The Electronegativity Equalization Method I: Parametrization and Validation for Atomic Charge Calculations

A polarizable valence electron density based force field for high-energy interactions between atoms and molecules

High-accuracy molecular force field models suited for hot gases and plasmas are not as abundant as those geared toward ambient pressure and temperature conditions. Here, we present an improved version of our previous electron-density based force field model that can now account for polarization effects by adjusting the atomic valence electron contributions to match ab initio calculated Mulliken partial charges. Using a slightly modified version of the Hohenberg-Kohn theorem, we also include an improved theoretical formulation of our model when applied to systems with degenerate ground states. We present two variants of our polarizable model, fitted from ab initio reference data calculated at CCSD(T)/cc-pVTZ and CCSD(T)/CEP-31G levels of theory, that both accurately model water dimer interaction energies. Further improvements include the additional interaction components with fictitious non-spherically symmetric, yet atom-centered, electron densities and fitting the exchange and correlation coefficients against analytical expressions. The latter removes all unphysical oscillations that are observed in the previous non-polarizable variant of our force field.

Computational Chemistry Strategies to Investigate the Antioxidant Activity of Flavonoids-An Overview

Despite several decades of research, the beneficial effect of flavonoids on health is still enigmatic. Here, we focus on the antioxidant effect of flavonoids, which is elementary to their biological activity. A relatively new strategy for obtaining a more accurate understanding of this effect is to leverage computational chemistry. This review systematically presents various computational chemistry indicators employed over the past five years to investigate the antioxidant activity of flavonoids. We categorize these strategies into five aspects: electronic structure analysis, thermodynamic analysis, kinetic analysis, interaction analysis, and bioavailability analysis. The principles, characteristics, and limitations of these methods are discussed, along with current trends.

Predicting Solvation Free Energies Using Electronegativity-Equalization Atomic Charges and a Dense Neural Network: A Generalized-Born Approach

I propose a dense Neural Network, ESE-GB-DNN, for evaluation of solvation free energies ΔG°solv for molecules and ions in water and nonaqueous solvents. As input features, it employs generalized-Born monatomic and diatomic terms, as well as atomic surface areas and the molecular volume. The electrostatics calculation is based on a specially modified version of electronegativity-equalization atomic charges. ESE-GB-DNN evaluates ΔG°solv in a simple and highly efficient way, yet it offers a high accuracy, often challenging that of standard DFT-based methods. For neutral solutes, ESE-GB-DNN yields an RMSE between 0.7 and 1.3 kcal/mol, depending on the solvent class. ESE-GB-DNN performs particularly well for nonaqueous solutions of ions, with an RMSE of about 0.7 kcal/mol. For ions in water, the RMSE is larger (2.9 kcal/mol).

Effect of preprocessing and simulation parameters on the performance of molecular docking studies

CONTEXT

Molecular docking is an important and rapid tool that provides a comprehensive view of different molecular mechanisms. It is often used to verify the binding interactions of many pairs of molecules and is much faster than more rigorous approaches. However, its application requires carefully preprocessing each molecule and selecting a series of simulation parameters, which is not always done correctly. We show how preprocessing and simulation parameters can positively or negatively impact molecular docking performance. For example, the inclusion of hydrogen atoms leads to better redocking scores, but molecular dynamics simulations must be performed under certain constraints; otherwise, it may worsen performance rather than improve it. This study clarifies the importance and influence of these different parameters in the simulation results.

METHODS

We analyzed the influence of different parameters on the predictive ability of molecular docking techniques using two software packages: AutoDock Vina and AutoDock-GPU. Thus, 90 receptor-ligand complexes were redocked, evaluating the root mean square deviation (RMSD) between the original position of the ligand (receptor-ligand complex obtained experimentally) and that obtained by the software for every analysis. We investigated the influence of hydrogen atoms (on the receptor and on the receptor-ligand complex), partial charges (QEq, QTPIE, EEM, EEM2015ha, MMFF94, Gasteiger-Marsili, and no charge), search boxes (size and exhaustiveness), ligand characteristics (size and number of torsions), and the use of molecular dynamics (of the receptor or the receptor-ligand complex) before docking analyses.

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.

In silico characterization of nanoparticles

Nanoparticles (NPs) make for intriguing heterogeneous catalysts due to their large active surface area and excellent and often size-dependent catalytic properties that emerge from a multitude of chemically different surface reaction sites. NP catalysts are, in principle, also highly tunable: even small changes to the NP size or surface facet composition, doping with heteroatoms, or changes of the supporting material can significantly alter their physicochemical properties. Because synthesis of size- and shape-controlled NP catalysts is challenging, the ability to computationally predict the most favorable NP structures for a catalytic reaction of interest is an in-demand skill that can help accelerate and streamline the material optimization process. Fundamentally, simulations of NP model systems present unique challenges to computational scientists. Not only must considerable methodological hurdles be overcome in performing calculations with hundreds to thousands of atoms while retaining appropriate accuracy to be able to probe the desired properties. Also, the data generated by simulations of NPs are typically more complex than data from simulations of, for example, single crystal surface models, and therefore often require different data analysis strategies. To this end, the present work aims to review analytical methods and data analysis strategies that have proven useful in extracting thermodynamic trends from NP simulations.

A quick solvation energy estimator based on electronegativity equalization

ESE-EE (Easy Solvation Estimation with Electronegativity equalization) is a quick method for estimation of solvation-free energies ΔGº_solv , which uses a thoroughly fitted electronegativity equalization (EE) scheme to obtain atomic charges, which are further employed in a scaled noniterative COSMO-like calculation to evaluate the electrostatic component of ΔGº_solv . Nonelectrostatic corrections including adjustable parameters are also added. For neutral solutes, ESE-EE yields a mean absolute error (MAE) in ΔG_solv ° of 1.5 kcal/mol for aqueous solutions; 1.0 kcal/mol for nonaqueous polar protic solvents; 0.9 kcal/mol for polar aprotic solvents; and about 0.6 kcal/mol for nonpolar solvents. Since ESE-EE only requires a molecular geometry as input for a ΔGº_solv prediction, it can be utilized for a rapid screening of ΔGº_solv for large neutral molecules. However, for ionic solutes, ESE-EE yields larger errors (typically several kcal/mol) and is recommendable for preliminary estimations only. Upon a special refitting, ESE-EE is able to yield partition coefficients with a good accuracy.

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.

From Density Functional Theory to Conceptual Density Functional Theory and Biosystems

The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Kernel charge equilibration: efficient and accurate prediction of molecular dipole moments with a machine-learning enhanced electron density model

State-of-the-art machine learning (ML) interatomic potentials use local representations of atomic environments to ensure linear scaling and size-extensivity. This implies a neglect of long-range interactions, most prominently related to electrostatics. To overcome this limitation, we herein present a ML framework for predicting charge distributions and their interactions termed kernel charge equilibration (kQEq). This model is based on classical charge equilibration (QEq) models expanded with an environment-dependent electronegativity. In contrast to previously reported neural network models with a similar concept, kQEq takes advantage of the linearity of both QEq and Kernel Ridge Regression to obtain a closed-form linear algebra expression for training the models. Furthermore, we avoid the ambiguity of charge partitioning schemes by using dipole moments as reference data. As a first application, we show that kQEq can be used to generate accurate and highly data-efficient models for molecular dipole moments.

Generalized Method for Charge-Transfer Equilibration in Reactive Molecular Dynamics

Variable charge models (e.g., electronegativity equalization method (EEM), charge equilibration (QEq), electrostatic plus (ES+)) used in reactive molecular dynamics simulations often inherently impose a global charge transfer between atoms (approximating each system as an ideal metal). Consequently, most surface processes (e.g., adsorption, desorption, deposition, sputtering) are affected, potentially causing dubious dynamics. This issue has been addressed by certain split charge variants (i.e., split charge equilibration (SQE), redoxSQE) through a distance-dependent bond hardness, by the atomic charge ACKS2 and QTPIE models, which are based on the Kohn-Sham density functional theory, as well as by an electronegativity screening extension to the QEq model (approximating each system as an ideal insulator). In a brief review of the QEq and the QTPIE model, their applicability for studying surface interactions is assessed in this work. Following this evaluation, a revised generalization of the QEq and QTPIE models is proposed and formulated, called the charge-transfer equilibration model or in short the QTE model. This method is based on the equilibration of charge-transfer variables, which locally constrain the split charge transfer per unit time (i.e., due to overlapping orbitals) without any kind of bond hardness specification. Furthermore, a formalism relying solely on atomic charges is obtained by a respective transformation, employing an extended Lagrangian method. We moreover propose a mirror boundary condition and its implementation to accelerate surface investigations. The models proposed in this work facilitate reactive molecular dynamics simulations, which describe various materials and surface phenomena appropriately.

ReaxFF/AMBER-A Framework for Hybrid Reactive/Nonreactive Force Field Molecular Dynamics Simulations

Combined quantum mechanical/molecular mechanical (QM/MM) models using semiempirical and ab initio methods have been extensively reported on over the past few decades. These methods have been shown to be capable of providing unique insights into a range of problems, but they are still limited to relatively short time scales, especially QM/MM models using ab initio methods. An intermediate approach between a QM based model and classical mechanics could help fill this time-scale gap and facilitate the study of a range of interesting problems. Reactive force fields represent the intermediate approach explored in this paper. A widely used reactive model is ReaxFF, which has largely been applied to materials science problems and is generally used as a stand-alone (i.e., the full system is modeled using ReaxFF). We report a hybrid ReaxFF/AMBER molecular dynamics (MD) tool, which introduces ReaxFF capabilities to capture bond breaking and formation within the AMBER MD software package. This tool enables us to study local reactive events in large systems at a fraction of the computational costs of QM/MM models. We describe the implementation of ReaxFF/AMBER, validate this implementation using a benzene molecule solvated in water, and compare its performance against a range of similar approaches. To illustrate the predictive capabilities of ReaxFF/AMBER, we carried out a Claisen rearrangement study in aqueous solution. In a first for ReaxFF, we were able to use AMBER's potential of mean force (PMF) capabilities to perform a PMF study on this organic reaction. The ability to capture local reaction events in large systems using combined ReaxFF/AMBER opens up a range of problems that can be tackled using this model to address both chemical and biological processes.

Incorporating charge transfer effects into a metallic empirical potential for accurate structure determination in (ZnMg)N nanoalloys

We report the results of a combined empirical potential-density functional theory (EP-DFT) study to assess the global minimum structures of free-standing zinc-magnesium nanoalloys of equiatomic composition and with up to 50 atoms. Within this approach, the approximate potential energy surface generated by an empirical potential is first sampled with unbiased basin hopping simulations, and then a selection of the isomers so identified is re-optimized at a first-principles DFT level. Bader charges calculated in a previous work [A. Lebon, A. Aguado and A. Vega, Corros. Sci., 2017, 124, 35-45] revealed a significant transfer of electrons from Mg to Zn atoms in these nanoalloys; so the main novelty in the present work is the development of an improved EP, termed Coulomb-corrected-Gupta potential, which incorporates an explicit charge-transfer correction term onto a metallic Gupta potential description. The Coulomb correction has a many-body character and is fed with parameterized values of the ab initio Bader charges. The potentials are fitted to a large training set containing DFT values of cluster energies and atomic forces, and the DFT results are used as benchmark data to assess the performance of Gupta and Coulomb-corrected-Gupta EP models. Quite surprisingly, the charge-transfer correction is found to represent only 6% of the nanoalloy binding energies, yet this quantitatively small correction has a sizable beneficial effect on the predicted relative energies of homotops. Zn-Mg bulk alloys are used as the sacrificial material in corrosion-protective coatings, and the long-term goal of our research is to disclose whether those corrosion-protected capabilities are enhanced at the nanoscale.

In-Silico Modeling in Drug Metabolism and Interaction: Current Strategies of Lead Discovery

BACKGROUND

Drug metabolism is a complex mechanism of human body systems to detoxify foreign particles, chemicals, and drugs through bio alterations. It involves many biochemical reactions carried out by invivo enzyme systems present in the liver, kidney, intestine, lungs, and plasma. After drug administration, it crosses several biological membranes to reach into the target site for binding and produces the therapeutic response. After that, it may undergo detoxification and excretion to get rid of the biological systems. Most of the drugs and its metabolites are excreted through kidney via urination. Some drugs and their metabolites enter into intestinal mucosa and excrete through feces. Few of the drugs enter into hepatic circulation where they go into the intestinal tract. The drug leaves the liver via the bile duct and is excreted through feces. Therefore, the study of total methodology of drug biotransformation and interactions with various targets is costly.

METHODS

To minimize time and cost, in-silico algorithms have been utilized for lead-like drug discovery. Insilico modeling is the process where a computer model with a suitable algorithm is developed to perform a controlled experiment. It involves the combination of both in-vivo and in-vitro experimentation with virtual trials, eliminating the non-significant variables from a large number of variable parameters. Whereas, the major challenge for the experimenter is the selection and validation of the preferred model, as well as precise simulation in real physiological status.

RESULTS

The present review discussed the application of in-silico models to predict absorption, distribution, metabolism, and excretion (ADME) properties of drug molecules and also access the net rate of metabolism of a compound.

CONCLUSION

It helps with the identification of enzyme isoforms; which are likely to metabolize a compound, as well as the concentration dependence of metabolism and the identification of expected metabolites. In terms of drug-drug interactions (DDIs), models have been described for the inhibition of metabolism of one compound by another, and for the compound-dependent induction of drug-metabolizing enzymes.

Deep Learning-Based Structure-Activity Relationship Modeling for Multi-Category Toxicity Classification: A Case Study of 10K Tox21 Chemicals With High-Throughput Cell-Based Androgen Receptor Bioassay Data

Deep learning (DL) has attracted the attention of computational toxicologists as it offers a potentially greater power for in silico predictive toxicology than existing shallow learning algorithms. However, contradicting reports have been documented. To further explore the advantages of DL over shallow learning, we conducted this case study using two cell-based androgen receptor (AR) activity datasets with 10K chemicals generated from the Tox21 program. A nested double-loop cross-validation approach was adopted along with a stratified sampling strategy for partitioning chemicals of multiple AR activity classes (i.e., agonist, antagonist, inactive, and inconclusive) at the same distribution rates amongst the training, validation and test subsets. Deep neural networks (DNN) and random forest (RF), representing deep and shallow learning algorithms, respectively, were chosen to carry out structure-activity relationship-based chemical toxicity prediction. Results suggest that DNN significantly outperformed RF (p < 0.001, ANOVA) by 22–27% for four metrics (precision, recall, F-measure, and AUPRC) and by 11% for another (AUROC). Further in-depth analyses of chemical scaffolding shed insights on structural alerts for AR agonists/antagonists and inactive/inconclusive compounds, which may aid in future drug discovery and improvement of toxicity prediction modeling.

Iterative Solvers for Empirical Partial Atomic Charges: Breaking the Curse of Cubic Numerical Complexity

Rational drug design involves a vast amount of computations to get thermodynamically reliable results and often relies on atomic charges as a means to model electrostatic interactions within the system. Computational inefficiency often hampers the development of new and wider dissemination of the known methods; thus, any source to speed up the calculations without a sacrifice in quality is warranted. At the heart of many empirical methods of calculating atomic charges is the solution of a system of linear algebraic equations (SLAE). The classical method of solving SLAE-the Gauss method-has in general case a cubic computational complexity. It is shown that the use of iterative methods for solving SLAE, characteristic to typical empirical atomic charge calculation methods, makes it possible to significantly reduce the amount of calculations and to obtain a computational complexity approaching a quadratic one. Despite the fact that this phenomenon is well-known in numerical methods, iterative solvers surprisingly do not seem to have been systematically applied to calculation of atomic charges via empirical schemes. Another finding is the relative values of the matrix elements, determined by the physical grounds of the interactions within the empirical system, generally lead to SLAE's with well-defined matrices, suited to use with iterative solvers to fasten computation compared to using the noniterative solvers. This finding broadens the applicability range of atomic charges obtained with empirical methods for such cases as, e.g., account of polarizability via "on-the-fly" recalculation of charges in changing surroundings within the force fields in molecular dynamics settings.

Evaluating Charge Equilibration Methods To Generate Electrostatic Fields in Nanoporous Materials

Charge equilibration (Qeq) methods can estimate the electrostatic potential of molecules and periodic frameworks by assigning point charges to each atom, using only a small fraction of the resources needed to compute density functional (DFT)-derived charges. This makes possible, for example, the computational screening of thousands of microporous structures to assess their performance for the adsorption of polar molecules. Recently, different variants of the original Qeq scheme were proposed to improve the quality of the computed point charges. One focus of this research was to improve the gas adsorption predictions in metal–organic frameworks (MOFs), for which many different structures are available. In this work, we review the evolution of the method from the original Qeq scheme, understanding the role of the different modifications on the final output. We evaluated the result of combining different protocols and set of parameters, by comparing the Qeq charges with high quality DFT-derived DDEC charges for 2338 MOF structures. We focused on the systematic errors that are attributable to specific atom types to quantify the final precision that one can expect from Qeq methods in the context of gas adsorption where the electrostatic potential plays a significant role, namely, CO₂ and H₂S adsorption. In conclusion, both the type of algorithm and the input parameters have a large impact on the resulting charges, and we draw some guidelines to help the user to choose the proper combination of the two for obtaining a meaningful set of charges. We show that, considering this set of MOFs, the accuracy of the original Qeq scheme is often still comparable with the most recent variants, even if it clearly fails in the presence of certain atom types, such as alkali metals.

Molden 2.0: quantum chemistry meets proteins

Since the first distribution of Molden in 1995 and the publication of the first article about this software in 2000 work on Molden has continued relentlessly. A few of the many improved or fully novel features such as improved and broadened support for quantum chemistry calculations, preparation of ligands for use in drug design related softwares, and working with proteins for the purpose of ligand docking.

Direct computation of parameters for accurate polarizable force fields

We present an improved electronic linear response model to incorporate polarization and charge-transfer effects in polarizable force fields. This model is a generalization of the Atom-Condensed Kohn-Sham Density Functional Theory (DFT), approximated to second order (ACKS2): it can now be defined with any underlying variational theory (next to KS-DFT) and it can include atomic multipoles and off-center basis functions. Parameters in this model are computed efficiently as expectation values of an electronic wavefunction, obviating the need for their calibration, regularization, and manual tuning. In the limit of a complete density and potential basis set in the ACKS2 model, the linear response properties of the underlying theory for a given molecular geometry are reproduced exactly. A numerical validation with a test set of 110 molecules shows that very accurate models can already be obtained with fluctuating charges and dipoles. These features greatly facilitate the development of polarizable force fields.

Can the electronegativity equalization method predict spectroscopic properties?

The electronegativity equalization method is classically used as a method allowing the fast generation of atomic charges using a set of calibrated parameters and provided knowledge of the molecular structure. Recently, it has started being used for the calculation of other reactivity descriptors and for the development of polarizable and reactive force fields. For such applications, it is of interest to know whether the method, through the inclusion of the molecular geometry in the Taylor expansion of the energy, would also allow sufficiently accurate predictions of spectroscopic data. In this work, relevant quantities for IR spectroscopy are considered, namely the dipole derivatives and the Cartesian Hessian. Despite careful calibration of parameters for this specific task, it is shown that the current models yield insufficiently accurate results.

Automatic classification of protein structures using physicochemical parameters

Protein classification is the first step to functional annotation; SCOP and Pfam databases are currently the most relevant protein classification schemes. However, the disproportion in the number of three dimensional (3D) protein structures generated versus their classification into relevant superfamilies/families emphasizes the need for automated classification schemes. Predicting function of novel proteins based on sequence information alone has proven to be a major challenge. The present study focuses on the use of physicochemical parameters in conjunction with machine learning algorithms (Naive Bayes, Decision Trees, Random Forest and Support Vector Machines) to classify proteins into their respective SCOP superfamily/Pfam family, using sequence derived information. Spectrophores™, a 1D descriptor of the 3D molecular field surrounding a structure was used as a benchmark to compare the performance of the physicochemical parameters. The machine learning algorithms were modified to select features based on information gain for each SCOP superfamily/Pfam family. The effect of combining physicochemical parameters and spectrophores on classification accuracy (CA) was studied. Machine learning algorithms trained with the physicochemical parameters consistently classified SCOP superfamilies and Pfam families with a classification accuracy above 90%, while spectrophores performed with a CA of around 85%. Feature selection improved classification accuracy for both physicochemical parameters and spectrophores based machine learning algorithms. Combining both attributes resulted in a marginal loss of performance. Physicochemical parameters were able to classify proteins from both schemes with classification accuracy ranging from 90-96%. These results suggest the usefulness of this method in classifying proteins from amino acid sequences.

Conceptual DFT: chemistry from the linear response function

Within the context of reactivity descriptors known in conceptual DFT, the linear response function (χ(r,r')) remained nearly unexploited. Although well known, in its time dependent form, in the solid state physics and time-dependent DFT communities the study of the "chemistry" present in the kernel was, until recently, relatively unexplored. The evaluation of the linear response function as such and its study in the time independent form are highlighted in the present review. On the fundamental side, the focus is on the approaches of increasing complexity to compute and represent χ(r,r'), its visualisation going from plots of the unintegrated χ(r,r') to an atom condensed matrix. The study on atoms reveals its physical significance, retrieving atomic shell structure, while the results on molecules illustrate that a variety of chemical concepts are retrieved: inductive and mesomeric effects, electron delocalisation, aromaticity and anti-aromaticity, σ and π aromaticity,…. The applications show that the chemistry of aliphatic (saturated and unsaturated) chains, saturated and aromatic/anti-aromatic rings, organic, inorganic or metallic in nature, can be retrieved via the linear response function, including the variation of the electronic structure of the reagents along a reaction path. The connection of the linear response function with the concept of nearsightedness and the alchemical derivatives is also highlighted.

Predicting p Ka values from EEM atomic charges

The acid dissociation constant p K_ais a very important molecular property, and there is a strong interest in the development of reliable and fast methods for p K_aprediction. We have evaluated the p K_aprediction capabilities of QSPR models based on empirical atomic charges calculated by the Electronegativity Equalization Method (EEM). Specifically, we collected 18 EEM parameter sets created for 8 different quantum mechanical (QM) charge calculation schemes. Afterwards, we prepared a training set of 74 substituted phenols. Additionally, for each molecule we generated its dissociated form by removing the phenolic hydrogen. For all the molecules in the training set, we then calculated EEM charges using the 18 parameter sets, and the QM charges using the 8 above mentioned charge calculation schemes. For each type of QM and EEM charges, we created one QSPR model employing charges from the non-dissociated molecules (three descriptor QSPR models), and one QSPR model based on charges from both dissociated and non-dissociated molecules (QSPR models with five descriptors). Afterwards, we calculated the quality criteria and evaluated all the QSPR models obtained. We found that QSPR models employing the EEM charges proved as a good approach for the prediction of p K_a(63% of these models had R² > 0.9, while the best had R² = 0.924). As expected, QM QSPR models provided more accurate p K_apredictions than the EEM QSPR models but the differences were not significant. Furthermore, a big advantage of the EEM QSPR models is that their descriptors (i.e., EEM atomic charges) can be calculated markedly faster than the QM charge descriptors. Moreover, we found that the EEM QSPR models are not so strongly influenced by the selection of the charge calculation approach as the QM QSPR models. The robustness of the EEM QSPR models was subsequently confirmed by cross-validation. The applicability of EEM QSPR models for other chemical classes was illustrated by a case study focused on carboxylic acids. In summary, EEM QSPR models constitute a fast and accurate p K_aprediction approach that can be used in virtual screening.

Charge profile analysis reveals that activation of pro-apoptotic regulators Bax and Bak relies on charge transfer mediated allosteric regulation

The pro-apoptotic proteins Bax and Bak are essential for executing programmed cell death (apoptosis), yet the mechanism of their activation is not properly understood at the structural level. For the first time in cell death research, we calculated intra-protein charge transfer in order to study the structural alterations and their functional consequences during Bax activation. Using an electronegativity equalization model, we investigated the changes in the Bax charge profile upon activation by a functional peptide of its natural activator protein, Bim. We found that charge reorganizations upon activator binding mediate the exposure of the functional sites of Bax, rendering Bax active. The affinity of the Bax C-domain for its binding groove is decreased due to the Arg94-mediated abrogation of the Ser184-Asp98 interaction. We further identified a network of charge reorganizations that confirms previous speculations of allosteric sensing, whereby the activation information is conveyed from the activation site, through the hydrophobic core of Bax, to the well-distanced functional sites of Bax. The network was mediated by a hub of three residues on helix 5 of the hydrophobic core of Bax. Sequence and structural alignment revealed that this hub was conserved in the Bak amino acid sequence, and in the 3D structure of folded Bak. Our results suggest that allostery mediated by charge transfer is responsible for the activation of both Bax and Bak, and that this might be a prototypical mechanism for a fast activation of proteins during signal transduction. Our method can be applied to any protein or protein complex in order to map the progress of allosteric changes through the proteins' structure.

Apoptosis is a physiological form of cell death that is fundamental for development, growth and homeostasis in multi-cellular organisms. Deviations in the apoptosis machinery are known to be involved in cancer, neurodegenerative disorders, and autoimmune diseases. The proteins Bax and Bak are essential for executing apoptosis, yet the mechanism of their activation is not properly understood at the structural level. To understand this mechanism, we investigated how the electronic density is reorganized (i.e., how charge is transferred) inside the Bax molecule when Bax binds a functional peptide of its natural activator protein. We identified the specific interactions responsible for the exposure of the functional sites of Bax, rendering Bax active. Furthermore, we found a network of charge transfer that conveys activation information from the Bax activation site, through the hydrophobic core of Bax, to the well-distanced functional sites of Bax. This network consists of three residues inside the hydrophobic core of Bax, which are present also in the hydrophobic core of Bak, suggesting that these residues are functionally important and thus potential drug targets. We provide a straightforward and accessible methodology to identify the key residues involved in the fast activation of proteins during signal transduction.

Assessment of Atomic Charge Models for Gas-Phase Computations on Polypeptides

The concept of the atomic charge is extensively used to model the electrostatic properties of proteins. Atomic charges are not only the basis for the electrostatic energy term in biomolecular force fields but are also derived from quantum mechanical computations on protein fragments to get more insight into their electronic structure. Unfortunately there are many atomic charge schemes which lead to significantly different results, and it is not trivial to determine which scheme is most suitable for biomolecular studies. Therefore, we present an extensive methodological benchmark using a selection of atomic charge schemes [Mulliken, natural, restrained electrostatic potential, Hirshfeld-I, electronegativity equalization method (EEM), and split-charge equilibration (SQE)] applied to two sets of penta-alanine conformers. Our analysis clearly shows that Hirshfeld-I charges offer the best compromise between transferability (robustness with respect to conformational changes) and the ability to reproduce electrostatic properties of the penta-alanine. The benchmark also considers two charge equilibration models (EEM and SQE), which both clearly fail to describe the locally charged moieties in the zwitterionic form of penta-alanine. This issue is analyzed in detail because charge equilibration models are computationally much more attractive than the Hirshfeld-I scheme. Based on the latter analysis, a straightforward extension of the SQE model is proposed, SQE+Q(0), that is suitable to describe biological systems bearing many locally charged functional groups.

Incorporation of charge transfer into the explicit polarization fragment method by grand canonical density functional theory

Molecular fragmentation algorithms provide a powerful approach to extending electronic structure methods to very large systems. Here we present a method for including charge transfer between molecular fragments in the explicit polarization (X-Pol) fragment method for calculating potential energy surfaces. In the conventional X-Pol method, the total charge of each fragment is preserved, and charge transfer between fragments is not allowed. The description of charge transfer is made possible by treating each fragment as an open system with respect to the number of electrons. To achieve this, we applied Mermin's finite temperature method to the X-Pol wave function. In the application of this method to X-Pol, the fragments are open systems that partially equilibrate their number of electrons through a quasithermodynamics electron reservoir. The number of electrons in a given fragment can take a fractional value, and the electrons of each fragment obey the Fermi-Dirac distribution. The equilibrium state for the electrons is determined by electronegativity equalization with conservation of the total number of electrons. The amount of charge transfer is controlled by re-interpreting the temperature parameter in the Fermi-Dirac distribution function as a coupling strength parameter. We determined this coupling parameter so as to reproduce the charge transfer energy obtained by block localized energy decomposition analysis. We apply the new method to ten systems, and we show that it can yield reasonable approximations to potential energy profiles, to charge transfer stabilization energies, and to the direction and amount of charge transferred.

Atom-Bond Electronegativity Equalization Method and its Applications Based on Density Functional Theory

The atom-bond electronegativity equalization method (ABEEM) and its applications for predicting intrinsic properties of large molecules, such as the charge distribution, the molecular energy, the local softness and the Fukui function, the regio- and stereo-selectivity of Diels–Alder reactions, the linear response function, and the charge polarization normal modes have been formulated. The examples show that there is a very good agreement of the ABEEM results with those of the corresponding ab initio quantum chemical calculations, demonstrating the reasonable and possible ABEEM's applications to the large molecular systems.