Several pieces of experimental evidence led us to hypothesize that the mechanism of action of paclitaxel (Taxol) could involve a two-steps binding process, with paclitaxel first binding within the outer wall of microtubules and then moving into the inner binding site. In this work, we first used multiply targeted molecular dynamics (MTMD) for steering paclitaxel from the outer toward the inner binding site. This rough trajectory was then submitted to a refinement procedure in the path collective variables space. Paclitaxel binding energy was monitored along the refined pathway, highlighting the relevance of residues belonging to the H6-H7 and the M- loops. Computational results were supported by kinetics studies performed on fluorescent paclitaxel derivatives.