Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Effect of Protein-Polarized Ligand Charges on Relative Protein Ligand Binding Affinities

A major challenge in computer-aided drug design is predicting relative binding energies of different molecules to a target protein using fast and accurate free-energy calculation methods. Free-energy calculations are primarily computed by utilizing classical molecular dynamics simulations based on all-atom force fields (FF) to model the interactions in the system. The present standard classical all-atom FFs contain fixed partial charges on the atoms, and hence electrostatic interactions are modeled between them. The parametrization process to determine these partial charges usually relies on quantum mechanics or semiempirical calculations of the molecule in the gas phase or homogeneous water surrounding. These present standard parametrization schemes of the partial charges neglect, therefore, polarization effects from the protein surrounding. The absence of protein polarization effects can lead to significant errors in free-energy calculations in proteins. We present a parametrization scheme for the partial charges of ligands, named protein-induced polarization (PIP) charges, which account for the electrostatic polarization due to the protein surrounding. The scheme involves single-point quantum mechanics/molecular mechanics calculations of the ligand charges in the protein/water surrounding. Using PIP ligand partial charges, we have calculated the relative binding free energies (RBFEs) of well-studied protein-ligand systems. We show here that RBFEs computed with PIP charges are either significantly improved or at least comparable to those computed with nonpolarized standard GAFF charges. Overall, we present a simple-to-use parametrization scheme to include protein polarization in any type of binding free-energy calculations. The parametrization scheme increases the accuracy in RBFE calculations, while it does not add significant computation time to standard parametrization procedures.

Non-negligible Outer-Shell Reorganization Energy for Charge Transfer in Nonpolar Systems

Many charge-transporting molecular systems function as ordered or disordered arrays of solid state materials composed of nonpolar (or weakly polar) molecules. Due to low dielectric constants for nonpolar systems, it is common to ignore the effects of outer-shell reorganization energy (λout). However, ignoring λout has not been properly supported and it can severely impact predictions and insights derived. Here, we estimate λout by two means: from experimental ultraviolet photoelectron spectra, in which vibronic progression in these spectra can be fitted with the widths of peaks determining the low-frequency component in reorganization energy, regarded to be closely associated with λout, and from molecular dynamic (MD) simulation of nonpolar molecules, in which disorder or fluctuation statistics for energies of charged molecules are calculated. An upper bound for λout was obtained as 505 and 549 meV for crystalline anthracene (140 K) and pentacene (50 K), respectively, by fitting of experimental data, and 212 and 170 meV, respectively, from MD simulations. These values are comparable to the inner-sphere reorganization energy (λin) arising from intramolecular vibration. With corresponding spectral density functions calculated, we found that λout is influenced both by low- and high-frequency dynamics, in which the former arises from constrained translational and rotational motions of surrounding molecules. In an amorphous state, about half of the λout's obtained are from high-frequency components, which is quite different from the conventional polar solvation. Moreover, crystalline systems exhibit super-Ohmic spectral density, whereas amorphous systems are sub-Ohmic.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

Effects of ion type and concentration on the structure and aggregation of the amyloid peptide A β 16 - 22 $$ {\boldsymbol{\beta}}_{16-22} $$

Among the various factors controlling the amyloid aggregation process, the influences of ions on the aggregation rate and the resulting structures are important aspects to consider, which can be studied by molecular simulations. There is a wide variety of protein force fields and ion models, raising the question of which model to use in such studies. To address this question, we perform molecular dynamics simulations of Aβ16-22 , a fragment of the Alzheimer's amyloid β peptide, using different protein force fields, AMBER99SB-disp (A99-d) and CHARMM36m (C36m), and different ion parameters. The influences of NaCl and CaCl2 at various concentrations are studied and compared with the systems without the addition of ions. Our results indicate a sensitivity of the peptide-ion interactions to the different ion models. In particular, we observe a strong binding of Ca2+ to residue E22 with C36m and also with the Åqvist ion model used together with A99-d, which slightly affects the monomeric Aβ16-22 structures and the aggregation rate, but significantly affects the oligomer structures formed in the aggregation simulations. For example, at high Ca2+ concentrations, there was a switch from an antiparallel to a parallel β-sheet. Such ionic influences are of biological relevance because local ion concentrations can change in vivo and could help explain the polymorphism of amyloid fibrils.

Accurate Calculation of Solvation Properties of Lithium Ions in Nonaqueous Solutions

We perform all-atom molecular dynamics simulations of lithium triflate in 1,2-dimethoxyethane using six different literature force fields. This system is representative of many experimental studies of lithium salts in solvents and polymers. We show that multiple historically common force fields for lithium ions give qualitatively incorrect results when compared with those from experiments and quantum chemistry calculations. We illustrate the importance of correctly selecting force field parameters and give recommendations on the force field choice for lithium electrolyte applications.

Computation of Electrical Conductivities of Aqueous Electrolyte Solutions: Two Surfaces, One Property

In this work, we computed electrical conductivities under ambient conditions of aqueous NaCl and KCl solutions by using the Einstein-Helfand equation. Common force fields (charge q = ±1 e) do not reproduce the experimental values of electrical conductivities, viscosities, and diffusion coefficients. Recently, we proposed the idea of using different charges to describe the potential energy surface (PES) and the dipole moment surface (DMS). In this work, we implement this concept. The equilibrium trajectories required to evaluate electrical conductivities (within linear response theory) were obtained by using scaled charges (with the value q = ±0.75 e) to describe the PES. The potential parameters were those of the Madrid-Transport force field, which accurately describe viscosities and diffusion coefficients of these ionic solutions. However, integer charges were used to compute the conductivities (thus describing the DMS). The basic idea is that although the scaled charge describes the ion-water interaction better, the integer charge reflects the value of the charge that is transported due to the electric field. The agreement obtained with experiments is excellent, as for the first time electrical conductivities (and the other transport properties) of NaCl and KCl electrolyte solutions are described with high accuracy for the whole concentration range up to their solubility limit. Finally, we propose an easy way to obtain a rough estimate of the actual electrical conductivity of the potential model under consideration using the approximate Nernst-Einstein equation, which neglects correlations between different ions.

Scaled charges for ions: An improvement but not the final word for modeling electrolytes in water

In this work, we discuss the use of scaled charges when developing force fields for NaCl in water. We shall develop force fields for Na⁺ and Cl^- using the following values for the scaled charge (in electron units): ±0.75, ±0.80, ±0.85, and ±0.92 along with the TIP4P/2005 model of water (for which previous force fields were proposed for q = ±0.85 and q = ±1). The properties considered in this work are densities, structural properties, transport properties, surface tension, freezing point depression, and maximum in density. All the developed models were able to describe quite well the experimental values of the densities. Structural properties were well described by models with charges equal to or larger than ±0.85, surface tension by the charge ±0.92, maximum in density by the charge ±0.85, and transport properties by the charge ±0.75. The use of a scaled charge of ±0.75 is able to reproduce with high accuracy the viscosities and diffusion coefficients of NaCl solutions for the first time. We have also considered the case of KCl in water, and the results obtained were fully consistent with those of NaCl. There is no value of the scaled charge able to reproduce all the properties considered in this work. Although certainly scaled charges are not the final word in the development of force fields for electrolytes in water, its use may have some practical advantages. Certain values of the scaled charge could be the best option when the interest is to describe certain experimental properties.

Maximum in density of electrolyte solutions: Learning about ion-water interactions and testing the Madrid-2019 force field

In this work, we studied the effect of Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ chlorides and sulfates on the temperature of maximum density (TMD) of aqueous solutions at room pressure. Experiments at 1 molal salt concentration were carried out to determine the TMD of these solutions. We also performed molecular dynamics simulations to estimate the TMD at 1 and 2 m with the Madrid-2019 force field, which uses the TIP4P/2005 water model and scaled charges for the ions, finding an excellent agreement between experiment and simulation. All the salts studied in this work shift the TMD of the solution to lower temperatures and flatten the density vs temperature curves (when compared to pure water) with increasing salt concentration. The shift in the TMD depends strongly on the nature of the electrolyte. In order to explore this dependence, we have evaluated the contribution of each ion to the shift in the TMD concluding that Na⁺, Ca²⁺, and SO₄ ^2- seem to induce the largest changes among the studied ions. The volume of the system has been analyzed for salts with the same anion and different cations. These curves provide insight into the effect of different ions upon the structure of water. We claim that the TMD of electrolyte solutions entails interesting physics regarding ion-water and water-water interactions and should, therefore, be considered as a test property when developing force fields for electrolytes. This matter has been rather unnoticed for almost a century now and we believe it is time to revisit it.

Anomalous Phase Behaviors of Monolayer NaCl Aqueous Solutions Induced by Effective Coulombic Interactions within Angstrom-Scale Slits

Interests in subnanofluidic devices have called for molecular dynamics (MD) simulation studies of the thermodynamic behavior of monolayer salt solution within angstrom-scale slits. However, it still remains a grand challenge to accurately describe the Coulombic interactions by incorporating the effects of charge transfer and electronic dielectric screening. Herein, by using the electronic continuum model, where the effective ion charges are fine-tuned with a scaling factor of λ, we present simulation evidence that the effective Coulombic interactions among Na⁺/Cl^- ions can strongly affect the behavior of monolayer ionic aqueous solution. Our microsecond-scale MD simulations show that only the counterions with moderate effective charges (0.3 ≤ λ ≤ 0.8) can dissolve in monolayer water, whereas the high effective charges (λ ≥ 0.85) induce ions to assemble into monolayer nanocrystals, and ions with the low effective charges (λ ≤ 0.2) exhibit gas-like nanobubble. These findings could provide deeper insights into the physical chemistry behind subnanofluidic iontronic devices.

Molecular Simulations of Aqueous Electrolytes: Role of Explicit Inclusion of Charge Transfer into Force Fields

We describe here simulations of aqueous salt solutions that are performed using an explicit charge transfer force field. The emphasis of the discussion is on the calculation of a dynamical property of the solutions: self-diffusion of water. While force fields that are based on pairwise additive potentials or on potentials with explicit inclusion of polarization or with scaled charges can provide at best a qualitative agreement with experiments, force fields with explicit inclusion of charge transfer can produce quantitative agreement with experiment for NaCl and KCl solutions. We argue that a force field with explicit charge transfer contains new physics absent in the previously used force fields described in recent reviews of molecular simulations of aqueous electrolytes.

Efficient Parametrization of Force Field for the Quantitative Prediction of the Physical Properties of Ionic Liquid Electrolytes

The prediction of transport properties of room-temperature ionic liquids from nonpolarizable force field-based simulations has long been a challenge. The uniform charge scaling method has been widely used to improve the agreement with the experiment by incorporating the polarizability and charge transfer effects in an effective manner. While this method improves the performance of the force fields, this prescription is ad hoc in character; further, a quantitative prediction is still not guaranteed. In such cases, the nonbonded interaction parameters too need to be refined, which requires significant effort. In this work, we propose a three-step semiautomated refinement procedure based on (1) atomic site charges obtained from quantum calculations of the bulk condensed phase; (2) quenched Monte Carlo optimizer to shortlist suitable force field candidates, which are then tested using pilot simulations; and (3) manual refinement to further improve the accuracy of the force field. The strategy is designed in a sequential manner with each step improving the accuracy over the previous step, allowing the users to invest the effort commensurate with the desired accuracy of the refined force field. The refinement procedure is applied on N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide (DEME-TFSI), a front-runner as an electrolyte for electric double-layer capacitors and single-molecule-based devices. The transferability of the refined force field is tested on N,N-dimethyl-N-ethyl-N-methoxyethoxyethylammonium bis(trifluoromethanesulfonyl)imide (N_112,2O2O1-TFSI). The refined force field is found to be better at predicting both structural and transport properties compared to the uniform charge scaling procedure, which showed a discrepancy in the X-ray structure factor. The refined force field showed quantitative agreement with structural (density and X-ray structure factor) and transport properties-diffusion coefficients, ionic conductivity, and shear viscosity over a wide temperature range, building a case for the wide adoption of the procedure.

Extended magnesium and calcium force field parameters for accurate ion-nucleic acid interactions in biomolecular simulations

Magnesium and calcium play an essential role in the folding and function of nucleic acids. To correctly describe their interactions with DNA and RNA in biomolecular simulations, an accurate parameterization is crucial. In most cases, the ion parameters are optimized based on a set of experimental solution properties such as solvation free energies, radial distribution functions, water exchange rates, and activity coefficient derivatives. However, the transferability of such bulk-optimized ion parameters to quantitatively describe biomolecular systems is limited. Here, we extend the applicability of our previous bulk-optimized parameters by including experimental binding affinities toward the phosphate oxygen on nucleic acids. In particular, we systematically adjust the combination rules that are an integral part of the pairwise interaction potentials of classical force fields. This allows us to quantitatively describe specific ion binding to nucleic acids without changing the solution properties in the most simple and efficient way. We show the advancement of the optimized Lorentz combination rule for two representative nucleic acid systems. For double-stranded DNA, the optimized combination rule for Ca²⁺ significantly improves the agreement with experiments, while the standard combination rule leads to unrealistically distorted DNA structures. For the add A-riboswitch, the optimized combination rule for Mg²⁺ improves the structure of two specifically bound Mg²⁺ ions as judged by the experimental distance to the binding site. Including experimental binding affinities toward specific ion binding sites on biomolecules, therefore, provides a promising perspective to develop a more accurate description of metal cations for biomolecular simulations.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

Polarization Effects in Water-Mediated Selective Cation Transport across a Narrow Transmembrane Channel

Despite the progress in modeling complex molecular systems of ever-increasing complexity, a quantitatively accurate computational treatment of ion permeation through narrow membrane channels remains challenging. An important factor to reach this goal is induced electronic polarization, which is likely to impact the permeation rate of small ions through narrow molecular pores. In this work, we extended the recently developed polarizable force field based on the classical Drude oscillators to assess the role of induced polarization effects on the energetics of sodium and potassium ion transport across the gramicidin A (gA) ion channel. The inclusion of induced polarization lowers barriers present in 1D potential of mean force (PMF) for cation permeation by ∼50% compared to those obtained with the additive force field. Conductance properties calculated with 1D PMFs from Drude simulations are in better agreement with experimental results. Polarization of single-file water molecules and protein atoms forming the narrow pore has a direct impact on the free-energy barriers and cation-specific solid-state NMR chemical shifts. Sensitivity analysis indicates that small changes to water-channel interactions can alter the free energy barrier for ion permeation. These results, illustrating polarization effects present in the complex electrostatic environment of the gA channel, have broad implications for revising proposed mechanisms of ion permeation and selectivity in a variety of ion channels.

Simple corrections for the static dielectric constant of liquid mixtures from model force fields

Pair-wise additive force fields provide fairly accurate predictions, through classical molecular simulations, for a wide range of structural, thermodynamic, and dynamical properties of many materials. However, one key property that has not been well captured is the static dielectric constant, which characterizes the response of a system to an applied electric field and is important in determining the screening of electrostatic interactions through a system. A simple correction has been found to provide a relatively robust method to improve the estimate of the static dielectric constant from molecular simulations for a broad range of compounds. This approach accounts for the electronic contribution to molecular polarizability and assumes that the charges that couple a molecule to an applied electric field are proportional to the effective force field charges. In this work, we examine how this correction performs for systems at different temperatures and for binary mixtures. Using a value for the electronic polarizability, based on the experimental index of refraction, and a charge scaling factor, determined at a single temperature, we find that the static dielectric constant can be predicted remarkably well, in comparison to the experimentally measured values. This provides good evidence that the effective charges that appear in pair-wise additive force fields developed to reproduce the potential energy surface of a system are not the same as those that determine the static dielectric constant; however, they can be captured in a relatively simple manner, which is dependent on the particular force field.

MD simulation reveals differential binding of Cm(III) and Th(IV) with serum transferrin at acidic pH

The iron carrier human serum transferrin (sTf) is known to transport other metals, including some actinides (An). Radiotoxic An are routinely involved in the nuclear fuel cycle and the possibility of their accidental exposure cannot be ruled out. Understanding An interaction with sTf assumes a greater significance for the development of safe and efficacious chelators for their removal from the blood stream. Here we report several 100 ns equilibrium MD simulations of Cm(III)- and Th(IV)-loaded sTf at various protonation states of the protein to explore the possibility of the two An ions release and speciation. The results demonstrate variation in protonation state of dilysine pair (K206 and K296) and the tyrosine (Y188) residue is necessary for the opening of Cm(III)-bound protein and the release of the ion. For the tetravalent thorium, protonation of dilysine pair suffices to cause conformational changes of protein. However, in none of the protonation states, Th(IV) releases from sTf because of its strong electrostatic interaction with D63 in the first shell of the sTf binding cleft. Analysis of hydrogen bond, water bridge, and the evaluation of potential of mean forces of the An ions' release from sTf, substantiate the differential behavior of Cm(III) and Th(IV) at endosomal pH. The results provide insight in the regulation of Cm(III) and Th(IV) bioavailability that may prove useful for effective design of their decorporating agents and as well may help the future design of radiotherapy based on tetravalent ions.

Pressure in Molecular Simulations with Scaled Charges. 1. Ionic Systems

Charge scaling, rationalized as MDEC (molecular dynamics in electronic continuum) or ECC (electronic continuum correction), has become a widely used simple approach to how to avoid self-consistent induced dipoles yet approximately take into account the effects of electronic polarizability. It has been assumed that the continuum permittivity does not depend on density; in turn, pressure is calculated by standard formulas. In this work, we elaborate a complementary approximation of density-independent molecular polarizability and derive formulas for pressure corrections within the MDEC framework; real behavior lies between these two extremes. The pressure corrections for test ionic systems are huge and negative, leading to sizable densities in constant-pressure MDEC simulations. A comparison of MDEC results with equivalent polarizable systems gives a good pressure match for a crystal but very low MDEC pressures for ionic liquids. These results witness about the importance of a correct density dependence not only of continuum permittivity in MDEC simulations but also of polarizability in polarizable simulations.

Molecular simulation of liquid-vapor coexistence for NaCl: Full-charge vs scaled-charge interaction models

Scaled-charge models have been recently introduced for molecular simulations of electrolyte solutions and molten salts to attempt to implicitly represent polarizability. Although these models have been found to accurately predict electrolyte solution dynamic properties, they have not been tested for coexistence properties, such as the vapor pressure of the melt. In this work, we evaluate the vapor pressure of a scaled-charge sodium chloride (NaCl) force field and compare the results against experiments and a non-polarizable full-charge force field. The scaled-charge force field predicts a higher vapor pressure than found in experiments, due to its overprediction of the liquid-phase chemical potential. Reanalyzing the trajectories generated from the scaled-charge model with full charges improves the estimation of the liquid-phase chemical potential but not the vapor pressure.

Molecular dynamics simulations of plutonium binding and its decorporation from the binding-cleft of human serum transferrin

The possibility of plutonium (Pu) intake by radiation workers can not be ruled out. Transportation of Pu(IV) to various organs/cells is mainly carried through iron-carrying protein, serum transferrin (sTf), by receptor-mediated endocytosis. Understanding the Pu-sTf interaction is a primary step toward future design of its decorporating agents. We report MD simulations of Pu(IV) binding with sTf and look out for its decorporation at extracellular pH using suitable ligands. MD simulations were carried out in polarizable water environment at different protonation states of the protein. Results unravel the binding motif of Pu(IV): (1) sTf binds the ion in closed conformation at extracellular serum pH with carbonate as synergistic anions, (2) change in protonation state of dilysine (K206 and K296)-trigger and that of the carbonate ion at acidic endosomal pH is found to cause conformational changes of protein, conducive for the heavy ion to be released, although; (3) strong electrostatic interaction between D63 in the binding-cleft and Pu(IV) is found not to ever set free the ion. In an endeavour to decorporate Pu(IV), fragmented molecular form of hydroxypyridinone (HOPO) and catechol (CAM)-based ligands are docked at the binding site (BS) of the protein and metadynamics simulations are conducted. Pu(IV) binding at BS is found to be so strong that it was not detached from BS with the docked HOPO. However, for the identical set of simulation parameters, CAM is found to facilitate dislodging the heavy ion from the protein's binding influence. Differential behaviour of the two chelators is further explored. Fragmented molecular form of hydroxy-pyridinone (HOPO) and catecholamide (CAM) ligands were docked at the binding-site (BS) of human serum transferrin (sTf) to explore their feasibility as plausible Pu(IV) decorporating agents by employing metadynamics method. CAM was found to dislodge Pu from the sTf BS, while HOPO could not.

Solvate ionic liquids based on lithium bis(trifluoromethanesulfonyl)imide–glyme systems: coordination in MD simulations with scaled charges

Charge scaling in molecular dynamics simulations of lithium bis(trifluoromethanesulfonyl)imide–glyme solvate ionic liquids yields better agreement with experiments.

Improved Cation Binding to Lipid Bilayers with Negatively Charged POPS by Effective Inclusion of Electronic Polarization

Phosphatidylserine (PS) lipids are important signaling molecules and the most common negatively charged lipids in eukaryotic membranes. The signaling can be often regulated by calcium, but its interactions with PS headgroups are not fully understood. Classical molecular dynamics (MD) simulations can potentially give detailed description of lipid-ion interactions, but the results strongly depend on the used force field. Here, we apply the electronic continuum correction (ECC) to the Amber Lipid17 parameters of 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (POPS) lipid to improve its interactions with K⁺, Na⁺, and Ca²⁺ ions. The partial charges of the headgroup, glycerol backbone, and carbonyls of POPS, bearing a unit negative charge, were scaled with a factor of 0.75, derived for monovalent ions, and the Lennard-Jones σ parameters of the same segments were scaled with a factor of 0.89. The resulting ECC-POPS model gives more realistic interactions with Na⁺ and Ca²⁺ cations than the original Amber Lipid17 parameters when validated using headgroup order parameters and the "electrometer concept". In ECC-lipids simulations, populations of complexes of Ca²⁺ cations with more than two PS lipids are negligible, and interactions of Ca²⁺ cations with only carboxylate groups are twice more likely than with only phosphate groups, while interactions with carbonyls almost entirely involve other groups as well. Our results pave the way for more realistic MD simulations of biomolecular systems with anionic membranes, allowing signaling processes involving PS and Ca²⁺ to be elucidated.

A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl-, and SO4 2- in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ and the anions Cl^- and SO₄ ^2-. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.

Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications

Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.

Binding of Cm(III) and Th(IV) with Human Transferrin at Serum pH: Combined QM and MD Investigations

Human serum transferrin (sTf) can also function as a noniron metal transporter since only 30% of it is typically saturated with a ferric ion. While this function of sTf can be fruitfully utilized for targeted delivery of certain metal therapeutics, it also runs the risk of trafficking the lethal radionuclides into cells. A large number of actinide (An) ions are known to bind to the iron sites of sTf although molecular-level understanding of their binding is unclear. Understanding the radionuclide interaction with sTf is a primary step toward future design of their decorporating agents since irrespective of the means of contamination, the radionuclides are absorbed and transported by blood before depositing into target organs. Here, we report an extensive multiscale modeling approach of two An (curium(III) and thorium(IV)) ions' binding with sTf at serum physiological pH. We find that sTf binds both the heavy ions in a closed conformation with carbonate as synergistic anions and the An-loaded sTf maintains its closed conformation even after 100 ns of equilibrium molecular dynamics (MD) simulations. MD simulations are performed in a polarizable water environment, which also incorporates electronic continuum corrections for ions via charge rescaling. The molecular details of the An coordination and An exchange free energies with iron in the interdomain cleft of the protein are evaluated through a combination of quantum mechanical (QM) and MD studies. In line with reported experimental observations, well-tempered metadynamics results of the ions' binding energetics show that An-sTf complexes are less stable than Fe-sTf. Additionally, curium(III) is found to bind more weakly than thorium(IV). The latter result might suggest relative attenuation of thorium(IV) cytotoxicity when compared with curium(III).

Temperature Induced Dynamical Transition of Biomolecules in Polarizable and Nonpolarizable TIP3P Water

Temperature induced dynamical transition (DT), associated with a sharp rise in molecular flexibility, is well-known to be exhibited between 270 and 280 K in glycerol to 200-230 K in hydrated biomolecules and is controlled by diffusivity (viscosity) of the solvation layer. In the molecular dynamics (MD) community, especially for water as a solvent, this has been an intense area of research despite decades of investigations. However, in general, water in these studies is described by empirical nonpolarizable force fields in which electronic polarizability is treated implicitly with effective charges and related parameters. This might have led to the present trait of discovery that DTs of biomolecules, irrespective of the potential functions for water models used, occur within a narrow band of temperature variation (30-40 K). Whereas a water molecule in a biomolecular surface and one in bulk are polarized differently, therefore explicit treatment of water polarizability would be a powerful approach toward the treatment of hydration water, believed to cause the DT manifestation. Using MD simulations, we investigated the effects of polarizable water on the DT of biomolecules and the dynamic properties of hydration water. We chose two types of solutes: globular protein (lysozyme) and more open and flexible RNAs (a hairpin and a riboswitch) with different natures of hydrophilic sites than proteins in general. We found that the characteristic temperature of DT ( T_DT) for the solutes in polarizable water is always higher than that in its nonpolarizable counterpart. In particular, for RNAs, the variations are found to be ∼45 K between the two water models, whereas for the more compact lysozyme, it is only ∼4 K. The results are discussed in light of the enormous increase in relaxation times of a liquid upon cooling in the paradigm of dynamic switchover in hydration water with liquid-liquid phase transition, derived from the existence of the second critical point. Our result supports the idea that structures of biomolecules and their interactions with the hydration water determines T_DT and provides evidence for the decisive role of polarizable water on the onset of DT, which has been hitherto ignored.

Tracing the Pathways of Waters and Protons in Photosystem II and Cytochrome c Oxidase

Photosystem II (PSII) uses water as the terminal electron donor, producing oxygen in the Mn4CaO5 oxygen evolving complex (OEC), while cytochrome c oxidase (CcO) reduces O2 to water in its heme–Cu binuclear center (BNC). Each protein is oriented in the membrane to add to the proton gradient. The OEC, which releases protons, is located near the P-side (positive, at low-pH) of the membrane. In contrast, the BNC is in the middle of CcO, so the protons needed for O2 reduction must be transferred from the N-side (negative, at high pH). In addition, CcO pumps protons from N- to P-side, coupled to the O2 reduction chemistry, to store additional energy. Thus, proton transfers are directly coupled to the OEC and BNC redox chemistry, as well as needed for CcO proton pumping. The simulations that study the changes in proton affinity of the redox active sites and the surrounding protein at different states of the reaction cycle, as well as the changes in hydration that modulate proton transfer paths, are described.

Free Energy of Classical Molecular Crystals by Thermodynamic Integration from a Harmonic Reference

We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and models of rigid molecules, and use it to obtain the harmonic free energy of a crystal. The anharmonic correction is then calculated by the conventional thermodynamic integration over temperature in the NVT ensemble. Attention is paid to finite-size errors, tail corrections, thermostat choice, ergodicity, and other sources of inaccuracies. The calculated free energy of ice XIV modeled by the TIP4P/2005 potential agrees with the previously reported value and is by one order more accurate.

On the importance of accounting for nuclear quantum effects in ab initio calibrated force fields in biological simulations

In many important processes in chemistry, physics, and biology the nuclear degrees of freedom cannot be described using the laws of classical mechanics. At the same time, the vast majority of molecular simulations that employ wide-coverage force fields treat atomic motion classically. In light of the increasing desire for and accelerated development of quantum mechanics (QM)-parameterized interaction models, we reexamine whether the classical treatment is sufficient for a simple but crucial chemical species: alkanes. We show that when using an interaction model or force field in excellent agreement with the "gold standard" QM data, even very basic simulated properties of liquid alkanes, such as densities and heats of vaporization, deviate significantly from experimental values. Inclusion of nuclear quantum effects via techniques that treat nuclear degrees of freedom using the laws of classical mechanics brings the simulated properties much closer to reality.

A Kirkwood-Buff derived force field for alkaline earth halide salts

The activity and function of many macromolecules in cellular environments are coupled with the binding of divalent ions such as calcium or magnesium. In principle, computer simulations can be used to understand the molecular level aspects of how many important macromolecules interact with ions. However, most of the force fields currently available often fail to accurately reproduce the properties of divalent ions in aqueous environments. Here we develop classical non-polarizable force fields for the aqueous alkaline earth metal halides (MX₂), where M = Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺ and X = Cl^-, Br^-, I^-, which can be used in bimolecular simulations and which are compatible with the Simple Point Charge/Extended (SPC/E) water model. The force field parameters are specifically developed to reproduce the experimental Kirkwood-Buff integrals for aqueous solutions and thereby the experimental activity derivatives, partial molar volumes, and excess coordination numbers. This ensures that a reasonable balance between ion-ion, ion-water, and water-water distributions is obtained. However, this requires a scaling of the cation to water oxygen interaction strength in order to accurately reproduce the integrals. The scaling factors developed for chloride salts are successfully transferable to the bromide and iodide salts. Use of these new models leads to reasonable diffusion constants and dielectric decrements. However, the performance of the models decreases with increasing salt concentration (>4m), and simulations of the pure crystals exhibited unstable behavior.

Evaluating Force Field Performance in Thermodynamic Calculations of Cyclodextrin Host-Guest Binding: Water Models, Partial Charges, and Host Force Field Parameters

Computational prediction of noncovalent binding free energies with methods based on molecular mechanical force fields has become increasingly routine in drug discovery projects, where they promise to speed the discovery of small molecule ligands to bind targeted proteins with high affinity. Because the reliability of free energy methods still has significant room for improvement, new force fields, or modifications of existing ones, are regularly introduced with the aim of improving the accuracy of molecular simulations. However, comparatively little work has been done to systematically assess how well force fields perform, particularly in relation to the calculation of binding affinities. Hardware advances have made these calculations feasible, but comprehensive force field assessments for protein–ligand sized systems still remain costly. Here, we turn to cyclodextrin host–guest systems, which feature many hallmarks of protein–ligand binding interactions but are generally much more tractable due to their small size. We present absolute binding free energy and enthalpy calculations, using the attach-pull-release (APR) approach, on a set of 43 cyclodextrin-guest pairs for which experimental ITC data are available. The test set comprises both α- and β-cyclodextrin hosts binding a series of small organic guests, each with one of three functional groups: ammonium, alcohol, or carboxylate. Four water models are considered (TIP3P, TIP4Pew, SPC/E, and OPC), along with two partial charge assignment procedures (RESP and AM1-BCC) and two cyclodextrin host force fields. The results suggest a complex set of considerations when choosing a force field for biomolecular simulations. For example, some force field combinations clearly outperform others at the binding enthalpy calculations but not for the binding free energy. Additionally, a force field combination which we expected to be the worst performer gave the most accurate binding free energies – but the least accurate binding enthalpies. The results have implications for the development of improved force fields, and we propose this test set, and potential future elaborations of it, as a powerful validation suite to evaluate new force fields and help guide future force field development.

Computational and structural evidence for neurotransmitter-mediated modulation of the oligomeric states of human insulin in storage granules

Human insulin is a pivotal protein hormone controlling metabolism, growth, and aging and whose malfunctioning underlies diabetes, some cancers, and neurodegeneration. Despite its central position in human physiology, the in vivo oligomeric state and conformation of insulin in its storage granules in the pancreas are not known. In contrast, many in vitro structures of hexamers of this hormone are available and fall into three conformational states: T6, T3Rf3, and R6 As there is strong evidence for accumulation of neurotransmitters, such as serotonin and dopamine, in insulin storage granules in pancreatic β-cells, we probed by molecular dynamics (MD) and protein crystallography (PC) if these endogenous ligands affect and stabilize insulin oligomers. Parallel studies independently converged on the observation that serotonin binds well within the insulin hexamer (site I), stabilizing it in the T3R3 conformation. Both methods indicated serotonin binding on the hexamer surface (site III) as well. MD, but not PC, indicated that dopamine was also a good site III ligand. Some of the PC studies also included arginine, which may be abundant in insulin granules upon processing of pro-insulin, and stable T3R3 hexamers loaded with both serotonin and arginine were obtained. The MD and PC results were supported further by in solution spectroscopic studies with R-state-specific chromophore. Our results indicate that the T3R3 oligomer is a plausible insulin pancreatic storage form, resulting from its complex interplay with neurotransmitters, and pro-insulin processing products. These findings may have implications for clinical insulin formulations.