In the multisite representation, each λ-coordinate is independent of the others and thus evolves on a one dimensional potential (equation 4), similar to that of "chemically" uncoupled sites. However, in contrast to the uncoupled sites, the correction potential V MM is multidimensional as its value depends on all λ i,k coordinates representing each of the possible protonation states of residue i. These potentials are obtained through a least-square fit of a multi-dimensional polynomial to the ensemble-averaged gradients of the potentials with respect to λ i,k evaluated on the (n i -1)-dimensional grid of the n i coupled λ-s, i. e.: