distribution changes during structure reduction, we compared the move distributions of the first and fourth quartile of the BMS-764459 reduction process. To avoid overlaps, we considered reduction sequences of length at least 4. A significant difference between the two BIBP 3226 quartiles emerged, as highlighted in Figure 7C. Moves with length up to 6 are more frequent toward the end of the reduction process, while long moves occur preferentially in the first reduction quartile. This behavior is also confirmed by comparing the first and second half of the reduction process. However, shorter final moves are in principle explained by an increase of the edges mean length, as can be seen in Figure 6. Finally, an interesting effect emerges when the frequencies of move lengths were analyzed as a function of the residual protein lengths at which they occur. By grouping move lengths in quartiles, while moves below the median reach the minimum frequency for a residual length around 60, the opposite behavior is attained by moves above the median. Interestingly, a residual length around 60 is the optimum of the reduction process, where the frequency of 0 moves reaches its minimum and contextually the frequency of long moves is maximum. We have presented a novel topological framework for the HOMFLY polynomial computation of polygonal paths based on the geometric construction of Conway skein triples. Validation on tabulated knots and links demonstrates the global method robustness and the effectiveness of the greedy selection of the crossing to be switched. These evidences have been further confirmed by the polynomial computation of protein structures, also leading to an upto date table of knotted structures. Whereas the performed topological checks allowed to discard artificially entangled proteins, two new right-handed trefoil knots have been detected. Remarkably, the application range of the presented framework is not limited to proteins and it can be extended to the topological analysis of biological and synthetic polymers. Particularly, the study of knotted synthetic polymers like polyethylene has led to insights into the mechanical properties of such structures. The presence of a knot strongly weakens the polymer that potentially breaks at the entrance to the knot. Furthermore, knots frequency depends on the solvent and is higher in the coil phase than the globular phase with the knotted core size that increases as a function of the number of monomers.