Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests

Refinement of the Drude Polarizable Force Field for Hexose Monosaccharides: Capturing Ring Conformational Dynamics with Enhanced Accuracy

We present a revised version of the Drude polarizable carbohydrate force field (FF), focusing on refining the ring and exocyclic torsional parameters for hexopyranose monosaccharides. This refinement addresses the previously observed discrepancies between calculated and experimental NMR 3J coupling values, particularly in describing ring dynamics and exocyclic rotamer populations within major hexose monosaccharides and their anomers. Specifically, α-MAN, β-MAN, α-GLC, β-GLC, α-GAL, β-GAL, α-ALT, β-ALT, α-IDO, and β-IDO were targeted for optimization. The optimization process involved potential energy scans (PES) of the ring and exocyclic dihedral angles computed using quantum mechanical (QM) methods. The target data for the reoptimization included PES of the inner ring dihedrals (C1-C2-C3-C4, C2-C3-C4-C5, C5-O5-C1-C2, C4-C5-O5-C1, O5-C1-C2-C3, C3-C4-C5-O5) and the exocyclic torsions, other than the pseudo ring dihedrals (O1-C1-O5-C5, O2-C2-C1-O5, and O4-C4-C5-O5) and hydroxyl torsions used in the previous parametrization efforts. These parameters, in conjunction with previously developed Drude parameters for hexopyranose monosaccharides, were validated against experimental observations, including NMR data and conformational energetics, in aqueous environments. The resulting polarizable model is shown to be in good agreement with a range of QM data, experimental NMR data, and conformational energetics of monosaccharides in aqueous solutions. This offers a significant improvement of the Drude carbohydrate force field, wherein the refinement enhances the accuracy of accessing the conformational dynamics of carbohydrates in biomolecular simulations.

Molecular simulation of the slurrying mechanism in microplastic semi-coke water slurry

CONTEXT

This study explores the interaction between particles in microplastic semi-coke water slurry at the molecular level using molecular simulation methods, specifically DFT calculations and MD simulations. In addition, the experiment of slurry preparation was carried out to study the viscosity and stability of the slurry. The electrostatic potential analysis shows that the interaction between microplastics and dispersant molecules occurs on atoms with large electronegativity or oxygen-containing functional groups, and the energy gap of frontier molecular orbitals indicated that PVC interacts most easily with the dispersant (0.39 eV), followed by PS (1.08 eV) and PET (3.65 eV). In addition, it is also noted that due to the steric hindrance effect, the adsorption energy was opposite to the DFT calculation results: PET was - 213.338 kcal/mol (NNO) which was highest, followed by PS (- 107.603 kcal/mol, NNO), and PVC (NNO) was lowest which was - 94.808 kcal/mol. And RDF shows similar results, which the probability of water molecules in the PET system was the highest, followed by PS, and finally, PVC. The MD results are consistent with the viscosity and stability characterization results of the slurry which PET has the lowest viscosity of 87.3 mPa·s. Finally, this study provides new ideas for the treatment of microplastics and the improvement of the performance of semi-coke water slurry and reveals the interaction mechanism between microplastics and semi-coke water slurry.

METHODS

All calculations were performed using Materials Studio (MS) version 2020 software, BIOVIA Corporation. The DFT calculation was carried out through the DMol3 module. The DFT calculations include electron density, electrostatics, orbitals, and population analysis. In DMol3 module, the GGA-PBE function was selected to consider gradient changes in density in the simulated calculation. The DFT-D correction was selected, and all electrons were calculated by DNP for accurate core potentials and the DNP file was 4.4. MD simulation was performed through the Forcite module. MD simulation mainly focuses on relative concentration distribution analysis, radial distribution function, and adsorption energy calculation. All molecular geometry optimizations are performed in the Forcite module. In the molecular dynamic part, all simulations used PCFF forcefield. The NVT ensemble was adopted and using the Nosé thermostat.

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.

Free Energy Density of a Fluid and Its Role in Solvation and Binding

The concept that a fluid has a position-dependent free energy density appears in the literature but has not been fully developed or accepted. We set this concept on an unambiguous theoretical footing via the following strategy. First, we set forth four desiderata that should be satisfied by any definition of the position-dependent free energy density, f(R), in a system comprising only a fluid and a rigid solute: its volume integral, plus the fixed internal energy of the solute, should be the system free energy; it deviates from its bulk value, fbulk, near a solute but should asymptotically approach fbulk with increasing distance from the solute; it should go to zero where the solvent density goes to zero; and it should be well-defined in the most general case of a fluid made up of flexible molecules with an arbitrary interaction potential. Second, we use statistical thermodynamics to formulate a definition of the free energy density that satisfies these desiderata. Third, we show how any free energy density satisfying the desiderata may be used to analyze molecular processes in solution. In particular, because the spatial integral of f(R) equals the free energy of the system, it can be used to compute free energy changes that result from the rearrangement of solutes as well as the forces exerted on the solutes by the solvent. This enables the use of a thermodynamic analysis of water in protein binding sites to inform ligand design. Finally, we discuss related literature and address published concerns regarding the thermodynamic plausibility of a position-dependent free energy density. The theory presented here has applications in theoretical and computational chemistry and may be further generalizable beyond fluids, such as to solids and macromolecules.

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.

Searching for Structure: Characterizing the Protein Conformational Landscape with Clustering-Based Algorithms

The identification and characterization of the main conformations from a protein population are a challenging and inherently high-dimensional problem. Here, we evaluate the performance of the Secondary sTructural Ensembles with machine LeArning (StELa) double-clustering method, which clusters protein structures based on the relationship between the φ and ψ dihedral angles in a protein backbone and the secondary structure of the protein, thus focusing on the local properties of protein structures. The classification of states as vectors composed of the clusters' indices arising naturally from the Ramachandran plot is followed by the hierarchical clustering of the vectors to allow for the identification of the main features of the corresponding free energy landscape (FEL). We compare the performance of StELa with the established root-mean-squared-deviation (RMSD)-based clustering algorithm, which focuses on global properties of protein structures and with Combinatorial Averaged Transient Structure (CATS), the combinatorial averaged transient structure clustering method based on distributions of the φ and ψ dihedral angle coordinates. Using ensembles of conformations from molecular dynamics simulations of intrinsically disordered proteins (IDPs) of various lengths (tau protein fragments) or short fragments from a globular protein, we show that StELa is the clustering method that identifies many of the minima and relevant energy states around the minima from the corresponding FELs. In contrast, the RMSD-based algorithm yields a large number of clusters that usually cover most of the FEL, thus being unable to distinguish between states, while CATS does not sample well the FELs for long IDPs and fragments from globular proteins.

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.

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.

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.

PyRESP: A Program for Electrostatic Parameterizations of Additive and Induced Dipole Polarizable Force Fields

Molecular modeling at the atomic level has been applied in a wide range of biological systems. The widely adopted additive force fields typically use fixed atom-centered partial charges to model electrostatic interactions. However, the additive force fields cannot accurately model polarization effects, leading to unrealistic simulations in polarization-sensitive processes. Numerous efforts have been invested in developing induced dipole-based polarizable force fields. Whether additive atomic charge models or polarizable induced dipole models are used, proper parameterization of the electrostatic term plays a key role in the force field developments. In this work, we present a Python program called PyRESP for performing atomic multipole parameterizations by reproducing ab initio electrostatic potential (ESP) around molecules. PyRESP provides parameterization schemes for several electrostatic models, including the RESP model with atomic charges for the additive force fields and the RESP-ind and RESP-perm models with additional induced and permanent dipole moments for the polarizable force fields. PyRESP is a flexible and user-friendly program that can accommodate various needs during force field parameterizations for molecular modeling of any organic molecules.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

Atomic Polarizabilities for Interactive Dipole Induction Models

Thole-style mutual induction models for molecular polarization have been adopted by several popular polarizable force fields (FFs) for their simplicity and transferability. The atomic polarizability parameters of these models are typically derived by fitting to ab initio or/and experimental molecular polarizabilities. In this work, we improve upon Thole polarizability parameters by employing both high-level quantum mechanics molecular polarizabilities and electrostatic potential (ESP) responses on three-dimensional grids. Our results indicate that the two approaches to derive atomic polarizability parameters are both effective, while the ESP approaches can also capture the polarization for the atoms with lone pair electrons. The resulting polarizability parameters have been validated on a set of over 7200 molecules covering the most common elements found in organic molecules (C, H, O, N, P, S, F, Cl, Br, and I). These parameters have also been tested on the experimentally measured molecular polarizabilities of 422 molecules. The final set of parameters derived in this work show notable improvement over the current AMOEBA set. The result is a highly transferable, expanded set of atomic polarizabilities defined by the local chemical environment in the form of SMARTS patterns. These parameters can be used directly in molecular mechanics polarizable potential energy functions such as AMOEBA, AMOEBA+, and other Thole-style models.

When Order Meets Disorder: Modeling and Function of the Protein Interface in Fuzzy Complexes

The degree of proteins structural organization ranges from highly structured, compact folding to intrinsic disorder, where each degree of self-organization corresponds to specific functions: well-organized structural motifs in enzymes offer a proper environment for precisely positioned functional groups to participate in catalytic reactions; at the other end of the self-organization spectrum, intrinsically disordered proteins act as binding hubs via the formation of multiple, transient and often non-specific interactions. This review focusses on cases where structurally organized proteins or domains associate with highly disordered protein chains, leading to the formation of interfaces with varying degrees of fuzziness. We present a review of the computational methods developed to provide us with information on such fuzzy interfaces, and how they integrate experimental information. The discussion focusses on two specific cases, microtubules and homologous recombination nucleoprotein filaments, where a network of intrinsically disordered tails exerts regulatory function in recruiting partner macromolecules, proteins or DNA and tuning the atomic level association. Notably, we show how computational approaches such as molecular dynamics simulations can bring new knowledge to help bridging the gap between experimental analysis, that mostly concerns ensemble properties, and the behavior of individual disordered protein chains that contribute to regulation functions.

Water-Mediated Oxidation of Guanine by a Repair Enzyme: Simulation Using the ABEEM Polarizable Force Field

The recognition mechanism of oxidative damage in organisms has long been a research hotspot. Water is an important medium in the recognition process, but its specific role remains unknown. There is a need to develop a suitable force field that can adequately describe the electrostatic, hydrogen bond, and other interactions among the molecules in the complex system of the repair enzyme and oxidized base. The developing ABEEM polarizable force field (PFF) has been used to simulate the repaired enzyme hOGG1 and oxidized DNA (PDB ID: 1EBM) in a biological environment, and the corresponding results are better than those of the fixed-charge force fields OPLS/AA and AMBER OL15. 8-Oxo-G is recognized by Gln315 of hOGG1 mainly through hydrogen bonds mediated by continuous exchange of 2 water molecules. Phe319 and Cys253 are stacked on both sides of the π planes of bases to form sandwich structures. The charge polarization effect gives an important signal to drive the exchange of water molecules and maintains the recognition of oxidation bases by enzymes. The mediated main water molecule A and mediated auxiliary water molecule B together pull Gln315 to recognize 8-oxo-G by hydrogen bond interactions. Then, the charge polarization signal of solvent water molecule C with a large absolute charge causes the absolute charge of O atoms in water molecule A or B to increase by approximately 0.2 e, and water molecule A or B leaves Gln315 and 8-oxo-G. The other water molecule and water molecule C synergistically recognize 8-oxo-G with Gln315. Even though the water molecules between Gln315 and 8-oxo-G are removed, the MD simulation results show that water molecules appear between Gln315 and 8-oxo-G in a very short time (<2 ps). The dwell time of each water molecule is approximately 60 ps. The radial distribution function and dwell time support the correctness of the above mechanism. These polarization effects and hydrogen bonding interactions cannot be simulated by a fixed-charge force field.

Efficient formulation of polarizable Gaussian multipole electrostatics for biomolecular simulations

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

Estimating the Roles of Protonation and Electronic Polarization in Absolute Binding Affinity Simulations

Accurate prediction of binding free energies is critical to streamlining the drug development and protein design process. With the advent of GPU acceleration, absolute alchemical methods, which simulate the removal of ligand electrostatics and van der Waals interactions with the protein, have become routinely accessible and provide a physically rigorous approach that enables full consideration of flexibility and solvent interaction. However, standard explicit solvent simulations are unable to model protonation or electronic polarization changes upon ligand transfer from water to the protein interior, leading to inaccurate prediction of binding affinities for charged molecules. Here, we perform extensive simulation totaling ∼540 μs to benchmark the impact of modeling conditions on predictive accuracy for absolute alchemical simulations. Binding to urokinase plasminogen activator (UPA), a protein frequently overexpressed in metastatic tumors, is evaluated for a set of 10 inhibitors with extended flexibility, highly charged character, and titratable properties. We demonstrate that the alchemical simulations can be adapted to utilize the MBAR/PBSA method to improve the accuracy upon incorporating electronic polarization, highlighting the importance of polarization in alchemical simulations of binding affinities. Comparison of binding energy prediction at various protonation states indicates that proper electrostatic setup is also crucial in binding affinity prediction of charged systems, prompting us to propose an alternative binding mode with protonated ligand phenol and Hid-46 at the binding site, a testable hypothesis for future experimental validation.

Xanthone glucoside 2-β-D-glucopyranosyl-1,3,6,7-tetrahydroxy-9H-xanthen-9-one binds to the ATP-binding pocket of glycogen synthase kinase 3β and inhibits its activity: implications in prostate cancer and associated cardiovascular disease risk

Glycogen synthase kinase 3 (GSK3) is a serine/threonine kinase which in the presence of ATP in its ATP-binding pocket transfers a phosphate to a primed substrate. GSK3β is an isoform of GSK3 which has been projected as a potent therapeutic target in human diseases including cancers and metabolic syndrome. Incidentally, cardiovascular disease is a common cause of non-cancer related deaths in prostate cancer (PCa) patients, mainly due to the effects of androgen-deprivation therapy (ADT), a mainstay for PCa treatment. Several small molecular inhibitors of GSK3 are either ATP-competitive (bind to the ATP-binding pocket), or non-ATP-competitive inhibitors (binding to the substrate-binding site of the enzyme). In this study, 2-β-D-glucopyranosyl-1,3,6,7-tetrahydroxy-9H-xanthen-9-one (βDGT), a natural xanthonoid present in many plant species, is reported to bind to the ATP-binding pocket of GSK3β and inhibit its activity, as demonstrated by the molecular docking and molecular dynamics simulation analysis and experimental validation in vitro. A comparison of the binding affinities with five known ATP-competitive inhibitors of GSK3β suggested similarity in binding site residues in the ATP-binding pocket of the enzyme. The optimum inhibitory concentration of the xanthonoid as determined by the luminescent kinase assay was 200 µM. The study envisages the use of βDGT as a natural ATP-competitive inhibitor of GSK3β and implicates its use in PCa patients on ADT, a cardiovascular disease risk, and other pathological conditions where GSK3 inhibition may be clinically important. HighlightsGSK3β is a multifaceted kinase known for its role in cancers, cardiovascular, and other diseases.In this study, βDGT, a xanthonoid, is reported to bind to the ATP-binding pocket of GSK3β.A comparison of βDGT binding with 5 known ATP-competitive inhibitors of GSK3β suggested the involvement of residues at the ATP binding site.The binding site analysis suggested an ATP-competitive mechanism of enzyme inhibition.Study envisages the use of βDGT as a natural ATP-competitive inhibitor of GSK3β and implicates its use in prostate cancer patients on androgen-deprivation therapy, a cardiovascular disease risk, and other pathological conditions.Communicated by Ramaswamy H. Sarma.

Recent Force Field Strategies for Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are widely distributed across eukaryotic cells, playing important roles in molecular recognition, molecular assembly, post-translational modification, and other biological processes. IDPs are also associated with many diseases such as cancers, cardiovascular diseases, and neurodegenerative diseases. Due to their structural flexibility, conventional experimental methods cannot reliably capture their heterogeneous structures. Molecular dynamics simulation becomes an important complementary tool to quantify IDP structures. This review covers recent force field strategies proposed for more accurate molecular dynamics simulations of IDPs. The strategies include adjusting dihedral parameters, adding grid-based energy correction map (CMAP) parameters, refining protein-water interactions, and others. Different force fields were found to perform well on specific observables of specific IDPs but also are limited in reproducing all available experimental observables consistently for all tested IDPs. We conclude the review with perspective areas for improvements for future force fields for IDPs.

Molecular simulations of IDPs: From ensemble generation to IDP interactions leading to disorder-to-order transitions

Intrinsically disordered proteins (IDPs) lack a well-defined three-dimensional structure but do exhibit some dynamical and structural ordering. The structural plasticity of IDPs indicates that entropy-driven motions are crucial for their function. Many IDPs undergo function-related disorder-to-order transitions upon by their interaction with specific binding partners. Approaches that are based on both experimental and theoretical tools enable the biophysical characterization of IDPs. Molecular simulations provide insights into IDP structural ensembles and disorder-to-order transition mechanisms. However, such studies depend strongly on the chosen force field parameters and simulation techniques. In this chapter, we provide an overview of IDP characteristics, review all-atom force fields recently developed for IDPs, and present molecular dynamics-based simulation methods that allow IDP ensemble generation as well as the characterization of disorder-to-order transitions. In particular, we introduce metadynamics, replica exchange molecular dynamics simulations, and also kinetic models resulting from Markov State modeling, and provide various examples for the successful application of these simulation methods to IDPs.

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

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

Further Optimization and Validation of the Classical Drude Polarizable Protein Force Field

The CHARMM Drude-2013 polarizable force field (FF) was developed to include the explicit treatment of induced electronic polarizability, resulting in a more accurate description of the electrostatic interactions in molecular dynamics (MD) simulations. While the Drude-2013 protein FF has shown success in improving the folding properties of α-helical peptides and to reproduce experimental observables in simulations up to 1 μs, some limitations were noted regarding the stability of β-sheet structures in simulations longer than 100 ns as well as larger deviations from crystal structures in simulations of a number of proteins compared to the additive CHARMM36 protein FF. The origin of the instability has been identified and appears to be primarily due to overestimated atomic polarizabilities and induced dipole-dipole interactions on the Cβ, Cγ, and Cδ side chain atoms. To resolve this and other issues, a number of aspects of the model were revisited, resulting in Drude-2019 protein FF. Backbone parameters were optimized targeting the conformational properties of the (Ala)5 peptide in solution along with gas phase properties of the alanine dipeptide. Dipeptides that contain N-acetylated and N'-methylamidated termini, excluding Gly, Pro, and Ala, were used as models to optimize the atomic polarizabilities and Thole screening factors on selected Cβ, Cγ, and Cδ carbons by targeting quantum mechanical (QM) dipole moments and molecular polarizabilities. In addition, to obtain better conformational properties, side chain χ1 and χ2 dihedral parameters were optimized targeting QM data for the respective side chain dipeptide conformations as well as Protein Data Bank survey data based on the χ1, χ2 sampling from Hamiltonian replica-exchange MD simulations of (Ala)4-X-(Ala)4 in solution, where X is the amino acid of interest. Further improvements include optimizing nonbonded interactions between charged residues to reproduce QM interaction energies of the charged-protein model compounds and experimental osmotic pressures. Validation of the optimized Drude protein FF includes MD simulations of a collection of peptides and proteins including β-sheet structures, as well as transmembrane ion channels. Results showed that the updated Drude-2019 protein FF yields smaller overall root-mean-square differences of proteins as compared to the additive CHARMM36m and Drude-2013 FFs as well as similar or improved agreement with experimental NMR properties, allowing for long time scale simulation studies of proteins and more complex biomolecular systems in conjunction with the remainder of the Drude polarizable FF.

Pairwise-additive and polarizable atomistic force fields for molecular dynamics simulations of proteins

Protein force fields have been undergoing continual development since the first complete parameter sets were introduced nearly four decades ago. The functional forms that underlie these models have many common elements for the treatment of bonded and nonbonded forces, which are reviewed here. The most widely used force fields to date use a fixed-charge convention in which electronic polarization effects are treated via a mean-field approximation during partial charge assignment. Despite success in modeling folded proteins over many years, the fixed-charge assumption has limitations that cannot necessarily be overcome within their potential energy equations. To overcome these limitations, several force fields have recently been derived that explicitly treat electronic polarization effects with straightforward extensions of the potential energy functions used by nonpolarizable force fields. Here, we review the history of the most popular nonpolarizable force fields (AMBER, CHARMM, OPLS, and GROMOS) as well as studies that have validated them and applied them to studies of protein folding and misfolding. Building upon these force fields are more recent polarizable interaction potentials, including fluctuating charge models, POSSIM, AMOEBA, and the classical Drude oscillator. These force fields differ in their implementations but all attempt to model electronic polarization in a computationally tractable manner. Despite their recent emergence in the field of protein folding, several studies have already applied these polarizable models to challenging problems in this domain, including the role of polarization in folding free energies and sequence-specific effects on the stability of α-helical structures.

Solution structure of macromolecules using small angle neutron scattering and molecular simulations

An introductory account of using molecular simulations to deduce solution structure of macromolecules using small angle neutron scattering data is presented for biologists. The presence of a liquid solution provides mobility to the molecules, making it difficult to pin down their structure. Here a simple introduction to molecular dynamics and Monte Carlo techniques is followed by a recipe to use the output of the simulations along with the scattering data in order to infer the structure of macromolecules when they are placed in a liquid solution. Some practical issues to be watched for are also highlighted.

Ameliorating amyloid aggregation through osmolytes as a probable therapeutic molecule against Alzheimer's disease and type 2 diabetes

Large numbers of neurological and metabolic disorders occurring in humans are induced by the aberrant growth of aggregated or misfolded proteins.

A force consistent method for electrostatic energy calculation in fluctuating charge model

A practical approach to include the polarization effect in a molecular force field is the fluctuating charge method in which atomic charges vary as the configuration of the molecular system changes. However, the use of the Coulomb formula to evaluate energy in a fluctuating charge method is theoretically inconsistent with the forces given by the fluctuating method. In this work, we propose a force-consistent method to correctly calculate electrostatic energies of molecular systems using a fluctuating charge model (Effective Polarizable Bond or EPB). In this protocol, the electrostatic energy is obtained by numerical interaction of the atomic forces along the MD trajectory, rather than using the default Coulomb formula in the EPB model. Test study on the benchmark Barnase-Barstar protein-protein interaction system demonstrates that although the total electrostatic energy of the system shows little deviation due to the averaging effect, specific residue-residue electrostatic interaction energy is affected and the level of the effect depends on the charges of the interacting residues with charged residues showing pronounced differences in calculated energies between using the current protocol and the standard Coulomb formula. It is recommended that the proposed numerical interaction method should be preferred in the calculation of electrostatic energy in fluctuating charge models used in molecular dynamics simulations.

Drude Polarizable Force Field Parametrization of Carboxylate and N-Acetyl Amine Carbohydrate Derivatives

In this work, we report the development of Drude polarizable force field parameters for the carboxylate and N-acetyl amine derivatives, extending the functionality of the existing Drude polarizable carbohydrate force field. The force field parameters have been developed in a hierarchical manner, reproducing the quantum mechanical gas-phase properties of small model compounds representing the key functional group in the carbohydrate derivatives, including optimization of the electrostatic and bonded parameters. The optimized parameters were then used to generate the models for carboxylate and N-acetyl amine carbohydrate derivatives. The transferred parameters were further tested and optimized to reproduce crystal geometries and J-coupling data from nuclear magnetic resonance experiments. The parameter development resulted in the incorporation of d-glucuronate, l-iduronate, N-acetyl-d-glucosamine (GlcNAc), and N-acetyl-d-galactosamine (GalNAc) sugars into the Drude polarizable force field. The parameters developed in this study were then applied to study the conformational properties of glycosaminoglycan polymer hyaluronan, composed of d-glucuronate and N-acetyl-d-glucosamine, in aqueous solution. Upon comparing the results from the additive and polarizable simulations, it was found that the inclusion of polarization improved the description of the electrostatic interactions observed in hyaluronan, resulting in enhanced conformational flexibility. The developed Drude polarizable force field parameters in conjunction with the remainder of the Drude polarizable force field parameters can be used for future studies involving carbohydrates and their conjugates in complex, heterogeneous systems.

Modeling Charge Flux by Interpolating Atomic Partial Charges

Although the charge flux effect or the geometric dependence of the atomic partial charges have been known for a long time, how it can be effectively handled is not yet established. Here, we present a charge interpolation scheme as a new general tool for representing the charge flux in an analytically well-defined manner. By applying it to the anionic GFP chromophore with the diabatically represented atomic charges, we show that the charge interpolation provides a substantial improvement on the accuracy of the geometry-dependent changes in the molecular dipole moments in the gas phase. We also test the scheme toward describing the electrostatic term in the solvation energy in the aqueous environment and observe that it is also improved but that the extent of the improvement is somewhat limited. We show that the remaining errors can be largely corrected by introducing atomic polarizabilities. Overall, our results show that charge interpolation is an amenable approach for describing the charge flux effect and that its description in the condensed phase should be accompanied by proper treatments of polarization effects.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration, and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model based on the AMOEBA+ framework captures various liquid-phase properties in molecular dynamics simulations while remaining consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.

Combining Iteration-Free Polarization with Large Time Step Stochastic-Isokinetic Integration

In order to accelerate molecular dynamics simulations using polarizable force fields, we combine a new extended Lagrangian approach that eliminates the self-consistent field step (iEL/0-SCF) with a stochastic integration scheme that allows for a long time step using a multiple time scale algorithm (SIN(R)). We consider different algorithms for the combined scheme that places different components of the nonbonded forces into different time scales, as well as splitting individual nonbonded forces across time scales, to demonstrate that the combined method works well for bulk water as well as for a concentrated salt solution, aqueous peptide, and solvated protein. Depending on system and desired accuracy, the iEL/0-SCF and SIN(R) combination yields lower bound computational speed-ups of ∼6-8 relative to a molecular dynamics Verlet integration using a standard SCF solver implemented in the reference program TINKER 8.1. The combined approach embodies a significant advance for equilibrium simulations in the canonical ensemble of many-body potential energy surfaces for condensed phase systems with speed-ups that exceed what is possible by either method alone.

Mutually polarizable QM/MM model with in situ optimized localized basis functions

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem - with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K⁺, and Cl^-. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface.

Development of Polarizable Gaussian Model for Molecular Mechanical Calculations I: Atomic Polarizability Parameterization To Reproduce ab Initio Anisotropy

A set of atomic polarizability parameters for a new polarizable Gaussian model (pGM) has been developed with the goal to accurately reproduce the polarizability anisotropy, taking advantage of its ability to attenuate all short-range electrostatic interactions, by fitting the ab initio molecular polarizability tensors ( A _pq) calculated at the B3LYP/aug-cc-pVTZ level. For comparison, we also rederived the parameters for three Thole models in which the 1-2 (bonded), 1-3 (separated by two bonds), and 1-4 (separated by three bonds) interactions are fully included. The average percent errors (APEs) of molecular polarizability tensors for 4842 molecules or dimers are 2.98, 3.76, 3.28, and 3.82% for the pGM, Thole linear, Thole exponential, and Thole Amoeba models, respectively, with atom-type independent, universal screening factors (USF). The APEs are reduced further to 2.30, 2.69, 2.25, and 2.48% for the four corresponding polarizable models with atom-type dependent, variable screening factors (VSF). It is encouraging that the pGM with variable screening factors achieved APEs of 1.83 for 1155 amino acid analogs, dipeptides, and tetrapeptides, 1.39 for 28 nucleic acid bases, 0.708 for 1464 water clusters, and 1.99 for 85 dimers of water and biological building blocks. Compared to the new set of models, the APEs of the old Thole models that were fitted to isotropic molecular polarizabilities are 8.7% for set A (without the 1-2 and 1-3 interactions) and 6.3% for set D (with the 1-2 and 1-3 interactions) models, respectively. MPAD, a metric of molecular polarization anisotropy difference based on the diagonal terms of molecular polarizability tensors was defined and applied to assess the polarizable models in reproducing the ab initio molecular polarization anisotropy. The MPADs are 3.71, 4.70, 4.11, and 4.77% for the pGM, Thole linear, Thole exponential, and Thole Amoeba USF models, respectively. The APEs are reduced further to 2.85, 3.58, 2.90, and 3.15% for the four corresponding VSF models. Thus, the new pGM and Thole models notably improve molecular polarization anisotropy. Since pGM attenuates all short-range electrostatic interactions, its application is expected to improve stability in charge fitting, energy, and force calculations and the accuracy of multibody polarization.

Force Fields for Small Molecules

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

The impact of interior dielectric constant and entropic change on HIV-1 complex binding free energy prediction

At present, the calculated binding free energy obtained using the molecular mechanics/Poisson-Boltzmann (Generalized-Born) surface area (MM/PB(GB)SA) method is overestimated due to the lack of knowledge of suitable interior dielectric constants in the simulation on the interaction of Human Immunodeficiency Virus (HIV-1) protease systems with inhibitors. Therefore, the impact of different values of the interior dielectric constant and the entropic contribution when using the MM/PB(GB)SA method to calculate the binding free energy was systemically evaluated. Our results show that the use of higher interior dielectric constants (1.4-2.0) can clearly improve the predictive accuracy of the MM/PBSA and MM/GBSA methods, and computational errors are significantly reduced by including the effects of electronic polarization and using a new highly efficient interaction entropy (IE) method to calculate the entropic contribution. The suitable range for the interior dielectric constant is 1.4-1.6 for the MM/PBSA method; within this range, the correlation coefficient fluctuates around 0.84, and the mean absolute error fluctuates around 2 kcal/mol. Similarly, an interior dielectric constant of 1.8-2.0 produces a correlation coefficient of approximately 0.76 when using the MM/GBSA method. In addition, the entropic contribution of each individual residue was further calculated using the IE method to predict hot-spot residues, and the detailed binding mechanisms underlying the interactions of the HIV-1 protease, its inhibitors, and bridging water molecules were investigated. In this study, the use of a higher interior dielectric constant and the IE method can improve the calculation accuracy of the HIV-1 system.

Mapping the Drude polarizable force field onto a multipole and induced dipole model

The induced dipole and the classical Drude oscillator represent two major approaches for the explicit inclusion of electronic polarizability into force field-based molecular modeling and simulations. In this work, we explore the equivalency of these two models by comparing condensed phase properties computed using the Drude force field and a multipole and induced dipole (MPID) model. Presented is an approach to map the electrostatic model optimized in the context of the Drude force field onto the MPID model. Condensed phase simulations on water and 15 small model compounds show that without any reparametrization, the MPID model yields properties similar to the Drude force field with both models yielding satisfactory reproduction of a range of experimental values and quantum mechanical data. Our results illustrate that the Drude oscillator model and the point induced dipole model are different representations of essentially the same physical model. However, results indicate the presence of small differences between the use of atomic multipoles and off-center charge sites. Additionally, results on the use of dispersion particle mesh Ewald further support its utility for treating long-range Lennard Jones dispersion contributions in the context of polarizable force fields. The main motivation in demonstrating the transferability of parameters between the Drude and MPID models is that the more than 15 years of development of the Drude polarizable force field can now be used with MPID formalism without the need for dual-thermostat integrators nor self-consistent iterations. This opens up a wide range of new methodological opportunities for polarizable models.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

An efficient computational approach for modeling protein electrostatic is developed according to static point-charge model distributions based on the linear-scaling EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) quantum mechanical (QM) method. In this approach, the Electrostatic-Potential atomic charges are obtained from ab initio calculation of protein, both polarization and charge transfer effect are taken into consideration. This approach shows a significant improvement in the description of electrostatic potential and solvation energy of proteins comparing with current popular molecular mechanics (MM) force fields. Therefore, it has gorgeous prospect in many applications, including accurate calculations of electric field or vibrational Stark spectroscopy in proteins and predicting protein-ligand binding affinity. It can also be applied in QM/MM calculations or electronic embedding method of ONIOM to provide a better electrostatic environment.

Synergistic approaches unraveling regulation and aggregation of intrinsically disordered β-amyloids implicated in Alzheimer's disease

Alzheimer's disease is a severe brain illness that causes vast numbers of nerve cells in the brain to die, driven by the production and deposition of amyloid beta (Aβ) peptides. Intrinsically disordered proteins (IDPs) generally lack stable structures and are abundant in nature. Aβ peptide is a well-known IDP with a wide range of oligomeric forms. Dysfunctions in Aβ lead to oligomerization, formation of fibrils, and neurodegenerative disorders or other forms of dementia. In this study, we used replica exchange molecular dynamics (REMD) to elucidate the roles of different osmolytes, particularly urea and trimethylamine N-oxide (TMAO), to study shifts in IDP populations. REMD samples the conformational space efficiently and at physiologically relevant temperatures, compared to conventional molecular dynamics that sample at a constant temperature. Urea is known to minimize the aggregation process, while TMAO is beneficial for its stabilizing action. The two osmolytes displayed characteristic effects on Aβ peptides and resulted in progressive modulation of conformations. The present study underlines the hypothesis of "modulation of conformational ensembles" to explain the regulation and aggregation of IDPs.

Computational Study of PCSK9-EGFA Complex with Effective Polarizable Bond Force Field

Inhibiting of Proprotein Convertase Subtilisin/Kexin-type 9 (PCSK9) and Low Density Lipoprotein Receptor (LDLR) binding is an effective way for reducing Low Density Lipoprotein cholesterol (LDL-C). Understanding the interaction between PCSK9 and LDLR is useful for PCSK9 inhibitor design. In this work, MD simulations with the standard (non-polarizable) AMBER force field and effective polarizable bond (EPB) force field were performed for wild type and four mutants of PCSK9 and EGFA (Epidermal Growth Factor-like repeat A) domain of LDLR complexes. These four mutants are gain-of-function mutants. The analysis of hydrogen bond dynamics and the relative binding free energy indicates that EPB is more reliable in simulating protein dynamics and predicting relative binding affinity. Structures sampled from MD simulations with the standard AMBER force field deviate too far away from crystal structures. Many important interaction components between of PCSK9 and EGFA no longer exist in the simulation with the Amber force field. For comparison, simulation using EPB force field gives more stable structures as shown by hydrogen bond analysis and produced relative binding free energies that are consistent with experimental results. Our study suggests that inclusion of polarization effects in MD simulation is important for studying the protein-protein interaction.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

A New Method for Treating Drude Polarization in Classical Molecular Simulation

With polarization becoming an increasingly common feature in classical molecular simulation, it is important to develop methods that can efficiently and accurately evaluate the many-body polarization solution. In this work, we expand the theoretical framework of our inertial extended Langrangian, self-consistent field iteration-free method (iEL/0-SCF), introduced for point induced dipoles, to the polarization model of a Drude oscillator. When applied to the polarizable simple point charge model (PSPC) for water, our iEL/0-SCF method for Drude polarization is as stable as a well-converged SCF solution and more stable than traditional extended Lagrangian (EL) approaches or EL formulations based on two temperature ensembles where Drude particles are kept "colder" than the real degrees of freedom. We show that the iEL/0-SCF method eliminates the need for mass repartitioning from parent atoms onto Drude particles, obeys system conservation of linear and angular momentum, and permits the extension of the integration time step of a basic molecular dynamics simulation to 6.0 fs for PSPC water.

Dielectric screening effect of electronic polarization and intramolecular hydrogen bonding

Recent site-resolved hydrogen exchange measurements have uncovered significant discrepancies between simulations and experimental data during protein folding, including the excessive intramolecular hydrogen bonds in simulations. This finding indicates a possibility that intramolecular charge-charge interactions have not included sufficient dielectric screening effect of the electronic polarization. Scaling down peptide atomic charges according to the optical dielectric constant is tested in this study. As a result, the number of intramolecular hydrogen bonds is lower than using unscaled atomic charges while reaching the same levels of helical contents or β-hairpin backbone hydrogen bonds, because van der Waals interactions contribute substantially to peptide folding in water. Reducing intramolecular charge-charge interactions and hydrogen bonding increases conformational search efficiency. In particular, it reduces the equilibrium helical content in simulations using AMBER force field and the energy barrier in folding simulations using CHARMM force field.

A charge equilibration formalism for treating charge transfer effects in MD simulations: Application to water clusters

Conventional classical force fields by construction do not explicitly partition intermolecular interactions to include polarization and charge transfer effects, whereas fully quantum mechanical treatments allow a means to effect this dissection (although not uniquely due to the lack of a charge transfer operator). Considering the importance of polarization in a variety of systems, a particular class of classical models, charge equilibration models, have been extensively developed to study those systems; since these types of interaction models are inherently based on movement of charge throughout a system, they are natural platform for including polarization and charge transfer effects within the context of molecular simulations. Here, we present two bond-space charge equilibration models we term as QE2 and mixed QE2 treat charge transfer in classical molecular mechanical calculations those provide practical solutions to two major drawbacks of charge equilibration models: (a) a nonvanishing amount of charge transfer between two heteroatoms at large separations, and (b) superlinear polarizability scaling during bond dissociation due to charge transfer over unphysical, large distances. To control charge transfer during dissociation of a bond in a molecular system, we introduce a distance-dependent scaling function (QE2 model) which, controls and recovers physical behavior of the homonuclear and heteronuclear charge transfer between two atoms at small and large values of internuclear separation; and the mixed QE2 model in which we combine the QE2 model under allow and disallow charge transfer situations that describe both charge transfer and polarizability in a distance-dependent manner. We demonstrate the utility of both models in the case of a water dimer, and compare the results with other existing models, and further, we perform short molecular dynamics simulations for few water clusters with the QE2 model to show the charge transfer and internuclear separation are correlated in dynamics. © 2017 Wiley Periodicals, Inc.