Modeling the interaction between a metal ion and small molecules can provide pivotal information to bridge and close the gap between two types of simulations: metal ions in water and metal ions in metalloproteins. As previously established, the 12-6-4 Lennard-Jones (LJ)-type nonbonded model, because of its ability to account for the induced dipole effect, has been highly successful in simulating metal ion systems. Using the potential of mean force (PMF) method, the polarizability of the metal-chelating nitrogen from two types of imidazole molecules, delta nitrogen protonated (HID) and epsilon nitrogen protonated (HIE), has been parametrized against experiment for 11 metals (Ag(I), Ca(II), Cd(II), Co(II), Cu(I), Cu(II), Fe(II), Mg(II), Mn(II), Ni(II), and Zn(II)) in conjunction with three commonly used water models (TIP3P, SPC/E, and OPC). We show that the standard 12-6 and unmodified 12-6-4 models are not able to accurately model these interactions and, indeed, predict that the complex should be unstable. The resultant parameters further establish the flexibility and the reliability of the 12-6-4 LJ-type nonbonded model, which can correctly describe three-component interactions between a metal, ligand, and solvent by simply tuning the polarizability of the chelating atom. Also, the transferability of this model was tested, showing the capability of describing metal–ligand interactions in various environments.

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.

ATPases associated with diverse cellular activities (AAA+) proteases utilize ATP hydrolysis to actively unfold native or misfolded proteins and translocate them into a protease chamber for degradation. This basic mechanism yields diverse cellular consequences, including the removal of misfolded proteins, control of regulatory circuits, and remodeling of protein conformation. Among various bacterial AAA+ proteases, FtsH is only membrane-integrated and plays a key role in membrane protein quality control. Previously, we have shown that FtsH has substantial unfoldase activity for degrading membrane proteins overcoming a dual energetic burden of substrate unfolding and membrane dislocation. Here, we asked how efficiently FtsH utilizes ATP hydrolysis to degrade membrane proteins. To answer this question, we measured degradation rates of the model membrane substrate GlpG at various ATP hydrolysis rates in the lipid bilayers. We find that the dependence of degradation rates on ATP hydrolysis rates is highly nonlinear: (i) FtsH cannot degrade GlpG until it reaches a threshold ATP hydrolysis rate; (ii) after exceeding the threshold, the degradation rates steeply increase and saturate at the ATP hydrolysis rates far below the maxima. During the steep increase, FtsH efficiently utilizes ATP hydrolysis for degradation, consuming only 40-60% of the total ATP cost measured at the maximal ATP hydrolysis rates. This behavior does not fundamentally change against water-soluble substrates as well as upon addition of the macromolecular crowding agent Ficoll 70. The Hill analysis shows that the nonlinearity stems from coupling of three to five ATP hydrolysis events to degradation, Abbreviations: 108, an amino acid sequence, SLLWS; AAA+, ATPases associated with diverse cellular activities; ATP, adenosine triphosphate; E. coli, Escherichia coli; E a,U , activation energy of unfolding; GFP, green fluorescent protein; mSA, monovalent streptavidin; NBD, nitrobenzoxadiazole; n H , the Hill coefficient; PAN, proteasome-activating AAA+ nucleotidase; TM, transmembrane; YccA N , the N-terminal tail of an E. coli membrane protein YccA; ΔG o U , free energy of unfolding. Additional Supporting Information may be found in the online version of this article.Significance statement: FtsH is a membrane-integrated ATP-dependent protease, playing a key role in membrane protein quality control. Here, we investigated how FtsH utilizes ATP hydrolysis to degrade proteins. We find that FtsH couples multiple ATP hydrolysis events to degradation in a highly cooperative and efficient manner. This mechanism explains how FtsH overcomes large energetic costs in unfolding substrates in the membranes and extracting them toward its protease domain located outside the membrane.which represents unique cooperativity compared to other AAA+ proteases including ClpXP, HslUV, Lon, and proteasomes.

As a fundamental property of all fluids, diffusion plays myriad roles in both science and our daily lives. Diffusive properties of many liquids including water have been extensively studied both experimentally and theoretically, while for transition metal ions, there exist significant experimental data that have not been extensively studied theoretically. Hence, high-confidence predictions for challenging systems like radioactive ions that are biohazardous cannot be reliably generated. In this work, a workflow named ISAIAH (Ion Simulation using AMBER for dIffusion Action when Hydrated) was designed to accurately simulate the diffusion coefficients of 15 monoatomic ions with charges varying from −1 to +3 in four water models. As the results indicate, good agreement with experimental values was achieved, leading us to select 239 Pu 4+ (for which no experimental data are available) as a candidate ion to make a theoretical prediction of its diffusion coefficient in water. Among all the force field parameter sets, the ones parametrized using an augmented 12-6-4 Lennard-Jones (LJ) potential showed lower average unsigned errors (AUE) for ions of various radii and electron configurations relative to some 12-6 LJ parameters. This observation agrees well with the fact that diffusion is affected by both the hydration free energy (HFE) and the ion-oxygen distance (IOD) between solute and solvent molecules, both of which are handled well by the 12-6-4 model.

A novel locally polarizable multisite model based on the original cation dummy atom (CDA) model is described for molecular dynamics simulations of ions in condensed phases. Polarization effects are introduced by the electronegativity equalization model (EEM) method where charges on the metal ion and its dummy atoms can fluctuate to respond to the environment. This model includes explicit polarization and ion-induced interactions and can be coupled with nonpolarizable or polarizable water models, making it more transferable to simpler force fields. This approach allows us to enhance the original fixed charge CDA model where the charge distribution cannot adapt to the local solvent structure. To illustrate the new CDA pol model, we examined properties of the Zn 2+ , Al 3+ , and Zr 4+ ions in aqueous solution. The polarizable model and Lennard-Jones parameters were refined for octahedrally coordinated Zn 2+ , Al 3+ , and Zr 4+ CDAs to reproduce thermodynamic and geometrical properties. Using this locally polarizable model, we were able to obtain the experimental hydration free energy, ion−oxygen distance, and coordination number coupled with the standard 12−6 Lennard-Jones model. This model can be used in myriad additional applications where local polarization and charge transfer is important.