Two approaches have been proposed: (i) direct coupling between each titratable residue and a water, or ion, and (ii) titratable buffers that collectively compensate changes in charge of all titratable residues. Here, we follow the latter approach, but with several improvements for all-atom simulations. Firstly, to avoid restraints, which were needed to minimize interactions between the buffers and the titrable sites in previous work, we introduced buffer particles with both small LJ radius and small partial charges of maximal |0.5| e, such that they do not disturb the hydrogen bond network, nor interact too strongly with the titratable sites or other buffers.