Extension of the LAP functional to include parallel spin correlation

The kinetic energy density-dependent correlation functional LAP1 is extended to include parallel-spin correlation beyond the exchange level. Two exchange–correlation schemes are considered, combining the new correlation functional (LAP3) with the GGA exchange of Becke and the GGA exchange of Perdew. Extensive tests on molecules and hydrogen-bonded systems are presented and discussed elucidating the role of parallel–spin correlation in different cases. Its inclusion in the LAP functional leads, on average, to a slight improvement of the calculated binding energies and equilibrium geometries of molecules. Particularly high sensitivity of the energy results on the relative share of parallel-spin correlation is observed for aromatic molecules and for systems involving weak hydrogen bonds. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 427–446, 1997     

Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field

Chorismate mutase is a key model system in the development of theories of enzyme catalysis. To analyze the physical nature of catalytic interactions within the enzyme active site and to estimate the stabilization of the transition state (TS) relative to the substrate (differential transition state stabilization, DTSS), we have carried out nonempirical variation-perturbation analysis of the electrostatic, exchange, delocalization, and correlation interactions of the enzyme-bound substrate and transition-state structures derived from ab initio QM/MM modeling of Bacillus subtilis chorismate mutase. Significant TS stabilization by approximately -23 kcal/mol [MP2/6-31G(d)] relative to the bound substrate is in agreement with that of previous QM/MM modeling and contrasts with suggestions that catalysis by this enzyme arises purely from conformational selection effects. The most important contributions to DTSS come from the residues, Arg90, Arg7, Glu78, a crystallographic water molecule, Arg116, and Arg63, and are dominated by electrostatic effects. Analysis of the differential electrostatic potential of the TS and substrate allows calculation of the catalytic field, predicting the optimal location of charged groups to achieve maximal DTSS. Comparison with the active site of the enzyme from those of several species shows that the positions of charged active site residues correspond closely to the optimal catalytic field, showing that the enzyme has evolved specifically to stabilize the TS relative to the substrate.     

Binding of aminoglycoside antibiotics to the small ribosomal subunit: a continuum electrostatics investigation

The binding of paromomycin and similar antibiotics to the small (30S) ribosomal subunit has been studied using continuum electrostatics methods. Crystallographic information from a complex of paromomycin with the 30S subunit was used as a framework to develop structures of similar antibiotics in the same ribosomal binding site. Total binding energies were calculated from electrostatic properties obtained by solution of the Poisson-Boltzmann equation combined with a surface area-dependent apolar term. These computed results showed good correlation with experimental data. Additionally, calculation of the ribosomal electrostatic potential in the paromomycin binding site provided insight into the electrostatic mechanisms for aminoglycoside binding and clues for the rational design of more effective antibiotics.     

Amine-hydrogen halide complexes: experimental electric dipole moments and a theoretical decomposition of dipole moments and binding energies

The Stark effect has been observed in the rotational spectra of several gas-phase amine-hydrogen halide complexes and the following electric dipole moments have been determined: H(3)(15)N-H(35)Cl (4.05865 +/- 0.00095 D), (CH(3))(3)(15)N-H(35)Cl (7.128 +/- 0.012 D), H(3)(15)N-H(79)Br (4.2577 +/- 0.0022 D), and (CH(3))(3)(15)N-H(79)Br (8.397 +/- 0.014 D). Calculations of the binding energies and electric dipole moments for the full set of complexes R(n)()(CH(3))(3)(-)(n)()N-HX (n = 0-3; X = F, Cl, Br) at the MP2/aug-cc-pVDZ level are also reported. The block localized wave function (BLW) energy decomposition method has been used to partition the binding energies into contributions from electrostatic, exchange, distortion, polarization, and charge-transfer terms. Similarly, the calculated dipole moments have been decomposed into distortion, polarization, and charge-transfer components. The complexes studied range from hydrogen-bonded systems to proton-transferred ion pairs, and the total interaction energies vary from 7 to 17 kcal/mol across the series. The individual energy components show a much wider variation than this, but cancellation of terms accounts for the relatively narrow range of net binding energies. For both the hydrogen-bonded complexes and the proton-transferred ion pairs, the electrostatic and exchange terms have magnitudes that increase with the degree of proton transfer but are of opposite sign, leaving most of the net stabilization to arise from polarization and charge transfer. In all of the systems studied, the polarization terms contribute the most to the induced dipole moment, followed by smaller but still significant contributions from charge transfer. A significant contribution to the induced moment of the ion pairs also arises from distortion of the HX monomer.     

Face-to-face arene-arene binding energies: dominated by dispersion but predicted by electrostatic and dispersion/polarizability substituent constants

Parallel face-to-face arene-arene complexes between benzene and substituted benzenes have been investigated at the MP2(full)/6-311G** and M05-2X/6-311G** levels of theory. A reasonably good correlation was found between the binding energies and the ∑|σ(m)| values of the substituted aromatics. It is proposed that a substituent |σ(m)| value informs on both the aromatic substituent dispersion/polarizability and the effect the substituent has on the aromatic electrostatics. Supporting this hypothesis, a combination of electrostatic (∑σ(m)) and dispersion/polarizability (∑M(r)) substituent constant terms gives an excellent, and statistically significant, correlation with the benzene-substituted benzene binding energy. Symmetry adapted perturbation theory energy decomposition calculations show the dominant attractive force is dispersion; however, the sum of all nonelectrostatic forces is essentially a constant, while the electrostatic component varies significantly. This explains the importance of including an electrostatic term when predicting benzene-substituted benzene binding energies.     

On the nature of stabilization in weak, medium, and strong charge-transfer complexes: CCSD(T)/CBS and SAPT calculations

Weak, medium, and strong charge-transfer (CT) complexes containing various electron donors (C(2)H(4), C(2)H(2), NH(3), NMe(3), HCN, H(2)O) and acceptors (F(2), Cl(2), BH(3), SO(2)) were investigated at the CCSD(T)/complete basis set (CBS) limit. The nature of the stabilization for these CT complexes was evaluated on the basis of perturbative NBO calculations and DFT-SAPT/CBS calculations. The structure of all of the complexes was determined by the counterpoise-corrected gradient optimization performed at the MP2/cc-pVTZ level, and most of complexes possess a linear-like contact structure. The total stabilization energies lie between 1 and 55 kcal/mol and the strongest complexes contain BH(3) as an electron acceptor. When ordering the electron donors and electron acceptors on the basis of these energies, we obtain the same order as that based on the perturbative E2 charge-transfer energies, which provides evidence that the charge-transfer term is the dominant energy contribution. The CCSD(T) correction term, defined as the difference between the CCSD(T) and MP2 interaction energies, is mostly small, which allows the investigation of the CT complexes of this type at the "cheap" MP2/CBS level. In the case of weak and medium CT complexes (with stabilization energy smaller than about 15 kcal/mol), the dominant stabilization originates in the electrostatic term; the dispersion as well as induction and δ(HF) terms covering the CT energy contribution are, however, important as well. For strong CT complexes, induction energy is the second (after electrostatic) most important energy term. The role of the induction and δ(HF) terms is unique and characteristic for CT complexes. For all CT complexes, the CCSD(T)/CBS and DFT-SAPT/CBS stabilization energies are comparable, and surprisingly, it is true even for very strong CT complexes with stabilization energy close to 50 kcal/mol characteristic by substantial charge transfer (more than 0.3 e). It is thus possible to conclude that perturbative DFT-SAPT analysis is robust enough to be applied even for dative-like complexes with substantial charge transfer.     

Spectroscopic and Ab Initio Investigation of C−H⋅⋅⋅N Hydrogen‐Bonded Complexes of Fluorophenylacetylenes: Frequency Shifts and Correlations

The C?H???N hydrogen‐bonded complexes of several fluorophenyacetylenes with ammonia and methylamine were characterized by a redshift in the acetylenic C?H stretching vibration of the phenylacetylene moiety. These redshifts were linearly correlated with the stabilization energies calculated at the CCSD(T)/CBS//MP2‐aug‐cc‐pVDZ level. Analysis of various components of the interaction energy indicated that the observed redshifts were weakly correlated with the electrostatic component. The weaker linear correlation between the frequency shifts and the electrostatic component between two data sets can perhaps be attributed to the marginal differences in the Stark tuning rate and zero‐field shifts. The induction and exchange‐repulsion components were linearly correlated. However, the dispersion component depends on the nature of the hydrogen‐bond acceptor and shows a quantum jump when the hydrogen‐bond acceptor is changed from ammonia to methylamine. The observed linear correlation between the redshifts in the C?H stretching frequencies and the total stabilization energies is due to mutual cancellation of deviations from linearity between various components.     

Ab initio quantum mechanical study of the binding energies of human estrogen receptor alpha with its ligands: an application of fragment molecular orbital method

We have theoretically examined the relative binding affinities (RBA) of typical ligands, 17beta-estradiol (EST), 17alpha-estradiol (ESTA), genistein (GEN), raloxifene (RAL), 4-hydroxytamoxifen (OHT), tamoxifen (TAM), clomifene (CLO), 4-hydroxyclomifene (OHC), diethylstilbestrol (DES), bisphenol A (BISA), and bisphenol F (BISF), to the alpha-subtype of the human estrogen receptor ligand-binding domain (hERalpha LBD), by calculating their binding energies. The ab initio fragment molecular orbital (FMO) method, which we have recently proposed for the calculations of macromolecules such as proteins, was applied at the HF/STO-3G level. The receptor protein was primarily modeled by 50 amino acid residues surrounding the ligand. The number of atoms in these model complexes is about 850, including hydrogen atoms. For the complexes with EST, RAL, OHT, and DES, the binding energies were calculated again with the entire ERalphaLBD consisting of 241 residues or about 4000 atoms. No significant difference was found in the calculated binding energies between the model and the real protein complexes. This indicates that the binding between the protein and its ligands is well characterized by the model protein with the 50 residues. The calculated binding energies relative to EST were very well correlated with the experimental RBA (the correlation coefficient r=0.837) for the ligands studied in this work. We also found that the charge transfer between ER and ligands is significant on ER-ligand binding. To our knowledge, this is the first achievement of ab initio quantum mechanical calculations of large molecules such as the entire ERalphaLBD protein.     

硝酰胺二聚体静电能和交换能的理论计算

根据对称性匹配微扰理论, 并运用多个微扰和非微扰方法, 计算了硝酰胺二聚体在不同分子间距(R)时静电能和交换能. 这些具有轨道弛豫的静电能不仅含有第4级单、双、四和三重激发态项, 而且含有CCSD的第5级和更高级的能量项. 同时发现: 第4级的三重激发态能量项比第5级和更高级的能量项之和还重要. 求得的含有分子内电子相关效应的交换能达到了CCSD水平. 用于计算交换能关联校正项的单对交换近似在硝酰胺二聚体的范德华最小距离0.42 nm附近区域才较合理. 在R为0.32～1.42 nm范围, 静电能与R的关系有两种: 一是在小于等于0.47 nm时, (R^－7.64; 二是大于0.47 nm时, (R^－3.97. 交换能具有明显的短程作用特点, 其与R间的关系为指数衰减: 21.061exp(－R/0.318). 最后发现: 在硝酰胺二聚体中, 分子内的电子相关效应对和的影响很显著.     

A quantum chemistry study of binding carotenoids in the bacterial light-harvesting complexes

Carotenoids play the dual function of light harvesting and photoprotection in photosynthetic organisms. Despite their functional importance, the molecular basis for binding of carotenoids in the photosynthetic proteins is poorly understood. We have discovered that all carotenoids are surrounded either by aromatic residues or by chlorophylls in all known crystal structures of the photosynthetic pigment-protein complexes. The intermolecular pi-pi stacking interactions between carotenoids and the surrounding aromatic residues in the light-harvesting complex II (LH-II) of Rhodospirillum molischianum were analyzed by high level ab initio electronic structure calculations. Intermolecular interaction energies were calculated with the second-order M?ller-Plesset perturbation method (MP2) using the modified 6-31G*(0.25) basis set with diffuse d-polarization by Hobza and co-workers. The MP2/6-31G*(0.25) calculations yield a total stabilization energy of -15.66 kcal/mol between the carotenoid molecule and the four surrounding aromatic residues (alpha-Trp-23, beta-Phe-20, beta-Phe-24, beta-Phe-27). It is thus concluded that pi-pi stacking interactions between carotenoids and the aromatic residues play an essential role in binding carotenoids in the LH-II complex of Rhodospirillum molischianum. The physical nature of the pi-pi stacking interactions was further analyzed, and the dispersion interactions were found to be the dominant intermolecular attraction force. There is also a substantial electrostatic contribution to the overall intermolecular stabilization energy.     

Physical quantity of residue electrostatic energy in flavin mononucleotide binding protein dimer

The electrostatic (ES) energy of each residue was for the first time quantitatively evaluated in a flavin mononucleotide binding protein (FBP). A residue electrostatic energy (RES) was obtained as the sum of the ES energies between atoms in each residue and all other atoms in the FBP dimer using atomic coordinates obtained by a molecular dynamics (MD) simulation. ES is one of the most important energies among the interaction energies in a protein. It is determined from the RES, the residues which mainly contribute to stabilize the structure of each subunit, and the binding energy between two subunits can be estimated. The RES of all residues in subunit A (Sub A) and subunit B (Sub B) were attractive forces, even though the residues contain net negative or positive charges. This reveals that the ES energies of any of the residues can contribute to stabilize the protein structure. The total binding ES energy over all residues among the subunits was distributed between −0.2 to −1.2 eV (mean = −0.67 eV) from the MD simulation time.     

Enhanced Li+ binding energies of some azines: a molecular orbital study

Summary Hartree-Fock calculations with the 6–31G* basis have been performed to investigate the structure and Li⁺ binding energies of the complexes between Li⁺ and pyridine, diazines, triazines and tetrazines. Structures have been fully optimized at the 3–21G level. As for azole-Li⁺ and methyldiazole-Li⁺ complexes, a topological analysis of the Laplacian of the electronic charge density reveals that the azine-Li⁺ is a typical closed-shell interaction and that the stabilization of the complex is mainly electrostatic. BSSE is quite significant, specially for Li⁺-bridging complexes. The correlation between calculated Li⁺ binding energies and proton affinities follows two different linear relationships, one for those cases where Li⁺ is singly coordinated and a different one for those cases in which an additional three-membered ring is formed. The enhanced stability of these particular conformations explains why while polyazines are less basic than pyridine when the reference acid is a proton; pyridazine and 1,2,4 triazine are more basic than pyridine when the reference acid is Li⁺. The effect on Li⁺ binding energies of systematic nitrogen substitution roughly follows an additive model.     

Basis set and correlation effects on computed positive ion hydrogen bond energies of the complexes AHn · AHn + 1+1: AHn = NH3, OH2, and FH

Basis set expansion and correlation effects on computed hydrogen bond energies of the positive ion complexes AH_n · AH_{n + 1}⁺¹, for AH_n = NH₃, OH₂ and FH, have been evaluated. The addition of diffuse functions on nonhydrogen atoms is the single most important enhancement of split-valence plus polarization basis sets for computing hydrogen bond energies. Basis set enhancement effects appear to be additive in these systems. The correlation energy contribution to the stabilization energies of these complexes is significant, with the second order term being the largest term and having a stabilizing effect. The third order term is smaller and of opposite sign, while the fourth order term is smaller yet and stabilizing. As a result, computed MP4 stabilization energies are bracketed by the MP2 and MP3 energies. The overall effect of basis set enhancement is to decrease hydrogen bond energies, whereas the addition of electron correlation increases stabilization energies.     

Halogen bonded complexes between volatile anaesthetics (chloroform, halothane, enflurane, isoflurane) and formaldehyde: a theoretical study

The structures and intermolecular interactions in the halogen bonded complexes of anaesthetics (chloroform, halothane, enflurane and isoflurane) with formaldehyde were studied by ab initio MP2 and CCSD(T) methods. The CCSD(T)/CBS calculated binding energies of these complexes are between -2.83 and -4.21 kcal mol(-1). The largest stabilization energy has been found for the C-Br···O bonded halothane···OCH(2) complex. In all complexes the C-X bond length (where X = Cl, Br) is slightly shortened, in comparison to a free compound, and an increase of the C-X stretching frequency is observed. The electrostatic interaction was excluded as being responsible for the C-X bond contraction. It is suggested that contraction of the C-X bond length can be explained in terms of the Pauli repulsion (the exchange overlap) between the electron pairs of oxygen and halogen atoms in the investigated complexes. This is supported by the DFT-SAPT results, which indicate that the repulsive exchange energy overcompensates the electrostatic one. Moreover, the dispersion and electrostatic contributions cover about 95% of the total attraction forces, in these complexes.     

Calculations of pH-dependent binding of proteins to biological membranes

Binding of proteins to membranes is often accompanied by titration of ionizable residues and is, therefore, dependent on pH. We present a theoretical treatment and computational approach for predicting absolute, pH-dependent membrane binding free energies. The standard free energy of binding, DeltaG, is defined as -RTln(P(b)/P(f)), where P(b) and P(f) are the amounts of bound and free protein. The apparent pK(a) of binding is the pH value at which P(b) and P(f) are equal. Proteins bind to the membrane in the pH range where DeltaG is negative. The components of the binding free energy are (a) the free energy cost of ionization state changes (DeltaG(ion)), (b) the effective energy of transfer from solvent to the membrane surface, (c) the translational/rotational entropy cost of binding, and (d) an ideal entropy term that depends on the relative volume of the bound and free state and therefore depends on lipid concentration. Calculation of the first term requires determination of pK(a) values in solvent and on the membrane surface. All energies required by the method are obtained from molecular dynamics trajectories on an implicit membrane (IMM1-GC). The method is tested on pentalysine and the helical peptide VEEKS, derived from the membrane-binding domain of phosphocholine cytidylyltransferase. The agreement between the measured and the calculated free energies of binding of pentalysine is good. The extent of membrane binding of VEEKS is, however, underestimated compared to experiment. Calculations of the interaction energy between two VEEKS helices on the membrane suggest that the discrepancy is mainly due to the neglect of protein-protein interactions on the membrane surface.     

Prediction of enzyme binding: human thrombin inhibition study by quantum chemical and artificial intelligence methods based on X-ray structures

Thrombin is a serine protease which plays important roles in the human body, the key one being the control of thrombus formation. The inhibition of thrombin has become a target for new antithrombotics. The aim of our work was to (i) construct a model which would enable us to predict Ki values for the binding of an inhibitor into the active site of thrombin based on a database of known X-ray structures of inhibitor-enzyme complexes and (ii) to identify the structural and electrostatic characteristics of inhibitor molecules crucially important to their effective binding. To retain as much of the 3D structural information of the bound inhibitor as possible, we implemented the quantum mechanical/molecular mechanical (QM/MM) procedure for calculating the molecular electrostatic potential (MEP) at the van der Waals surfaces of atoms in the protein's active site. The inhibitor was treated quantum mechanically, while the rest of the complex was treated by classical means. The obtained MEP values served as inputs into the counter-propagation artificial neural network (CP-ANN), and a genetic algorithm was subsequently used to search for the combination of atoms that predominantly influences the binding. The constructed CP-ANN model yielded Ki values predictions with a correlation coefficient of 0.96, with Ki values extended over 7 orders of magnitude. Our approach also shows the relative importance of the various amino acid residues present in the active site of the enzyme for inhibitor binding. The list of residues selected by our automatic procedure is in good correlation with the current consensus regarding the importance of certain crucial residues in thrombin's active site.     

Transfer Thermodynamics of Protein in Denaturing and Stabilizing Media

Free energies of transfer (ΔG_t) of RibonucleaseA (RNaseA) from water to aqueous solutions of urea (4 M, 6 M and 8 M), a protein denaturing solvent as well as ΔG_t of RibonucleaseA, β‐Lactoglobulin, α‐Chymotripsin and ChymotrypsinogenA from water to aqueous glycerol (10%, 20%, 30% and 40%), a protein stabilizing solvent has been dissected into cavity term [ΔG_t(cav)] and interaction term [ΔG_t(int)]. The interaction free energy includes all types of interactions like hard‐soft, hydrogen bonding, electrostatic, etc. The cavity forming free energies have been calculated using the standard version of scaled particle theory (SPT) with well‐reported SPT parameters. It has been found that transfer free energies of cavity terms ΔG_t(cav) for native protein from water to urea‐water and water to aqueous glycerol follow almost opposite trends. This primarily indicates there may be some correlation between cavity creation energies and protein denaturing and stabilizing ability of a solvent. The results are in agreement with those obtained from preferential binding coefficient studies in these media.     

牛视紫红质蛋白质中视黄醛的活性位点

视紫红质蛋白是一个跨膜蛋白, 视黄醛(RET)在该蛋白中的活性结合位点涉及到视觉过程机理, 与一些眼科疾病病理有关. 基于牛视紫红质蛋白1U19的蛋白质晶体结构数据, 采用密度泛函理论的B3LYP方法计算RET-Lys296残基与视黄醛分子周围半径为0.6 nm的空间范围30个氨基酸残基相互作用和结合能. 数值显示1U19蛋白中的残基Glu113、Glu181和Glu122是质子化的RET-Lys296残基的活性结合位点, 结合能分别为-333.38、-205.67和-194.56 kJ·mol-1. 这些氨基酸残基带有一个负电荷, 与质子化的RET-Lys296残基发生强烈的离子静电相互作用. 另外几个残基Ala292、Cys187、Phe293、Pro291以及Trp265等与质子化RET-Lys296残基也有相互吸引作用. 当RET-Lys296残基非质子化, 上述相互作用消失, 促使视黄醛分子与视蛋白分离. 研究发现残基Glu113和Glu181周围各自有一个结晶水分子通过双氢键形式起着稳定作用.     

Pseudoreceptor model for ryanodine derivatives at calcium release channels

This paper describes the generation of a pseudoreceptor model for ryanodine receptor (RyR) modulating ryanoids in rabbit skeletal muscle. For this purpose, the molecular modelling software PrGen was applied to correlate experimentally determined and calculated free energies of binding for a set of 15 ryanodine derivatives. The final model indicates a narrow cleft with hydrogen bond donor and acceptor capacities (represented by an Asn) as most crucial for binding the pyrrole carboxylate substituent at C3 of ryanodine. In addition, hydrophobic residues flank the aromatic pyrrole ring (Tyr, Phe, and Ile). Two of those residues (Tyr and Ile) interact with the 2-isopropyl moiety, which seems to contribute to binding. Opposite to the pyrrole locus, a second hydrophobic region (represented by a Leu) restricts ryanodine derivatives in their longitudinal axis and leads to the discrimination of equatorial and axial positioned methyl groups and of polar substituents at C9. Finally, a charged glutamate residue generates strong hydrogen bonding and electrostatic interactions with the hydroxyl groups at C10 and C15. For this binding-site model – composed of six amino acid residues – a correlation for the training set ligands of R = 0.99 (Q² = 0.975) and a root mean square (rms) deviation of 0.568 kcal/mol for the prediction of the binding energies of four test set ligands was obtained. Based on this pseudoreceptor model the putative topology of the real binding site of ryanoids will be discussed.