Consequences of Overfitting the van der Waals Radii of Ions

Abstract

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.

Thermodynamics of Metal–Acetate Interactions

“…The results from this study show that two histidine residues contributing to the metal coordination sites lose their interactions with the metal ion. Two oxygen atoms from the negatively charged residues in the binding site then take over and coordinate with the metal ion in a bidentate mode.…”

“…To assess our parameters beyond a system composed exclusively of acetate and a metal ion, we applied them to a system containing the Escherichia coli Glyoxalase I metalloprotein (PDB ID: 1F9Z). A previous study on this protein indicates that the z12–6 parameters fail to maintain the coordination modes of both Ni­(II) binding sites after 80 ns of MD simulations . This metalloprotein is a homodimer comprising two metal-binding sites, with each binding site including His5, His74, Glu122, and Glu56 and two water molecules coordinating with one nickel (see Figure ).…”

Frontiers and Challenges of Computing ncRNAs Biogenesis, Function and Modulation

“…Conversely, Jungwirth and co-workers modified the description of the electrostatic term by exploiting an additional charge-scaling term . Finally, Schwierz and colleagues have introduced long-range interaction potential and optimized Lorentz combination rules. , Nevertheless, it remains questionable the generalizability and transferability of nonbonded 12–6 Mg 2+ models to RNA systems …”

Modeling Lanthanide Ions in Solution: A Versatile Force Field in Aqueous and Organic Solvents

“…Li’s methodology was a significant breakthrough because it provided a method for accurately simulating the behavior of a wide range of cations across the periodic table, including those with charges of +1, , + 2, , +3, and +4. , The comparison of the structural properties, namely the Ln 3+ first coordination shell, and hydration free energies (HFEs) with experimental Marcus’ values is crucial in determining the accuracy of this approach. This thorough investigation demonstrated that Li’s approach yielded excellent results for a wide range of cations while significantly reducing the computational overhead associated with polarization calculations . Such an approach has already been used for refining previous force fields of mono-atomic cations in interaction with nucleic acids, proteins, and imidazole .…”