Scalable Indirect Free Energy Method Applied to Divalent Cation-Metalloprotein Binding

Many biological processes are based on molecular recognition between highly charged molecules such as nucleic acids, inorganic ions, charged amino acids, etc. For such cases, it has been demonstrated that molecular simulations with fixed partial charges often fail to achieve experimental accuracy. Although incorporation of more advanced electrostatic models (such as multipoles, mutual polarization, etc.) can significantly improve simulation accuracy, it increases computational expense by a factor of 5-20x. Indirect free energy (IFE) methods can mitigate this cost by modeling intermediate states at fixed-charge resolution. For example, an efficient reference model such as a pairwise Amber, CHARMM, or OPLS-AA force field can be used to derive an initial estimate, followed by thermodynamic corrections to a more advanced target potential such as the polarizable AMOEBA model. Unfortunately, all currently described IFE methods encounter difficulties reweighting more than similar to 50 atoms between resolutions due to extensive scaling of both the magnitude of the thermodynamic corrections and their statistical uncertainty. We present an approach called simultaneous bookending (SB) that is fundamentally different from existing IFE methods based on a tunable sampling approximation, which permits scaling to thousands of atoms. SB is demonstrated on the relative binding affinity of Mg2+/Ca2+ to a set of metalloproteins with up to 2972 atoms, finding no statistically significant difference between direct AMOEBA results and those from correcting Amber to AMOEBA. The ability to change the resolution of thousands of atoms during reweighting suggests the approach may be applicable in the future to protein-protein binding affinities or nucleic acid thermodynamics.