Bridging the 12-6-4 Model and the Fluctuating Charge Model

Metal ions play important roles in various biological systems. Molecular dynamics (MD) using classical force field has become a popular research tool to study biological systems at the atomic level. However, meaningful MD simulations require reliable models and parameters. Previously we showed that the 12-6 Lennard-Jones nonbonded model for ions could not reproduce the experimental hydration free energy (HFE) and ion-oxygen distance (IOD) values simultaneously when ion has a charge of +2 or higher. We discussed that this deficiency arises from the overlook of the ion-induced dipole interaction in the 12-6 model, and this term is proportional to 1/r4 based on theory. Hence, we developed the 12-6-4 model and showed it could solve this deficiency in a physically meaningful way. However, our previous research also found that the 12-6-4 model overestimated the coordination numbers (CNs) for some highly charged metal ions. And we attributed this artifact to that the current 12-6-4 scheme lacks a correction for the interactions among the first solvation shell water molecules. In the present study, we considered the ion-included dipole interaction by using the 12-6 model with adjusting the atomic charges of the first solvation shell water molecules. This strategy not only considers the ion-induced dipole interaction between ion and the first solvation shell water molecules but also well accounts for the increased repulsion among these water molecules compared to the bulk water molecules. We showed this strategy could well reproduce the experimental HFE and IOD values for Mg2+, Zn2+, Al3+, Fe3+, and In3+ and solve the CN overestimation issue of the 12-6-4 model for Fe3+ and In3+. Moreover, our simulation results showed good agreement with previous ab initio MD simulations. In addition, we derived the physical relationship between the C4 parameter and induced dipole moment, which agreed well with our simulation results. Finally, we discussed the implications of the present work for simulating metalloproteins. Due to the fluctuating charge model uses a similar concept to the 12-6 model with adjusting atomic charges, we believe the present study builds a bridge between the 12-6-4 model and the fluctuating charge model.