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A fully atomistic modelling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and it a posteriori analysis. This difficulty can be overcome with the use of multi-resolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive atomistic detail is crucial in the modelling of the active site in order to capture e.g. the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme (HEWL) with the inhibitor di-N-acetylchitotriose. Particular attention is posed to the impact of the mapping, i.e. the selection of atomistic and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.