Rational Design of Nonbonded Point Charge Models for Divalent Metal Cations with Lennard-Jones 12-6 Potential

Metallicious: Automated Force-Field Parameterization of Covalently Bound Metals for Supramolecular Structures

Metal ions play a central, functional, and structural role in many molecular structures, from small catalysts to metal-organic frameworks (MOFs) and proteins. Computational studies of these systems typically employ classical or quantum mechanical approaches or a combination of both. Among classical models, only the covalent metal model reproduces both geometries and charge transfer effects but requires time-consuming parameterization, especially for supramolecular systems containing repetitive units. To streamline this process, we introduce metallicious, a Python tool designed for efficient force-field parameterization of supramolecular structures. Metallicious has been tested on diverse systems including supramolecular cages, knots, and MOFs. Our benchmarks demonstrate that parameters accurately reproduce the reference properties obtained from quantum calculations and crystal structures. Molecular dynamics simulations of the generated structures consistently yield stable simulations in explicit solvent, in contrast to similar simulations performed with nonbonded and cationic dummy models. Overall, metallicious facilitates the atomistic modeling of supramolecular systems, key for understanding their dynamic properties and host-guest interactions. The tool is freely available on GitHub (https://github.com/duartegroup/metallicious).

Modeling solvation dynamics of transition metal redox ion through on-the-fly multi-objective Bayesian-optimized force field

Modeling solvation dynamics and properties is crucial for developing electrolytes for electrochemical energy storage and conversion devices. This work reports an on-the-fly multi-objective Bayesian optimization (OTF-MOBO) method to parameterize force fields for modeling ionic solvation structures, thermodynamics, and transport properties using molecular dynamics simulations. By leveraging solvation-free energy and solvation radii as training data, we employ the data-driven OTF-MOBO algorithm to actively optimize the force field parameters. The modeling accuracy was evaluated in molecular dynamics simulations until the Pareto front in the parameter space was reached through minimized prediction errors in both solvation-free energy and solvation radii. Using transition metal redox ions (Fe3+/Fe2+, Cr3+/Cr2+, and Cu2+/Cu+) in aqueous solution as examples, we demonstrate that simple force fields combining the Lenard-Jones potential and Coulombic potential can achieve relative error below 2% in both solvation free energy and solvation radii. The optimized force fields can be further extrapolated to predict solvation entropy and diffusivities with relative error below 10% compared with experiments.

Simulating Metal-Imidazole Complexes

One commonly observed binding motif in metalloproteins involves the interaction between a metal ion and histidine's imidazole side chains. Although previous imidazole-M(II) parameters established the flexibility and reliability of the 12-6-4 Lennard-Jones (LJ)-type nonbonded model by simply tuning the ligating atom's polarizability, they have not been applied to multiple-imidazole complexes. To fill this gap, we systematically simulate multiple-imidazole complexes (ranging from one to six) for five metal ions (Co(II), Cu(II), Mn(II), Ni(II), and Zn(II)) which commonly appear in metalloproteins. Using extensive (40 ns per PMF window) sampling to assemble free energy association profiles (using OPC water and standard HID imidazole charge models from AMBER) and comparing the equilibrium distances to DFT calculations, a new set of parameters was developed to focus on energetic and geometric features of multiple-imidazole complexes. The obtained free energy profiles agree with the experimental binding free energy and DFT calculated distances. To validate our model, we show that we can close the thermodynamic cycle for metal-imidazole complexes with up to six imidazole molecules in the first solvation shell. Given the success in closing the thermodynamic cycles, we then used the same extended sampling method for six other metal ions (Ag(I), Ca(II), Cd(II), Cu(I), Fe(II), and Mg(II)) to obtain new parameters. Since these new parameters can reproduce the one-imidazole geometry and energy accurately, we hypothesize that they will reasonably predict the binding free energy of higher-level coordination numbers. Hence, we did not extend the analysis of these ions up to six imidazole complexes. Overall, the results shed light on metal-protein interactions by emphasizing the importance of ligand-ligand interaction and metal-π-stacking within metalloproteins.

Binding of Phosphate Species to Ca2+ and Mg2+ in Aqueous Solution

Phosphate derivatives and their interaction with metal cations are involved in many important biological phenomena, so an accurate characterization of the phosphate-metal interaction is necessary to properly understand the role of phosphate-metal contacts in mediating biological function. Herein, we improved the standard 12-6 Lennard-Jones (LJ) potential via the usage of the 12-6-4 LJ model, which incorporates ion-induced dipole interactions. Via parameter scanning, we fine-tuned the 12-6-4 LJ polarizability values to obtain accurate absolute binding free energies for the phosphate anions H2PO4-, HPO42-, PO43- coordinating with Ca2+ and Mg2+. First, we modified the phosphate 12-6-4 LJ parameters to reproduce the solvation free energies of the series of phosphate anions using the thermodynamic integration (TI) method. Then, using the potential mean force (PMF) method, the polarizability of the metal-phosphate interaction was obtained. We show that the free energy profiles of phosphate ions coordinated to Ca2+ and Mg2+ generally show similar trends at longer metal-phosphate distances, while the absolute binding energy values increased with deprotonation. The resulting parameters demonstrate the flexibility of the 12-6-4 LJ-type nonbonded model and its usefulness in accurately describing cation-anion interactions.

Evidence of Sharp Transitions between Octahedral and Capped Trigonal Prism States of the Solvation Shell of the Aqueous Fe3+ Ion

The structure of the solvation shell of the aqueous Fe3+ ion has been a subject of controversy due to discrepancies between experiments and different levels of theory. We address this issue by performing simulations for a wide range of ion concentrations, using various potential energy functions, supplemented by density functional theory calculations of selected configurations. The solvation shell undergoes abrupt transitions between two states: a hexacoordinated octahedral (OH) state and a capped trigonal prism (CTP) state with 7-fold coordination. The lifetime of these states is dependent on concentration. In dilute FeCl3 solutions, the lifetimes of both are similar (≈1 ns). However, the lifetime of the OH state increases with ion concentration, while that of the CTP state decreases slightly. When a uniform negative background charge is used instead of explicit counterions, the lifetime of the OH state is greatly overestimated. These findings underscore the need for further experimental measurements and higher-level simulations.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

Surface/interfacial transport through pores control desalination mechanisms in 2D carbon-based membranes

The shortage of freshwater is a critical concern for contemporary society, and reverse osmosis desalination technology has gathered considerable attention as a potential solution to this problem. It has been recognized that the desalination process involving water flow through angstrom-sized pores has tremendous potential. However, it is challenging to obtain angstrom-sized pore structures with internal mass transfer and surface/interface properties matching the application conditions. Herein, a two-dimensional (2D) zeolite-like carbon structure (Carzeo-ANG) was constructed with unique angstrom-sized pores in the zeolite structure; then, the surface/interfacial transport behavior and percolation effect of the Carzeo-ANG desalination membrane were evaluated by density functional theory (DFT) calculations and classical molecular dynamics. The first-principles calculations in density functional theory were implemented through the Vienna ab initio simulation package (VASP), which is a commercial package for the simulation of carbon-based materials. The results show that Carzeo-ANG is periodically distributed with angstrom-sized pores (effective diameter = 5.4 Å) of dodecacyclic carbon rings, which ensure structural stability while maintaining sufficient mechanical strength. The remarkable salt-ion adsorption properties and mass transfer activity combined with the reasonable density distribution and free energy barrier for water molecules endow the membrane with superior desalination ability. At the pressure of 80 MPa, the rejection efficiency of Cl- and Na+ were 100% and 96.25%, and the membrane could achieve a water flux of 132.71 L cm-2 day-1 MPa-1. Moreover, the interconnected electronic structure of Carzeo-ANG imparts a self-cleaning effect.

Repurposing of World-Approved Drugs for Potential Inhibition against Human Carbonic Anhydrase I: A Computational Study

Human carbonic anhydrases (hCAs) have enzymatic activities for reversible hydration of CO2 and are acknowledged as promising targets for the treatment of various diseases. Using molecular docking and molecular dynamics simulation approaches, we hit three compounds of methyl 4-chloranyl-2-(phenylsulfonyl)-5-sulfamoyl-benzoate (84Z for short), cyclothiazide, and 2,3,5,6-tetrafluoro-4-piperidin-1-ylbenzenesulfonamide (3UG for short) from the existing hCA I inhibitors and word-approved drugs. As a Zn2+-dependent metallo-enzyme, the influence of Zn2+ ion models on the stability of metal-binding sites during MD simulations was addressed as well. MM-PBSA analysis predicted a strong binding affinity of -18, -16, and -14 kcal/mol, respectively, for these compounds, and identified key protein residues for binding. The sulfonamide moiety bound to the Zn2+ ion appeared as an essential component of hCA I inhibitors. Vina software predicted a relatively large (unreasonable) Zn2+-sulfonamide distance, although the relative binding strength was reproduced with good accuracy. The selected compounds displayed potent inhibition against other hCA isoforms of II, XIII, and XIV. This work is valuable for molecular modeling of hCAs and further design of potent inhibitors.

Reduced Chitosan as a Strategy for Removing Copper Ions from Water

Toxic heavy metals are priority pollutants in wastewater, commonly present in dangerous concentrations in many places across the globe. Although in trace quantities copper is a heavy metal essential to human life, in excess it causes various diseases, whereby its removal from wastewater is a necessity. Among several reported materials, chitosan is a highly abundant, non-toxic, low-cost, biodegradable polymer, comprising free hydroxyl and amino groups, that has been directly applied as an adsorbent or chemically modified to increase its performance. Taking this into account, reduced chitosan derivatives (RCDs 1-4) were synthesised by chitosan modification with salicylaldehyde, followed by imine reduction, characterised by RMN, FTIR-ATR, TGA and SEM, and used to adsorb Cu(II) from water. A reduced chitosan (RCD3), with a moderate modification percentage (43%) and a high imine reduction percentage (98%), proved to be more efficient than the remainder RCDs and even chitosan, especially at low concentrations under the best adsorption conditions (pH 4, R_S/L = 2.5 mg mL^-1). RCD3 adsorption data were better described by the Langmuir-Freundlich isotherm and the pseudo-second-order kinetic models. The interaction mechanism was assessed by molecular dynamics simulations, showing that RCDs favour Cu(II) capture from water compared to chitosan, due to a greater Cu(II) interaction with the oxygen of the glucosamine ring and the neighbouring hydroxyl groups.

Machines on Genes through the Computational Microscope

Macromolecular machines acting on genes are at the core of life's fundamental processes, including DNA replication and repair, gene transcription and regulation, chromatin packaging, RNA splicing, and genome editing. Here, we report the increasing role of computational biophysics in characterizing the mechanisms of "machines on genes", focusing on innovative applications of computational methods and their integration with structural and biophysical experiments. We showcase how state-of-the-art computational methods, including classical and ab initio molecular dynamics to enhanced sampling techniques, and coarse-grained approaches are used for understanding and exploring gene machines for real-world applications. As this review unfolds, advanced computational methods describe the biophysical function that is unseen through experimental techniques, accomplishing the power of the "computational microscope", an expression coined by Klaus Schulten to highlight the extraordinary capability of computer simulations. Pushing the frontiers of computational biophysics toward a pragmatic representation of large multimegadalton biomolecular complexes is instrumental in bridging the gap between experimentally obtained macroscopic observables and the molecular principles playing at the microscopic level. This understanding will help harness molecular machines for medical, pharmaceutical, and biotechnological purposes.

Benchmarking biomolecular force field-based Zn2+ for mono- and bimetallic ligand binding sites

Zn²⁺ is one of the most versatile biologically available metal ions, but accurate modeling of Zn²⁺ -containing metalloproteins at the biomolecular force field level can be challenging. Since most Zn²⁺ models are parameterized in bulk solvent, in-depth knowledge about their performance in a protein environment is limited. Thus, we systematically investigate here the behavior of non-polarizable Zn²⁺ models for their ability to reproduce experimentally determined metal coordination and ligand binding in metalloproteins. The benchmarking is performed in challenging environments, including mono- (carbonic anhydrase II) and bimetallic (metallo-β-lactamase VIM-2) ligand binding sites. We identify key differences in the performance between the Zn²⁺ models with regard to the preferred ligating atoms (charged/non-charged), attraction of water molecules, and the preferred coordination geometry. Based on these results, we suggest suitable simulation conditions for varying Zn²⁺ site geometries that could guide the further development of biomolecular Zn²⁺ models.

Accurate Metal-Imidazole Interactions

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.

Impacts of targeting different hydration free energy references on the development of ion potentials

Hydration free energy (HFE) as the most important solvation parameter is often targeted in ion model development, even though the reported values differ by dozens of kcal mol^-1 mainly due to the experimentally undetermined HFE of the proton ΔG°(H⁺). The choice of ΔG°(H⁺) obviously affects the hydration of single ions and the relative HFE between the ions with different (magnitude or sign) charges, and the impacts of targeted HFEs on the ion solvation and ion-ion interactions are largely unrevealed. Here we designed point charge models of K⁺, Mg²⁺, Al³⁺, and Cl^- ions targeting a variety of HFE references and then investigated the HFE influences on the simulations of dilute and concentrated ion solutions and of the salt ion pairs in gas, liquid, and solid phases. Targeting one more property of ion-water oxygen distances (IOD) leaves the ion-water binding distance invariant, while the binding strength increases with the decreasing (more negative) HFE of ions as a result of a decrease in ΔG°(H⁺) for the cation and an increase in ΔG°(H⁺) for the anion. The increase in ΔG°(H⁺) leads to strengthened cation-anion interactions and thus to close ion-ion contacts, low osmotic pressures, and small activity derivatives in concentrated ion solutions as well as too stable ion pairs of the salts in different phases. The ion diffusivity and water exchange rates around the ions are simply not HFE dependent but rather more complex. Targeting both the aqueous IOD and salt crystal properties of KCl was also attempted and the comparison between different models indicates the complexity and challenge in obtaining a balanced performance between different phases using classical force fields. Our results also support that a real ΔG°(H⁺) value of -259.8 kcal mol^-1 recommended by Hünenberger and Reif guides ion models to reproduce ion-water and ion-ion interactions reasonably at relatively low salt concentrations. Simulations of a metalloprotein show that a relatively more positive ΔG°(H⁺) for Mg²⁺ model is better for a reasonable description of the metal binding network.

Rational Design of Nonbonded Point Charge Models for Monovalent Ions with Lennard-Jones 12-6 Potential

Ions are of central importance in nature, and a variety of potential models was proposed to model ions in different phases for an in-depth exploration of ion-related systems. Here, we developed point charge models of 14 monovalent ions with the traditional 12-6 Lennard-Jones (LJ) potential for use in conjunction with 11 water models of TIP3P, OPC3, SPC/E, SPC/E_b, TIP3P-FB, a99SB-disp, TIP4P-Ew, OPC, TIP4P/2005, TIP4P-D, and TIP4P-FB. The designed models reproduced the real hydration free energy (HFE) of ions and the ion-oxygen distance (IOD) in the first hydration shell accurately and simultaneously, a performance similar to the previously reported 12-6-4 LJ-type ion models (12-6 LJ plus an attractive C₄ term for cations or a repulsive one for anions). This work, along with our previous work on di-, tri-, and tetravalent metal cations (J. Chem. Inf. Model. 2021, 61, 4031-4044; J. Chem. Inf. Model. 2021, 61, 4613-4629), demonstrates the feasibility of the simple 12-6 LJ potential in ion modeling. In order for the 12-6 LJ potential to reproduce both the HFE and IOD, the LJ R parameters need to be close to Shannon's ionic radii for the highly charged cations and to the Stokes's van der Waals (vdW) radii for the monovalent ions. With an additional C₄ term, the R parameters of 12-6-4 LJ ion models agree well with the Stokes's vdW radii and have a more physical meaning. It appears that the C₄ term can be merged into the 12-6 LJ potential by a rational tuning of R and the LJ well depth. Simulations of the osmotic coefficients of alkali chloride solutions and the properties of gaseous and solid alkali halides indicate the necessity of further optimizing ion-ion interactions via, for instance, targeting more properties or using a more physical (polarizable) model.

Rational Design of Nonbonded Point Charge Models for Highly Charged Metal Cations with Lennard-Jones 12-6 Potential

Here, we developed nonbonded point charge models using a simple Lennard-Jones (LJ) 12-6 potential for highly charged metal cations (18 trivalent and 6 tetravalent ions) for use with 11 water models of TIP3P, OPC3, SPC/E, SPC/E_b, TIP3P-FB, a99SB-disp, TIP4P-Ew, OPC, TIP4P/2005, TIP4P-D, and TIP4P-FB. The designed models simultaneously reproduce the hydration free energy (HFE) and ion-oxygen distance (IOD) in the first hydration shell with an error within 1 kcal/mol and 0.01 Å on average, respectively, and yield reasonable coordination numbers for most cations. Such performance is equivalent to the previously reported point charge models using a more complex 12-6-4 LJ-type potential, while the LJ R parameters of our models are much close to Shannon's revised effective ion radii than that of the 12-6-4 models. Our designed models overestimate the diffusion constants of several trivalent ions by 5-68%. The performance in predicting osmotic coefficients of trivalent chlorides in aqueous solution depends on the salt type. A calibration of cation-anion interacting LJ parameters reproduces the experimental osmotic coefficients of an AlCl₃ solution at 0.2-3.0 mol/L. The effectiveness of our new models is further demonstrated by simulating a metalloprotein system with four force field/water combinations. This work facilitates accurate modeling of metal-containing systems by a variety of force fields and water models in aqueous solution.