We selected 10 interatomic distances (Figure , d1-d10) between the residues of the catalytic triad and the substrate (PET4 or PEF4) to describe the acylation step. In the case of deacylation, we included a further distance (d11) and three coordination numbers (c1, c2, c3) describing the interactions of the water molecule within the active site. We considered the coordination numbers between the O atom of the water molecule (c1), the Ne atom of H237 (c2) or the hydroxyl Og atom of S160 (c3) with the two H atoms of water to account for the cleavage or formation of covalent bonds independent of which of the two H atoms is involved. Moreover, since the acylation reaction involves comparing descriptors with different physical meanings (distances and coordination numbers), the descriptor values were preprocessed by subtracting the mean of each descriptor's dataset, considering both distributions simultaneously, and normalizing the final data to a range of -1 to +1 before applying HLDA. The selected descriptors are defined in Table along with the coefficients obtained via HLDA, whereas the atoms involved are illustrated in Figure . A representation of the distances and coordination numbers included in the analysis is provided in Figure and Figure for the PETase-PET4 and PETase-PEF4 systems, respectively. , which were used to construct the reaction coordinate via HLDA. PETase is depicted as a transparent grey cartoon, with the catalytic triad (S160, H237, and D206) highlighted. The two tetramers, PET4 and PEF4, are shown in a linear configuration for clarity.