Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.     

Insight into Markovnikov regioselectivity rule via molecular face and ABEEM‐σπ theory

Electrophilic additions of HCl to a series of asymmetric alkenes in the gas phase are investigated by the Molecular Face (MF) theory and ABEEM‐σπ model. The interesting features of regioselectivity for these reactions are characterized by the electron density (ED) encoded on the MF of alkenes and charge distribution of alkenes obtained via the ABEEM‐σπ model, respectively. It is then demonstrated that for a series of alkenes, the Hammett constant σ_p (substituent constant) has a good linear correlation with K_ED, where K_ED is character of the ED at the π region in the initial state of alkenes. Comparison between investigations using MF, ABEEM‐σπ, molecular electrostatic potential, and DFT theories, in essence, give similar conclusions for explaining the regioselectivity of the electrophilic additions to alkenes, although from different points of view. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model

Uracil–(H₂O)_n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.     

Valence state parameters of all transition metal atoms in metalloproteins—development of ABEEMσπ fluctuating charge force field

To promote accuracy of the atom‐bond electronegativity equalization method (ABEEMσπ) fluctuating charge polarizable force fields, and extend it to include all transition metal atoms, a new parameter, the reference charge is set up in the expression of the total energy potential function. We select over 700 model molecules most of which model metalloprotein molecules that come from Protein Data Bank. We set reference charges for different apparent valence states of transition metals and calibrate the parameters of reference charges, valence state electronegativities, and valence state hardnesses for ABEEMσπ through linear regression and least square method. These parameters can be used to calculate charge distributions of metalloproteins containing transition metal atoms (Sc‐Zn, Y‐Cd, and Lu‐Hg). Compared the results of ABEEMσπ charge distributions with those obtained by ab initio method, the quite good linear correlations of the two kinds of charge distributions are shown. The reason why the STO‐3G basis set in Mulliken population analysis for the parameter calibration is specially explained in detail. Furthermore, ABEEMσπ method can also quickly and quite accurately calculate dipole moments of molecules. Molecular dynamics optimizations of five metalloproteins as the examples show that their structures obtained by ABEEMσπ fluctuating charge polarizable force field are very close to the structures optimized by the ab initio MP2/6–311G method. This means that the ABEEMσπ/MM can now be applied to molecular dynamics simulations of systems that contain metalloproteins with good accuracy. © 2014 Wiley Periodicals, Inc.     

σ–π Continuum in Indole–Palladium(II) Complexes

The intrinsic features of (hetero‐arene)–metal interactions have been elusive mainly because the systematic structure analysis of non‐anchored hetero‐arene–metal complexes has been hampered by their labile nature. We report successful isolation and systematic structure analysis of a series of non‐anchored indole–palladium(II) complexes. It was revealed that there is a σ–π continuum for the indole–metal interaction, while it has been thought that the dominant coordination mode of indole to a metal center is the Wheland‐intermediate‐type σ‐mode in light of the seemingly strong electron‐donating ability of indole. Several factors which affect the σ‐ or π‐character of indole–metal interactions are discussed.     

Ab initio study of the π–π interactions between CO2 and benzene,pyridine, and pyrrole

The π–π interactions between CO₂ and three aromatic molecules, namely benzene (C₆H₆), pyridine (C₅H₅N), and pyrrole (C₄H₅N), which represent common functional groups in metal‐organic/zeoliticimidazolate framework materials, were characterized using high‐level ab initio methods. The coupled‐cluster with single and double excitations and perturbative treatment of triple excitations (CCSD(T)) method with a complete basis set (CBS) was used to calibrate Hartree–Fock, density functional theory, and second‐order M?ller–Plesset (MP2) with resolution of the identity approximation calculations. Results at the MP2/def2‐QZVPP level showed the smallest deviations (only about 1 kJ/mol) compared with those at the CCSD(T)/CBS level of theory. The strength of π–π binding energies (BEs) followed the order C₄H₅N > C₆H₆ ～ C₅H₅N and was roughly correlated with the aromaticity and the charge transfer between CO₂ and aromatic molecule in clusters. Compared with hydrogen‐bond or electron donor–acceptor interactions observed during BE calculations at the MP2/def2‐QZVPP level of theory, π–π interactions significantly contribute to the total interactions between CO₂ and aromatic molecules. © 2013 Wiley Periodicals, Inc.     

Phenylcarbamoylated β‐CD: π‐Acidic and π‐basic chiral selectors for HPLC

Two types of chiral stationary phases for HPLC based on π‐acidic or π‐basic perphenylcarbamoylated β‐CDs were synthesized. The relative structural features of the two effective chiral selectors are discussed and compared in both normal‐phase and RP modes. In addition, the nature and concentration of alcoholic modifiers were varied for optimal separation in normal phase and the structural variation of the analytes was also examined. The results showed that hydrogen bonding, steric effect and π‐acidic–π‐basic interaction contributed greatly to enantioseparation. Upon comparison, some of the differences in the separation behavior of the two types of chiral stationary phases might be due to the π‐acidic or π‐basic phenylcarbamate groups.     

The Bright Future of Unconventional σ/π‐Hole Interactions

Non‐covalent interactions play a crucial role in (supramolecular) chemistry and much of biology. Supramolecular forces can indeed determine the structure and function of a host–guest system. Many sensors, for example, rely on reversible bonding with the analyte. Natural machineries also often have a significant non‐covalent component (e.g. protein folding, recognition) and rational interference in such ‘living’ devices can have pharmacological implications. For the rational design/tweaking of supramolecular systems it is helpful to know what supramolecular synthons are available and to understand the forces that make these synthons stick to one another. In this review we focus on σ‐hole and π‐hole interactions. A σ‐ or π‐hole can be seen as positive electrostatic potential on unpopulated σ* or π⁽*⁾ orbitals, which are thus capable of interacting with some electron dense region. A σ‐hole is typically located along the vector of a covalent bond such as X?H or X?Hlg (X=any atom, Hlg=halogen), which are respectively known as hydrogen and halogen bond donors. Only recently it has become clear that σ‐holes can also be found along a covalent bond with chalcogen (X?Ch), pnictogen (X?Pn) and tetrel (X?Tr) atoms. Interactions with these synthons are named chalcogen, pnigtogen and tetrel interactions. A π‐hole is typically located perpendicular to the molecular framework of diatomic π‐systems such as carbonyls, or conjugated π‐systems such as hexafluorobenzene. Anion–π and lone‐pair–π interactions are examples of named π‐hole interactions between conjugated π‐systems and anions or lone‐pair electrons respectively. While the above nomenclature indicates the distinct chemical identity of the supramolecular synthon acting as Lewis acid, it is worth stressing that the underlying physics is very similar. This implies that interactions that are now not so well‐established might turn out to be equally useful as conventional hydrogen and halogen bonds. In summary, we describe the physical nature of σ‐ and π‐hole interactions, present a selection of inquiries that utilise σ‐ and π‐holes, and give an overview of analyses of structural databases (CSD/PDB) that demonstrate how prevalent these interactions already are in solid‐state structures.     

Facile Fabrication of Solid‐state Electrochemiluminescence Sensor via Non‐covalent π‐π Stacking and Covalent Bonding on Graphite Electrode

Herein, a facile and efficient method was developed for fabrication of solid‐state electrochemiluminescence (ECL) sensor via non‐covalent π‐π stacking and covalent bonding on the graphite electrode (GE) surface. The electrode was firstly modified with 1‐aminopyrene via π‐π stacking between GE surface and the pyrene moiety. Thereafter a stable and efficient solid‐state ECL sensor was fabricated by covalent immobilization of ruthenium(II) onto the GE surface via amidation reaction between the 1‐aminopyrene and bis(2,2′‐bipyridyl)(4‐methyl‐4′‐carboxypropyl‐2,2′‐bipyridyl) ruthenium(II) bishexafluorophosphate. The sensor has been investigated using tripropylamine and tetracycline as representative analytes, and low detection limits of 0.7 nM and 3.5 nM (S/N=3) were reached, respectively.     

Structure determination of three furan‐substituted benzimidazoles and calculation of π–π and C—H...π interaction energies

The synthesis and structural characterization of 2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazole [C₁₆H₁₂N₂O₂, (I)], 2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazol‐3‐ium chloride monohydrate [C₁₆H₁₃N₂O₂⁺·Cl⁻·H₂O, (II)] and the hydrobromide salt 5,6‐dimethyl‐2‐(furan‐2‐yl)‐1‐(furan‐2‐ylmethyl)‐1H‐benzimidazol‐3‐ium bromide [C₁₈H₁₇N₂O₂⁺·Br⁻, (III)] are described. Benzimidazole (I) displays two sets of aromatic interactions, each of which involves pairs of molecules in a head‐to‐tail arrangement. The first, denoted set (Ia), exhibits both intermolecular C—H...π interactions between the 2‐(furan‐2‐yl) (abbreviated as Fn) and 1‐(furan‐2‐ylmethyl) (abbreviated as MeFn) substituents, and π–π interactions involving the Fn substituents between inversion‐center‐related molecules. The second, denoted set (Ib), involves π–π interactions involving both the benzene ring (Bz) and the imidazole ring (Im) of benzimidazole. Hydrated salt (II) exhibits N—H...OH₂...Cl hydrogen bonding that results in chains of molecules parallel to the a axis. There is also a head‐to‐head aromatic stacking of the protonated benzimidazole cations in which the Bz and Im rings of one molecule interact with the Im and Fn rings of adjacent molecules in the chain. Salt (III) displays N—H...Br hydrogen bonding and π–π interactions involving inversion‐center‐related benzimidazole rings in a head‐to‐tail arrangement. In all of the π–π interactions observed, the interacting moieties are shifted with respect to each other along the major molecular axis. Basis set superposition energy‐corrected (counterpoise method) interaction energies were calculated for each interaction [DFT, M06‐2X/6‐31+G(d)] employing atomic coordinates obtained in the crystallographic analyses for heavy atoms and optimized H‐atom coordinates. The calculated interaction energies are −43.0, −39.8, −48.5, and −55.0 kJ mol⁻¹ for (Ia), (Ib), (II), and (III), respectively. For (Ia), the analysis was used to partition the interaction energies into the C—H...π and π–π components, which are 9.4 and 24.1 kJ mol⁻¹, respectively. Energy‐minimized structures were used to determine the optimal interplanar spacing, the slip distance along the major molecular axis, and the slip distance along the minor molecular axis for 2‐(furan‐2‐yl)‐1H‐benzimidazole.     

Comparative studies on group III σ‐hole and π‐hole interactions

The σ‐hole of M₂H₆ (M = Al, Ga, In) and π‐hole of MH₃ (M = Al, Ga, In) were discovered and analyzed, the bimolecular complexes M₂H₆···NH₃ and MH₃···N₂P₂F₄ (M = Al, Ga, In) were constructed to carry out comparative studies on the group III σ‐hole interactions and π‐hole interactions. The two types of interactions are all partial‐covalent interactions; the π‐hole interactions are stronger than σ‐hole interactions. The electrostatic energy is the largest contribution for forming the σ‐hole and π‐hole interaction, the polarization energy is also an important factor to form the M···N interaction. The electrostatic energy contributions to the interaction energy of the σ‐hole interactions are somewhat greater than those of the π‐hole interactions. However, the polarization contributions for the π‐hole interactions are somewhat greater than those for the σ‐hole interactions. © 2016 Wiley Periodicals, Inc.     

Photophysical properties of σ–π‐conjugated alternating oligothienylene–oligosilylene polymers

UV‐visible absorption and fluorescence properties of three series of σ–π‐conjugated polymers (copolymers of alternative oligothienylene and oligosilylene units) have been studied in dioxane solution. The energies of the absorption maximum, fluorescence maximum, and the 0–0 transition are found to be linearly dependent on the reciprocal of the number of thiophene rings in the repeating unit of the polymer chain, but almost independent of the silicon atom number. The σ–π‐conjugation in the polymers results in red shift in the absorption and fluorescence maxima, higher fluorescence quantum yields, and longer fluorescence lifetimes of the polymers, with respect to their corresponding analogous α‐oligothiophenes. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1873–1880, 1999     

Study on the Cation-π Interactions between Ammonium Ion and Aromatic π Systems

The nature and strength of the cation-π interactions between NH4^＋ and toluene, p-cresol, or Me-indole were studied in terms of the topological properties of molecular charge density and binding energy decomposition. The results display that the diversity in the distribution pattern of bond and cage critical points reflects the profound influence of the number and nature of substituent on the electron density of the aromatic rings. On the other hand, the energy decomposition shows that dispersion and repulsive exchange forces play an important role in the organic cation （NH4^＋）-π interaction, although the electrostatic and induction forces dominate the interaction. In addition, it is intriguing that there is an excellent correlation between the electrostatic energy and ellipticity at the bond critical point of the aromatic π systems, which would be helpful to further understand the electrostatic interaction in the cation-π complexes.     

Cooperation of σ–π and σ*–π* Conjugation in the UV/Vis and Fluorescence Spectra of 9,10-Disilylanthracene

In 1996, we reported that silyl groups of 9,10-disilylanthracenes significantly affect the UV/Vis and fluorescence spectra. Although the results indicate that the silyl groups have strong electronic effects on anthracene, the details of the mechanisms responsible for this have not yet been clarified. This article describes the analysis of the UV/Vis and fluorescence spectra of 9,10-bis(diisopropylsilyl)anthracene by theoretical calculations. This study reveals that π conjugation of anthracene is extended by cooperation of σ–π and σ*–π* conjugation between the silyl groups and anthracene. This effect increases the transition moment of the π–π* transition of anthracene. As a result, the molecular extinction coefficient of the ¹L_a band and the fluorescence quantum yield are increased.     

Preparation of σ- and π-Benzyl Type Derivatives of Molybdenum

The reaction of -LiM₀(CO)₂Cp with α-chloromethylnaphthalene gives a yellow, crystalline σ-benzyl type derivative of molybdenum (1). Irridation of (1) in n-hexane gives a red π-benzyl type derivative (2). Both complexes (1) and (2) are stable in air.     

Insight into the π‐hole···π‐electrons tetrel bonds between F2ZO (Z = C,Si, Ge) and unsaturated hydrocarbons

The intermolecular π‐hole···π‐electrons interactions between F₂ZO (Z = C, Si, Ge) molecules and unsaturated hydrocarbons including acetylene, ethylene, 1,3‐butadiene and benzene were constructed to reveal the differences of tetrel bonds forming by carbon and heavier tetrel atoms. The ab initio computation in association with topological analysis of electron density, natural bond orbital, and energy decomposition analysis demonstrate that the strength of Si···π and Ge···π tetrel bonds is much stronger than that of C···π tetrel bonds. The Si···π and Ge···π tetrel bonds exhibit covalent or partially covalent interaction nature, while the weak C···π tetrel bonds display the hallmarks of noncovalent interaction, the electrostatic interaction is the primary influencing factor. The Si···π and Ge···π interactions are determined by both the σ‐ and π‐electron densities, while the C···π interactions are dominated mainly by the π‐electron densities. The π‐hole···π‐electrons tetrel bonds are dominated by electrostatic interaction, and polarization has a comparable contribution in the Si···π and Ge···π tetrel bonds.