Polarization effects in protein-ligand calculations extend farther than the actual induction energy

The various roles that polarizabilities play in the calculation of protein-ligand interaction energies with a polarizable force field are investigated, and the importance and distance dependence of some common approximations is determined for each of these roles separately, using quantum-mechanical calculations as the reference. It is found that the pure induction energy, if defined as the energetic gain from the charge redistribution upon interaction between the protein and ligand, is a rather short-ranged effect that becomes independent of the exact implementation at distances above similar to 4 angstrom. On the other hand, the polarization between the protein residues in the assembly of a protein from separately computed fragments (as is routinely done in force field development) has a significant effect on the computed interaction energies, even for residues as far as 15 angstrom from the ligand. Finally, polarization improves the transferability of partial charges, but the simple polarization model used in, for example, the Amber force field explains only 14-19% of the conformational variation of the charges. In all cases, more advanced polarization models, especially involving anisotropic polarizabilities, seem to give significantly better descriptions of these effects. The study suggests that an accurate treatment of polarization can be important even in systems where the actual induction energy is small in magnitude.