Electronegativity Equalization Research Articles

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.

Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method

The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the electronegativity equalization method.

Local HSAB rationalization of diels–alder reactions by means of ab initio and ABEEMσπ methods: Stereoselectivity and reaction rate

AbstractIn this article, four series of Diels–Alder (DA) reactions (totally, 68 reactions) have been investigated, including their transition states, by means of ab initio method at MP2/6‐311+G(d,p) level and atom‐bond electronegativity equalization method (ABEEMσπ) method. The rationalization of stereoselectivities of these DA reactions has been done in the light of the local hard and soft acids and bases (HSAB) criterion. The results show that the finite difference approximation with ab initio method can not always be used to predict the stereoselectivities of these reactions, while ABEEMσπ method can properly be applied to predict the stereoselectivities of these DA reactions. Moreover, we have proposed the generalized Fukui function and local softness which involve the number of the atoms of a molecule. For the first time, we here demonstrate that local HSAB criterion with the generalized local softness can be utilized not only to predict the main products of these DA reactions but also to rationalize the relative magnitudes of the reaction rate constants of these DA reactions. © 2013 Wiley Periodicals, Inc.

On the electrophilic character of molecules through its relation with electronegativity and chemical hardness.

Electrophilicity is an intrinsic property of atoms and molecules. It probably originates logistically with the involvement in the physical process of electrostatics of soaked charge in electronic shells and the screened nuclear charge of atoms. Motivated by the existing view of conceptual density functional theory that similar to electronegativity and hardness equalization, there should be a physical process of equalization of electrophilicity during the chemical process of formation of hetero nuclear molecules, we have developed a new theoretical scheme and formula for evaluating the electrophilicity of hetero nuclear molecules. A comparative study with available bench marking reveals that the hypothesis of electrophilicity and equalization, and the present method of evaluating equalized electrophilicity, are scientifically promising.

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.

Computation of Charge Distribution and Electrostatic Potential in Silicates with the Use of Chemical Potential Equalization Models

New parameters for the electronegativity equalization model (EEM) and the split-charge equilibration (SQE) model are calibrated for silicate materials, based on an extensive training set of representative isolated systems. In total, four calibrations are carried out, two for each model, either using iterative Hirshfeld (HI) charges or ESP grid data computed with density functional theory (DFT) as a reference. Both the static (ground state) reference quantities and their responses to uniform electric fields are included in the fitting procedure. The EEM model fails to describe the response data, whereas the SQE model quantitatively reproduces all of the training data. For the ESP-based parameters, we found that the reference ESP data are only useful at those grid points where the electron density is lower than 10–3 a.u. The density value correlates with a distance criterion used for selecting grid points in common ESP fitting schemes. All parameters are validated with DFT computations on an independent set...

Theoretical study on the hydration of hydrogen peroxide in terms of ab initio method and atom-bond electronegativity equalization method fused into molecular mechanics

In this paper, the interaction between hydrogen peroxide (HP) and water were systemically studied by atom-bond electronegativity equalization method fused into molecular mechanics (ABEEM/MM) and ab initio method. The results show that the optimized geometries, interaction energies and dipole moments of hydrated HP clusters HP(H2O) n (n = 1–6) calculated by ABEEM/MM model are fairly consistent with the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ results. The ABEEM/MM results indicate that n = 4 is the transition state structure from 2D planar structure to 3D network structure. The variations of the average hydrogen bond length with the increasing number of water molecules given by ABEEM/MM model agree well with those of ab initio studies. Moreover, the radial distribution functions (RDFs) of water molecule around HP in HP aqueous solution have been analyzed in detail. It can be confirmed that HP is a good proton donor and poor proton acceptor in aqueous solution by analysis of the RDFs.

Development predictive QSAR models for artemisinin analogues by various feature selection methods: A comparative study

Quantitative structure–activity relationship (QSAR) models were derived for 179 analogues of artemisinin, a potent antimalarial agent. The activities of these compounds were investigated by means of multiple linear regression (MLR). To select relevant descriptors, several methods including stepwise selection, successive projection algorithm and an ant colony optimization algorithm (called memorized_ACS) were employed. A wide variety of molecular descriptors belonging to various structural properties were calculated for each molecule. Two matrixes (D1 and D2) of molecular properties were built. The D1 matrix included the calculated descriptors and the D2 matrix contained the first to third orders of the calculated descriptors and the logarithm of absolute values of the calculated descriptors. For both data matrixes, significant QSAR models were obtained by the memorized_ACS algorithm. The reactive and PEOE (partial equalization of orbital electronegativity) descriptors represented the highest impact on the antimalarial activity. The PEOE descriptors belong to partial charge descriptors and the reactive descriptor is an indicator of the presence of the reactive groups in the molecule. The best MLR model has a training error of 0.71 log RA units (r 2 = 0.81) and a prediction error of 0.48 log RA units (r 2 = 0.88).

Calculating atomic charges in molecules and crystals by a new electronegativity equalization method

The new method of the electronegativity equalization of atoms in molecules and crystals based on Mulliken’ scale is proposed. Calculating the atomic charges by this method gives results which are in accordance with the chemical intuition and empirical estimations.

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.

The Hirshfeld-I method: atoms in molecules and chemical bonding perspective

The Hirshfeld method for the atom in the molecule (AIM) was born from crystallography and relies on the use of a so-called promolecule [1]. The promolecule is composed of all atoms in their respective locations in the molecule and a promolecular density is obtained as the sum of all isolated atomic densities. At every point in space, the share of an (isolated) atom in the promolecular density can be easily computed via their ratio and the key element of the Hirshfeld method is that this ratio is then used to extract an AIM density from the molecular electron density . That is: Unfortunately, the results of Hirshfeld analysis depend heavily on the isolated atom states used to compute the AIM weight functions. In the improved Hirshfeld-I method, the Hirshfeld process is repeated until self consistency is reached. In other words: the charge on the AIM and the isolated atom are the same. In this presentation the information theoretic context of Hirshfeld-I is sketched, performance of the method compared to regular Hirshfeld analysis discussed, its impact on the nature of atom condensed Fukui functions described, and its use for good quality monopole approximation electrostatic potentials is shown [2-6]. Electron delocalization indices, as obtained using the Hirshfeld-I method, are described [7] and the excellent Hirshfeld-I AIM charge performance in electronegativity equalization methods discussed [9]. Finally, based on Hirshfeld-I derived density matrices [10], an AIM is formulated in momentum space. [1] F.L. Hirshfeld, Theor. Chim. Acta, 1977, 44, 129. [2] P. Bultinck, C. Van Alsenoy, P.W. Ayers, and R. J. Carbo-Dorca, J. Chem. Phys., 2007, 126, 144111. [3] P. Bultinck, P. Faraday Discussions, 2007, 135, 244. [4] P. Bultinck, P.W. Ayers, S. Fias, K. Tiels, C. Van Alsenoy, Chem. Phys. Lett., 2007, 444, 205. [5] P. Bultinck, P., S. Fias, C. Van Alsenoy, P.W. Ayers, and R. Carbo-Dorca, J. Chem. Phys., 2007, 127, 034102. [6] S. Van Damme, P. Bultinck, and S. Fias, J. Chem. Theory and Comput., 2009, 5, 334. [7] Heyndrickx, W.; Matito, E.; Salvador, P.; Sola, M.; Bultinck, P. J. Comput. Chem., 2011, 32, 386. [9] Verstraelen, T.; Bultinck, P.; Van Speybroeck, V.; Ayers, P.W.; Van Neck, D.; Waroquier, M. J. Chem. Theor. Comput. In press, 2011. [10] Vanfleteren, D.; Van Neck, D.; Bultinck, P.; Ayers, P.W.; Waroquier, M. J. Chem. Phys., 2010, 132, 164111.

水合锰(Ⅱ)结构的量子化学和ABEEM/MM研究

For the next-generation polarizable force field, atom-bond electronegativity equalization fluctuating charge force field (ABEEM/MM), and quantum chemistry method, an accurate Mn2+-H2O potential function was constructed, and its parameters were determined via fitting to quantum chemistry results. Then the potential function was employed to calculate the structure and binding energies of the hydrated manganous ionic clusters Mn2+(H2O) n ( n =1-12). The results were in good agreement with those from quantum chemistry. Furthermore, the structural properties of the Mn2+ aqueous solution were simulated using ABEEM/MM molecular dynamics. This includes the radial distribution function (RDF), angular distribution function (ADF), water structure, and charge distribution. The first and second peaks of Mn2+-O RDF are located at 0.218 nm and 0.435 nm. The coordination numbers for the first and second hydration shells, which were integrated from the RDF, are 7.03 and 17.74. The first and second peaks of the O-Mn2+-O ADF are located at 80° and 140°. These results are consistent with those from experimental measurements and other theoretical simulations. The water molecules in the first hydration shell were polarized by the Mn2+ ions, and their bond lengths were stretched, but their bond angles were reduced. Mn2+ does not measurably affect the structures of the water molecules outside the first hydration shell. Our analysis of the charge distributions showed that, compared with ABEEM-7P liquid water, the charges of the H atom and lone pairs vary more in the Mn2+ aqueous solution. Moreover, there was evident charge transfer between the Mn2+ ions and their adjacent water molecules.

Calculating solvation energies by means of a fluctuating charge model combined with continuum solvent model

Continuum solvent models have shown to be very efficient for calculating solvation energy of biomolecules in solution. However, in order to produce accurate results, besides atomic radii or volumes, an appropriate set of partial charges of the molecule is needed. Here, a set of partial charges produced by a fluctuating charge model-the atom-bond electronegativity equalization method model (ABEEMσπ) fused into molecular mechanics is used to fit for the analytical continuum electrostatics model of generalized-Born calculations. Because the partial atomic charges provided by the ABEEMσπ model can well reflect the polarization effect of the solute induced by the continuum solvent in solution, accurate and rapid calculations of the solvation energies have been performed for series of compounds involving 105 small neutral molecules, twenty kinds of dipeptides and several protein fragments. The solvation energies of small neutral molecules computed with the combination of the GB model with the fluctuating charge protocol (ABEEMσπ∕GB) show remarkable agreement with the experimental results, with a correlation coefficient of 0.97, a slope of 0.95, and a bias of 0.34 kcal∕mol. Furthermore, for twenty kinds of dipeptides and several protein fragments, the results obtained from the analytical ABEEMσπ∕GB model calculations correlate well with those from ab initio and Poisson-Boltzmann calculations. The remarkable agreement between the solvation energies computed with the ABEEMσπ∕GB model and PB model provides strong motivation for the use of ABEEMσπ∕GB solvent model in the simulation of biochemical systems.

The Significance of Parameters in Charge Equilibration Models.

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

Whether there is a hardness equalization principle analogous to the electronegativity equalization principle—A quest

AbstractIn this report, we have attempted to explore whether the hardness equalization principle can be conceived analogous to the well‐established electronegativity equalization principle. We have relied upon the fact that the hardness, like the electronegativity, is a qualitative property, and there is commonality in the basic philosophy of the origin and the operational significance of these two fundamental descriptors—the electronegativity and the hardness of atoms in physics and chemistry. Starting from the empirical radial dependent formula of computing the hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that hardness equalization principle is operative and justifiably valid. For a validity test, we have applied the suggested ansatz to compute the hardness of as many as four sets of compounds with widely divergent physical and chemical nature. As hardness is not an experimentally measurable property, there is no benchmark to perform any validity test of our computed data. We have, therefore, computed the hardness data of these four different sets of the compound invoking the approximate and operational formula of Parr and Pearson, (I − A)/2, to evaluate hardness values and to compute I and A, we have invoked Koopmans' theorem and an ab initio quantum chemical method. We have observed that there is a close correlation between the four sets of hardness data computed through the semi‐empirical ansatz of this work and the quantum mechanical method. Thus, it appears that the ansatz of computing molecular hardness derived on the basis of the hardness equalization principle is efficacious in computing molecular hardness. The detailed comparative study suggests that the paradigm of the hardness equalization principle may be another law of nature like the established electronegativity equalization principle. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Electronegativity and Chemical Hardness: Different Patterns in Quantum Chemistry

Five levels for emphasizing the electronegativity and chemical hardness quantum chemical differences were reviewed: the analysis of their quantum definitions in Fock space, their reliability in providing atomic patterns of periodicity within density functional softness as well as the semiclassical quantum propagator/Green function based theories as compared to the traditional finite difference methods based on ionization potential and electronic affinity, in providing viable relationships with other aromaticity energetic, magnetic, topologic and geometric criteria, and exposing their sensitivity to the media or solvent effects. The revealed differences reflect the special role electronegativity and chemical hardness play in modeling chemical reactivity and chemical bonding by associating fundamental principles along with the conceptual and computational quantum methods in approximating, implementing, and combining the energy and density quantities and related properties of a multi-electronic multi-nuclei system; still, based on revealed quantum differences, the associate hierarchy of principles in chemical bonding is established and the idea of chemical orthogonal space having electronegativity and chemical hardness as main vectors is advanced. Keywords: Fock space, chemical reactivity principles, density functional theory, path integral semiclassical theory, atomic scales, aromaticity, quantitative structure aromaticity relationships (QSArR), solvent effects, Quantum Chemistry, chemical orthogonal space, Coulombic interacting systems, electronegativity equalization, DFT approach, AIM configuration, MOL configuration

A new algorithm for the evaluation of the global hardness of polyatomic molecules

Relying upon the commonality of the basic philosophy of the origin and development of electronegativity and hardness, we have attempted to explore whether a hardness equalization principle can be conceived for polyatomic molecules analogous to the electronegativity equalization principle. Starting from the new radial-dependent electrostatic definition of hardness of atoms suggested by the present authors and assuming that the hardness equalization principle is operative and valid, we have derived a formula for evaluating the hardness of polyatomic molecule, , where n is the number of ligands, ri is the atomic radius of the ith atom and C is a constant. The formula has been used to calculate the hardness values of 380 polyatomic molecules with widely divergent physico-chemical properties. The computed hardness data of a set of representative molecules are in good agreement with the corresponding hardness data evaluated quantum mechanically. The hardness data of the present work are found to be quite efficacious in explaining the known reaction surfaces of some well-known hard–soft acid–base exchange reactions in the real world. However, the hardness data evaluated through the ansatz and operational and approximate formula of Parr and Pearson poorly correlate the same reaction surface. This study reveals that the new definition of hardness and the assumed model of hardness equalization are scientifically acceptable valid propositions.

A new algorithm for the evaluation of equilibrium inter nuclear bond distance of heteronuclear diatomic molecules based on the hardness equalization principle

In this report, we have derived a formula for evaluating the equilibrium inter nuclear bond distances of heteronuclear diatomics relying upon the concept of hardness equalization principle. We have relied upon the fact that the hardness, like the electronegativity, is a qualitative property and since there is much commonality in the basic philosophy of the origin and the operational significance of these two fundamental descriptors – the electronegativity and the hardness, there should be a physical process of hardness equalization similar to the electronegativity equalization. Starting from the radial dependent formula of computing hardness of atoms suggested by us and relying upon the hypothesis of hardness equalization principle, we have derived an algorithm for computing the equilibrium inter nuclear bond distance of hetero nuclear diatomics as RAB(A) ≈C(14.4/\(\eta_{\rm AB}\)), where \(\eta_{\rm AB}\)(eV) is the molecular hardness, C is the constant depends on the fundamental nature of hardness e.g. the bond type, steric factor etc. The optimized value of C is 0.95. We have invoked the algorithm stated above to compute the equilibrium inter nuclear bond lengths of as many as four different sets of compounds with widely divergent chemico-physical properties. In order to explore the efficaciousness of the formula derived in the present work, we have performed a validity test by comparing the theoretically evaluated bond distances vis-a-vis their corresponding spectroscopic counterparts. The comparative study reveals the surprising results that in majority of cases, the theoretical bond distances just superimpose upon the experimental bond distances. Thus, it is transparent that the hardness equalization principle is justifiably a physical process during the formation of molecule.

An estimation method of binding free energy in terms of ABEEMσπ/MM and continuum electrostatics fused into LIE method

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. The linear interaction energy method is combined with atom-bond electronegativity equalization method at σπ level Force field (fused into molecular mechanics) and generalized Born continuum model calculation of electrostatic solvation for the estimation of the absolute free energy of binding. The parameters of this method are calibrated by using a training set of 24 HIV-1 protease-inhibitor complexes (PDB entry 1AAQ). A correlation coefficient of 0.93 was obtained with a root mean square deviation of 0.70 kcal mol(-1) . This approach is further tested on seven inhibitor and protease complexes, and it provides small root mean square deviation between the calculated binding free energy and experimental binding free energy without reparametrization. By comparing the radii of gyration and the hydrogen bond distances between ligand and protein of three training model molecules, the consistent comparison result of binding free energy is obtained. It proves that this method of calculating the binding free energy with appropriate structural analysis can be applied to quickly assess new inhibitors of HIV-1 proteases. To test whether the parameters of this method can apply to other drug targets, we have validated this method for the drug target cyclooxygenase-2.

Molecular Dynamics Simulations of a β‐Hairpin Fragment of Protein G by Means of Atom‐Bond Electronegativity Equalization Method Fused into Molecular Mechanics (ABEEMδπ/MM)

AbstractThere are some controversial opinions about the origin of folding β‐hairpin stability in aqueous solution. In this study, the structural and dynamic behavior of a 16‐residue β‐hairpin from B1 domain of protein G has been investigated at 280, 300, 350 and 450 K using molecular dynamics (MD) simulations by means of Atom‐Bond Electronegativity Equalization Method Fused into Molecular Mechanics i.e., ABEEMδπ/MM and the explicit ABEEM‐7P water solvent model. In addition, a 300 K simulation of one mutant having the aromatic residues substituted with alanines has been performed. The hydrophobic surface area, hydrophilic surface area and some structural properties have been used to measure the role of the hydrophobic interactions. It is found that the aromatic residues substituted with alanines have shown an evident destabilization of the structure and unfolding started after 1.5 ns. It is also found that the number of the main chain hydrogen bonds have different distributions through three different simulations. All above demonstrate that the hydrophobic interactions and the main chain hydrogen bonds play an important role in the stability of the folding structure of β‐hairpin in solution. Furthermore, through the structural analyses of the β‐hairpin structures from four temperature simulations and the comparison with other MD simulations of β‐hairpin peptides, the new ABEEMδπ force field can reproduce the structural data in good agreement with the experimental data.