The configurational dependence of binding free energies: A Poisson–Boltzmann study of Neuraminidase inhibitors

The linear finite difference Poisson-Boltzmann (FDPB) equation is applied to the calculation of the electrostatic binding free energies of a group of inhibitors to the Neuraminidase enzyme. An ensemble of enzyme-inhibitor complex conformations was generated using Monte Carlo simulations and the electrostatic binding free energies of subtly different configurations of the enzyme-inhibitor complexes were calculated. It was seen that the binding free energies calculated using FDPB depend strongly on the configuration of the complex taken from the ensemble. This configurational dependence was investigated in detail in the electrostatic hydration free energies of the inhibitors. Differences in hydration energies of up to 7 kcal mol^–1 were obtained for root mean square (RMS) structural deviations of only 0.5 Å. To verify the result, the grid size and parameter dependence of the calculated hydration free energies were systematically investigated. This showed that the absolute hydration free energies calculated using the FDPB equation were very sensitive to the values of key parameters, but that the configurational dependence of the free energies was independent of the parameters chosen. Thus just as molecular mechanics energies are very sensitive to configuration, and single-structure values are not typically used to score binding free energies, single FDPB energies should be treated with the same caution.     

A computational analysis of the binding model of MDM2 with inhibitors

Abstract  

It is a new and promising strategy for anticancer drug design to block the MDM2-p53 interaction using a non-peptide small-molecule inhibitor. We carry out molecular dynamics simulations to study the binding of a set of six non-peptide small-molecule inhibitors with the MDM2. The relative binding free energies calculated using molecular mechanics Poisson–Boltzmann surface area method produce a good correlation with experimentally determined results. The study shows that the van der Waals energies are the largest component of the binding free energy for each complex, which indicates that the affinities of these inhibitors for MDM2 are dominated by shape complementarity. The A-ligands and the B-ligands are the same except for the conformation of 2,2-dimethylbutane group. The quantum mechanics and the binding free energies calculation also show the B-ligands are the more possible conformation of ligands. Detailed binding free energies between inhibitors and individual protein residues are calculated to provide insights into the inhibitor-protein binding model through interpretation of the structural and energetic results from the simulations. The study shows that G1, G2 and G3 group mimic the Phe19, Trp23 and Leu26 residues in p53 and their interactions with MDM2, but the binding model of G4 group differs from the original design strategy to mimic Leu22 residue in p53.     

硝酸甲酯分子间相互作用的DFT和ab initio比较

用密度泛函理论(DFT)和从头算(ab initio)方法,分别在B3LYP/6 31G和HF/6 31G水平上求得硝酸甲酯三种二聚体的全优化几何构型和电子结构,并用6 311G和6 311＋＋G基组进行总能量计算.对HF/6 31G计算结果进行MP4SDTQ电子相关校正.在各基组下均进行基组叠加误差(BSSE)和零点能(ZPE)校正求得结合能.对6 31G优化构型作振动分析并基于统计热力学求得200～600 K温度下单体和二聚体的热力学性质.详细比较两种方法的相应计算结果,发现DFT求得的分子间距离较短,分子内键长较长,所得结合能均小于相应ab initio计算值.     

A Molecular Modeling for the Complexation of Cyclobis(paraquat-p-phenylene) with Substituted Benzenes and Biphenyls

The molecular recognition of cyclobis(paraquat-p-phenylene), 14+, has drawn great attention recently, due to its important applications in the design and synthesis of electrochemically and chemically switchable rotaxanes, photoactive rotaxanes, and other molecular devices1. Usually, this type of molecular recognition was investigated with the methods including X-ray, NMR, UV, and IR. However, since these methods usually have difficulties in providing a detailed understanding of the energeti…     

1S core-level shifts of Al and Ar atoms in aluminum clusters

Theoretical 1s core-electron binding energies are presented for Al and Ar atoms in free space and in AlAl₁₂, AlAl₁₂Al₆, and ArAl₁₂ clusters. The binding energies have been calculated by the self-consistent field Xα scattered-wave (SCF Xα SW ) method using various exchange parameters and different atomic-sphere overlaps. The atom/cluster binding-energy shifts have been obtained both from the Slater's transition-state energies and from the total-energy differences; these values are in better agreement with each other if calculated with proper overlapping than if with nonoverlapping spheres. A comparison with available experimental and theoretical data is given as well.     

Binding energies of the silver ion to alcohols and amides: a theoretical and experimental study

The silver ion binding energies to alcohols (methanol, ethanol, n-propanol, i-propanol, and n-butanol) and to amides (acetamide, N-methylacetamide, N, N-dimethylacetamide, formamide, N-methylformamide, and N, N-dimethylformamide) have been calculated using density functional theory (DFT) and measured using the threshold collision-induced dissociation (TCID) method. For DFT, the combined basis sets of ECP28MWB for silver and 6-311++G(2df,2pd) for the other atoms were found to be optimal using a series of test calculations on Ag (+) binding to methanol and to formamide. In addition, the Ag (+) binding energies of all ligands were evaluated with nine functionals after full geometric optimizations. TCID binding energies were measured using a triple quadrupole mass spectrometer. Reasonable to good agreements were obtained between the calculated and experimental silver(I) binding energies. Ligation of Ag (+) to the alcohols was primarily via the oxygen, although n-propanol and n-butanol exhibited additional, bidentate coordination via the CH hydrogens. By contrast, silver(I) binding to the amides was all monodentate via the carbonyl oxygen. There appears to be strong correlations between the binding energies and the polarizabilities of the ligands.     

Many-body interaction in glycine-(water)3 complex using density functional theory method

Various configurations were investigated to find the most stable structures of glycine-(water)3 complex. Five different optimized conformers of glycine-(water)3 complex are obtained from density functional theory calculations using 6-311++G* basis set. Relaxation energy and many body interaction energies (two, three, and four body) are also calculated for these conformers. Out of the five conformers, the most stable conformer has the BSSE corrected total energy -513.917 967 7 Hartree and binding energy -27.28 Kcal/mol. It has been found that the relaxation energies, two body energies and three body energies have significant contribution to the total binding energy whereas four body energies are very small. The chemical hardness and chemical potential also confirmed the stability of the conformer having lowest total energy.     

Binding energies of germanium clusters, Gen (n = 2−5)

Gaussian-2 (G2) theory for third-row non-transition elements is used to calculate energies of germanium clusters, Ge_n (n = 2−5). The G2 energies are used to derive accurate binding energies for the clusters. The results for Ge₂ and Ge₃ are in agreement with experiment while there is some disagreement for Ge₄ and Ge₅. The binding energies are also calculated using the B3LYP density functional method with the 6–311 + G(3df,2p) basis set and compared with the G2 results and experiment.     

EGFR和4-苯胺喹唑啉类抑制剂之间相互作用模式的研究

采用分子动力学和MM/PBSA相结合的方法预测了表皮生长因子受体和4-苯胺喹 啉类抑制剂的相互作用模式。在分子动力学采样的基础上,采用MM/PBSA的方法分 别预测了四种可能结合模式下表皮生长因子受体和4-苯胺喹唑啉类抑制剂间的结合 自由能。在MM/PBSA计算中,受体和抑制剂之间的非键相互作用能采用分子力学 (MM)的方法得到;溶剂效应中极性部分对自由能的贡献通过解Possion- Boltzmanne (PB)方程的方法得到;溶液效应中非极性部分对自由能的贡献则通过 分子表面积计算(SA)的方法得到。计算表明,在四种结合模式下,表皮生长因子受 体和4-苯胺喹唑啉类抑制剂之间的结合自由能有较大的差别。在最佳的相互作用模 式中,抑制剂的苯胺部分位于活性口袋的底部,能够与受体残基的非极性侧链产生 很强的范德华和疏水相互作用。抑制剂喹唑啉环上的N(1)原子能够和Met-769上的 NH形成稳定的氢键,而抑制剂上的N(3)原子则和周围的一个水分子形成氢键。同时 ,抑制剂双环上的取代基团也能和活性口袋外部的部分残基形成一定的范德华和疏 水相互作用。最佳结合模式能够很好地解释已有抑制剂结构和活性间的关系。     

Accurate prediction of protonation state as a prerequisite for reliable MM-PB(GB)SA binding free energy calculations of HIV-1 protease inhibitors

Binding free energies were calculated for the inhibitors lopinavir, ritonavir, saquinavir, indinavir, amprenavir, and nelfinavir bound to HIV-1 protease. An MMPB/SA-type analysis was applied to conformational samples from 3 ns explicit solvent molecular dynamics simulations of the enzyme-inhibitor complexes. Binding affinities and the sampled conformations of the inhibitor and enzyme were compared between different HIV-1 protease protonation states to find the most likely protonation state of the enzyme in the complex with each of the inhibitors. The resulting set of protonation states leads to good agreement between calculated and experimental binding affinities. Results from the MMPB/SA analysis are compared with an explicit/implicit hybrid scheme and with MMGB/SA methods. It is found that the inclusion of explicit water molecules may offer a slight advantage in reproducing absolute binding free energies while the use of the Generalized Born approximation significantly affects the accuracy of the calculated binding affinities.     

Can MM/GBSA calculations be sped up by system truncation?

We have studied whether calculations of the binding free energy of small ligands to a protein by the MM/GBSA approach (molecular mechanics combined with generalized Born and surface area solvation) can be sped up by including only a restricted number of atoms close to the ligand. If the protein is truncated before the molecular dynamics (MD) simulations, quite large changes are observed for the calculated binding energies, for example, 4 kJ/mol average difference for a radius of 19 Å for the binding of nine phenol derivatives to ferritin. The results are improved if no atoms are fixed in the simulations, with average and maximum errors of 2 and 3 kJ/mol at 19 Å and 3 and 6 kJ/mol at 7 Å. Similar results are obtained for two additional proteins, p38α MAP kinase and factor Xa. On the other hand, if energies are calculated on snapshots that are truncated after the MD simulation, all residues more than 8.5 Å from the ligand can be omitted without changing the energies by more than 1 kJ/mol on average (maximum error 1.4 kJ/mol). At the molecular mechanics level, the gain in computer time for such an approach is small. However, it shows what size of system should be used if the energies instead are calculated with a more demanding method, for example, quantum‐mechanics. © 2017 Wiley Periodicals, Inc.     

Calculation of core-level electron spectra of ionic liquids

On the example of 40 ion pairs (5 cations times 8 anions), this study demonstrates how the core-level binding energy values can be calculated and used to plot theoretical spectra at low computational cost using density functional theory methods. Three approaches for obtaining the binding energy values are based on delta Kohn–Sham (ΔKS) calculations, 1s KS orbital energies, and atomic charges. The ΔKS results show reasonable agreement with the available experimental X-ray photoelectron data. The 1s KS orbital energies correlate well with the ΔKS results. Atomic charge correlation with ΔKS is improved by accounting for the charges of neighboring atoms. Assignment of binding energies to atoms and the applicability of the mentioned methods to model systems of ionic liquids are discussed.     

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.     

Quantum chemistry benchmarking of binding and selectivity for lanthanide extractants

Computer‐aided screening methods facilitate the discovery of new extractants for heavy and rare‐earth metal separations. In this work, we have benchmarked the accuracy of different quantum chemistry methods for calculating extractant binding energies and selectivities. Specifically, we compare calculated data from different exchange correlation functionals (B3LYP‐D3, ωB97X‐D3, and M06‐L) and different basis sets (including large‐core effective core potentials and all‐electron basis sets). We report aqueous‐phase binding energy and selectivity trends for 1:1 and 3:1 extractant/lanthanide models for the complexes. We find that binding selectivities are not particularly sensitive to model chemistry, but binding energies are sensitive. Furthermore, calculated trends in selectivity using 3:1 extractant/lanthanide models are in better agreement with available experimental trends than trends using 1:1 extractant/lanthanide models. Lastly, we find that the B3LYP‐D3/6‐31 + G* model chemistry with the Stuttgart large‐core relativistic effective core potentials on the lanthanide sufficiently reproduces results from larger basis set calculations and is confirmed as suitable for relatively fast and efficient screening of lanthanide binding energies and selectivities.     

An ab initio benchmark study of hydrogen bonded formamide dimers

The five singly and doubly hydrogen bonded dimers of formamide are calculated at the correlated level by using resolution of identity M?ller-Plesset second-order perturbation theory (RIMP2) and the coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] method. All structures are optimized with the Dunning aug-cc-pVTZ and aug-cc-pVQZ basis sets. The binding energies are extrapolated to the complete basis set (CBS) limit by using the aug-cc-pVXZ (X = D, T, Q) basis set series. The effect of extending the basis set to aug-cc-pV5Z on the geometries and binding energies is studied for the centrosymmetric doubly N-H...O bonded dimer FA1 and the doubly C-H...O bonded dimer FA5. The MP2 CBS limits range from -5.19 kcal/mol for FA5 to -14.80 kcal/mol for the FA1 dimer. The DeltaCCSD(T) corrections to the MP2 CBS limit binding energies calculated with the 6-31+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are mutually consistent to within < or =0.03 kcal/mol. The DeltaCCSD(T) correction increases the binding energy of the C-H...O bonded FA5 dimer by 0.4 kcal/mol or approximately 9% over the distance range +/-0.5 Angstrom relative to the potential minimum. This implies that the ubiquitous long-range C-H...O interactions in proteins are stronger than hitherto calculated.     

Substituent effects on axle binding in amide pseudorotaxanes: comparison of NMR titration and ITC data with DFT calculations

The binding behaviour of differently substituted diamide axle molecules to Hunter/V?gtle tetralactam macrocycles was studied with a combination of NMR titration, isothermal titration calorimetry (ITC) experiments and calculations employing density functional theory (DFT), along with dispersion-corrected exchange-correlation functionals. Guests with alkyl or alkenyl chains attached to the diamide carbonyl groups have a significantly higher binding affinity to the macrocycle than guests with benzoyl amides and their substituted analogues. While the binding of the benzoyl and alkenyl substituted axles is enthalpically driven, the alkyl-substituted guest binds mainly because of a positive binding entropy. The electronic effects of para-substituents at the benzoyl moieties have an influence on the binding affinities. Electron donating substituents increase, while electron-withdrawing substituents decrease the binding energies. The binding affinities obtained from both NMR titration and ITC experiments correlate well with each other. The substituent effects observed in the experimental data are reflected in adiabatic interaction energies calculated with density functional methods. The calculated structures also agree well with pseudorotaxane crystal structures.     

Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition

Equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) method has been applied to exciton states of polyethylene using ab initio crystal Hartree-Fock method with one-dimensional periodic boundary condition. Full transformation of two-electron integrals from atomic-orbital basis to crystal-orbital basis has been performed for EOM-CCSD calculations. In order to make transformed integrals to have correct properties of translational symmetry, a lattice summation scheme has been proposed. The EOM-CCSD excitation energies have been obtained for the lowest singlet and triplet exciton states of polyethylene. The excitation energies converge with system size much faster than oligomer calculations using n-alkanes. Quasiparticle energy-level calculations by second-order many-body perturbation theory and by solving the inverse Dyson equation have also been performed to obtain exciton binding energies. Basis set dependencies on excitation energy, quasiparticle band gap, and exciton binding energy have been investigated. At the 6-31+G level, the excitation energy of the lowest singlet-exciton state and its binding energy are calculated to be 8.1 and 3.2 eV, respectively. The calculated excitation energy is well comparable with the corresponding experimental value, 7.6 eV.     

Hydrogen bonding interaction in sarcosine–water complex using ab initio and DFT method

The hydrogen bonding interaction in the Sarcosine (N‐methylglycine)–water complex is studied using ab initio, MP2, and density functional theory (DFT/B3LYP). For this complex, binding energies, dipole–dipole interactions, chemical hardness, and chemical potential have been calculated. Three different basis sets, viz. 6‐311+G, 6‐311++G, and 6‐311++G*, have been used to optimize the geometries by all three methods. The basis set superposition errors are also calculated, and the corrected binding energies are reported for this complex. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

On the contribution of vibrational anharmonicity to the binding energies of water clusters

The second-order vibrational perturbation theory method has been used together with the B3LYP and MP2 electronic structure methods to investigate the effects of anharmonicity on the vibrational zero-point energy (ZPE) contributions to the binding energies of (H2O)n, n = 2-6, clusters. For the low-lying isomers of (H2O)6, the anharmonicity correction to the binding energy is calculated to range from -248 to -355 cm(-1). It is also demonstrated that although high-order electron correlation effects are important for the individual vibrational frequencies, they are relatively unimportant for the net ZPE contributions to the binding energies of water clusters.