Fragment‐based quantum mechanical calculation of protein–protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE‐GMFCC) method has been successfully utilized for efficient linear‐scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE‐GMFCC method for calculation of binding affinity of Endonuclease colicin–immunity protein complex. The binding free energy changes between the wild‐type and mutants of the complex calculated by EE‐GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6‐31G*‐D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein–protein binding affinities. Moreover, the self‐consistent calculation of PB solvation energy is required for accurate calculations of protein–protein binding free energies. This study demonstrates that the EE‐GMFCC method is capable of providing reliable prediction of relative binding affinities for protein–protein complexes. © 2018 Wiley Periodicals, Inc.     

Site‐directed analysis on protein hydrophobicity

Hydrophobicity of a protein is considered to be one of the major intrinsic factors dictating the protein aggregation propensity. Understanding how protein hydrophobicity is determined is, therefore, of central importance in preventing protein aggregation diseases and in the biotechnological production of human therapeutics. Traditionally, protein hydrophobicity is estimated based on hydrophobicity scales determined for individual free amino acids, assuming that those scales are unaltered when amino acids are embedded in a protein. Here, we investigate how the hydrophobicity of constituent amino acid residues depends on the protein context. To this end, we analyze the hydration free energy—free energy change on hydration quantifying the hydrophobicity—of the wild‐type and 21 mutants of amyloid‐beta protein associated with Alzheimer's disease by performing molecular dynamics simulations and integral‐equation calculations. From detailed analysis of mutation effects on the protein hydrophobicity, we elucidate how the protein global factor such as the total charge as well as underlying protein conformations influence the hydrophobicity of amino acid residues. Our results provide a unique insight into the protein hydrophobicity for rationalizing and predicting the protein aggregation propensity on mutation, and open a new avenue to design aggregation‐resistant proteins as biotherapeutics. © 2014 Wiley Periodicals, Inc.     

A scheme of numerical solution for three‐dimensional isoelectronic series of hydrogen atom using one‐dimensional basis functions

The solution of three‐dimensional Schrödinger wave equations of the hydrogen atoms and their isoelectronic ions (Z = 1 − 4) are obtained from the linear combination of one‐dimensional hydrogen wave functions. The use of one‐dimensional basis functions facilitates easy numerical integrations. An iteration technique is used to obtain accurate wave functions and energy levels. The obtained ground state energy level for the hydrogen atom converges stably to −0.498 a.u. The result shows that the novel approach is efficient for the three‐dimensional solution of the wave equation, extendable to the numerical solution of general many‐body problems, as has been demonstrated in this work with hydrogen anion.     

Modified AutoDock for accurate docking of protein kinase inhibitors

Protein kinases are an important class of enzymes controlling virtually all cellular signaling pathways. Consequently, selective inhibitors of protein kinases have attracted significant interest as potential new drugs for many diseases. Computational methods, including molecular docking, have increasingly been used in the inhibitor design process [1]. We have considered several docking packages in order to strengthen our kinase inhibitor work with computational capabilities. In our experience, AutoDock offered a reasonable combination of accuracy and speed, as opposed to methods that specialize either in fast database searches or detailed and computationally intensive calculations.However, AutoDock did not perform well in cases where extensive hydrophobic contacts were involved, such as docking of SB203580 to its target protein kinase p38. Another shortcoming was a hydrogen bonding energy function, which underestimated the attraction component and, thus, did not allow for sufficiently accurate modeling of the key hydrogen bonds in the kinase-inhibitor complexes.We have modified the parameter set used to model hydrogen bonds, which increased the accuracy of AutoDock and appeared to be generally applicable to many kinase-inhibitor pairs without customization. Binding to largely hydrophobic sites, such as the active site of p38, was significantly improved by introducing a correction factor selectively affecting only carbon and hydrogen energy grids, thus, providing an effective, although approximate, treatment of solvation.     

Hydrogen‐bonded two‐ and three‐dimensional polymeric structures in the ammonium salts of 3,5‐dinitrobenzoic acid, 4‐nitrobenzoic acid and 2,4‐dichlorobenzoic acid

The structures of ammonium 3,5‐dinitrobenzoate, NH₄⁺·C₇H₃N₂O₆⁻, (I), ammonium 4‐nitrobenzoate dihydrate, NH₄⁺·C₇H₄NO₄⁻·2H₂O, (II), and ammonium 2,4‐dichlorobenzoate hemihydrate, NH₄⁺·C₇H₃Cl₂O₂⁻·0.5H₂O, (III), have been determined and their hydrogen‐bonded structures are described. All three salts form hydrogen‐bonded polymeric structures, viz. three‐dimensional in (I) and two‐dimensional in (II) and (III). With (I), a primary cation–anion cyclic association is formed [graph set R₄³(10)] through N—H...O hydrogen bonds, involving a carboxylate group with both O atoms contributing to the hydrogen bonds (denoted O,O′‐carboxylate) on one side and a carboxylate group with one O atom involved in two hydrogen bonds (denoted O‐carboxylate) on the other. Structure extension involves N—H...O hydrogen bonds to both carboxylate and nitro O‐atom acceptors. With structure (II), the primary inter‐species interactions and structure extension into layers lying parallel to (001) are through conjoined cyclic hydrogen‐bonding motifs, viz.R₄³(10) (one cation, an O,O′‐carboxylate group and two water molecules) and centrosymmetric R₄²(8) (two cations and two water molecules). The structure of (III) also has conjoined R₄³(10) and centrosymmetric R₄²(8) motifs in the layered structure but these differ in that the first motif involves one cation, an O,O′‐carboxylate group, an O‐carboxylate group and one water molecule, and the second motif involves two cations and two O‐carboxylate groups. The layers lie parallel to (100). The structures of salt hydrates (II) and (III), displaying two‐dimensional layered arrays through conjoined hydrogen‐bonded nets, provide further illustration of a previously indicated trend among ammonium salts of carboxylic acids, but the anhydrous three‐dimensional structure of (I) is inconsistent with that trend.     

Layer structure estimation of three‐dimensional crystal and two‐dimensional molecular film for fluorinated comb copolymers

Comb copolymers containing both hydrogenated and fluorinated side‐chains were prepared by copolymerization using acrylic or methacrylic monomers in several ratios. The crystal structures of these copolymers and layer structures of their organized molecular films were investigated by wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and out‐of plane X‐ray diffraction. Further, to selectively estimate the regularity of shorter fluorocarbon side‐chains, organized molecular films of copolymers were investigated by polarized near‐edge X‐ray adsorption fine structure (NEXAFS) spectroscopy. From the results of these measurements, it was inferred that these copolymers formed highly ordered layer structures, and a long spacing was predominantly determined by the arrangement of hydrogenated side‐chains, except in copolymers having extremely high fluorocarbon contents. In the case of the organized molecular films, the fluorinated side‐chains of methacrylate copolymers cannot form a highly ordered arrangement, whereas those of acrylate copolymers were oriented on monolayers. However, in both cases, the hydrogenated side‐chains predominantly formed layer structures in the organized films, and the fluorinated side‐chains did not contribute to the formation of the layer structures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 534–546, 2008     

The three‐dimensional hydrogen‐bonded structures in the ammonium and sodium salt hydrates of 4‐aminophenylarsonic acid

The structures of two hydrated salts of 4‐aminophenylarsonic acid (p‐arsanilic acid), namely ammonium 4‐aminophenylarsonate monohydrate, NH₄⁺·C₆H₇AsNO₃⁻·H₂O, (I), and the one‐dimensional coordination polymer catena‐poly[[(4‐aminophenylarsonato‐κO)diaquasodium]‐μ‐aqua], [Na(C₆H₇AsNO₃)(H₂O)₃]_n, (II), have been determined. In the structure of the ammonium salt, (I), the ammonium cations, arsonate anions and water molecules interact through inter‐species N—H...O and arsonate and water O—H...O hydrogen bonds, giving the common two‐dimensional layers lying parallel to (010). These layers are extended into three dimensions through bridging hydrogen‐bonding interactions involving the para‐amine group acting both as a donor and an acceptor. In the structure of the sodium salt, (II), the Na⁺ cation is coordinated by five O‐atom donors, one from a single monodentate arsonate ligand, two from monodentate water molecules and two from bridging water molecules, giving a very distorted square‐pyramidal coordination environment. The water bridges generate one‐dimensional chains extending along c and extensive interchain O—H...O and N—H...O hydrogen‐bonding interactions link these chains, giving an overall three‐dimensional structure. The two structures reported here are the first reported examples of salts of p‐arsanilic acid.     

Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system‐specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.     

sDFIRE: Sequence‐specific statistical energy function for protein structure prediction by decoy selections

An important unsolved problem in molecular and structural biology is the protein folding and structure prediction problem. One major bottleneck for solving this is the lack of an accurate energy to discriminate near‐native conformations against other possible conformations. Here we have developed sDFIRE energy function, which is an optimized linear combination of DFIRE (the Distance‐scaled Finite Ideal gas Reference state based Energy), the orientation dependent (polar‐polar and polar‐nonpolar) statistical potentials, and the matching scores between predicted and model structural properties including predicted main‐chain torsion angles and solvent accessible surface area. The weights for these scoring terms are optimized by three widely used decoy sets consisting of a total of 134 proteins. Independent tests on CASP8 and CASP9 decoy sets indicate that sDFIRE outperforms other state‐of‐the‐art energy functions in selecting near native structures and in the Pearson's correlation coefficient between the energy score and structural accuracy of the model (measured by TM‐score). © 2016 Wiley Periodicals, Inc.     

New angle‐dependent potential energy function for backbone–backbone hydrogen bond in protein–protein interactions

Backbone–backbone hydrogen bonds (BBHBs) are one of the most abundant interactions at the interface of protein–protein complex. Here, we propose an angle‐dependent potential energy function for BBHB based on density functional theory (DFT) calculations and the operation of a genetic algorithm to find the optimal parameters in the potential energy function. The angular part of the energy funtion is assumed to be the product of the power series of sine and cosine functions with respect to the two angles associated with BBHB. Two radial functions are taken into account in this study: Morse and Leonard‐Jones 12‐10 potential functions. Of these two functions under consideration, the former is found to be more accurate than the latter in terms of predicting the binding energies obtained from DFT calculations. The new HB potential function also compares well with the knowledge‐based potential derived by applying Boltzmann statistics for a variety of protein–protein complexes in protein data bank. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Structural and spectropscopic studies of a three‐dimensional hydrogen‐bonded copper(II) complex: aqua[bis(pyridin‐2‐ylcarbonyl)amidato]cyanidocopper(II)

The preparation and X‐ray and spectroscopic studies of the title copper(II) complex, [Cu(C₁₂H₈N₃O₂)(CN)(H₂O)], are reported. The Cu^II cation is five‐coordinated, forming a distorted square‐planar pyramid with an Addison τ parameter of 0.14. The UV–vis spectrum shows a d–d transition of the Cu^II centre at 638 nm, and the electron paramagnetic resonance (EPR) spectrum confirms that the Cu^II cation has an axial symmetry coordination and that the unpaired electrons occupy the d_x2–y2 orbital. Cyclic voltammetric studies show two irreversible oxidation and reduction peaks.     

Sonochemical synthesis of a two‐dimensional supramolecular polymer with nanoporous morphology,linear thallophilic and covalent hydrogen‐bonding interactions

A new thallium‐based supramolecular polymer [Tl(μ₃–3‐HClb)(μ₃–3‐Clb)]_n ( 1 ), (3‐HClb = 3‐chloroperbenzoic acid), has been synthesized and structurally characterized by single crystal X‐ray crystallography. It has a two‐dimensional structure with linear thallophilic and covalent hydrogen‐bonding interactions. In order to evaluate the effects of concentration, ultrasonic irradiation and type of solvents on structure, morphology and thermal behavior of 1 , some experiments were designed, and eight samples of 1 were synthesized under different conditions. These samples were characterized by IR spectroscopy, thermogravimetric and differential thermal analyses, X‐ray powder diffraction and scanning electron microscopy.     

Implicit allowance for “specific” hydrogen bonding contributions to hydration energies in quantum chemically based continuum models: a phenomenological perspective

The abilities of some quantum mechanically based continuum models to accurately predict hydration energies, even where “specific” hydrogen bonding interactions to the aqueous solvent are anticipated, suggests that such effects are implicitly allowed for in the electrostatic model. Examples of this phenomenon involving various ’onium ions are presented and discussed in the context of COSMO, SM2, and a revised version of the authors’ previously described PCM method.     

(5RS)‐5‐(4‐Methoxyphenyl)‐2‐(methylsulfanyl)benzo[g]pyrimido[4,5‐b]quinoline‐4,6,11(3H,5H,12H)‐trione,with Z′ = 3, forms a three‐dimensional hydrogen‐bonded framework containing five types of hydrogen bond

The title compound, C₂₃H₁₇N₃O₄S, crystallizes with Z′ = 3 in the space group P. Two of the three independent molecules are broadly similar in terms of both their molecular conformations and their participation in hydrogen bonds, but the third molecule differs from the other two in both of these respects. The molecules are linked by a combination of N—H...O, N—H...N, C—H...O, C—H...N and C—H...π(arene) hydrogen bonds to form a continuous three‐dimensional framework structure within which a centrosymmetric six‐molecule aggregate can be identified as a key structural element.     

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction‐Field Method for the Solvation Free Energies of Amino Acid Side‐Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model’s accuracy in predicting conformational free‐energy differences. The solvation free energies of neutral and polar amino acid side‐chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol^?1. The new parameters were evaluated for charged side‐chain analogs. The HADES results were compared with explicit‐solvent, generalized Born, Poisson–Boltzmann, and QM‐based methods. The potentials of mean force (PMFs) between pairs of side‐chain analogs obtained by using HADES and explicit‐solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.     

Time‐dependent density functional theory study on the electronic excited‐state geometric structure,infrared spectra,and hydrogen bonding of a doubly hydrogen‐bonded complex

The geometric structures and infrared (IR) spectra in the electronically excited state of a novel doubly hydrogen‐bonded complex formed by fluorenone and alcohols, which has been observed by IR spectra in experimental study, are investigated by the time‐dependent density functional theory (TDDFT) method. The geometric structures and IR spectra in both ground state and the S₁ state of this doubly hydrogen‐bonded FN‐2MeOH complex are calculated using the DFT and TDDFT methods, respectively. Two intermolecular hydrogen bonds are formed between FN and methanol molecules in the doubly hydrogen‐bonded FN‐2MeOH complex. Moreover, the formation of the second intermolecular hydrogen bond can make the first intermolecular hydrogen bond become slightly weak. Furthermore, it is confirmed that the spectral shoulder at around 1700 cm^?1 observed in the IR spectra should be assigned as the doubly hydrogen‐bonded FN‐2MeOH complex from our calculated results. The electronic excited‐state hydrogen bonding dynamics is also studied by monitoring some vibraitonal modes related to the formation of hydrogen bonds in different electronic states. As a result, both the two intermolecular hydrogen bonds are significantly strengthened in the S₁ state of the doubly hydrogen‐bonded FN‐2MeOH complex. The hydrogen bond strengthening in the electronically excited state is similar to the previous study on the singly hydrogen‐bonded FN‐MeOH complex and play important role on the photophysics of fluorenone in solutions. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Synthesis,crystal structure and photoluminescence of a three‐dimensional zinc coordination compound with NBO‐type topology

The assembly of metal–organic frameworks (MOFs) with metal ions and organic ligands is currently attracting considerable attention in crystal engineering and materials science due to their intriguing architectures and potential applications. A new three‐dimensional MOF, namely poly[[diaqua(μ₈‐para‐terphenyl‐3,3′,5,5′‐tetracarboxylato)dizinc(II)] dimethylformamide disolvate monohydrate], {[Zn₂(C₂₂H₁₀O₈)(H₂O)₂]·2C₃H₇NO·H₂O}_n, was synthesized by the self‐assembly of Zn(NO₃)₂·6H₂O and para‐terphenyl‐3,3′,5,5′‐tetracarboxylic acid (H₄TPTC) under solvothermal conditions. The compound was structurally characterized by FT–IR spectroscopy, elemental analysis and single‐crystal X‐ray diffraction analysis. Each Zn^II ion is located in a square‐pyramidal geometry and is coordinated by four carboxylate O atoms from four different TPTC^4? ligands. Pairs of adjacent equivalent Zn^II ions are bridged by four carboxylate groups, forming [Zn₂(O₂CR)₄] (R = terphenyl) paddle‐wheel units. One aqua ligand binds to each Zn^II centre along the paddle‐wheel axis. Each [Zn₂(O₂CR)₄] paddle wheel is further linked to four terphenyl connectors to give a three‐dimensional framework with NBO‐type topology. The thermal stability and solid‐state photoluminescence properties of the title compound have also been investigated.     

Atomistic detailed free‐energy landscape of intrinsically disordered protein studied by multi‐scale divide‐and‐conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α‐helix form in the presence Ca²⁺‐loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺‐loaded CaM must be simultaneously treated. However, it is time‐consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi‐scale divide‐and‐conquer MD (MSDC‐MD), which combines AAM‐MD and coarse‐grained model MD (CGM‐MD). To speed up the conformation sampling, MSDC‐MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM‐MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC‐MD; the root‐mean‐square distance (RMSD) with respect to the experimental structure was 2.23 Å.     

Identifying and reducing error in cluster‐expansion approximations of protein energies

Protein design involves searching a vast space for sequences that are compatible with a defined structure. This can pose significant computational challenges. Cluster expansion is a technique that can accelerate the evaluation of protein energies by generating a simple functional relationship between sequence and energy. The method consists of several steps. First, for a given protein structure, a training set of sequences with known energies is generated. Next, this training set is used to expand energy as a function of clusters consisting of single residues, residue pairs, and higher order terms, if required. The accuracy of the sequence‐based expansion is monitored and improved using cross‐validation testing and iterative inclusion of additional clusters. As a trade‐off for evaluation speed, the cluster‐expansion approximation causes prediction errors, which can be reduced by including more training sequences, including higher order terms in the expansion, and/or reducing the sequence space described by thecluster expansion. This article analyzes the sources of error and introduces a method whereby accuracy can be improved by judiciously reducing the described sequence space. The method is applied to describe the sequence–stability relationship for several protein structures: coiled‐coil dimers and trimers, a PDZ domain, and T4 lysozyme as examples with computationally derived energies, and SH3 domains in amphiphysin‐1 and endophilin‐1 as examples where the expanded pseudo‐energies are obtained from experiments. Our open‐source software package Cluster Expansion Version 1.0 allows users to expand their own energy function of interest and thereby apply cluster expansion to custom problems in protein design. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Synthesis,decomposition studies and crystal structure of a three‐dimensional CuCN network structure with protonated N‐methylethanolamine as the guest cation

The compound poly[2‐hydroxy‐N‐methylethan‐1‐aminium [μ₃‐cyanido‐κ³C:C:N‐di‐μ‐cyanido‐κ⁴C:N‐dicuprate(I)]], {(C₃H₁₀NO)[Cu₂(CN)₃]}_n or [meoenH]Cu₂(CN)₃, crystallizes in the tetragonal space group P4₃. The structure consists of a three‐dimensional (3D) anionic Cu^ICN network with noncoordinated protonated N‐methylethanolamine cations providing charge neutrality. Pairs of cuprophilic Cu atoms are bridged by the C atoms of μ₃‐cyanide ligands, which link these units into a 4₃ spiral along the c axis. The spirals are linked together into a 3D anionic network by the two other cyanide groups. The cationic moieties are linked into their own 4₃ spiral via N—H…O and O—H…O hydrogen bonds, and the cations interact with the 3D network via an unusual pair of N—H…N hydrogen bonds to one of the μ₂‐cyanide groups. Thermogravimetric analysis indicates an initial loss of the base cation and one cyanide as HCN at temperatures in the range 130–250 °C to form CuCN. We show how loss of a specific cyanide group from the 3D CuCN structure could form the linear CuCN structure. Further heating leaves a residue of elemental copper, isolated as the oxide.