Cation−π and π–π Interactions in Aqueous Solution Studied Using Polarizable Potential Models

Ternary Synergy of Lys, Dopa, and Phe Results in Strong Cohesion of Peptide Films

Synergistic interactions between 3,4-dihydroxyphenylalanine (Dopa, Y*), cationic residues, and the aromatic rings have been recently highlighted as influential factors that enhance the underwater adhesion strength of mussel foot proteins and their derivatives. In this study, we report the first ever evidence of a cation-catechol-benzene ternary synergy between Y*, lysine (Lys, K), and phenylalanine (Phe, F) in adhesive peptides. We synthesized three hexapeptides containing a different combination of Y*, K, and F, i.e., (KY*)₃, (KF)₃, and (KY*F)₂, respectively, exploring the relationship between the cohesive performance and molecular architecture of peptides. The peptide with the (KY*F)₂ sequence displays the strongest underwater cohesion energy of 10.3 ± 0.3 mJ m^-2 from direct nanoscale surface force measurements. Combined with molecular dynamics simulation, we demonstrated that there are more bonding interactions (including cation-π, π-π, and hydrogen bond interactions) in (KY*F)₂ compared to the other two peptides. In addition, peptide (KY*F)₂ still shows the strongest cohesive energies of 7.6 ± 0.7 and 3.7 ± 0.5 mJ m^-2 in acidic and high-ionic strength environments, respectively, although the cohesive energy decreases compared to the value in pure water. Our results further explain the underwater cohesion mechanisms combining multiple interactions and offer insights on designing Dopa containing underwater adhesives.

Comparative study of the unbinding process of some HTLV-1 protease inhibitors using unbiased molecular dynamics simulations

The HTLV-1 protease is one of the major antiviral targets to overwhelm this virus. Several research groups have developed protease inhibitors, but none has been successful. In this regard, developing new HTLV-1 protease inhibitors to fix the defects in previous inhibitors may overcome the lack of curative treatment for this oncovirus. Thus, we decided to study the unbinding pathways of the most potent (compound 10, PDB ID 4YDF, Ki = 15 nM) and one of the weakest (compound 9, PDB ID 4YDG, Ki = 7900 nM) protease inhibitors, which are very structurally similar. We conducted 12 successful short and long simulations (totaling 14.8 μs) to unbind the compounds from two monoprotonated (mp) forms of protease using the Supervised Molecular Dynamics (SuMD) without applying any biasing force. The results revealed that Asp32 or Asp32′ in the two forms of mp state similarly exert powerful effects on maintaining both potent and weak inhibitors in the binding pocket of HTLV-1 protease. In the potent inhibitor’s unbinding process, His66′ was a great supporter that was absent in the weak inhibitor’s unbinding pathway. In contrast, in the weak inhibitor’s unbinding process, Trp98/Trp98′ by pi-pi stacking interactions were unfavorable for the stability of the inhibitor in the binding site. In our opinion, these results will assist in designing more potent and effective inhibitors for the HTLV-1 protease.

Corrections in the CHARMM36 Parametrization of Chloride Interactions with Proteins, Lipids, and Alkali Cations, and Extension to Other Halide Anions

The nonpolarizable CHARMM force field is one of the most widely used energy functions for all-atom biomolecular simulations. Chloride is the only halide ion included in the latest version, CHARMM36m, and is used widely in simulation studies, often as an electrolyte ion but also as the biological substrate of transport proteins and enzymes. Here, we find that existing parameters systematically underestimate the interaction of Cl^- with proteins and lipids. Accordingly, when examined in solution, little to no Cl^-association can be observed with most components of the protein, including backbone, polar side chains and aromatic rings. The strength of the interaction with cationic side chains and with alkali ions is also incongruent with experimental measurements, specifically osmotic coefficients of concentrated solutions. Consistent with these findings, a 4-μs trajectory of the Cl^--specific transport protein CLC-ec1 shows irreversible Cl^- dissociation from the so-called S_cen binding site, even in a 150 mM NaCl buffer. To correct for these deficiencies, we formulate a series of pair-specific Lennard-Jones parameters that override those resulting from the conventional Lorentz-Berthelot combination rules. These parameters, referred to as NBFIX, are systematically calibrated against available experimental data as well as ab initio geometry optimizations and energy evaluations, for a wide set of binary and ternary Cl^- complexes with protein and lipid analogs and alkali cations. Analogously, we also formulate parameter sets for the other three biological halide ions, namely, fluoride, bromide, and iodide. The resulting parameters are used to calculate the potential of mean force defining the interaction of each anion and each of the protein and lipid analogues in bulk water, revealing association free energies in the range of -0.3 to -3.3 kcal/mol, with the F^- complexes being the least stable. The NBFIX corrections also preserve the Cl^- occupancy of CLC-ec1 in a second 4-μs trajectory. We posit that these optimized molecular-mechanics models provide a more realistic foundation for all-atom simulation studies of processes entailing changes in hydration, recognition, or transport of halide anions.

Physisorption of bio oil nitrogen compounds onto montmorillonite

We assess computationally the adsorption of a series of nitrogen containing heterocycles and fatty acid amides from bio-oil on a model clay surface, Na-montmorillonite. The adsorption energies and conformations predicted by atomistic detail molecular dynamics (MD) simulations are compared against density functional theory (DFT) based molecular electrostatic potentials (MEP) and Hirshfeld, AIM, Merz-Singh-Kollman, and ChelpG charges. MD predicts systematically adsorption via cation bridging with adsorption strength of the heterocycles following purine > pyridine > imidazole > pyrrole > indole > quinoline. The fatty acid amides adsorption strength follows the steric availability and bulkiness of the head group. A comparison against the DFT calculations shows that MEP predicts adsorption geometries and the MD simulations reproduce the conformations for single adsorption site species. However, the DFT derived charge distibutions show that MD force-fields with non-polarizable fixed partial charge representations parametrized for aqueous environments cannot be used in apolar solvent environments without careful accuracy considerations. The overall trends in adsorption energies are reproduced by the Charmm GenFF employed in the MD simulations but the adsorption energies are systematically overestimated in this apolar solvent environment. The work has significance both for revealing nitrogen compound adsorption trends in technologically relevant bio oil environments but also as a methodological assessment revealing the limits of state of the art biomolecular force-fields and simulation protocols in apolar bioenvironments.

Hydrated cation-π interactions of π-electrons with hydrated Li+, Na+, and K+ cations

Cation-π interactions are essential for many chemical, biological, and material processes, and these processes usually involve an aqueous salt solution. However, there is still a lack of a full understanding of the hydrated cation-π interactions between the hydrated cations and the aromatic ring structures on the molecular level. Here, we report a molecular picture of hydrated cation-π interactions, by using the calculations of density functional theory (DFT). Specifically, the graphene sheet can distort the hydration shell of the hydrated K+ to interact with K+ directly, which is hereafter called water-cation-π interactions. In contrast, the hydration shell of the hydrated Li+ is quite stable and the graphene sheet interacts with Li+ indirectly, mediated by water molecules, which we hereafter call the cation-water-π interactions. The behavior of hydrated cations adsorbed on a graphene surface is mainly attributed to the competition between the cation-π interactions and hydration effects. These findings provide valuable details of the structures and the adsorption energy of hydrated cations adsorbed onto the graphene surface.

Accuracy of Alternate Nonpolarizable Force Fields for the Determination of Protein-Ligand Binding Affinities Dominated by Cation-π Interactions

Modifying pair-specific Lennard-Jones parameters through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field has proven cost-effective for improving the description of cation-π interactions in biological objects by means of pairwise additive potential energy functions. Here, two sets of newly optimized CHARMM36 force-field parameters including NBFIX corrections, coined CHARMM36m-NBF and CHARMM36-WYF, and the original force fields, namely CHARMM36m and Amber ff14SB, are used to determine the standard binding free energies of seven protein-ligand complexes containing cation-π interactions. Compared with precise experimental measurements, our results indicate that the uncorrected, original force fields significantly underestimate the binding free energies, with a mean error of 5.3 kcal/mol, while the mean errors of CHARMM36m-NBF and CHARMM36-WYF amount to 0.8 and 2.1 kcal/mol, respectively. The present study cogently demonstrates that the use of modified parameters jointly with NBFIX corrections dramatically increases the accuracy of the standard binding free energy of protein-ligand complexes dominated by cation-π interactions, most notably with CHARMM36m-NBF.

3D Interaction Homology: Hydropathic Analyses of the "π-Cation" and "π-π" Interaction Motifs in Phenylalanine, Tyrosine, and Tryptophan Residues

Three-dimensional (3D) maps of the hydropathic environments of protein amino acid residues are information-rich descriptors of preferred conformations, interaction types and energetics, and solvent accessibility. The interactions made by each residue are the primary factor for rotamer selection and the secondary, tertiary, and even quaternary protein structure. Our evolving basis set of environmental data for each residue type can be used to understand the protein structure. This work focuses on the aromatic residues phenylalanine, tyrosine, and tryptophan and their structural roles. We calculated and analyzed side chain-to-environment 3D maps for over 70,000 residues of these three types that reveal, with respect to hydrophobic and polar interactions, the environment around each. After binning with backbone ϕ/ψ and side chain χ₁, we clustered each bin by 3D similarities between map-map pairs. For each of the three residue types, four bins were examined in detail: one in the β-pleat, two in the right-hand α-helix, and one in the left-hand α-helix regions of the Ramachandran plot. For high degrees of side chain burial, encapsulation of the side chain by hydrophobic interactions is ubiquitous. The more solvent-exposed side chains are more likely to be involved in polar interactions with their environments. Evidence for π-π interactions was observed in about half of the residues surveyed [phenylalanine (PHE): 53.3%, tyrosine (TYR): 34.1%, and tryptophan (TRP): 55.7%], but on an energy basis, this contributed to only ∼4% of the total. Evidence for π-cation interactions was observed in 14.1% of PHE, 8.3% of TYR, and 26.8% of TRP residues, but on an energy basis, this contributed to only ∼1%. This recognition of even these subtle interactions in the 3D hydropathic environment maps is key support for our interaction homology paradigm of protein structure elucidation and possibly prediction.

Ion Solvation and Transport in Narrow Carbon Nanotubes: Effects of Polarizability, Cation-π Interaction, and Confinement

Understanding ion solvation and transport under confinement is critical for a wide range of emerging technologies, including water desalination and energy storage. While molecular dynamics (MD) simulations have been widely used to study the behavior of confined ions, considerable deviations between simulation results depending on the specific treatment of intermolecular interactions remain. In the following, we present a systematic investigation of the structure and dynamics of two representative solutions, that is, KCl and LiCl, confined in narrow carbon nanotubes (CNTs) with a diameter of 1.1 and 1.5 nm, using a combination of first-principles and classical MD simulations. Our simulations show that the inclusion of both polarization and cation-π interactions is essential for the description of ion solvation under confinement, particularly for large ions with weak hydration energies. Beyond the variation in ion solvation, we find that cation-π interactions can significantly influence the transport properties of ions in CNTs, particularly for KCl, where our simulations point to a strong correlation between ion dehydration and diffusion. Our study highlights the complex interplay between nanoconfinement and specific intermolecular interactions that strongly control the solvation and transport properties of ions.

Modeling Shows that Rotation about the Peroxide O-O Bond Assists Protein and Lipid Functional Groups in Discriminating between H2O2 and H2O

Long associated with cell death, hydrogen peroxide (H₂O₂) is now known to perform many physiological roles. Unraveling its biological mechanisms of action requires atomic-level knowledge of its association with proteins and lipids, which we address here. High-level [MP2(full)/6-311++G(3df,3pd)] ab initio calculations reveal skew rotamers as the lowest-energy states of isolated H₂O₂ (ϕ_HOOH ∼ 112°) with minimum and maximum electrostatic potentials (kcal/mol) of -24.8 (V_s,min) and 36.5 (V_s,max), respectively. Transition-state, nonpolar trans rotamers (ϕ_HOOH ∼ 180°) at 1.2 kcal/mol higher in energy are poorer H-bond acceptors (V_s,min = -16.6) than the skew rotamers, while highly polar cis rotamers (ϕ_HOOH ∼ 0°) at 7.8 kcal/mol are much better H-bond donors (V_s,max = 52.7). Modeling H₂O₂ association with neutral and charged analogs of protein residues and lipid groups (e.g., ester, phosphate, choline) reveals that skew rotamers (ϕ_HOOH = 84-122°) are favored in the neutral and cationic complexes, which display gas-phase interaction energies (E^CP, kcal/mol) of -1.5 to -18. The neutral and cationic complexes of H₂O exhibit a similar range of stabilities (E^CP ∼ -1 to -18). However, considerably higher energies (E^CP ∼ -14 to -36) are found for the H₂O₂ complexes of the anionic ligands, which are stabilized by charge-assisted H-bond donation from cis and distorted cis rotamers (ϕ_HOOH = 0-60°). H₂O is a much poorer H-bond donor (V_s,max = 33.4) than cis-H₂O₂, so its anionic complexes are significantly weaker (E^CP ∼ -11 to -20). Thus, by dictating the rotamer preference of H₂O₂, functional groups in biomolecules can discriminate between H₂O₂ and H₂O. Finally, exploiting the present ab initio data, we calibrated and validated our published molecular mechanics model for H₂O₂ (Orabi, E. A.; English, A. M. J. Chem. Theory Comput. 2018, 14, 2808-2821) to provide an important tool for simulating H₂O₂ in biology.

Dividing the Periodic Box into Subdivisions with Their Surroundings to Accelerate Molecular Dynamics Simulation with High Accuracy

A major field of current research in chemistry and biology is the development of the tools that enable in situ analysis of complex systems. However, the long-time dynamics simulation for an extremely large system in solution is almost impossible by an all-atom force field combined with an explicit solvent model. The results show that the larger the periodic box is, the closer the properties of the system are to the experimental values. Therefore, how can we carry out simulations for systems that are fast, accurate, and large enough? A method of dividing the periodic box into subdivisions with their surroundings (DBSS) is presented here, and it clearly increases the computation speed without losing accuracy and enables the simulation of extremely large systems by strongly decreasing the dimension of the charge matrix. The DBSS method divides a single periodic box or unit in an extremely large system into several subdivisions with a suitable choice according to atomic coordinates. This method ensures that these subdivisions are always changing and allows the atoms to communicate with each other. Intermolecular communication is important for molecular properties and functions but is not possible with other fragment methods. The partial charges are calculated in each subdivision with an overlapping surrounding used to take hydrogen bond interaction between the subdivisions into account. This is an iterative process because the charge population will be recalculated at intervals during the dynamics simulations. Taking a water system as an example, each subdivision is extended by 4 Å as the surrounding. The computation time scales almost linearly with the size of the system, and the slope is small. MD simulations for several properties have been performed by the ABEEM-DBSS method. The results indicate that the ABEEM-DBSS method can accurately simulate the properties of water system, and the accuracy can reach or approach that of the experimental data or of other water potentials. Interestingly, the properties become closer to the experimental data as the sizes of the periodic box increase, further validating the need for the simulation of a large system and demonstrating the value of the DBSS method.

Explicit Representation of Cation-π Interactions in Force Fields with 1/r4 Nonbonded Terms

The binding energies for cation-π complexation are underestimated by traditional fixed-charge force fields owing to their lack of explicit treatment of ion-induced dipole interactions. To address this deficiency, an explicit treatment of cation-π interactions has been introduced into the OPLS-AA force field. Following prior work with atomic cations, it is found that cation-π interactions can be handled efficiently by augmenting the usual 12-6 Lennard-Jones potentials with 1/r⁴ terms. Results are provided for prototypical complexes as well as protein-ligand systems of relevance for drug design. Alkali cation, ammonium, guanidinium, and tetramethylammonium were chosen for the representative cations, while benzene and six heteroaromatic molecules were used as the π systems. The required nonbonded parameters were fit to reproduce structure and interaction energies for gas-phase complexes from density functional theory (DFT) calculations at the ωB97X-D/6-311++G(d,p) level. The impact of the solvent was then examined by computing potentials of mean force (pmfs) in both aqueous and tetrahydrofuran (THF) solutions using the free-energy perturbation (FEP) theory. Further testing was carried out for two cases of strong and one case of weak cation-π interactions between druglike molecules and their protein hosts, namely, the JH2 domain of JAK2 kinase and macrophage migration inhibitory factor. FEP results reveal greater binding by 1.5-4.4 kcal/mol from the addition of the explicit cation-π contributions. Thus, in the absence of such treatment of cation-π interactions, errors for computed binding or inhibition constants of 10¹-10³ are expected.

Accurate Description of Cation-π Interactions in Proteins with a Nonpolarizable Force Field at No Additional Cost

Cation-π interactions play a significant role in a host of processes eminently relevant to biology. However, polarization effects arising from the interaction of cations with aromatic moieties have long been recognized to be inadequately described by pairwise additive force fields. In the present work, we address this longstanding shortcoming through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field, modifying pair-specific Lennard-Jones (LJ) parameters, while circumventing the limitations of the Lorentz-Berthelot combination rules. The potentials of mean force (PMFs) characterizing prototypical cation-π interactions in aqueous solutions are first determined using a hybrid quantum mechanical/molecular mechanics (QM/MM) strategy in conjunction with an importance-sampling algorithm. The LJ parameters describing the cation-π pairs are then optimized to match the QM/MM PMFs. The standard binding free energies of nine cation-π complexes, i.e., toluene, para-cresol, and 3-methyl-indole interacting with either ammonium, guanidinium, or tetramethylammonium, determined with this new set of parameters agree well with the experimental measurements. Additional simulations were carried out on three different classes of biological objects featuring cation-π interactions, including five individual proteins, three protein-ligand complexes, and two protein-protein complexes. Our results indicate that the description of cation-π interactions is overall improved using NBFIX corrections, compared with the standard pairwise additive force field. Moreover, an accurate binding free energy calculation for a protein-ligand complex containing cation-π interactions (2BOK) shows that using the new parameters, the experimental binding affinity can be reproduced quantitatively. Put together, the present work suggests that the NBFIX parameters optimized here can be broadly utilized in the simulation of proteins in an aqueous solution to enhance the representation of cation-π interactions, at no additional computational cost.

New Molecular-Mechanics Model for Simulations of Hydrogen Fluoride in Chemistry and Biology

Hydrogen fluoride (HF) is the most polar diatomic molecule and one of the simplest molecules capable of hydrogen-bonding. HF deviates from ideality both in the gas phase and in solution and is thus of great interest from a fundamental standpoint. Pure and aqueous HF solutions are broadly used in chemical and industrial processes, despite their high toxicity. HF is a stable species also in some biological conditions, because it does not readily dissociate in water unlike other hydrogen halides; yet, little is known about how HF interacts with biomolecules. Here, we set out to develop a molecular-mechanics model to enable computer simulations of HF in chemical and biological applications. This model is based on a comprehensive high-level ab initio quantum chemical investigation of the structure and energetics of the HF monomer and dimer; (HF)_n clusters, for n = 3-7; various clusters of HF and H₂O; and complexes of HF with analogs of all 20 amino acids and of several commonly occurring lipids, both neutral and ionized. This systematic analysis explains the unique properties of this molecule: for example, that interacting HF molecules favor nonlinear geometries despite being diatomic and that HF is a strong H-bond donor but a poor acceptor. The ab initio data also enables us to calibrate a three-site molecular-mechanics model, with which we investigate the structure and thermodynamic properties of gaseous, liquid, and supercritical HF in a wide range of temperatures and pressures; the solvation structure of HF in water and of H₂O in liquid HF; and the free diffusion of HF across a lipid bilayer, a key process underlying the high cytotoxicity of HF. Despite its inherent simplifications, the model presented significantly improves upon previous efforts to capture the properties of pure and aqueous HF fluids by molecular-mechanics methods and to our knowledge constitutes the first parameter set calibrated for biomolecular simulations.

Improved Modeling of Cation-π and Anion-Ring Interactions Using the Drude Polarizable Empirical Force Field for Proteins

Cation-π interactions are noncovalent interactions between a π-electron system and a positively charged ion that are regarded as a strong noncovalent interaction and are ubiquitous in biological systems. Similarly, though less studied, anion-ring interactions are present in proteins along with in-plane interactions of anions with aromatic rings. As these interactions are between a polarizing ion and a polarizable π system, the accuracy of the treatment of these interactions in molecular dynamics (MD) simulations using additive force fields (FFs) may be limited. In the present work, to allow for a better description of ion-π interactions in proteins in the Drude-2013 protein polarizable FF, we systematically optimized the parameters for these interactions targeting model compound quantum mechanical (QM) interaction energies with atom pair-specific Lennard-Jones parameters along with virtual particles as selected ring centroids introduced to target the QM interaction energies and geometries. Subsequently, MD simulations were performed on a series of protein structures where ion-π pairs occur to evaluate the optimized parameters in the context of the Drude-2013 FF. The resulting FF leads to a significant improvement in reproducing the ion-π pair distances observed in experimental protein structures, as well as a smaller root-mean-square differences and fluctuations of the overall protein structures from experimental structures. Accordingly, the optimized Drude-2013 protein polarizable FF is suggested for use in MD simulations of proteins where cation-π and anion-ring interactions are critical. © 2019 Wiley Periodicals, Inc.

Progressive Hydrophobicity of Fluorobenzenes

The potentials of mean force for the dimers of fluorobenzenes sample both π-stacked and T-shaped structures for partially fluorinated benzenes, namely, 1,4-difluorobenzene, 1,3,5-trifluorobenzene, and 1,2,4,5-tetrafluorobenzene, and sample only the T-shaped structures for benzene and hexafluorobenzene. While the free energy for the dimerization in water is very weakly dependent on the number of fluorine atoms, the formation of π-stacked structures is entropy-driven and the T-shaped structures appear due to an enthalpic minimum. Interestingly, the solvation behavior suggests that the accumulation of water around the contact and solvent-separated pairs decreases with the increase in the number of fluorine atoms, which signifies progressive hydrophobicity of fluorobenzenes.

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

Cation-π Interactions between Quaternary Ammonium Ions and Amino Acid Aromatic Groups in Aqueous Solution

Cation-π interactions play important roles in the stabilization of protein structures and protein-ligand complexes. They contribute to the binding of quaternary ammonium ligands (mainly RNH₃⁺ and RN(CH₃)₃⁺) to various protein receptors and are likely involved in the blockage of potassium channels by tetramethylammonium (TMA⁺) and tetraethylammonium (TEA⁺). Polarizable molecular models are calibrated for NH₄⁺, TMA⁺, and TEA⁺ interacting with benzene, toluene, 4-methylphenol, and 3-methylindole (representing aromatic amino acid side chains) based on the ab initio MP2(full)/6-311++G(d,p) properties of the complexes. Whereas the gas-phase affinity of the ions with a given aromatic follows the trend NH₄⁺ > TMA⁺ > TEA⁺, molecular dynamics simulations using the polarizable models show a reverse trend in water, likely due to a contribution from the hydrophobic effect. This reversed trend follows the solubility of aromatic hydrocarbons in quaternary ammonium salt solutions, which suggests a role for cation-π interactions in the salting-in of aromatic compounds in solution. Simulations in water show that the complexes possess binding free energies ranging from -1.3 to -3.3 kcal/mol (compared to gas-phase binding energies between -8.5 and -25.0 kcal/mol). Interestingly, whereas the most stable complexes involve TEA⁺ (the largest ion), the most stable solvent-separated complexes involve TMA⁺ (the intermediate-size ion).

An assessment of the random-phase approximation functional and characteristics analysis for noncovalent cation-π interactions

The binding energy is of great importance in understanding the formation and stability of noncovalent interactions. However, the determination of the binding energy with high precision and efficiency in medium- and long-range noncovalent interactions is still challenging for quantum chemistry. Here, we assess the performance of random-phase approximation (RPA), a fully non-local fifth-rung of the Jacob ladder functional, in determining the binding energy of cation-π systems (cation = Li⁺, Na⁺, Be²⁺, Mg²⁺, Al⁺, and NH₄⁺; π = C₆H₆), which, to the best of our knowledge, has not been investigated. Using experimental results as the benchmark, we systematically compared the RPA method to the other ab initio methods (DFT/B3LYP, MP2, CCSD(T), and QCISD(T)) both in calculation accuracy and efficiency. From the perspective of accuracy, RPA is the best among these approaches, followed by the CCSD(T) and QCISD(T) methods. DFT/B3LYP and MP2 provide the worst accuracy. In addition, the computational efficiency of RPA is much faster than that of CCSD(T) and QCISD(T). We believe that RPA is a robust method for the precise description of medium- and long-range noncovalent interactions and is capable of providing benchmarking data. The interaction strength and interaction nature of cation-π systems are further analyzed by atoms in molecules (AIM) and the color-mapped reduced density gradient (RDG) isosurface, which are consistent with the characteristics of a typical cation-π interaction.

Cation-π interactions in competition with cation microhydration: a theoretical study of alkali metal cation-pyrene complexes

Cation–π interactions were systematically investigated for the adsorption of H⁺ and alkali metal cations M⁺ to pyrene by means of Møller–Plesset perturbation theory (MP2) and density functional theory (DFT). The main aims were to determine the preferred adsorption sites and how the microhydration shell influences the adsorption process. The preferred adsorption sites were characterized in terms of structural parameters and energetic stability. Stability analysis of the M⁺–pyrene complexes revealed that the binding strength and the barrier to transitions between neighboring sites generally decreased with increasing cation size from Li⁺ to Cs⁺. Such transitions were practically barrierless (<<1 kcal/mol) for the large Rb⁺ and Cs⁺ ions. Further, the influence of the first hydration shell on the adsorption behavior was investigated for Li⁺ and K⁺ as representatives of small and large (alkali metal) cations, respectively. While the isolated complexes possessed only one minimum, two minima—corresponding to an inner and an outer complex—were observed for microhydrated complexes. The small Li⁺ ion formed a stable hydration shell and preferentially interacted with water rather than pyrene. In contrast, K⁺ favored cation–π over cation–water interactions. It was found that the mechanism for complex formation depends on the balance between cation–π interactions, cation–water complexation, and the hydrogen bonding of water to the π-system.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Improving the Force Field Description of Tyrosine-Choline Cation-π Interactions: QM Investigation of Phenol-N(Me)4+ Interactions

Cation-π interactions between tyrosine amino acids and compounds containing N,N,N-trimethylethanolammonium (N(CH3)3) are involved in the recognition of histone tails by chromodomains and in the recognition of phosphatidylcholine (PC) phospholipids by membrane-binding proteins. Yet, the lack of explicit polarization or charge transfer effects in molecular mechanics force fields raises questions about the reliability of the representation of these interactions in biomolecular simulations. Here, we investigate the nature of phenol-tetramethylammonium (TMA) interactions using quantum mechanical (QM) calculations, which we also use to evaluate the accuracy of the additive CHARMM36 and Drude polarizable force fields in modeling tyrosine-choline interactions. We show that the potential energy surface (PES) obtained using SAPT2+/aug-cc-pVDZ compares well with the large basis-set CCSD(T) PES when TMA approaches the phenol ring perpendicularly. Furthermore, the SAPT energy decomposition reveals comparable contributions from electrostatics and dispersion in phenol-TMA interactions. We then compared the SAPT2+/aug-cc-pVDZ PES obtained along various approach directions to the corresponding PES obtained with CHARMM, and we show that the force field accurately reproduces the minimum distances while the interaction energies are underestimated. The use of the Drude polarizable force field significantly improves the interaction energies but decreases the agreement on distances at energy minima. The best agreement between force field and QM PES is obtained by modifying the Lennard-Jones terms for atom pairs involved in the phenol-TMA cation-π interactions. This is further shown to improve the correlation between the occupancy of tyrosine-choline cation-π interactions obtained from molecular dynamics simulations of a bilayer-bound bacterial phospholipase and experimental affinity data of the wild-type protein and selected mutants.

An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications

Molecular mechanics force fields that explicitly account for induced polarization represent the next generation of physical models for molecular dynamics simulations. Several methods exist for modeling induced polarization, and here we review the classical Drude oscillator model, in which electronic degrees of freedom are modeled by charged particles attached to the nuclei of their core atoms by harmonic springs. We describe the latest developments in Drude force field parametrization and application, primarily in the last 15 years. Emphasis is placed on the Drude-2013 polarizable force field for proteins, DNA, lipids, and carbohydrates. We discuss its parametrization protocol, development history, and recent simulations of biologically interesting systems, highlighting specific studies in which induced polarization plays a critical role in reproducing experimental observables and understanding physical behavior. As the Drude oscillator model is computationally tractable and available in a wide range of simulation packages, it is anticipated that use of these more complex physical models will lead to new and important discoveries of the physical forces driving a range of chemical and biological phenomena.

Probing the Ca(2+)-assisted π-π interaction during Ca(2+)-dependent protein folding

Protein folding is governed by a balance of non-covalent interactions, of which cation-π and π-π play important roles. Theoretical calculations revealed a strong cooperativity between cation-π involving alkali and alkaline earth metal ions and π-π interactions, but however, no experimental evidence was provided in this regard. Here, we characterized a Ca(2+)-binding self-processing module (SPM), which mediates a highly-specific Ca(2+)-dependent autocatalytic processing of iron-regulated protein FrpC secreted by the pathogenic Gram-negative bacterium Neisseria meningitidis. The SPM undergoes a Ca(2+)-induced transition from an intrinsically unstructured conformation to the compact protein fold that is ultimately stabilized by the π-π interaction between two unique tryptophan residues arranged in the T-shaped orientation. Moreover, the pair of tryptophans is located in a close vicinity of a calcium-binding site, suggesting the involvement of a Ca(2+)-assisted π-π interaction in the stabilization of the tertiary structure of the SPM. This makes the SPM an excellent model for the investigation of the Ca(2+)-assisted π-π interaction during Ca(2+)-induced protein folding.

Estimating the binding ability of onium ions with CO2 and π systems: a computational investigation

The impact of increasing methyl substitution on onium ions in their complexes with CO₂ and aromatic systems has been analyzed using DFT calculations.

Cation-π interactions of methylated ammonium ions: a quantum mechanical study

Cation-π interactions of methylated ammonium ions play a key role in a broad range of biochemical systems. These include methyl-lysine binding proteins which bind to methylated sites on histone proteins, lysine demethylase enzymes which demethylate these sites, and neurotransmitter receptor complexes which bind choline-derived ligands. Recognition in these systems is achieved through an 'aromatic cage' motif in the binding site. Here we use high-level quantum mechanical calculations to address how cation-π interactions of methylated ammonium ions are modulated by a change in methylation state and interaction geometry. We survey methyl-lysine and choline-derived complexes in the Protein Databank to validate our results against available structural data. A quantitative description of cation-π interactions of methylated ammonium systems is critical to structure-based efforts to target methyl-lysine binding proteins and demethylase enzymes in the treatment of unregulated transcriptional control, and neurotransmitter receptors in the treatment of neurological disease. It is our hope that our work will serve as a benchmark for the development of physical chemistry based force fields that can accurately model the contribution of cation-π interactions to binding and specificity in these systems.

Different hydration patterns in the pores of AmtB and RhCG could determine their transport mechanisms

The ammonium transporters of the Amt/Rh family facilitate the diffusion of ammonium across cellular membranes. Functional data suggest that Amt proteins, notably found in plants, transport the ammonium ion (NH4(+)), whereas human Rhesus (Rh) proteins transport ammonia (NH3). Comparison between the X-ray structures of the prokaryotic AmtB, assumed to be representative of Amt proteins, and the human RhCG reveals important differences at the level of their pore. Despite these important functional and structural differences between Amt and Rh proteins, studies of the AmtB transporter have led to the suggestion that proteins of both subfamilies work according to the same mechanism and transport ammonia. We performed molecular dynamics simulations of the AmtB and RhCG proteins under different water and ammonia occupancy states of their pore. Free energy calculations suggest that the probability of finding NH3 molecules in the pore of AmtB is negligible in comparison to finding water. The presence of water in the pore of AmtB could support the transport of proton. The pore lumen of RhCG is found to be more hydrophobic due to the presence of a phenylalanine conserved among Rh proteins. Simulations of RhCG also reveal that the signature histidine dyad is occasionally exposed to the extracellular bulk, which is never observed in AmtB. These different hydration patterns are consistent with the idea that Amt and Rh proteins are not functionally equivalent and that permeation takes place according to two distinct mechanisms.

Matching of additive and polarizable force fields for multiscale condensed phase simulations

Inclusion of electronic polarization effects is one of the key aspects in which the accuracy of current biomolecular force fields may be improved. The principal drawback of such approaches is the computational cost, which typically ranges from 3 - 10 times that of the equivalent additive model, and may be greater for more sophisticated treatments of polarization or other many-body effects. Here, we present a multiscale approach which may be used to enhance the sampling in simulations with polarizable models, by using the additive model as a tool to explore configuration space. We use a method based on information theory to determine the charges for an additive model that has optimal overlap with the polarizable one, and we demonstrate the feasibility of enhancing sampling via a hybrid replica exchange scheme for several model systems. An additional advantage is that, in the process, we obtain a systematic method for deriving charges for an additive model that will be the natural complement to its polarizable parent. The additive charges are found by an effective coarse-graining of the polarizable force field, rather than by ad hoc procedures.

Effects of the aromatic substitution pattern in cation-π sandwich complexes

A computational study investigating the effects of the aromatic substitution pattern on the structure and binding energies of cation-π sandwich complexes is reported. The correlation between the binding energies (Ebind) and Hammett substituent constants is approximately the same as what is observed for cation-π half-sandwich complexes. For cation-π sandwich complexes where both aromatics contain substituents the issue of relative conformation is a possible factor in the strength of the binding; however, the work presented here shows the Ebind values are approximately the same regardless of the relative conformation of the two substituted aromatics. Finally, recent computational work has shown conflicting results on whether cation-π sandwich Ebind values (Ebind,S) are approximately equal to twice the respective half-sandwich Ebind values (Ebind,HS), or if cation-π sandwich Ebind,S values are less than double the respective half-sandwich Ebind,HS values. The work presented here shows that for cation-π sandwich complexes involving substituted aromatics the Ebind,S values are less than twice the respective half-sandwich Ebind,HS values, and this is termed nonadditive. The extent to which the cation-π sandwich complexes investigated here are nonadditive is greater for B3LYP calculated values than for MP2 calculated values and for sandwich complexes with electron-donating substituents than those with electron-withdrawing groups.