基于分子动力学模拟和连续介质模型的自由能计算方法*

近些年,基于分子动力学模拟和连续介质模型的自由能计算方法受到了越来越多的关注,其中MM/PBSA就是最具代表性的方法.在MM/PBSA中,体系的焓变采用分子力学(MM)的方法计算得到;溶剂效应中极性部分对自由能的贡献通过解Poisson-Boltzmann(PB)方程的方法计算得到;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(SA)计算得到.本文结合我们科研组的工作,就近几年MM/PBSA方法的最新进展做了较为详细的阐述,同时对MM/PBSA的发展前景进行了展望.     

Computational study of structures and proton transfer in hydrogen‐bonded ammonia complexes using semiempirical valence‐bond approach

In this study, the seGVB method was implemented for the N H bonding system, specifically for hydrogen‐bonded ammonia complexes, and the model well reproduces the MP2 geometries and energetics. A comparison between the ammonia dimer and water dimer is given from the viewpoint of valance‐bond structures in terms of the calculated bond energies and pair–pair interactions. The linear hydrogen bond is found to be stronger than the bent bonds in both cases, with the difference in energy between the linear and cyclic structures being comparable in both cases although the NH bonds are generally weaker. The energy decomposition clearly demonstrates that the changes in electronic energy are quite different in the two cases due to the presence of an additional lone pair on the water molecule, and it is this effect which leads to the net stabilization of the cyclic structure for the ammonia dimer. Proton‐transfer profiles for hydrogen‐bonded ammonia complexes [NH₂ H NH₂]⁻ and [NH₃ H NH₃]⁺ were calculated. The barrier for proton transfer in [NH₃ H NH₃]⁺ is larger than that in [NH₂ H NH₂]⁻, but smaller than that in the protonated water dimer. The different bonding structures substantially affect the barrier to proton transfer, even though they are isoelectronic systems. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 357–367, 1999     

Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA

In the drug discovery process, accurate methods of computing the affinity of small molecules with a biological target are strongly needed. This is particularly true for molecular docking and virtual screening methods, which use approximated scoring functions and struggle in estimating binding energies in correlation with experimental values. Among the various methods, MM‐PBSA and MM‐GBSA are emerging as useful and effective approaches. Although these methods are typically applied to large collections of equilibrated structures of protein‐ligand complexes sampled during molecular dynamics in water, the possibility to reliably estimate ligand affinity using a single energy‐minimized structure and implicit solvation models has not been explored in sufficient detail. Herein, we thoroughly investigate this hypothesis by comparing different methods for the generation of protein‐ligand complexes and diverse methods for free energy prediction for their ability to correlate with experimental values. The methods were tested on a series of structurally diverse inhibitors of Plasmodium falciparum DHFR with known binding mode and measured affinities. The results showed that correlations between MM‐PBSA or MM‐GBSA binding free energies with experimental affinities were in most cases excellent. Importantly, we found that correlations obtained with the use of a single protein‐ligand minimized structure and with implicit solvation models were similar to those obtained after averaging over multiple MD snapshots with explicit water molecules, with consequent save of computing time without loss of accuracy. When applied to a virtual screening experiment, such an approach proved to discriminate between true binders and decoy molecules and yielded significantly better enrichment curves. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Interaction identification of Zif268 and TATAZF proteins with GC‐/AT‐rich DNA sequence: A theoretical study

Molecular dynamics (MD) simulations for Zif268 (a zinc‐finger‐protein binding specifically to the GC‐rich DNA)‐d(A₁G₂C₃G₄T₅G₆G₇G₈C₉A₁₀C₁₁)₂ and TATA_ZF (a zinc‐finger‐protein recognizing the AT‐rich DNA)‐d(A₁C₂G₃C₄T₅A₆T₇A₈A₉A₁₀A₁₁G₁₂G₁₃)₂ complexes have been performed for investigating the DNA binding affinities and specific recognitions of zinc fingers to GC‐rich and AT‐rich DNA sequences. The binding free energies for the two systems have been further analyzed by using the molecular mechanics Poisson‐Boltzmann surface area (MM‐PBSA) method. The calculations of the binding free energies reveal that the affinity energy of Zif268‐DNA complex is larger than that of TATA_ZF‐DNA one. The affinity between the zinc‐finger‐protein and DNA is mainly driven by more favorable van‐der‐Waals and nonpolar/solvation interactions in both complexes. However, the affinity energy difference of the two binding systems is mainly caused by the difference of van‐der‐Waals interactions and entropy components. The decomposition analysis of MM‐PBSA free energies on each residue of the proteins predicts that the interactions between the residues with the positive charges and DNA favor the binding process; while the interactions between the residues with the negative charges and DNA behave in the opposite way. The interhydrogen‐bonds at the protein‐DNA interface and the induced intrafinger hydrogen bonds between the residues of protein for the Zif268‐DNA complex have been identified at some key contact sites. However, only the interhydrogen‐bonds between the residues of protein and DNA for TATA_ZF‐DNA complex have been found. The interactions of hydrogen‐bonds, electrostatistics and van‐der‐Waals type at some new contact sites have been identified. Moreover, the recognition characteristics of the two studied zinc‐finger‐proteins have also been discussed. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Computation of the binding affinities of catechol‐O‐methyltransferase inhibitors: Multisubstate relative free energy calculations

Alchemical free energy simulations are amongst the most accurate techniques for the computation of the free energy changes associated with noncovalent protein–ligand interactions. A procedure is presented to estimate the relative binding free energies of several ligands to the same protein target where multiple, low‐energy configurational substates might coexist, as opposed to one unique structure. The contributions of all individual substates were estimated, explicitly, with the free energy perturbation method, and combined in a rigorous fashion to compute the overall relative binding free energies and dissociation constants. It is shown that, unless the most stable bound forms are known a priori, inaccurate results may be obtained if the contributions of multiple substates are ignored. The method was applied to study the complex formed between human catechol‐O‐methyltransferase and BIA 9‐1067, a newly developed tight‐binding inhibitor that is currently under clinical evaluation for the therapy of Parkinson's disease. Our results reveal an exceptionally high‐binding affinity (K_d in subpicomolar range) and provide insightful clues on the interactions and mechanism of inhibition. The inhibitor is, itself, a slowly reacting substrate of the target enzyme and is released from the complex in the form of O‐methylated product. By comparing the experimental catalytic rate (k_cat) and the estimated dissociation rate (k_off) constants of the enzyme‐inhibitor complex, one can conclude that the observed inhibition potency (K_i) is primarily dependent on the catalytic rate constant of the inhibitor's O‐methylation, rather than the rate constant of dissociation of the complex. © 2012 Wiley Periodicals, Inc.     

Effect of sampling on BACE‐1 ligands binding free energy predictions via MM‐PBSA calculations

The BACE‐1 enzyme is a prime target to find a cure to Alzheimer's disease. In this article, we used the MM‐PBSA approach to compute the binding free energies of 46 reported ligands to this enzyme. After showing that the most probable protonation state of the catalytic dyad is mono‐protonated (on ASP32), we performed a thorough analysis of the parameters influencing the sampling of the conformational space (in total, more than 35 μs of simulations were performed). We show that ten simulations of 2 ns gives better results than one of 50 ns. We also investigated the influence of the protein force field, the water model, the periodic boundary conditions artifacts (box size), as well as the ionic strength. Amber03 with TIP3P, a minimal distance of 1.0 nm between the protein and the box edges and a ionic strength of I = 0.2 M provides the optimal correlation with experiments. Overall, when using these parameters, a Pearson correlation coefficient of R = 0.84 (R ² = 0.71) is obtained for the 46 ligands, spanning eight orders of magnitude of K _d (from 0.017 nm to 2000 μM, i.e., from −14.7 to −3.7 kcal/mol), with a ligand size from 22 to 136 atoms (from 138 to 937 g/mol). After a two‐parameter fit of the binding affinities for 12 of the ligands, an error of RMSD = 1.7 kcal/mol was obtained for the remaining ligands. © 2017 Wiley Periodicals, Inc.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Surface characterization and sorption efficacy of tire‐obtained carbon: experimental and semiempirical study of rhodamine B adsorption

This work focuses on the surface characterization and sorption activity of carbon derived from waste tires. The carbon was prepared by thermal treatment of waste rubber tires, followed by exposure to nitric acid and hydrogen peroxide. The tired‐obtained activated carbon (AC) was evaluated using a variety of techniques. Fourier transform infrared spectroscope and Raman spectra reveal existence of hydroxyl and carboxylic groups on AC surface. Scanning electron microscope and Brunauer–Emmett–Teller revealed the porosity of AC is well developed with mesopore structure (mesopore volume of 0.96 cm³/g). AC was tested for Rhodamine B sorption, and the adsorption kinetics well fitted using a pseudo second‐order kinetic model. The adsorption isotherm data could be well described by the Langmuir model. Semiempirical calculations using Austin Model 1 were performed to explain the adsorption at molecular level. Binding enthalpies in the range of 0.5–4 kcal/mol of four possible scenarios were computed. We believe the combination between experimental work and semiempirical calculations allows for a better understanding of Rhodamine B molecules adsorption on the AC surface. Copyright © 2015 John Wiley & Sons, Ltd.     

DNA脱碱基位点存在下非氢键配体的增强结合研究

众所周知,插入剂的DNA特性结合位点位于DNA碱基对之间,然而这种非共价相互作用对于含脱碱基（AP）位点的DNA来讲还没有引起足够的重视,虽然在生物细胞中总是存在着DNA脱碱基位点。本文以原黄素（proflavine,PF）为例研究了插入剂对DNA中AP位点的结合特性。实验结果表明,相对于插入位点而言,AP位点是PF的优先结合位点,AP位点的本征结合常数比插入结合常数高一个数量级以上。此外,PF的结合使含脱碱基位点DNA的热稳定性明显提高,表明PF在脱碱基位点的结合构像明显不同于插入结合时的分子定向。本文结果将有助于判断小分子的DNA结合方式所决定的药物的生物化学及生物物理效用。     

Fast and accurate determination of the relative binding affinities of small compounds to HIV‐1 protease using non‐equilibrium work

The fast pulling ligand (FPL) out of binding cavity using non‐equilibrium molecular dynamics (MD) simulations was demonstrated to be a rapid, accurate and low CPU demand method for the determination of the relative binding affinities of a large number of HIV‐1 protease (PR) inhibitors. In this approach, the ligand is pulled out of the binding cavity of the protein using external harmonic forces, and the work of pulling force corresponds to the relative binding affinity of HIV‐1 PR inhibitor. The correlation coefficient between the pulling work and the experimental binding free energy of shows that FPL results are in good agreement with experiment. It is thus easier to rank the binding affinities of HIV‐1 PR inhibitors, that have similar binding affinities because the mean error bar of pulling work amounts to . The nature of binding is discovered using the FPL approach. © 2016 Wiley Periodicals, Inc.     

Hot spot computational identification: Application to the complex formed between the hen egg white lysozyme (HEL) and the antibody HyHEL‐10

The definition and comprehension of the hot spots in an interface is a subject of primary interest for a variety of fields, including structure‐based drug design. Therefore, to achieve an alanine mutagenesis computational approach that is at the same time accurate and predictive, capable of reproducing the experimental mutagenesis values is a major challenge in the computational biochemistry field. Antibody/protein antigen complexes provide one of the greatest models to study protein–protein recognition process because they have three fundamentally features: specificity, high complementary association and a small epitope restricted to the diminutive complementary determining regions (CDR) region, while the remainder of the antibody is largely invariant. Thus, we apply a computational mutational methodological approach to the study of the antigen–antibody complex formed between the hen egg white lysozyme (HEL) and the antibody HyHEL‐10. A critical evaluation that focuses essentially on the limitations and advantages between different computational methods for hot spot determination, as well as between experimental and computational methodological approaches, is presented. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Computational study of ligand binding in lipid transfer proteins: Structures,interfaces, and free energies of protein‐lipid complexes

Plant nonspecific lipid transfer proteins (nsLTPs) bind a wide variety of lipids, which allows them to perform disparate functions. Recent reports on their multifunctionality in plant growth processes have posed new questions on the versatile binding abilities of these proteins. The lack of binding specificity has been customarily explained in qualitative terms on the basis of a supposed structural flexibility and nonspecificity of hydrophobic protein‐ligand interactions. We present here a computational study of protein‐ligand complexes formed between five nsLTPs and seven lipids bound in two different ways in every receptor protein. After optimizing geometries in molecular dynamics calculations, we computed Poisson‐Boltzmann electrostatic potentials, solvation energies, properties of the protein‐ligand interfaces, and estimates of binding free energies of the resulting complexes. Our results provide the first quantitative information on the ligand abilities of nsLTPs, shed new light into protein‐lipid interactions, and reveal new features which supplement commonly held assumptions on their lack of binding specificity. © 2012 Wiley Periodicals, Inc.     

Calculating pKa values for substituted phenols and hydration energies for other compounds with the first‐order fuzzy‐border continuum solvation model

We have computed pK_a values for 11 substituted phenol compounds using the continuum Fuzzy‐Border (FB) solvation model. Hydration energies for 40 other compounds, including alkanes, alkenes, alkynes, ketones, amines, alcohols, ethers, aromatics, amides, heterocycles, thiols, sulfides, and acids have been calculated. The overall average unsigned error in the calculated acidity constant values was equal to 0.41 pH units and the average error in the solvation energies was 0.076 kcal/mol. We have also reproduced pK_a values of propanoic and butanoic acids within about 0.1 pH units from the experimental values by fitting the solvation parameters for carboxylate ion carbon and oxygen atoms. The FB model combines two distinguishing features. First, it limits the amount of noise which is common in numerical treatment of continuum solvation models by using fixed‐position grid points. Second, it uses either second‐ or first‐order approximation for the solvent polarization, depending on a particular implementation. These approximations are similar to those used for solute and explicit solvent fast polarization treatment which we developed previously. This article describes results of using the first‐order technique. This approximation places the presented methodology between the Generalized Born and Poisson‐Boltzmann continuum solvation models with respect to their accuracy of reproducing the many‐body effects in modeling a continuum solvent. © 2012 Wiley Periodicals, Inc.     

A theoretical study on cyclacenes: Analytical tight‐binding approach

We present a theoretical study of cyclacene molecules performed at tight‐binding level. The orbital energies and eigenvectors have been analytically computed, and exact expressions for the axial component of the total position spread and polarizability tensors have been obtained. In absence of dimerization, the system has a D_nh symmetry, where n is the number of hexagonal units. The energy bands present no gap at the Fermi level, and to this fact it corresponds a diverging (per‐electron) polarizability for in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the σ_h symmetry plane, conversely, remain finite for . The total position spread tensor presents a qualitatively different behavior, since all the three components of the position spread per electron remain finite for . The results are analyzed and discussed for both axial and planar components separately as these are affected differently with respect to the increasing system size. Both dipole polarizability and total position spread have been computed using an ab initio approach for the smallest systems, to compare the analytical tight‐binding expressions with a higher‐level theory.     

Relationship between dye–iodine binding and cell voltage in dye‐sensitized solar cells: A quantum‐mechanical look

It has been proposed that iodine binding to dyes may actually decrease the cell efficiency of a dye‐sensitized solar cell. A previous experimental study showed that a two‐atom change from oxygen to sulfur increased recombination of iodine with injected electrons by a factor of approximately 2. Here, it is shown that iodine binding is a plausible explanation for this effect. The steric and conjugation effects are quantified separately using a set of model compounds. Quantum‐chemical calculations show that elongation of the hydrocarbon chain has only an insignificant effect on the iodine and bromine binding to the chalcogen atoms (O, S, Se). The conjugation, however, significantly disfavors the iodine and bromine interaction. Iodine and bromine binding to the dye and model compounds containing sulfur is significantly more favorable than to their oxygen containing counterparts. Bromine binding to dyes is shown to be stronger than that of iodine. Accordingly, bromine binding to dyes may contribute significantly to the observed lower efficiencies in cells using Br/Br^? as the redox couple. © 2012 Wiley Periodicals, Inc.     

A combined computational and experimental approach for investigating a hydrogen‐bonded supermolecular compound comprising benzimidazole and malonic acid

A hydrogen‐bonded tetramer supramolecular motif of 2:2 benzimidazole (BIZ) and malonic acid (MLA) has been synthesized and characterized by elemental analysis, infrared (IR), and X‐ray single crystal diffraction. Thermal stability analyses demonstrate that this supramolecular adduct is a new material and it is not the ordinary superposition of the original monomers. Density function theory (DFT) calculations for the models of dimers, trimers, and tetramer comprising BIZ and MLA have been carried out at B3LYP/6‐31G* and PBE1PBE/6‐31G* levels of theory, respectively. By comparing the calculated results with the experiments (single crystal structure, IR spectra, and thermal analysis) and based on the statistic thermodymnamic calculations, it is concluded that the dimers cannot exist at room temperature and the tetramer can simulate the title supramolecular complex better than the two trimers. Further studies on the model of tetramer indicate that the hydrogen bond of N···H? O is stronger than that of O···H? N. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

NANOPACK: Parallel codes for semiempirical quantum chemical calculations of large systems in the sp‐ and spd‐basis

A parallel implementation of the conventionally used NDDO (MNDO, AM1, PM3, CLUSTER‐Z1) and modified NDDO‐WF (CLUSTER‐Z2) techniques for semiempirical quantum chemical calculations of large molecular systems in the sp‐ and spd‐basis, respectively, is described. The atom‐pair distribution of data over processors forms the basis of the parallelization. The technological aspects of designing scalable parallel calculations on supercomputers (using ScaLAPACK and MPI libraries) are discussed. The scaling of individual algorithms and the entire package was carried out for model systems with 894, 1920, and 2014 atomic orbitals. The package speed‐up provided by different multiprocessor systems involving a cluster of Intel PIII processors, Alpha‐21264‐processor‐built machine MBC‐1000M, and Cray‐T3E is analyzed. The effect of computer characteristics on the package performance is discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002