An Estimation of Hybrid Quantum Mechanical Molecular Mechanical Polarization Energies for Small Molecules Using Polarizable Force-Field Approaches

Fluoride Ion Binding and Translocation in the CLCF Fluoride/Proton Antiporter: Molecular Insights from Combined Quantum-Mechanical/Molecular-Mechanical Modeling

CLCF fluoride/proton antiporters move fluoride ions out of bacterial cells, leading to fluoride resistance in these bacteria. However, many details about their operating mechanisms remain unclear. Here, we report a combined quantum-mechanical/molecular-mechanical (QM/MM) study of a CLCF homologue from Enterococci casseliflavus (Eca), in accord with the previously proposed windmill mechanism. Our multiscale modeling sheds light on two critical steps in the transport cycle: (i) the external gating residue E118 pushing a fluoride in the external binding site into the extracellular vestibule and (ii) an incoming fluoride reconquering the external binding site by forcing out E118. Both steps feature competitions for the external binding site between the negatively charged carboxylate of E118 and the fluoride. Remarkably, the displaced E118 by fluoride accepts a proton from the nearby R117, initiating the next transport cycle. We also demonstrate the importance of accurate quantum descriptions of fluoride solvation. Our results provide clues to the mysterious E318 residue near the central binding site, suggesting that the transport activities are unlikely to be disrupted by the glutamate interacting with a well-solvated fluoride at the central binding site. This differs significantly from the structurally similar CLC chloride/proton antiporters, where a fluoride trapped deep in the hydrophobic pore causes the transporter to be locked down. A free-energy barrier of 10-15 kcal/mol was estimated via umbrella sampling for a fluoride ion traveling through the pore to repopulate the external binding site.

Structure and Dynamics of Confined Water Inside Diphenylalanine Peptide Nanotubes

Diphenylalanine (FF) peptides exhibit a unique ability to self-assemble into nanotubes with confined water molecules playing pivotal roles in their structure and function. This study investigates the structure and dynamics of diphenylalanine peptide nanotubes (FFPNTs) using all-atom molecular dynamics (MD) and grand canonical Monte Carlo combined with MD (GCMC/MD) simulations with both the CHARMM additive and Drude polarizable force fields. The occupancy and dynamics of confined water molecules were also examined. It was found that less than 2 confined water molecules per FF help stabilize the FFPNTs on the x-y plane. Analyses of the kinetics of confined water molecules revealed distinctive transport behaviors for bound and free water, and their respective diffusion coefficients were compared. Our results validate the importance of polarizable force field models in studying peptide nanotubes and provide insights into our understanding of nanoconfined water.

Anion Pathways in the NarK Nitrate/Nitrite Exchanger

NarK nitrate/nitrite antiporter imports nitrate (a mineral form of the essential element nitrogen) into the cell and exports nitrite (a metabolite that can be toxic in high concentrations) out of the cell. However, many details about its operational mechanism remain poorly understood. In this work, we performed steered molecular dynamics simulations of anion translocations and quantum-chemistry model calculations of the binding sites to study the wild-type NarK protein and its R89K mutant. Our results shed light on the importance of the two strictly conserved binding-site arginine residues (R89 and R305) and two glycine-rich signature motifs (G164-M176 and G408-F419) in anion movement through the pore. We also observe conformational changes of the protein during anion migration. For the R89K mutant, our quantum calculations reveal a competition for a proton between the anion (especially nitrite) and lysine, which can potentially slow down or even trap the anion in the pore. Our findings provide a possible explanation for the striking experimental finding that the arginine-to-lysine mutation, despite preserving the charge, impedes or abolishes anion transport in such mutants of NarK and other similar nitrate/nitrite exchangers.

Unifying Charge-Flow Polarization Models

We show that several models where electric polarization in molecular systems is modeled by charge-flow between atoms can all be considered as different manifestations of a general underlying mathematical structure. The models can be classified according to whether they employ atomic or bond parameters and whether they employ atom/bond hardness or softness. We show that an ab initio calculated charge response kernel can be considered as the inverse screened Coulombic matrix projected onto the zero-charge subspace, and this may provide a method for deriving charge screening functions to be used in force fields. The analysis suggests that some models contain redundancies, and we argue that a parameterization of charge-flow models in terms of bond softness is preferable as it depends on local quantities and decay to zero upon bond dissociation, while bond hardness depends on global quantities and increases toward infinity upon bond dissociation.

Binding Energy and Free Energy of Calcium Ion to Calmodulin EF-Hands with the Drude Polarizable Force Field

Calcium ions are important messenger molecules in cells, which bind calcium-binding proteins to trigger many biochemical processes. We constructed four model systems, each containing one EF-hand loop of calmodulin with one calcium ion bound, and investigated the binding energy and free energy of Ca²⁺ by the quantum mechanics symmetry-adapted perturbation theory (SAPT) method and the molecular mechanics with the additive CHARMM36m (C36m) and the polarizable Drude force fields (FFs). Our results show that the explicit introduction of polarizability in the Drude not only yields considerably improved agreement with the binding energy calculated from the SAPT method but is also able to capture each component of the binding energies including electrostatic, induction, exchange, and dispersion terms. However, binding free energies computed with the Drude and the C36m FFs both deviated significantly from the experimental measurements. Detailed analysis indicated that one of main reasons might be that the strong interactions between Ca²⁺ and the side chain nitrogen of Asn/Gln in the Drude FF caused the distorted coordination geometries of calcium. Our work illustrated the importance of polarization in modeling ion-protein interactions and the difficulty in generating accurate and balanced FF models to represent the polarization effects.

Doubly Polarized QM/MM with Machine Learning Chaperone Polarizability

A major shortcoming of semiempirical (SE) molecular orbital methods is their severe underestimation of molecular polarizability compared with experimental and ab initio (AI) benchmark data. In a combined quantum mechanical and molecular mechanical (QM/MM) treatment of solution-phase reactions, solute described by SE methods therefore tends to generate inadequate electronic polarization response to solvent electric fields, which often leads to large errors in free energy profiles. To address this problem, here we present a hybrid framework that improves the response property of SE/MM methods through high-level molecular-polarizability fitting. Specifically, we place on QM atoms a set of corrective polarizabilities (referred to as chaperone polarizabilities), whose magnitudes are determined from machine learning (ML) to reproduce the condensed-phase AI molecular polarizability along the minimum free energy path. These chaperone polarizabilities are then used in a machinery similar to a polarizable force field calculation to compensate for the missing polarization energy in the conventional SE/MM simulations. Because QM atoms in this treatment host SE wave functions as well as classical polarizabilities, both polarized by MM electric fields, we name this method doubly polarized QM/MM (dp-QM/MM). We demonstrate the new method on the free energy simulations of the Menshutkin reaction in water. Using AM1/MM as a base method, we show that ML chaperones greatly reduce the error in the solute molecular polarizability from 6.78 to 0.03 ų with respect to the density functional theory benchmark. The chaperone correction leads to ∼10 kcal/mol of additional polarization energy in the product region, bringing the simulated free energy profiles to closer agreement with the experimental results. Furthermore, the solute-solvent radial distribution functions show that the chaperone polarizabilities modify the free energy profiles through enhanced solvation corrections when the system evolves from the charge-neutral reactant state to the charge-separated transition and product states. These results suggest that the dp-QM/MM method, enabled by ML chaperone polarizabilities, provides a very physical remedy for the underpolarization problem in SE/MM-based free energy simulations.

Quality of force fields and sampling methods in simulating pepX peptides: a case study for intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are a group of proteins that lack well-defined structures under native conditions and carry out crucial physiological functions in various biochemical pathways. Due to the heterogeneous nature of IDPs, molecular dynamics simulations have been extensively adopted to investigate the conformational ensembles and dynamic properties of these proteins. However, their accuracy remains limited by the development of force fields and sampling algorithms. Here, we evaluated the quality of both force fields and enhanced sampling algorithms based on five short pepX peptides. Our results show that the more extended conformational ensembles sampled by the AMOEBA polarizable force field present a higher ability to reproduce experimental NMR observables than AMBER and CHARMM classical force fields. Moreover, a better agreement with experiments is achieved in the simulation of IaMD (integrated accelerated molecular dynamics) than in aMD (accelerated molecular dynamics). The results together indicate that the combination of AMOEBA force field and IaMD enhanced sampling might be a better choice for simulating IDPs. This work may provide important clues for developments and applications of force fields and enhanced sampling methods in future simulations of IDPs.

Methylguanidinium at the Air/Water Interface: A Simulation Study with the Drude Polarizable Force Field

Methylguanidinium is an important molecular ion, which also serves as the model compound for the arginine side chain. We studied the structure and dynamics of the methylguanidium ion at the air/water interface by molecular dynamics simulations employing the Drude polarizable force field. We found out that methylguanidinium accumulated at the interface, with a majority adopting tilted conformations. We also demonstrated that methylguanidinium and guanidinium ions had different preference toward the air/water interface. Detailed analysis of induced dipole moments showed how ions adjusted their charge distribution at the interface and revealed how the anisotropy in molecular polarizability impacted the orientation of molecular ions. Our results illustrate the importance of explicitly including the electronic polarization effects in modeling interfacial properties.

On the faithfulness of molecular mechanics representations of proteins towards quantum-mechanical energy surfaces

Force fields based on molecular mechanics (MM) are the main computational tool to study the relationship between protein structure and function at the molecular level. To validate the quality of such force fields, high-level quantum-mechanical (QM) data are employed to test their capability to reproduce the features of all major conformational substates of a series of blocked amino acids. The phase-space overlap between MM and QM is quantified in terms of the average structural reorganization energies over all energy minima. Here, the structural reorganization energy is the MM potential-energy difference between the structure of the respective QM energy minimum and the structure of the closest MM energy minimum. Thus, it serves as a measure for the relative probability of visiting the QM minimum during an MM simulation. We evaluate variants of the AMBER, CHARMM, GROMOS and OPLS biomolecular force fields. In addition, the two blocked amino acids alanine and serine are used to demonstrate the dependence of the measured agreement on the QM method, the phase, and the conformational preferences. Blocked serine serves as an example to discuss possible improvements of the force fields, such as including polarization with Drude particles, or using tailored force fields. The results show that none of the evaluated force fields satisfactorily reproduces all energy minima. By decomposing the average structural reorganization energies in terms of individual energy terms, we can further assess the individual weaknesses of the parametrization strategies of each force field. The dominant problem for most force fields appears to be the van der Waals parameters, followed to a lesser degree by dihedral and bonded terms. Our results show that performing a simple QM energy optimization from an MM-optimized structure can be a first test of the validity of a force field for a particular target molecule.

Predicting partition coefficients of drug-like molecules in the SAMPL6 challenge with Drude polarizable force fields

The water-octanol partition coefficient is an important physicochemical property for small molecule drug design. Here, we report our participation in the SAMPL6 logP prediction challenge with free energy perturbation (FEP) calculations in the water phase and in the 1-octanol phase using Drude polarizable force fields. Root mean square error (RMSE) and mean absolute error (MAE) of our prediction are equal to 1.85 and 1.25 logP units. The errors are not evenly distributed. Out of eleven SAMPL6 solutes, FEP/Drude performed very badly on three molecules (deviations all larger than 2 logP units) but good on the remaining eight (deviations all less than 1 logP unit). We find while FEP converges well within one nanosecond in water, simulations in 1-octanol need much longer simulation time and possibly more independent runs for sampling. We also find out that 1-octanol, albeit being a non-polar solvent, still polarizes solute molecules and forms stable hydrogen bonds with them. At the end, we attempt to reweight FEP trajectories with QM/Drude calculations and discuss possible caveats in our simulation setup.

Solvation Free Energy Calculation Using a Fixed-Charge Model: Implicit and Explicit Treatments of the Polarization Effect

In this work, IPolQ-Mod charges and the reference potential scheme are used to calculate the solvation free energies of a set of organic molecules. Both methods could capture the phase transfer of a solute with accompanying polarization cost utilizing a fixed-charge model. The IPolQ-Mod charges, which are the average of two charge sets fitted in a vacuum state and a condensed phase, take account of the polarization effect implicitly. For the reference potential method, the quantum mechanics polarization corrections are calculated explicitly by thermodynamic perturbation. The polarization effect captured by the IPolQ-Mod charges is an approximation to that of the reference potential method theoretically. In the present study, the reference potential method shows a slight improvement over the classical restrained electrostatic potential (RESP) charges, which perform pretty well in predicting the solvation free energy. However, IPolQ-Mod(MP2) shows a poor agreement with the experimental data. Compared with IPolQ-Mod(MP2), IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) is found to give more appropriate prediction of the molecule's dipole and the solvation free energies calculated by IPolQ-Mod(M06-2X) or IPolQ-Mod(ωB97X) are more compatible with those of the RESP charges. If the other force field parameters remain unchanged, M06-2X or ωB97X is recommended to derive the IPolQ-Mod charges.

Higher Accuracy Achieved in the Simulations of Protein Structure Refinement, Protein Folding, and Intrinsically Disordered Proteins Using Polarizable Force Fields

The accuracy of molecular mechanics force fields is of vital importance in biomolecular simulations. However, the admittedly more accurate polarizable force fields were recently reported to be less able to reproduce the experimental properties in comparison to additive force fields in some cases. Here, we perform long-time-scale molecular dynamics simulations to systematically evaluate the effect of explicit electronic polarization in polarizable force fields. The results show that the inclusion of electrostatic polarization effect in polarizable force fields can improve their accuracies in protein structure refinement and generate conformational ensembles more approximate to experiments for intrinsically disordered proteins. In contrast, it is difficult for polarizable force fields to approach the native structure, let alone to predict the native state when it is unknown a priori in the real protein structure predictions. We speculate that these effects might be attributed to the preference of protein-water interactions in polarizable force fields.

A Multiscale Simulation Approach to Modeling Drug-Protein Binding Kinetics

Drug-target binding kinetics has recently emerged as a sometimes critical determinant of in vivo efficacy and toxicity. Its rational optimization to improve potency or reduce side effects of drugs is, however, extremely difficult. Molecular simulations can play a crucial role in identifying features and properties of small ligands and their protein targets affecting the binding kinetics, but significant challenges include the long time scales involved in (un)binding events and the limited accuracy of empirical atomistic force fields (lacking, e.g., changes in electronic polarization). In an effort to overcome these hurdles, we propose a method that combines state-of-the-art enhanced sampling simulations and quantum mechanics/molecular mechanics (QM/MM) calculations at the BLYP/VDZ level to compute association free energy profiles and characterize the binding kinetics in terms of structure and dynamics of the transition state ensemble. We test our combined approach on the binding of the anticancer drug Imatinib to Src kinase, a well-characterized target for cancer therapy with a complex binding mechanism involving significant conformational changes. The results indicate significant changes in polarization along the binding pathways, which affect the predicted binding kinetics. This is likely to be of widespread importance in binding of ligands to protein targets.

Analysis of the conformational properties of amine ligands at the gold/water interface with QM, MM and QM/MM simulations

We describe a strategy of integrating quantum mechanical (QM), hybrid quantum mechanical/molecular mechanical (QM/MM) and MM simulations to analyze the physical properties of a solid/water interface.