Atomic radii play important roles in scientific research. The covalent radii of atoms, ionic radii of ions, and van der Waals (VDW) radii of neutral atoms can all be derived from crystal structures. However, the VDW radii of ions are a challenge to determine because the atomic distances in crystal structures were determined by a combination of VDW interactions and electrostatic interactions, making it unclear how to define the VDW sphere of ions in such an environment. In the present study, we found that VDW radii, which were determined based on the 0.0015 au electron density contour through a wavefunction analysis on atoms, have excellent agreement with the VDW radii of noble-gas atoms determined experimentally. Based on this criterion, we calculated the VDW radii for various atomic ions across the periodic table, providing a systematic set of VDW radii of ions. Previously we have shown that the 12-6 Lennard-Jones nonbonded model could not simultaneously reproduce the hydration free energy (HFE) and ion−oxygen distance (IOD) for an atomic ion when its charge is +2 or higher. Because of this, we developed the 12-6-4 model to reproduce both properties at the same time by explicitly considering the ion-induced dipole interactions. However, recent studies showed it was possible to use the 12-6 model to simulate both properties simultaneously when an ion has the R min /2 parameter (i.e., the VDW radius) close to the Shannon ionic radius. In the present study, we show that such a "success" is due to an unphysical overfitting, as the VDW radius of an ion should be significantly larger than its ionic radius. Through molecular dynamics simulations, we show that such overfitting causes significant issues when transferring the parameters from ion−water systems to ion− ligand and metalloprotein systems. In comparison, the 12-6-4 model shows significant improvement in comparison to the overfitted 12-6 model, showing excellent transferability across different systems. In summary, although both the 12-6-4 and 12-6 models could reproduce HFE and IOD for an ion, the 12-6-4 model accomplishes such a task based on the consideration of the physics involved, while the 12-6 model accomplishes this through overfitting, which brings significant transferability issues when simulating other systems. Hence, we strongly recommend the use of the 12-6-4 model (or even more sophisticated models) instead of overfitted 12-6 models when simulating complex systems such as metalloproteins.

Atomic radii play important role in scientific research. The covalent radii of atoms, ionic radii of ions, and van der Waals (VDW) radii of neutral atoms can all be derived from crystal structures. However, the VDW radii of ions are a challenge to determine because the atomic distances in crystal structures were determined by a combination of the VDW interactions plus the electrostatic interactions, making it unclear how to define the VDW sphere of ions in such an environment. In the present study, we found that the VDW radii, which were determined based on the 0.0015 au electron density contour through a wavefunction analysis on atoms, have excellent agreement with the VDW radii of noble gas atoms determined experimentally. Based on this criterion, we calculated the VDW radii for various atomic ions across the periodic table, providing a systematic set of VDW radii of ions. Previously we have shown that the 12-6 Lennard-Jones nonbonded model could not simultaneously reproduce the hydration free energy (HFE) and ion-oxygen distance (IOD) for an atomic ion when its charge is +2 or higher. Because of this, we developed the 12-6-4 model to reproduce both properties at the same time by explicitly considering the ion-induced dipole interactions. However, recent studies showed it was possible to use the 12-6 model to simulate both properties simultaneously when an ion has the Rmin/2 parameter (i.e., the VDW radius) close to the Shannon ionic radius. In the present study, we show that such a “success” is due to an unphysical overfitting, as the VDW radius of an ion should be significantly larger than its ionic radius. Through molecular dynamics simulations, we show that such overfitting causes significant issues when transferring the parameters from ion-water systems to ion-ligand and metalloprotein systems. In comparison, the 12-6-4 model shows significant improvement in comparison to the overfitted 12-6 model, showing excellent transferability across different systems. In summary, although both the 12-6-4 and 12-6 models could reproduce HFE and IOD for an ion, the 12-6-4 model accomplishes such a task based on the consideration of the physics involved, while the 12-6 model accomplishes this through overfitting, which brings significant transferability issues when simulating other systems. Hence, we strongly recommend the use of the 12-6-4 model (or even more sophisticated models) instead of overfitted 12-6 models when simulating complex systems such as metalloproteins.

Atomic radii play important role in scientific research. The covalent radii of atoms, ionic radii of ions, and van der Waals (VDW) radii of neutral atoms can all be derived from crystal structures. However, the VDW radii of ions are a challenge to determine because the atomic distances in crystal structures were determined by a combination of the VDW interactions plus the electrostatic interactions, making it unclear how to define the VDW sphere of ions in such an environment. In the present study, we found that the VDW radii, which were determined based on the 0.0015 au electron density contour through a wavefunction analysis on atoms, have excellent agreement with the VDW radii of noble gas atoms determined experimentally. Based on this criterion, we calculated the VDW radii for various atomic ions across the periodic table, providing a systematic set of VDW radii of ions. Previously we have shown that the 12-6 Lennard-Jones nonbonded model could not simultaneously reproduce the hydration free energy (HFE) and ion-oxygen distance (IOD) for an atomic ion when its charge is +2 or higher. Because of this, we developed the 12-6-4 model to reproduce both properties at the same time by explicitly considering the ion-induced dipole interactions. However, recent studies showed it was possible to use the 12-6 model to simulate both properties simultaneously when an ion has the Rmin/2 parameter (i.e., the VDW radius) close to the Shannon ionic radius. In the present study, we show that such a “success” is due to an unphysical overfitting, as the VDW radius of an ion should be significantly larger than its ionic radius. Through molecular dynamics simulations, we show that such overfitting causes significant issues when transferring the parameters from ion-water systems to ion-ligand and metalloprotein systems. In comparison, the 12-6-4 model shows significant improvement in comparison to the overfitted 12-6 model, showing excellent transferability across different systems. In summary, although both the 12-6-4 and 12-6 models could reproduce HFE and IOD for an ion, the 12-6-4 model accomplishes such a task based on the consideration of the physics involved, while the 12-6 model accomplishes this through overfitting, which brings significant transferability issues when simulating other systems. Hence, we strongly recommend the use of the 12-6-4 model (or even more sophisticated models) instead of overfitted 12-6 models when simulating complex systems such as metalloproteins.

The fluctuating charge (FQ) model can generate atomic charges much more efficiently than quantum mechanical methods. The FQ model has been developed for a wide range of applications, but few models were specifically tailored for calculating atomic charges of metalloproteins. Zinc-containing proteins widely exist in biology and play important roles in various processes. In this study, we present a fluctuating charge model for zinc-containing metalloproteins based on the charge equilibration (Qeq) scheme. Our model was parameterized to reproduce CM5 charges, which demonstrated excellent performance in reproducing molecular dipole moments. During our study, we found that adding the Pauling-bond-order-like term (referred to as the "+C term" in a previous study) between the zinc ion and ligating atoms significantly improves the model's performance. Although our model was trained for four-coordinated zinc sites only, our tests indicated it can well describe the atomic charges in five- and six-coordinated zinc sites as well. Finally, we adapted our model to generate partial charges for the metal site in a zinc finger domain. These charges exhibited comparable performance to the widely used restrained electrostatic potential (RESP) charges in molecular dynamics (MD) simulations. The current model can be extended to other metal-containing systems and serve the molecular modeling community.