Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Amino Acid Transfer Free Energies Reveal Thermodynamic Driving Forces in Biomolecular Condensate Formation

The self-assembly of intrinsically disordered proteins into biomolecular condensates shows a dependence on the primary sequence of the protein, leading to sequence-dependent phase separation. Methods to investigate this sequence-dependent phase separation rely on effective residue-level interaction potentials that quantify the propensity for the residues to remain in the dilute phase versus the dense phase. The most direct measure of these effective potentials are the distribution coefficients of the different amino acids between the two phases, but due to the lack of availability of these coefficients, proxies, most notably hydropathy, have been used. However, recent work has demonstrated the limitations of the assumption of hydropathy-driven phase separation. In this work, we address this fundamental gap by calculating the transfer free energies associated with transferring each amino acid side chain analog from the dilute phase to the dense phase of a model biomolecular condensate. We uncover an interplay between favorable protein-mediated and unfavorable water-mediated contributions to the overall free energies of transfer. We further uncover an asymmetry between the contributions of positive and negative charges in the driving forces for condensate formation. The results presented in this work provide an explanation for several non-trivial trends observed in the literature and will aid in the interpretation of experiments aimed at elucidating the sequence-dependent driving forces underlying the formation of biomolecular condensates.

Force Field Limitations of All-Atom Continuous Constant pH Molecular Dynamics

All-atom constant pH molecular dynamics simulations offer a powerful tool for understanding pH-mediated and proton-coupled biological processes. As the protonation equilibria of protein side chains are shifted by electrostatic interactions and desolvation energies, pKa values calculated from the constant pH simulations may be sensitive to the underlying protein force field and water model. Here we investigated the force field dependence of the all-atom particle mesh Ewald (PME) continuous constant pH (PME-CpHMD) simulations of a mini-protein BBL. The replica-exchange titration simulations based on the Amber ff19sb and ff14sb force fields with the respective water models showed significantly overestimated pKa downshifts for a buried histidine (His166) and for two glutamic acids (Glu141 and Glu161) that are involved in salt-bridge interactions. These errors (due to undersolvation of neutral histidines and overstabilization of salt bridges) are consistent with the previously reported pKa's based on the CHARMM c22/CMAP force field, albeit in larger magnitudes. The pKa calculations also demonstrated that ff19sb with OPC water is significantly more accurate than ff14sb with TIP3P water, and the salt-bridge related pKa downshifts can be partially alleviated by the atom-pair specific Lennard-Jones corrections (NBFIX). Together, these data suggest that the accuracies of the protonation equilibria of proteins from constant pH simulations can significantly benefit from improvements of force fields.

Towards targeting EGFR and COX-2 inhibitors: comprehensive computational studies on the role of chlorine group in novel thienyl-pyrazoline derivative

To enhance the effectiveness of chemotherapy and overcome resistance, scientists must develop novel drugs or scaffolds that have a combined effect, such as the inhibition of EGFR and COX-2. This research employed virtual screening techniques, such as docking, and dynamics simulation, to predict chlorinated thienyl-pyrazoline derivatives that inhibit these proteins. The study proposed eleven (11) ligands with binding energies ranging from -7.8 kcal/mol to -8.7 kcal/mol for EGFR and -6.4 kcal/mol to -8.4 kcal/mol for COX-2. Ligands P1 and P11 exhibited the highest binding affinity for both proteins. The results of RMSD, RMSF, RoG, SASA the number of hydrogen bonds, and BAR free binding energy demonstrated the good stability of ligands P1 and P11 when binding to both proteins over 180 ns simulations. In addition, the absorption, distribution, metabolism, excretion, and toxicity properties of the selected ligands were assessed to predict their toxicity and drug likeliness. Based on the results, these compounds can be proposed for further synthesis and in vitro studies.Communicated by Ramaswamy H. Sarma.

Self-Consistent Implementation of a Solvation Free Energy Framework to Predict the Salt Solubilities of Six Alkali Halides

To assess the salt solubilities of six alkali halides in aqueous systems, we proposed a thermodynamic cycle and an efficient molecular modeling methodology. The Gibbs free energy changes for vaporization, dissociation, and dissolution were calculated using the experimental data of ionic thermodynamic properties obtained from the NBS tables. Additionally, the Marcus' and Tissandier's solvation free energy data for Li+, Na+, K+, Cl-, and Br- ions were compared with the conventional solvation free energies by substituting into our self-consistent thermodynamic cycle. Furthermore, Tissandier's absolute solvation free energy data were used as the training set to refit the Lennard-Jones parameters of OPLS-AA force field for ions. To predict salt solubilities, an assumption of a pseudo-solvent was proposed to characterize the coupling work of a solute with its environment from infinitely diluted to saturated solutions, indicating that the Gibbs energy change of solvation process is a function of ionic strength. Following the self-consistency of the cycle, the newly derived formulas were used to determine the salt solubilities by interpolating the intersection of Gibbs free energy of dissolution and the zero free energy line. The refined ion parameters can also predict the structure and thermodynamic properties of aqueous electrolyte solutions, such as densities, pair correlation functions, hydration numbers, mean activity coefficients, vapor pressures, and the radial dependences of the net charge at 298.15 K and 1 bar. Our method can be used to characterize the solid-liquid equilibria of ions or charged particles in aqueous systems. Furthermore, for highly concentrated strong electrolyte systems, it is essential to introduce accurate water models and polarizable force fields.

Polarizability Plays a Decisive Role in Modulating Association between Molecular Cations and Anions

Electrostatic interactions involving proteins depend on not only the ionic charges involved but also their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein-protein and protein-ligand interactions. Cationic analogues of the basic amino acid side chains are simulated, along with oxyanionic analogues of cation-exchange ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a nonpolarizable model. An effective continuum correction to account for electronic polarizability can capture both trends better but at the expense of fidelity to the underlying free energy landscape for ion-pair association. A polarizable model proves decisive in capturing experimentally suggested trends with respect to both cations and anions; critically, the free energy landscape for ion-pair association is itself altered, thus altering configurational sampling.

Solvation of Manganese(III) Ion in Water and in Ammonia

In this work, we have studied the solvation of manganese(III) ion in water and in ammonia using three levels of theory: MP2, MN15, and ωB97XD associated with the aug-cc-pVDZ basis set. The studied systems are constituted of Mn³⁺(H₂O)₆ and Mn³⁺(NH₃)₆ in gas and solvent phases as well as Mn³⁺(H₂O)₁₈ and Mn³⁺(NH₃)₁₈ in the gas phase. Four aspects of the solvation of manganese(III) ion have been examined for the aforementioned systems at the three levels of theory. First, we started by locating the Jahn-Teller elongated and compressed configuration in Mn³⁺(H₂O)₆ and Mn³⁺(NH₃)₆. Second, we calculated the spin state energies and the spin state free energies for temperatures ranging from 50 to 400 K to look at possible spin crossover in the studied systems. Third, we carried out a quantum theory of atoms in molecules (QTAIM) analysis, and we determined the ionic radii of manganese(III) ion in water and in ammonia. Fourth, we calculated the solvation free energies and the solvation enthalpies of manganese(III) ion in water and in ammonia using the cluster continuum solvation model. For these four aspects of the solvation of manganese(III) ion, most of the reported properties are provided in this work for the first time. We particularly found that the calculated solvation enthalpy of the manganese(III) ion in water is in good agreement with an experimental estimate.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

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.

Force-Field-Based Computational Study of the Thermodynamics of a Large Set of Aqueous Alkanolamine Solvents for Post-Combustion CO2 Capture

The ability to predict the thermodynamic properties of amine species in CO₂-loaded aqueous solutions, including their deprotonation (pK_a) and carbamate to bicarbonate reversion (pK_c) equilibrium constants and their corresponding standard reaction enthalpies, is of critical importance for the design of improved carbon capture solvents. In this study, we used isocoulombic forms of both reactions to determine these quantities for a large set of aqueous alkanolamine solvent systems. Our hybrid approach involves using classical molecular dynamics simulations with the general amber force field (GAFF) and semi-empirical AM1-BCC charges (GAFF/AM1-BCC) in the solution phase, combined with high-level composite quantum chemical ideal-gas calculations. We first determined a new force field (FF) for the hydronium ion (H₃O⁺) by matching to the single experimental pK_a data point for the well-known monoethanolamine system at 298.15 K. We then used this FF to predict the pK_a values for 76 other amines at 298.15 K and for all 77 amines at elevated temperatures. Additionally, we indirectly relate the H₃O⁺ hydration free energy to that of H⁺ and provide expressions for intrinsic hydration free energy and enthalpy of the proton. Using the derived H₃O⁺ FF, we predicted the pK_a values of a diverse set of alkanolamines with an overall average absolute deviation of less than 0.72 pK_a units. Furthermore, the derived H₃O⁺ FF is able to predict the protonation enthalpy of these amines when used with the GAFF. We also predicted the carbamate reversion constants of the primary and secondary amine species in the data set and their corresponding standard heats of reaction, which we compared with the scarcely available experimental data, which are often subject to significant uncertainty. Finally, we also described the influence of electronic and steric effects of different molecular fragments/groups on the stabilities of the carbamates.

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.

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

Exploring a metal-involved biochemical process at a molecular level often requires a reliable description of metal properties in aqueous solution by classical nonbonded models. An additional C₄ term for considering ion-induced dipole interactions was previously proposed to supplement the widely used Lennard-Jones 12-6 potential (known as the 12-6-4 LJ-type model) with good accuracy. Here, we demonstrate an alternative to modeling divalent metal cations (M²⁺) with the traditional 12-6 LJ potential by developing nonbonded point charge models for use with 11 water models: TIP3P, SPC/E, SPC/E_b, TIP4P-Ew, TIP4P-D, and TIP4P/2005 and the more recent OPC3, TIP3P-FB, OPC, TIP4P-FB, and a99SB-disp. Our designed models simultaneously reproduce the experimental hydration free energy, ion-oxygen distance, and coordination number in the first hydration shell accurately for most of the metal cations, an accuracy equivalent to that of the complex 12-6-4 LJ-type and double exponential potential models. A systematic comparison with the existing M²⁺ models is presented as well in terms of effective ion radii, diffusion constants, water exchange rates, and ion-water interactions. Molecular dynamics simulations of metal substitution in Escherichia coli glyoxalase I variants show the great potential of our new models for metalloproteins.

Developing and Assessing Nonbonded Dummy Models of Magnesium Ion with Different Hydration Free Energy References

A large diversity in the targeted hydration free energies (HFEs) during model parameterization of metal ions was reported in the literature with a difference by dozens of kcal/mol. Here, we developed a series of nonbonded dummy models of the Mg²⁺ ion targeting different HFE references in TIP3P water, followed by assessments of the designed models in the simulations of MgCl₂ solution and biological systems. Together with the comparison of existing models, we conclude that the difference in the targeted HFEs has a limited influence on the model performance, while the usability of these models differs from case to case. The feasibility of reproducing more properties of Mg²⁺ such as diffusion constants and water exchange rates using a nonbonded dummy model is demonstrated. Underestimated activity derivative and osmotic coefficient of MgCl₂ solutions in high concentration reveal a necessity for further optimization of ion-pair interactions. The developed dummy models are applicable to metal coordination with Asp, Glu, and His residues in metalloenzymes, and the performance in predicting monodentate or bidentate binding modes of Asp/Glu residues depends on the complexity of metal centers and the choice of protein force fields. When both the binding modes coexist, the nonbonded dummy models outperform point charge models, probably in need of considering polarization of metal-binding residues by, for instance, charge calibration in classical force fields. This work is valuable for the use and further development of magnesium ion models for simulations of metal-containing systems with good accuracy.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

Molecular dynamics simulations of Y(iii) coordination and hydration properties

Y mainly exists in ionic rare-earth resources. During rare-earth carbonate precipitation, rare-earth ion loss in the precipitated rare-earth mother liquor often occurs due to CO₃²⁻ coordination and Y(iii) hydration. Microscopic information on the coordination and hydration of CO₃²⁻ and H₂O to Y(iii) has not yet been elucidated. Therefore, in this study, the macroscopic dissolution of Y(iii) in different aqueous solutions of Na₂CO₃ was studied. The radial distribution function and coordination number of Y(iii) by CO₃²⁻ and H₂O were systematically analyzed using molecular dynamics (MD) simulations to obtain the complex ion form of Y(iii) in carbonate solutions. Density functional theory (DFT) was used to geometrically optimize and calculate the UV spectrum of Y(iii) complex ions. This spectrum was then analyzed and compared with experimentally determined ultraviolet-visible spectra to verify the reliability of the MD simulation results. Results showed that Y(iii) in aqueous solution exists in the form of [Y·3H₂O]³⁺ and that CO₃²⁻ is present in the bidentate coordination form. In 0–0.8 mol L⁻¹ CO₃²⁻ solutions, Y(iii) was mainly present as the 5-coordinated complex [YCO₃·3H₂O]⁺. When the concentration of CO₃²⁻ was increased to 1.2 mol L⁻¹, [YCO₃·3H₂O]⁺ was converted into a 6-coordinated complex [Y(CO₃)₂·2H₂O]⁻. Further increases in CO₃²⁻ concentration promoted Y(iii) dissolution in solution in the form of complex ions. These findings can be used to explain the problem of incomplete precipitation of rare earths in carbonate solutions.

Based on MD results, DFT was used to geometrically optimize and calculate the UV spectrum of Y(iii) complex ions. Data validation was further performed using UV-vis experiments to reveal Y(iii) coordination and hydration properties.

Prediction of Partition Coefficients of Environmental Toxins Using Computational Chemistry Methods

The partitioning of compounds between aqueous and other phases is important for predicting toxicity. Although thousands of octanol-water partition coefficients have been measured, these represent only a small fraction of the anthropogenic compounds present in the environment. The octanol phase is often taken to be a mimic of the inner parts of phospholipid membranes. However, the core of such membranes is typically more hydrophobic than octanol, and other partition coefficients with other compounds may give complementary information. Although a number of (cheap) empirical methods exist to compute octanol-water (log k _OW) and hexadecane-water (log k _HW) partition coefficients, it would be interesting to know whether physics-based models can predict these crucial values more accurately. Here, we have computed log k _OW and log k _HW for 133 compounds from seven different pollutant categories as well as a control group using the solvation model based on electronic density (SMD) protocol based on Hartree-Fock (HF) or density functional theory (DFT) and the COSMO-RS method. For comparison, XlogP3 (log k _OW) values were retrieved from the PubChem database, and KowWin log k _OW values were determined as well. For 24 of these compounds, log k _OW was computed using potential of mean force (PMF) calculations based on classical molecular dynamics simulations. A comparison of the accuracy of the methods shows that COSMO-RS, KowWin, and XlogP3 all have a root-mean-square deviation (rmsd) from the experimental data of ≈0.4 log units, whereas the SMD protocol has an rmsd of 1.0 log units using HF and 0.9 using DFT. PMF calculations yield the poorest accuracy (rmsd = 1.1 log units). Thirty-six out of 133 calculations are for compounds without known log k _OW, and for these, we provide what we consider a robust prediction, in the sense that there are few outliers, by averaging over the methods. The results supplied may be instrumental when developing new methods in computational ecotoxicity. The log k _HW values are found to be strongly correlated to log k _OW for most compounds.

QligFEP: an automated workflow for small molecule free energy calculations in Q

The process of ligand binding to a biological target can be represented as the equilibrium between the relevant solvated and bound states of the ligand. This which is the basis of structure-based, rigorous methods such as the estimation of relative binding affinities by free energy perturbation (FEP). Despite the growing capacity of computing power and the development of more accurate force fields, a high throughput application of FEP is currently hampered due to the need, in the current schemes, of an expert user definition of the "alchemical" transformations between molecules in the series explored. Here, we present QligFEP, a solution to this problem using an automated workflow for FEP calculations based on a dual topology approach. In this scheme, the starting poses of each of the two ligands, for which the relative affinity is to be calculated, are explicitly present in the MD simulations associated with the (dual topology) FEP transformation, making the perturbation pathway between the two ligands univocal. We show that this generalized method can be applied to accurately estimate solvation free energies for amino acid sidechain mimics, as well as the binding affinity shifts due to the chemical changes typical of lead optimization processes. This is illustrated in a number of protein systems extracted from other FEP studies in the literature: inhibitors of CDK2 kinase and a series of A2A adenosine G protein-coupled receptor antagonists, where the results obtained with QligFEP are in excellent agreement with experimental data. In addition, our protocol allows for scaffold hopping perturbations to identify the binding affinities between different core scaffolds, which we illustrate with a series of Chk1 kinase inhibitors. QligFEP is implemented in the open-source MD package Q, and works with the most common family of force fields: OPLS, CHARMM and AMBER.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

SAMPL6: calculation of macroscopic pKa values from ab initio quantum mechanical free energies

Macroscopic pK_a values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pK_a values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pK_as with a maximum likelihood estimator and appropriately summed to yield macroscopic pK_a values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pK_as: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pK_a. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pK_a units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pK_a values for novel compounds with reasonable accuracy.

Study of interactions between metal ions and protein model compounds by energy decomposition analyses and the AMOEBA force field

The interactions between metal ions and proteins are ubiquitous in biology. The selective binding of metal ions has a variety of regulatory functions. Therefore, there is a need to understand the mechanism of protein-ion binding. The interactions involving metal ions are complicated in nature, where short-range charge-penetration, charge transfer, polarization, and many-body effects all contribute significantly, and a quantitative description of all these interactions is lacking. In addition, it is unclear how well current polarizable force fields can capture these energy terms and whether these polarization models are good enough to describe the many-body effects. In this work, two energy decomposition methods, absolutely localized molecular orbitals and symmetry-adapted perturbation theory, were utilized to study the interactions between Mg²⁺/Ca²⁺ and model compounds for amino acids. Comparison of individual interaction components revealed that while there are significant charge-penetration and charge-transfer effects in Ca complexes, these effects can be captured by the van der Waals (vdW) term in the AMOEBA force field. The electrostatic interaction in Mg complexes is well described by AMOEBA since the charge penetration is small, but the distance-dependent polarization energy is problematic. Many-body effects were shown to be important for protein-ion binding. In the absence of many-body effects, highly charged binding pockets will be over-stabilized, and the pockets will always favor Mg and thus lose selectivity. Therefore, many-body effects must be incorporated in the force field in order to predict the structure and energetics of metalloproteins. Also, the many-body effects of charge transfer in Ca complexes were found to be non-negligible. The absorption of charge-transfer energy into the additive vdW term was a main source of error for the AMOEBA many-body interaction energies.