CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations

Cryptolepine-transferrin nanosystem preparation and the anticancer effects on human malignant glioblastoma U87MG cells

In this study, the synthesis and characterization of the human transferrin (hTf)-cryptolepine complex nanostructure were performed. The interaction of hTf in the forms of native and nanostructures with cryptolepine was evaluated through various spectroscopic methods, molecular docking, and molecular dynamic (MD) simulation studies. Finally, the anticancer mechanisms of the prepared complex nanostructure on the Human malignant glioblastoma U87MG cell line and normal astrocytes were assessed using cell viability, RT-PCR, and ELISA assays. The data showed that hTf and hTf-cryptolepine complex nanostructures exhibited particle sizes of 149.37 ± 28.98 and 161.85 ± 33.44 nm, and average zeta potential values of -11.85 ± 1.98 and -23.87 ± 2.202 mV, respectively. It was also found that the drug release behavior from the hTf-cryptolepine complex nanostructures displayed a pH-sensitive pattern, demonstrating a strong correlation with the Higuchi model and a moderate correlation with the Korsmeyer-Peppas model. Spectroscopy and MD simulation studies revealed that the interaction of hTf and cryptolepine did not induce significant changes in the structure of the protein. Moreover, binding parameters were determined to be greater for hTf-cryptolepine complex nanostructures compared to the hTf-cryptolepine complex. Cellular assays showed that the calculated IC50 concentrations of cryptolepine, hTf-cryptolepine complex, and hTf-cryptolepine complex nanostructures in Human malignant glioblastoma U87MG cells were 16.1, 14.31, and 4.60 μM, respectively. Furthermore, it was demonstrated that Human malignant glioblastoma U87MG cells treated with hTf-cryptolepine complex nanostructures had a more significant increase in caspase-3 expression and activity compared to free cryptolepine or the hTf-cryptolepine complex. In conclusion, this paper may hold great promise for the introduction of bionanotherapeutics, which require further evaluation in future studies.

Polarizable Water Model with Ab Initio Neural Network Dynamic Charges and Spontaneous Charge Transfer

Simulating water accurately has been a challenge due to the complexity of describing polarization and intermolecular charge transfer. Quantum mechanical (QM) electronic structures provide an accurate description of polarization in response to local environments, which is nevertheless too expensive for large water systems. In this study, we have developed a polarizable water model integrating Charge Model 5 atomic charges at the level of the second-order Mo̷ller-Plesset perturbation theory, predicted by an accurate and transferable charge neural network (ChargeNN) model. The spontaneous intermolecular charge transfer has been explicitly accounted for, enabling a precise treatment of hydrogen bonds and out-of-plane polarization. Our ChargeNN water model successfully reproduces various properties of water in gas, liquid, and solid phases. For example, ChargeNN correctly captures the hydrogen-bond stretching peak and bending-libration combination band, which are absent in the spectra using fixed charges, highlighting the significance of accurate polarization and charge transfer. Finally, the molecular dynamical simulations using ChargeNN for liquid water and a large water droplet with a ∼4.5 nm radius reveal that the strong interfacial electric fields are concurrently induced by the partial collapse of the hydrogen-bond network and surface-to-interior charge transfer. Our study paves the way for QM-polarizable force fields, aiming for large-scale molecular simulations with high accuracy.

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

Minimal Basis Iterative Stockholder Decomposition with Multipole Constraints

The minimal basis iterative Stockholder (MBIS) decomposition of molecular electron densities into atomic quantities is an attractive approach for deriving electrostatic parameters in force fields. The MBIS-derived atomic charges, however, in general tend to overestimate the molecular dipole and quadrupole moments by ∼10%. We show that it is possible to derive a constrained MBIS model where the atomic charges or a combination of atomic charges and dipoles exactly reproduce the molecular dipole and quadrupole moments for molecules. The atomic multipole moments derived by the constrained procedure are better at reproducing the molecular electrostatic potential (ESP) than the unconstrained atomic multipole moments. They are, furthermore, significantly less conformationally dependent than atomic charges obtained by fitting to the molecular electrostatic potential.

Refinement of Atomic Polarizabilities for a Polarizable Gaussian Multipole Force Field with Simultaneous Considerations of Both Molecular Polarizability Tensors and In-Solution Electrostatic Potentials

Atomic polarizabilities are considered to be fundamental parameters in polarizable molecular mechanical force fields that play pivotal roles in determining model transferability across different electrostatic environments. In an earlier work, the atomic polarizabilities were obtained by fitting them to the B3LYP/aug-cc-pvtz molecular polarizability tensors of mainly small molecules. Taking advantage of the recent PCMRESPPOL method, we refine the atomic polarizabilities for condensed-phase simulations using a polarizable Gaussian Multipole (pGM) force field. Departing from earlier works, in this work, we incorporated polarizability tensors of a large number of dimers and electrostatic potentials (ESPs) in multiple solvents. We calculated 1565 × 4 ESPs of small molecule monomers and dimers of noble gas and small molecules and 4742 × 4 ESPs of small molecule dimers in four solvents (diethyl ether, ε = 4.24, dichloroethane, ε = 10.13, acetone, ε = 20.49, and water, ε = 78.36). For the gas-phase polarizability tensors, we supplemented the molecule set that was used in our earlier work by adding both the 4252 monomer and dimer sets studied by Shaw and co-workers and the 7211 small molecule monomers listed in the QM7b database to a combined total of 13,523 molecular polarizability tensors of monomers and dimers. The QM7b polarizability set was obtained from quantum-machine.org and was calculated at the LR-CCSD/d-aug-cc-pVDZ level of theory. All other polarizability tensors and all ESPs were calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The atomic polarizabilities were developed using all polarizability tensors and the 1565 × 4 ESPs of small molecule monomers and were then assessed by comparing them to the 4742 × 4 ab initio ESPs of small molecule dimers. The predicted dimer ESPs had an average relative root-mean-square error (RRMSE) of 9.30%, which was only slightly larger than the average fitting RRMSE of 9.15% of the monomer ESPs. The transferability of the polarizability set was further evaluated by comparing the ESPs calculated using parameters developed in another dielectric environment for both tetrapeptide and DES monomer data sets. It was observed that the polarizabilities of this work retained or slightly improved the transferability over the one discussed in earlier work even though the number of parameters in the present set is about half of that in the earlier set. Excluding the gas-phase data, for the DES monomer set, the average transfer RRMSEs were 16.25% and 10.83% for pGM-ind and pGM-perm methods, respectively, comparable to the average fitting RRMSEs of 16.03% and 10.54%; for tetrapeptides, the average transfer RRMSEs were 5.62% and 3.95% for pGM-ind and pGM-perm methods, respectively, slightly larger than 5.41% and 3.61% of the fitting RRMSEs. Therefore, we conclude that the pGM methods with updated polarizabilities achieved remarkable transferability from monomer to dimer and from one solvent to another.

Balancing Group 1 Monoatomic Ion-Polar Compound Interactions in the Polarizable Drude Force Field: Application in Protein and Nucleic Acid Systems

An accurate force field (FF) is the foundation of reliable results from molecular dynamics (MD) simulations. In our recently published work, we developed a protocol to generate atom pair-specific Lennard-Jones (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) parameters in the context of the Drude polarizable FF based on readily accessible quantum mechanical (QM) data to fit condensed phase experimental thermodynamic benchmarks, including the osmotic pressure, diffusion coefficient, ionic conductivity, and solvation free energy, when available. In the present work, the developed protocol is applied to generate NBFIX and NBTHOLE parameters for interactions between monatomic ions (specifically Li+, Na+, K+, Rb+, Cs+, and Cl-) and common functional groups found in proteins and nucleic acids. The parameters generated for each ion-functional group pair were then applied to the corresponding functional groups within proteins or nucleic acids followed by MD simulations to analyze the distribution of ions around these biomolecules. The modified FF successfully addresses the issue of overbinding observed in a previous iteration of the Drude FF. Quantitatively, the model accurately reproduces the effective charge of proteins and demonstrates a level of charge neutralization for a double-helix B-DNA in good agreement with the counterion condensation theory. Additionally, simulations involving ion competition correlate well with experimental results, following the trend Li+ > Na+ ≈ K+ > Rb+. These results validate the refined model for group 1 ion-biomolecule interactions that will facilitate the application of the polarizable Drude FF in systems in which group 1 ions play an important role.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Exploring Ion Polarizabilities and Their Correlation with van der Waals Radii: A Theoretical Investigation

Polarizability (α) is a fundamental property which measures the tendency of the electron cloud of an atom, ion, or molecule to be distorted by electric field. Polarizability contributes to important physical properties such as molecular interactions or dielectric constants; thus, it is essential to have accurate polarizabilities in molecular simulations. However, it remains a challenge to develop polarizable force fields (FFs) for ions in computational chemistry. In particular, a comprehensive set of polarizabilities for ions has not been derived. Herein, we derived a systematic set of polarizabilities for atoms and ions across the periodic table based on high-level quantum mechanics calculations. These values have excellent agreement with experimental data. Furthermore, we examined the relationship between the obtained polarizabilities and the van der Waals (VDW) radii (RVDW) that we previously determined (J. Chem. Theory Comput., 2023, 19, 2064). Two relationships, RVDW ∝ α1/7 and RVDW ∝ α1/3, proposed in previous studies were examined in the present work. Our results indicated the former relationship, which was derived based on the quantum harmonic oscillator model, prevails for atoms and cations, but neither relationship provides a satisfactory fit for anions. This is consistent with the tight-binding nature of the electrons in atoms and cations, while it is more challenging to quantify the polarizabilities of anions because of their more dispersed electron clouds. Moreover, we compared different approaches to determine the dispersion coefficients, including the London equation, Slater-Kirkwood equation, symmetry-adapted perturbation theory (SAPT) calculations, and time-dependent density functional theory method, along with the approach based on VDW constants. Our results indicated that although different approaches predict deviated magnitudes for the dispersion coefficients, their predictions are highly correlated, implying that each of these approaches can be used to evaluate dispersion interactions after proper scaling. Finally, we have developed a parametrization strategy for the 12-6-4 model based on the obtained insights. We specifically compared the performance of the 12-6-4 model with SAPT and SobEDA analyses to model interactions involving Na+/Mg2+ and various ligands containing He, Ne, Ar, H2O, NH3, [H2PO4]-, and [HPO4]2-. Our results demonstrate that the 12-6-4 parameters effectively reproduce both the total interaction energy and the individual energy components (electrostatics, exchange-repulsion, dispersion, and induction), highlighting the physical robustness of the 12-6-4 model and the effectiveness of our parametrization approach. This study has significant implications for advancing the development of next-generation ion models and polarizable FFs.

Molecular permeation through large pore channels: computational approaches and insights

Computational methods such as molecular dynamics (MD) have illuminated how single-atom ions permeate membrane channels and how selectivity among them is achieved. Much less is understood about molecular permeation through eukaryotic channels that mediate the flux of small molecules (e.g. connexins, pannexins, LRRC8s, CALHMs). Here we describe computational methods that have been profitably employed to explore the movements of molecules through wide pores, revealing mechanistic insights, guiding experiments, and suggesting testable hypotheses. This review illustrates MD techniques such as voltage-driven flux, potential of mean force, and mean first-passage-time calculations, as applied to molecular permeation through wide pores. These techniques have enabled detailed and quantitative modeling of molecular interactions and movement of permeants at the atomic level. We highlight novel contributors to the transit of molecules through these wide pathways. In particular, the flexibility and anisotropic nature of permeant molecules, coupled with the dynamics of pore-lining residues, lead to bespoke permeation dynamics. As more eukaryotic large-pore channel structures and functional data become available, these insights and approaches will be important for understanding the physical principles underlying molecular permeation and as guides for experimental design.

Methods for Classical-Mechanical Molecular Simulation in Chemistry: Achievements, Limitations, Perspectives

More than a half century ago it became feasible to simulate, using classical-mechanical equations of motion, the dynamics of molecular systems on a computer. Since then classical-physical molecular simulation has become an integral part of chemical research. It is widely applied in a variety of branches of chemistry and has significantly contributed to the development of chemical knowledge. It offers understanding and interpretation of experimental results, semiquantitative predictions for measurable and nonmeasurable properties of substances, and allows the calculation of properties of molecular systems under conditions that are experimentally inaccessible. Yet, molecular simulation is built on a number of assumptions, approximations, and simplifications which limit its range of applicability and its accuracy. These concern the potential-energy function used, adequate sampling of the vast statistical-mechanical configurational space of a molecular system and the methods used to compute particular properties of chemical systems from statistical-mechanical ensembles. During the past half century various methodological ideas to improve the efficiency and accuracy of classical-physical molecular simulation have been proposed, investigated, evaluated, implemented in general simulation software or were abandoned. The latter because of fundamental flaws or, while being physically sound, computational inefficiency. Some of these methodological ideas are briefly reviewed and the most effective methods are highlighted. Limitations of classical-physical simulation are discussed and perspectives are sketched.

Evaluating Polarizable Biomembrane Simulations against Experiments

Owing to the increase of available computational capabilities and the potential for providing a more accurate description, polarizable molecular dynamics force fields are gaining popularity in modeling biomolecular systems. It is, however, crucial to evaluate how much precision is truly gained with increasing cost and complexity of the simulation. Here, we leverage the NMRlipids open collaboration and Databank to assess the performance of available polarizable lipid models─the CHARMM-Drude and the AMOEBA-based parameters─against high-fidelity experimental data and compare them to the top-performing nonpolarizable models. While some improvement in the description of ion binding to membranes is observed in the most recent CHARMM-Drude parameters, and the conformational dynamics of AMOEBA-based parameters are excellent, the best nonpolarizable models tend to outperform their polarizable counterparts for each property we explored. The identified shortcomings range from inaccuracies in describing the conformational space of lipids to excessively slow conformational dynamics. Our results provide valuable insights for the further refinement of polarizable lipid force fields and for selecting the best simulation parameters for specific applications.

Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.

Origin of Enantioselectivity in Engineered Cytochrome c-Catalyzed Carbon-Radical FePP Hydrolysis Revealed Using QM/MM (ABEEM Polarizable Force Field) and MD Simulations

The origin of highly efficient asymmetric aminohydroxylation of styrene catalyzed by engineered cytochrome c is investigated by the developed Atom-Bond Electronegativity Equalization Method polarizable force field (ABEEM PFF), which is a combined outcome of electronic and steric effects. Model molecules were used to establish the charge parameters of the ABEEM PFF, for which the bond-stretching and angle-bending parameters were obtained by using a combination of modified Seminario and scan methods. The interactions between carbon-radical Fe-porphyrin (FePP) and waters are simulated by molecular dynamics, which shows a clear preference for the pre-R over the pre-S. This preference is attributed to the hydrogen-bond between the mutated 100S and 101P residues as well as van der Waals interactions, enforcing a specific conformation of the carbon-radical FePP complex within the binding pocket. Meanwhile, the hydrogen-bond between water and the nitrogen atom in the active intermediate dictates the stereochemical outcome. Quantum mechanics/molecular mechanics (QM/MM (ABEEM PFF)) and free-energy perturbation calculations elucidate that the 3RTS is characterized by sandwich-like structure among adjacent amino acid residues, which exhibits greater stability than crowed arrangement in 3STS and enables the R enantiomer to form more favorably. Thus, this study provides mechanistic insight into the catalytic reaction of hemoproteins.

Assessment of Amino Acid Electrostatic Parametrizations of the Polarizable Gaussian Multipole Model

Accurate parametrization of amino acids is pivotal for the development of reliable force fields for molecular modeling of biomolecules such as proteins. This study aims to assess amino acid electrostatic parametrizations with the polarizable Gaussian Multipole (pGM) model by evaluating the performance of the pGM-perm (with atomic permanent dipoles) and pGM-ind (without atomic permanent dipoles) variants compared to the traditional RESP model. The 100-conf-combterm fitting strategy on tetrapeptides was adopted, in which (1) all peptide bond atoms (-CO-NH-) share identical set of parameters and (2) the total charges of the two terminal N-acetyl (ACE) and N-methylamide (NME) groups were set to neutral. The accuracy and transferability of electrostatic parameters across peptides with varying lengths and real-world examples were examined. The results demonstrate the enhanced performance of the pGM-perm model in accurately representing the electrostatic properties of amino acids. This insight underscores the potential of the pGM-perm model and the 100-conf-combterm strategy for the future development of the pGM force field.

A Fast, Convenient, Polarizable Electrostatic Model for Molecular Dynamics

We present an efficient polarizable electrostatic model, utilizing typed, atom-centered polarizabilities and the fast direct approximation, designed for efficient use in molecular dynamics (MD) simulations. The model provides two convenient approaches for assigning partial charges in the context of atomic polarizabilities. One is a generalization of RESP, called RESP-dPol, and the other, AM1-BCC-dPol, is an adaptation of the widely used AM1-BCC method. Both are designed to accurately replicate gas-phase quantum mechanical electrostatic potentials. Benchmarks of this polarizable electrostatic model against gas-phase dipole moments, molecular polarizabilities, bulk liquid densities, and static dielectric constants of organic liquids show good agreement with the reference values. Of note, the model yields markedly more accurate dielectric constants of organic liquids, relative to a matched nonpolarizable force field. MD simulations with this method, which is currently parametrized for molecules containing elements C, N, O, and H, run only about 3.6-fold slower than fixed charge force fields, while simulations with the self-consistent mutual polarization average 4.5-fold slower. Our results suggest that RESP-dPol and AM1-BCC-dPol afford improved accuracy relative to fixed charge force fields and are good starting points for developing general, affordable, and transferable polarizable force fields. The software implementing these approaches has been designed to utilize the force field fitting frameworks developed and maintained by the Open Force Field Initiative, setting the stage for further exploration of this approach to polarizable force field development.

Development of a Fluctuating Charge Model for Zinc-Containing Metalloproteins

Metalloproteins widely exist in biology and play important roles in various processes. To accurately simulate metalloprotein systems, modeling polarization and charge transfer effects is vital. The fluctuating charge (FQ) model can efficiently generate atomic charges and simulate the charge transfer effect; it has been developed for a wide range of applications, but few models have been specifically tailored for metalloproteins. In this study, we present a fluctuating charge model specifically for zinc-containing metalloproteins based on the extended charge equilibration (EQeq) scheme. Our model was parametrized to reproduce CM5 charges instead of RESP/CHELPG charges because the former is less dependent on the conformation or basis set, does not suffer from unphysical charges for buried atoms, and is still being able to well reproduce the molecular dipoles. During our study, we found that adding the Pauling-bond-order-like term (referred to as the "+C term" in a previous study) between the zinc ion and ligating atoms significantly improves the model's performance. Although our model was trained for four-coordinated zinc sites only, our results indicated it can well describe the atomic charges in diverse zinc sites. Morever, our model was used to generate partial charges for the metal sites in three different zinc-containing metalloproteins (with four-, five-, and six-coordinated metal sites, respectively). These charges exhibited performance comparable to that of the RESP charges in molecular dynamics (MD) simulations. Additional tests indicated our model could also well reproduce the CM5 charges when geometric changes were involved. Those results indicate that our model can efficiently calculate the atomic charges for metal sites and well simulate the charge transfer effect, which marks an important step toward developing versatile polarizable force fields for metalloproteins.

Computational approaches to delivery of anticancer drugs with multidimensional nanomaterials

Functionalized nanotubes (NTs), nanosheets, nanorods, and porous organometallic scaffolds are potential in vivo carriers for cancer therapeutics. Precise delivery through these agents depends on factors like hydrophobicity, payload capacity, bulk/surface adsorption, orientation of molecules inside the host matrix, bonding, and nonbonding interactions. Herein, we summarize advances in simulation techniques, which are extremely valuable in initial geometry optimization and evaluation of the loading and unloading behavior of encapsulated drug molecules. Computational methods broadly involve the use of quantum and classical mechanics for studying the behavior of molecular properties. Combining theoretical processes with experimental techniques, such as X-ray crystallography, NMR spectroscopy, and bioassays, can provide a more comprehensive understanding of the structure and function of biological molecules. This integrated approach has led to numerous breakthroughs in drug discovery, enzyme design, and the study of complex biological processes. This short review provides an overview of results and challenges described from erstwhile investigations on the molecular interaction of anticancer drugs with nanocarriers of different aspect ratios.

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.

Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. We show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr-Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

Evidence That Less Can Be More for Transferable Force Fields

Graph-based parameter assignment has been the basis for developing transferable force fields for molecular dynamics simulations for decades. Nevertheless, transferable force fields vary in how specifically terms are defined with respect to the molecular graph and the procedures for generating parametrization data. More-specific force-field terms increase the complexity of the force field, theoretically increasing accuracy but also increasing training data requirements. In contrast, less-specific force fields can be reused across larger regions of chemical space, theoretically reducing accuracy but also reducing the number of parameters and training data requirements. Here, the tradeoffs between force-field specificity and accuracy are quantified by parametrizing three new sets of force fields with varying levels of graph specificity, using a shared procedure for generating training data. These force fields are benchmarked for their ability to reproduce the structural features and liquid properties of 87 organic molecules at 146 distinct state points. The overall accuracy for properties that were directly trained on rapidly saturates as the graph specificity of the force-field increases. From this, we conclude there is at best a marginal benefit of using less transferable and more complex force fields with common sources of quantum-chemically derived training data. When looking at properties unseen during training, there is some evidence that the more-complex force fields even perform slightly worse. These results are rationalized by the fortuitous regularization of force fields based on less-specific and more-transferable atom types. Both the saturation in the accuracy of training properties and the marginally worse performance on off-target properties fundamentally contradict the expectation that bespoke force fields are generally more accurate, given their larger number of parameters, and suggests that increasing force-field complexity should be carefully justified against performance gains and balanced against available training data.

Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model

Accuracy and transferability are the two highly desirable properties of molecular mechanical force fields. Compared with the extensively used point-charge additive force fields that apply fixed atom-centered point partial charges to model electrostatic interactions, polarizable force fields are thought to have the advantage of modeling the atomic polarization effects. Previous works have demonstrated the accuracy of the recently developed polarizable Gaussian multipole (pGM) models. In this work, we assessed the transferability of the electrostatic parameters of the pGM models with (pGM-perm) and without (pGM-ind) atomic permanent dipoles in terms of reproducing the electrostatic potentials surrounding molecules/oligomers absent from electrostatic parameterizations. Encouragingly, both the pGM-perm and pGM-ind models show significantly improved transferability than the additive model in the tests (1) from water monomer to water oligomer clusters; (2) across different conformations of amino acid dipeptides and tetrapeptides; (3) from amino acid tetrapeptides to longer polypeptides; and (4) from nucleobase monomers to Watson-Crick base pair dimers and tetramers. Furthermore, we demonstrated that the double-conformation fittings using amino acid tetrapeptides in the αR and β conformations can result in good transferability not only across different tetrapeptide conformations but also from tetrapeptides to polypeptides with lengths ranging from 1 to 20 repetitive residues for both the pGM-ind and pGM-perm models. In addition, the observation that the pGM-ind model has significantly better accuracy and transferability than the point-charge additive model, even though they have an identical number of parameters, strongly suggest the importance of intramolecular polarization effects. In summary, this and previous works together show that the pGM models possess both accuracy and transferability, which are expected to serve as foundations for the development of next-generation polarizable force fields for modeling various polarization-sensitive biological systems and processes.

Development of a QM/MM(ABEEM) method combined with a polarizable force field to investigate the excision reaction mechanism of damaged thymine

This paper focuses on the development of a quantum mechanics/molecular mechanics method using the ABEEM polarizable force field (QM/MM(ABEEM) method) to investigate the excision reaction mechanism of damaged thymine. This method does not simply combine the QM method with the polarizable force field. A valence electronegativity piecewise function with the distance between atoms as a variable is introduced to describe the atomic partial charges, and changes greatly during the reaction process. At the same time, the charge transfer effect is treated using the condition of local charge conservation. Compared with the traditional QM/MM method, the QM/MM(ABEEM) method can more accurately simulate the polarization effect and charge transfer effect in the reaction process. Focusing on the controversial problems of the excision of damaged bases, six reaction pathways were designed for monofunctional and difunctional deglycosylation of neutral bases and protonated bases. The results show that the QM/MM(ABEEM) method accurately simulates the polarization effect, charge transfer effect, activation energy and other properties of the reaction process. The process in which the active residue Asp activates the nucleophile H₂O to attack the protonated base is the preferred path. The average activation energy and free activation energy of the protonated base are 7.00-14.00 kcal mol^-1 lower than that of the neutral base. The study in this paper is helpful to understand the mechanism of repair enzymes in repairing bases.

Quantum chemical studies on hydrogen bonds in helical secondary structures

We present a brief review of our recent computational studies of hydrogen bonds (H-bonds) in helical secondary structures of proteins, α-helix and 3₁₀-helix, using a Negative Fragmentation Approach with density functional theory. We found that the depolarized electronic structures of the carbonyl oxygen of the ith residue and the amide hydrogen of the (i + 4)th residue cause weaker H-bond in an α-helix than in an isolated H-bond. Our calculations showed that the H-bond energies in the 3₁₀-helix were also weaker than those of the isolated H-bonds. In the 3₁₀-helices, the adjacent N-H group at the (i + 1)th residue was closer to the C=O group of the H-bond pair than the adjacent C=O group in the 3₁₀-helices, whereas the adjacent C=O group at the (i + 1)th residue was close to the H-bond acceptor in α-helices. Therefore, the destabilization of the H-bond is attributed to the depolarization caused by the adjacent residue of the helical backbone connecting the H-bond donor and acceptor. The differences in the change in electron density revealed that such depolarizations were caused by the local electronic interactions in their neighborhood inside the helical structure and redistributed the electron density. We also present the improvements in the force field of classical molecular simulation, based on our findings.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12551-022-01034-5.

Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field

We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.

A new framework for frequency-dependent polarizable force fields

A frequency-dependent extension of the polarizable force field "Atom-Condensed Kohn-Sham density functional theory approximated to the second-order" (ACKS2) [Verstraelen et al., J. Chem. Phys. 141, 194114 (2014)] is proposed, referred to as ACKS2ω. The method enables theoretical predictions of dynamical response properties of finite systems after partitioning of the frequency-dependent molecular response function. Parameters in this model are computed simply as expectation values of an electronic wavefunction, and the hardness matrix is entirely reused from ACKS2 as an adiabatic approximation is used. A numerical validation shows that accurate models can already be obtained with atomic monopoles and dipoles. Absorption spectra of 42 organic and inorganic molecular monomers are evaluated using ACKS2ω, and our results agree well with the time-dependent DFT calculations. Also for the calculation of C₆ dispersion coefficients, ACKS2ω closely reproduces its TDDFT reference. When parameters for ACKS2ω are derived from a PBE/aug-cc-pVDZ ground state, it reproduces experimental values for 903 organic and inorganic intermolecular pairs with an MAPE of 3.84%. Our results confirm that ACKS2ω offers a solid connection between the quantum-mechanical description of frequency-dependent response and computationally efficient force-field models.

Development of QM/MM (ABEEM polarizable force field) method to simulate the excision reaction mechanism of damaged cytosine

DNA damages are regarded as having harmful effects on cell. The base excision repair mechanism combats these effects by removing damaged bases. The deglycosylation mechanism of excising damaged bases by DNA glycosylase and the state of the leaving base have been controversial. The enzymatic reaction of DNA glycosylase to remove the damaged bases involves not only the formation and breaking of chemical bonds, but also complex polarization effect and charge transfer, which cannot be accurately simulated by the QM/MM method combined with the fixed charge force field. This work has developed the ABEEM fluctuating polarizable force field combining with the QM method, that is (QM/MM[ABEEM]), to accurately simulate the proton transfer, charge transfer and the charge distribution. The piecewise function is used as the valence-state electronegativity in the QM/MM (ABEEM) to realize the accurate fitting of the charge distribution in reaction. And the charge transfer is accurately simulated by the local charge conservation conditions. Four deglycosylation mechanisms including the monofunctional and difunctional mechanisms of four neutral and protonated cytosine derivatives are explored. It is confirmed that the monofunctional mechanism of Asp-activated nucleophile water is a better deglycosylation mechanism and the base is protonated before the reaction occurs. Protonization of the base reduced the activation energy by 10.00-17.00 kcal/mol. Asp provides the necessary charge for the reaction, and DNA glycosylase preferentially cleaves ɛC. This work provides a theoretical basis for the research of excising damaged bases by DNA glycosylase.

Accurate Reproduction of Quantum Mechanical Many-Body Interactions in Peptide Main-Chain Hydrogen-Bonding Oligomers by the Polarizable Gaussian Multipole Model

A key advantage of polarizable force fields is their ability to model the atomic polarization effects that play key roles in the atomic many-body interactions. In this work, we assessed the accuracy of the recently developed polarizable Gaussian Multipole (pGM) models in reproducing quantum mechanical (QM) interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions for peptide main-chain hydrogen-bonding conformers, using glycine dipeptide oligomers as the model systems. Two types of pGM models were considered, including that with (pGM-perm) and without (pGM-ind) permanent atomic dipoles. The performances of the pGM models were compared with several widely used force fields, including two polarizable (Amoeba13 and ff12pol) and three additive (ff19SB, ff15ipq, and ff03) force fields. Encouragingly, the pGM models outperform all other force fields in terms of reproducing QM interaction energies, many-body interaction energies, as well as the nonadditive and additive contributions to the many-body interactions, as measured by the root-mean-square errors (RMSEs) and mean absolute errors (MAEs). Furthermore, we tested the robustness of the pGM models against polarizability parameterization errors by employing alternative polarizabilities that are either scaled or obtained from other force fields. The results show that the pGM models with alternative polarizabilities exhibit improved accuracy in reproducing QM many-body interaction energies as well as the nonadditive and additive contributions compared with other polarizable force fields, suggesting that the pGM models are robust against the errors in polarizability parameterizations. This work shows that the pGM models are capable of accurately modeling polarization effects and have the potential to serve as templates for developing next-generation polarizable force fields for modeling various biological systems.

Extension of the CHARMM Classical Drude Polarizable Force Field to N- and O-Linked Glycopeptides and Glycoproteins

Molecular dynamic simulations are an effective tool to study complex molecular systems and are contingent upon the availability of an accurate and reliable molecular mechanics force field. The Drude polarizable force field, which allows for the explicit treatment of electronic polarization in a computationally efficient fashion, has been shown to reproduce experimental properties that were difficult or impossible to reproduce with the CHARMM additive force field, including peptide folding cooperativity, RNA hairpin structures, and DNA base flipping. Glycoproteins are essential components of glycoconjugate vaccines, antibodies, and many pharmaceutically important molecules, and an accurate polarizable force field that includes compatibility between the protein and carbohydrate aspect of the force field is essential to study these types of systems. In this work, we present an extension of the Drude polarizable force field to glycoproteins, including both N- and O-linked species. Parameter optimization focused on the dihedral terms using a reweighting protocol targeting NMR solution J-coupling data for model glycopeptides. Validation of the model include eight model glycopeptides and four glycoproteins with multiple N- and O-linked glycosylations. The new glycoprotein carbohydrate force field can be used in conjunction with the remainder of Drude polarizable force field through a variety of MD simulation programs including GROMACS, OPENMM, NAMD, and CHARMM and may be accessed through the Drude Prepper module in the CHARMM-GUI.

Is an Inductive Effect Explicit Account Required for Atomic Charges Aimed at Use within the Force Fields?

Polarization and inductive effects are the concepts that have been widely used in qualitative and even quantitative descriptions of experimentally observed properties in chemistry. The polarization effect has proven to be important in cases of biomolecular modeling though still the vast majority of molecular simulations use the classical non-polarizable force fields. In the last few decades, a lot of effort has been put into promoting the polarization effect and incorporating it into modern force fields and charge calculation methods. In contrast, the inductive effect has not attracted such attention and is effectively absent in both classic and modern force fields. Thus, a question is whether this difference corresponds to the difference in the physical significance of the effects and their explicit account, or is an artifact that should be corrected in the next generation of force fields. The significance of the electronic effects is studied in this paper through the prism of performance of specific models for atomic charge calculation that take into explicit account a nested set of effects: the formal charge, the nearest neighbors, the inductive effect, and finally the model, which takes into account all effects, which are possible to account for using atomic charges. The specific choice for the methods is the following: formal charges, MMFF94 bond charge increments, Dynamic Electronegativity Relaxation (DENR), and RESP. We propose a special scheme for the separate estimation of each particular effect contribution. By pairwise comparing the residual molecular electrostatic potential (MEP) errors of those charge models (aimed at best reproducing the quantum chemical reference MEP), we sequentially revealed how the account of each effect contributes to the better-quality MEP reproduction. The following relative importance of effects was estimated; thus, the natural hierarchy of the effects was established. First, the account of formal charges is of primordial importance. Second, the nearest neighbors account is the next in significance. Third, the explicit account of inductive effect in empirical charge calculation schemes was shown to significantly─both qualitatively and quantitatively─improve the quality of MEP reproduction. Fourth, the contribution of polarization is indirectly assessed. Surprisingly, it is of the order of magnitude of the inductive effect even for the molecular systems, for which it is anticipated to be more significant. Finally, the relative importance of anisotropic effects in neutral molecules was additionally reviewed.

Depolarizing Effects in Hydrogen Bond Energy in 310-Helices Revealed by Quantum Chemical Analysis

Hydrogen-bond (H-bond) energies in 3₁₀-helices of short alanine peptides were systematically examined by precise DFT calculations with the negative fragmentation approach (NFA), a modified method based on the molecular tailoring approach. The contribution of each H-bond was evaluated in detail from the 3₁₀-helical conformation of total energies (whole helical model, WH_3-10 model), and the results were compared with the property of H-bond in α-helix from our previous study. The H-bond energies of the WH_3-10 model exhibited tendencies different from those exhibited by the α-helix in that they depended on the helical position of the relevant H-bond pair. H-bond pairs adjacent to the terminal H-bond pairs were observed to be strongly destabilized. The analysis of electronic structures indicated that structural characteristics cause the destabilization of the H-bond in 3₁₀-helices. We also found that the longer the helix length, the more stable the H-bond in the terminal pairs of the WH_3-10 model, suggesting the action of H-bond cooperativity.

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Molecular Docking and Molecular Dynamics Simulation of Fisetin, Galangin, Hesperetin, Hesperidin, Myricetin, and Naringenin against Polymerase of Dengue Virus

Dengue fever is a disease spread by the DENV virus through mosquitoes. This disease is dangerous because there is no specific drug, vaccine, or antiviral against the DENV virus, insisting on drug discovery for dengue fever. RNA-dependent RNA polymerase (RdRp) enzyme in DENV can be a drug target because it has an important role in the virus replication process. In this research, in silico simulations were carried out on bioflavonoid compounds, namely, Fisetin, Galangin, Hesperetin, Hesperidin, Myricetin, and Naringenin with Quercetin as control ligand. QSAR analysis showed that all ligand has the probability to be antiviral and RNA synthesis inhibitor. Docking scores showed that Myricetin, Hesperidin, and Fisetin show strong performance while Hesperidin, Hesperetin, and Naringenin showed strong performance in MM/GBSA. Only Hesperidin showed strong performance in both scorings. Further investigation by ADMET analysis was done to investigate toxicology and pharmacological properties. Our molecular dynamics study through RMSD showed that even though Quercetin does not give good scoring values in both docking score and MM/GBSA, it has robust stable interaction to RdRp. The strong performance of Hesperidin was also validated by protein-ligand contact fraction in 5 ns. Overall, we observed that Hesperidin shows good potential as a DENV-3-RdRp inhibitor in par with Quercetin, although further in vitro study should be conducted.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

Bayesian-Inference-Driven Model Parametrization and Model Selection for 2CLJQ Fluid Models

A high level of physical detail in a molecular model improves its ability to perform high accuracy simulations but can also significantly affect its complexity and computational cost. In some situations, it is worthwhile to add complexity to a model to capture properties of interest; in others, additional complexity is unnecessary and can make simulations computationally infeasible. In this work, we demonstrate the use of Bayesian inference for molecular model selection, using Monte Carlo sampling techniques accelerated with surrogate modeling to evaluate the Bayes factor evidence for different levels of complexity in the two-centered Lennard-Jones + quadrupole (2CLJQ) fluid model. Examining three nested levels of model complexity, we demonstrate that the use of variable quadrupole and bond length parameters in this model framework is justified only for some chemistries. Through this process, we also get detailed information about the distributions and correlation of parameter values, enabling improved parametrization and parameter analysis. We also show how the choice of parameter priors, which encode previous model knowledge, can have substantial effects on the selection of models, penalizing careless introduction of additional complexity. We detail the computational techniques used in this analysis, providing a roadmap for future applications of molecular model selection via Bayesian inference and surrogate modeling.

Modeling Electronic Response Properties with an Explicit-Electron Machine Learning Potential

Explicit-electron force fields introduce electrons or electron pairs as semiclassical particles in force fields or empirical potentials, which are suitable for molecular dynamics simulations. Even though semiclassical electrons are a drastic simplification compared to a quantum-mechanical electronic wave function, they still retain a relatively detailed electronic model compared to conventional polarizable and reactive force fields. The ability of explicit-electron models to describe chemical reactions and electronic response properties has already been demonstrated, yet the description of short-range interactions for a broad range of chemical systems remains challenging. In this work, we present the electron machine learning potential (eMLP), a new explicit electron force field in which the short-range interactions are modeled with machine learning. The electron pair particles will be located at well-defined positions, derived from localized molecular orbitals or Wannier centers, naturally imposing the correct dielectric and piezoelectric behavior of the system. The eMLP is benchmarked on two newly constructed data sets: eQM7, an extension of the QM7 data set for small molecules, and a data set for the crystalline β-glycine. It is shown that the eMLP can predict dipole moments, polarizabilities, and IR-spectra of unseen molecules with high precision. Furthermore, a variety of response properties, for example, stiffness or piezoelectric constants, can be accurately reproduced.

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Polarization Switching Method for Effective Free Energy Calculation of Membrane Translocation on the Nano-scale

Free-energy calculations are crucial for investigating biomolecular interactions on the Nano-scale level. However, in theoretical studies, the neglect of electronic polarization can jeopardize their accuracy and correct predictive capabilities, specifically...

Generation of Quantum Configurational Ensembles Using Approximate Potentials

Conformational analysis is of paramount importance in drug design: it is crucial to determine pharmacological properties, understand molecular recognition processes, and characterize the conformations of ligands when unbound. Molecular Mechanics (MM) simulation methods, such as Monte Carlo (MC) and molecular dynamics (MD), are usually employed to generate ensembles of structures due to their ability to extensively sample the conformational space of molecules. The accuracy of these MM-based schemes strongly depends on the functional form of the force field (FF) and its parametrization, components that often hinder their performance. High-level methods, such as ab initio MD, provide reliable structural information but are still too computationally expensive to allow for extensive sampling. Therefore, to overcome these limitations, we present a multilevel MC method that is capable of generating quantum configurational ensembles while keeping the computational cost at a minimum. We show that FF reparametrization is an efficient route to generate FFs that reproduce QM results more closely, which, in turn, can be used as low-cost models to achieve the gold standard QM accuracy. We demonstrate that the MC acceptance rate is strongly correlated with various phase space overlap measurements and that it constitutes a robust metric to evaluate the similarity between the MM and QM levels of theory. As a more advanced application, we present a self-parametrizing version of the algorithm, which combines sampling and FF parametrization in one scheme, and apply the methodology to generate the QM/MM distribution of a ligand in aqueous solution.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Molecular dynamics free energy simulations of ATP:Mg2+ and ADP:Mg2+ using the polarizable force field AMOEBA

ATPases and GTPases are two important classes of protein that play critical roles in energy transduction, cellular signaling, gene regulation and catalysis. These proteins use cofactors such as nucleoside di and tri-phosphates (NTP, NDP) and can detect the difference between NDP and NTP which then induce different protein conformations. Mechanisms that drive proteins into the NTP or NDP conformation may depend on factors such as ligand structure and how Mg²⁺ coordinates with the ligand, amino acids in the pocket and water molecules. Here, we have used the advanced electrostatic and polarizable force field AMOEBA and molecular dynamics free energy simulations (MDFE) to examine the various binding mechanisms of ATP:Mg²⁺ and ADP:Mg²⁺.We compared the ATP:Mg²⁺ binding with previous studies using non-polarizable force fields and experimental data on the binding affinity. It was found that the total free energy of binding for ATP:Mg²⁺ (-7.00 ± 2.13 kcal/mol) is in good agreement with experimental values (-8.6 ± .2 kcal/mol)¹. In addition, parameters for relevant protonation states of ATP, ADP, GTP and GDP have been derived. These parameters will allow for researchers to investigate biochemical phenomena involving NTP's and NDP's with greater accuracy than previous studies involving non-polarizable force fields.

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.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

Multipolar electrostatics for hairpin and pseudoknots in RNA: Improving the accuracy of force field potential energy function

Molecular dynamics (MD) simulations that rely on force field methods has been widely used to explore the structure and function of RNAs. However, the current commonly used force fields are limited by the electrostatic description offered by atomic charge, dipole and at most quadrupole moments, failing to capture the anisotropic picture of electronic features. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. A multipolar electrostatic model based on high rank multipole moments is described in this work, which allows us to combine polarizability and anisotropy of electron density. RNA secondary structure was taken as a research system, and its substructures including stem, loops (hairpin loop, bulge loop, internal loop, and multi-branch loop), and pseudoknots (H-type and K-type) were investigated, respectively, as well as the hairpin. First, the atom-atom electrostatic properties derived from one chain of a duplex RNA 2MVY in our previous work (Ref. 58) were measured by the pilot RNA systems of hairpin, hairpin loop, stem, and H-type pseudoknot, respectively. The prediction results were not satisfactory. Consequently, to obtain a general set of electrostatic parameters for RNA force fields, the convergence behavior of the atom-atom electrostatic interactions in the pilot RNA systems was explored using high rank atomic multipole moments. The pilot RNA systems were cut into four types of different-sized molecular fragments, and the single nucleotide fragment and nucleotide-paired fragment proved to be the most reasonable systems for base-unpairing regions and base-pairing regions to investigate the convergence behavior of all types of atom-atom electrostatic interactions, respectively. Transferability of the electrostatic properties drawn from the pilot RNA systems to the corresponding test systems was also investigated. Furthermore, the convergence behavior of atomic electrostatic interactions in other substructures including bulge loop, internal loop, multi-branch loop, and K-type pseudoknot was expected to be modeled via the hairpin.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

An electrostatic energy-based charge model for molecular dynamics simulation

The interactions of the polar chemical bonds such as C=O and N-H with an external electric field were investigated, and a linear relationship between the QM/MM interaction energies and the electric field along the chemical bond is established in the range of weak to intermediate electrical fields. The linear relationship indicates that the electrostatic interactions of a polar group with its surroundings can be described by a simple model of a dipole with constant moment under the action of an electric field. This relationship is employed to develop a general approach to generating an electrostatic energy-based charge (EEC) model for molecules containing single or multiple polar chemical bonds. Benchmark test studies of this model were carried out for (CH₃)₂-CO and N-methyl acetamide in explicit water, and the result shows that the EEC model gives more accurate electrostatic energies than those given by the widely used charge model based on fitting to the electrostatic potential (ESP) in direct comparison to the energies computed by the QM/MM method. The MD simulations of the electric field at the active site of ketosteroid isomerase based on EEC demonstrated that EEC gave a better representation of the electrostatic interaction in the hydrogen-bonding environment than the Amber14SB force field by comparison with experiment. The current study suggests that EEC should be better suited for molecular dynamics study of molecular systems with polar chemical bonds such as biomolecules than the widely used ESP or RESP (restrained ESP) charge models.

ParaMol: A Package for Automatic Parameterization of Molecular Mechanics Force Fields

The ensemble of structures generated by molecular mechanics (MM) simulations is determined by the functional form of the force field employed and its parameterization. For a given functional form, the quality of the parameterization is crucial and will determine how accurately we can compute observable properties from simulations. While accurate force field parameterizations are available for biomolecules, such as proteins or DNA, the parameterization of new molecules, such as drug candidates, is particularly challenging as these may involve functional groups and interactions for which accurate parameters may not be available. Here, in an effort to address this problem, we present ParaMol, a Python package that has a special focus on the parameterization of bonded and nonbonded terms of druglike molecules by fitting to ab initio data. We demonstrate the software by deriving bonded terms' parameters of three widely known drug molecules, viz. aspirin, caffeine, and a norfloxacin analogue, for which we show that, within the constraints of the functional form, the methodologies implemented in ParaMol are able to derive near-ideal parameters. Additionally, we illustrate the best practices to follow when employing specific parameterization routes. We also determine the sensitivity of different fitting data sets, such as relaxed dihedral scans and configurational ensembles, to the parameterization procedure, and discuss the features of the various weighting methods available to weight configurations. Owing to ParaMol's capabilities, we propose that this software can be introduced as a routine step in the protocol normally employed to parameterize druglike molecules for MM simulations.