This document contains additional information regarding the details of the three methods for free energy calculations employed in the study. All three methods are based on molecular dynamics. For methods I and II the binding free energy is obtained by numerical integrationas: ∆Fbind = Fbound − Ffree =∫ 10〈 dHdλ〉N V T ; λdλ . (1)The ensemble average is calculated as a time average from a molecular dynamics simulations in the canonical (NVT) ensemble. The coupling parameter, λ, is chosen such that the Hamiltonian is changed from describing the bound state to describing the free state of theZn ion. If the transformation process is reversible, the free energy change is independent of the reaction path and only depends on the initial and final states. Therefore we are free to choose the path of integration in Eq. (1) as long as the reversibility condition is met. Determining differences between two large numbers, as is the case in Eq. (1), can be problematic since the statistical errors involved are large as well. If λ is constructed wisely, large energy differences and their errors can be made to cancel in the final result. In general 2 it is non-trivial to find ways which allow for such cancellations. In our case we are comparing two states where the long-range electrostatics are very similar and therefore minimises the otherwise serious issues linked to changing charges in free energy calculations.