MMP-2和Hydroxamate类抑制剂绝对自由能的计算

采用基于线性响应近似的自由能计算方法计算了一类hydroxamate抑制剂和MMP-2的绝对结合自由能。计算中,催化锌离子和MMP-2以及配体之间采用了非键模型。分子动力学模拟结果显示,采用非键模型时,催化Zn离子采用五配位的形式,但配位键的形式和初始结构比较有很大的差别。通过拟合,分别得到了单参数、双参数以及三参数的自由能预测模型,其中,含有常数校正项的三参数模型具有最佳的预测能力,预测自由能和实际自由能之间平均绝对误差仅为2.38kJ/mol。     

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.     

Potent Inhibitors of Malarial Aspartic Proteases,the Plasmepsins,by Hydroformylation of Substituted 7‐Azanorbornenes

The increasing prevalence of multidrug‐resistant strains of the malarial parasite Plasmodium falciparum requires the urgent development of new therapeutic agents with novel modes of action. The vacuolar malarial aspartic proteases plasmepsin (PM) I, II, and IV are involved in hemoglobin degradation and play a central role in the growth and maturation of the parasite in the human host. We report the structure‐based design, synthesis, and in vitro evaluation of a new generation of PM inhibitors featuring a highly decorated 7‐azabicyclo[2.2.1]heptane core. While this protonated central core addresses the catalytic Asp dyad, three substituents bind to the flap, the S1/S3, and the S1′ pockets of the enzymes. A hydroformylation reaction is the key synthetic step for the introduction of the new vector reaching into the S1′ pocket. The configuration of the racemic ligands was confirmed by extensive NMR and X‐ray crystallographic analysis. In vitro biological assays revealed high potency of the new inhibitors against the three plasmepsins (IC₅₀ values down to 6 nM ) and good selectivity towards the closely related human cathepsins D and E. The occupancy of the S1′ pocket makes an essential contribution to the gain in binding affinity and selectivity, which is particularly large in the case of the PM IV enzyme. Designing non‐peptidic ligands for PM II is a valid route to generate compounds that inhibit the entire family of vacuolar plasmepsins.     

Binding affinity prediction with different force fields: examination of the linear interaction energy method

A systematic study of the linear interaction energy (LIE) method and the possible dependence of its parameterization on the force field and system (receptor binding site) is reported. We have calculated the binding free energy for nine different ligands in complex with P450cam using three different force fields (Amber95, Gromos87, and OPLS-AA). The results from these LIE calculations using our earlier parameterization give relative free energies of binding that agree remarkably well with the experimental data. However, the absolute energies are too positive for all three force fields, and it is clear that an additional constant term (gamma) is required in this case. Out of five examined LIE models, the same one emerges as the best for all three force fields, and this, in fact, corresponds to our earlier one apart from the addition of the constant gamma, which is almost identical for the three force fields. Thus, the present free energy calculations clearly indicate that the coefficients of the LIE method are independent of the force field used. Their relation to solvation free energies is also demonstrated. The only free parameter of the best model is gamma, which is found to depend on the hydrophobicity of the binding site. We also attempt to quantify the binding site hydrophobicity of four different proteins which shows that the ordering of gamma's for these sites reflects the fraction of hydrophobic surface area.     

Computational Characterization of Binding of Small Molecule Inhibitors to HIV‐1 gp41

Developing orally available small molecule inhibitors of HIV‐1 fusion has attracted significant interest over many years. Frey had recently reported several synthetic compounds which are experimentally shown to inhibit cell‐cell fusion in the low micromolar range. We carried out computational study to help identify possible binding modes by docking these compounds onto the hydrophobic pocket on gp41 and to characterize structures of binding complexes. The detailed gp41‐molecule binding interactions and free energies of binding are obtained through molecular dynamics simulation and MM‐PBSA calculation. Specific molecular interactions in the gp41‐inhibitor complexes are identified. The present computational study complements the corresponding experimental investigation and helps establish a good starting point for further refinement of small molecular gp41 inhibitors.     

Fast,metadynamics‐based method for prediction of the stereochemistry‐dependent relative free energies of ligand–receptor interactions

The computational approach applicable for the molecular dynamics (MD)‐based techniques is proposed to predict the ligand–protein binding affinities dependent on the ligand stereochemistry. All possible stereoconfigurations are expressed in terms of one set of force‐field parameters [stereoconfiguration‐independent potential (SIP)], which allows for calculating all relative free energies by only single simulation. SIP can be used for studying diverse, stereoconfiguration‐dependent phenomena by means of various computational techniques of enhanced sampling. The method has been successfully tested on the β₂‐adrenergic receptor (β₂‐AR) binding the four fenoterol stereoisomers by both metadynamics simulations and replica‐exchange MD. Both the methods gave very similar results, fully confirming the presence of stereoselective effects in the fenoterol‐β₂‐AR interactions. However, the metadynamics‐based approach offered much better efficiency of sampling which allows for significant reduction of the unphysical region in SIP. © 2014 Wiley Periodicals, Inc.     

Computational prediction of monosaccharide binding free energies to lectins with linear interaction energy models

The linear interaction energy (LIE) method to compute binding free energies is applied to lectin‐monosaccharide complexes. Here, we calculate the binding free energies of monosaccharides to the Ralstonia solanacearum lectin (RSL) and the Pseudomonas aeruginosa lectin‐II (PA‐IIL). The standard LIE model performs very well for RSL, whereas the PA‐IIL system, where ligand binding involves two calcium ions, presents a major challenge. To overcome this, we explore a new variant of the LIE model, where ligand–metal ion interactions are scaled separately. This model also predicts the saccharide binding preference of PA‐IIL on mutation of the receptor, which may be useful for protein engineering of lectins. © 2012 Wiley Periodicals, Inc.     

Calculation of ligand binding free energies from molecular dynamics simulations

A recently developed method for predicting binding affinities in ligand–receptor complexes, based on interaction energy averaging and conformational sampling by molecular dynamics simulation, is presented. Polar and nonpolar contributions to the binding free energy are approximated by a linear scaling of the corresponding terms in the average intermolecular interaction energy for the bound and free states of the ligand. While the method originally assumed the validity of electrostatic linear response, we show that incorporation of systematic deviations from linear response derived from free energy perturbation calculations enhances the accuracy of the approach. The method is applied to complexes of wild-type and mutant human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors. It is shown that a binding energy accuracy of about 1 kcal/mol is attainable even for multiply ionized compounds, such as methotrexate, for which electrostatic interactions energies are very large. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 77–88, 1998     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.     

Fast and flexible gpu accelerated binding free energy calculations within the amber molecular dynamics package

Alchemical free energy (AFE) calculations based on molecular dynamics (MD) simulations are key tools in both improving our understanding of a wide variety of biological processes and accelerating the design and optimization of therapeutics for numerous diseases. Computing power and theory have, however, long been insufficient to enable AFE calculations to be routinely applied in early stage drug discovery. One of the major difficulties in performing AFE calculations is the length of time required for calculations to converge to an ensemble average. CPU implementations of MD‐based free energy algorithms can effectively only reach tens of nanoseconds per day for systems on the order of 50,000 atoms, even running on massively parallel supercomputers. Therefore, converged free energy calculations on large numbers of potential lead compounds are often untenable, preventing researchers from gaining crucial insight into molecular recognition, potential druggability and other crucial areas of interest. Graphics Processing Units (GPUs) can help address this. We present here a seamless GPU implementation, within the PMEMD module of the AMBER molecular dynamics package, of thermodynamic integration (TI) capable of reaching speeds of >140 ns/day for a 44,907‐atom system, with accuracy equivalent to the existing CPU implementation in AMBER. The implementation described here is currently part of the AMBER 18 beta code and will be an integral part of the upcoming version 18 release of AMBER. © 2018 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.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

FEW: A workflow tool for free energy calculations of ligand binding

In the later stages of drug design projects, accurately predicting relative binding affinities of chemically similar compounds to a biomolecular target is of utmost importance for making decisions based on the ranking of such compounds. So far, the extensive application of binding free energy approaches has been hampered by the complex and time‐consuming setup of such calculations. We introduce the free energy workflow (FEW) tool that facilitates setup and execution of binding free energy calculations with the AMBER suite for multiple ligands. FEW allows performing free energy calculations according to the implicit solvent molecular mechanics (MM‐PB(GB)SA), the linear interaction energy, and the thermodynamic integration approaches. We describe the tool's architecture and functionality and demonstrate in a show case study on Factor Xa inhibitors that the time needed for the preparation and analysis of free energy calculations is considerably reduced with FEW compared to a fully manual procedure. © 2013 Wiley Periodicals, Inc.     

The application of three approximate free energy calculations methods to structure based ligand design: Trypsin and its complex with inhibitors

Three approximate free energy calculation methods are examined and applied to an example ligand design problem. The first of the methods uses a single simulation to estimate the relative binding free energies for related ligands that are not simulated. The second method is similar, except that it uses only first derivatives of free energy with respect to atomic parameters (most often charge, van der Waals equilibrium distance, and van der Waals well depth) to calculate free energy differences. The last method PROFEC (Pictorial Representation of Free Energy Components), generates contour maps that show how binding free energy changes when additional particles are added near the ligand. These three methods are applied to a benzamidine/trypsin complex. They each reproduce the general trends in the binding free energies, indicating that they might be useful for suggesting how ligands could be modified to improve binding and, consequently, useful in structure-based drug design.     

Influence of the solvent representation on vibrational entropy calculations: Generalized born versus distance‐dependent dielectric model

The harmonic model is the most popular approximation for estimating the “configurational” entropy of a solute in molecular mechanics/Poisson‐Boltzmann solvent accessible surface area (MM/PBSA)‐type binding free energy calculations. Here, we investigate the influence of the solvent representation in the harmonic model by comparing estimates of changes in the vibrational entropies for 30 trypsin/ligand complexes on ligand binding. Second derivatives of Amber generalized Born (GB) solvation models are available in the nucleic acid builder code. They allow one to use these models for the calculation of vibrational entropies instead of using a simpler solvation model based on a distance‐dependent dielectric (DDD) constant. Estimates of changes in the vibrational entropies obtained with a DDD model are systematically and significantly larger, by on average, 6 kcal mol^?1 (at T = 300 K), than estimates obtained with a GB model and so are more favorable for complex formation. The difference becomes larger the more the vibrational entropy contribution disfavors complex formation, that is, the larger the ligand is (for the complexes considered here). A structural decomposition of the estimates into per‐residue contributions reveals polar interactions between the ligand and the surrounding protein, in particular involving charged nitrogens, as a main source of the differences. Snapshots minimized with the DDD model showed a structural deviation from snapshots minimized in explicit water that is larger by, on average, 0.5 Å RMSD compared to snapshots that were minimized with GB^HCT. As experimental vibrational entropies of biomacromolecules are elusive, there is no direct way to establish a solvent model's superiority. Thus, we can only recommend using the GB harmonic model for vibrational entropy calculations based on the reasoning that smaller structural deviations should point to the implicit solvent model that closer approximates the energy landscape of the solute in explicit solvent. © 2012 Wiley Periodicals, Inc.     

Free energy perturbation and molecular dynamics calculations of copper binding to azurin

Free energy perturbation/molecular dynamics simulations have been carried out on copper/azurin systems calculating the binding affinities of copper (II) ion to azurin either in the native or in the unfolded state. In order to test the validity of the strategy adopted for the calculations and to establish what force field is suitable for these kinds of calculations, three different force fields, AMBER, CVFF, and CFF, have been alternatively used for the calculations and the results have been compared with experimental data obtained by spectroscopic titrations of copper (II)/azurin solutions and denaturation experiments. Our findings have pointed out that only CFF gives satisfactory results, thus providing a reliable tool for copper binding simulations in copper protein.     

Incorporating the effect of ionic strength in free energy calculations using explicit ions

The incorporation of explicit ions to mimic the effect of ionic strength or to neutralize the overall charge on a system in free energy calculations using molecular dynamics simulations is investigated. The difference in the free energy of hydration between two triosephosphate isomerase inhibitors calculated at five different ion concentrations is used as an example. We show that the free energy difference can be highly sensitive to the presence of explicit ions even in cases where the mutation itself does not involve a change in the overall charge. The effect is most significant if the molecule carries a net charge close to the site mutated. Furthermore, it is shown that the introduction of a small number of ions can lead to very severe sampling problems suggesting that in practical calculations convergence can best be achieved by incorporating either no counterions or by simulating at high ionic strength to ensure sufficient sampling of the ion distribution.     

A novel approach to the calculation of the free energy due to molecular flexibility

The contribution of the molecular flexibility to the solvation excess free energy is expressed in terms of probabilities of reaching hard limits on intramolecular coordinates in a series of calculations successively relaxing those limits. Numerical tests on the harmonic oscillator are also presented and used to make suggestion about computational issues.