Given the prominent role of the changes in water solvation around the Zr 4+ upon binding to DFO and 4HMS, it is interesting to understand whether this has any impact on the thermodynamics reported in Fig. . Specifically, the free energy curves discussed earlier are along one reaction coordinate only, namely the CN collective variable which counts the oxygen atoms belonging to the chelator hydroxamate groups coordinating the ion. From the 1dimensional umbrella sampling simulations, it is also possible to reconstruct a 2-dimensional free energy surface along our original CN variable and another variable that counts the number of water molecules coordinating the Zr 4+ (labeled as CN Zr 4+ --O W , see Methods section for definition). Fig. shows the 2-dimensional free energy surfaces constructed for DFO (left panel) and 4HMS (right panel) as a function of the original CN we used earlier (labeled as CN Zr 4+ --O X on the x-axes) and of the CN Zr 4+ --O W (on the y-axes) . For both DFO and 4HMS, we observe that explicit inclusion of solvation in the reaction coordinate does not change our conclusions. For DFO, the free energy minimum involves a structure where there are three to four oxygen atoms of DFO coordinated to Zr 4+ while for 4HMS, the minimum occurs approximately at 8 hydroxamate oxygen atoms. Furthermore, the free energy differences between the stable and high energy structures are also consistent between the 1-d and 2-d analyses.