新型二氟甲基磷酸类酪氨酸蛋白磷酸酯酶1B抑制剂的分子动力学模拟和结合自由能计算

通过分子对接建立了一系列含二氟甲基磷酸基团(DFMP)或二氟甲基硫酸基团(DFMS)的抑制剂与酪氨酸蛋白磷酸酯酶1B(PTP1B)的相互作用模式, 并通过1 ns的分子动力学模拟和molecular mechanics/generalized Born surface area (MM/GBSA)方法计算了其结合自由能. 计算获得的结合自由能排序和抑制剂与靶酶间结合能力排序一致; 通过基于主方程的自由能计算方法, 获得了抑制剂与靶酶残基间相互作用的信息, 这些信息显示DFMP/DFMS基团的负电荷中心与PTP1B的221位精氨酸正电荷中心之间的静电相互作用强弱决定了此类抑制剂的活性, 进一步的分析还显示位于DFMP/DFMS基团中的氟原子或其他具有适当原子半径的氢键供体原子会增进此类抑制剂与PTP1B活性位点的结合能力.     

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

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

Solvent interaction energy calculations on molecular dynamics trajectories: increasing the efficiency using systematic frame selection

End-point methods such as linear interaction energy (LIE) analysis, molecular mechanics generalized Born solvent-accessible surface (MM/GBSA), and solvent interaction energy (SIE) analysis have become popular techniques to calculate the free energy associated with protein-ligand binding. Such methods typically use molecular dynamics (MD) simulations to generate an ensemble of protein structures that encompasses the bound and unbound states. The energy evaluation method (LIE, MM/GBSA, or SIE) is subsequently used to calculate the energy of each member of the ensemble, thus providing an estimate of the average free energy difference between the bound and unbound states. The workflow requiring both MD simulation and energy calculation for each frame and each trajectory proves to be computationally expensive. In an attempt to reduce the high computational cost associated with end-point methods, we study several methods by which frames may be intelligently selected from the MD simulation including clustering and address the question of how the number of selected frames influences the accuracy of the SIE calculations.     

Crystal molecular dynamics simulations to speed up MM/PB(GB)SA evaluation of binding free energies of di-mannose deoxy analogs with P51G-m4-Cyanovirin-N

Complexes of two Cyanovirin-N (CVN) mutants, m4-CVN and P51G-m4-CVN, with deoxy di-mannose analogs were employed as models to generate conformational ensembles using explicit water Molecular Dynamics (MD) simulations in solution and in crystal environment. The results were utilized for evaluation of binding free energies with the molecular mechanics Poisson-Boltzmann (or Generalized Born) surface area, MM/PB(GB)SA, methods. The calculations provided the ranking of deoxy di-mannose ligands affinity in agreement with available qualitative experimental evidences. This confirms the importance of the hydrogen-bond network between di-mannose 3'- and 4'-hydroxyl groups and the protein binding site B(M) as a basis of the CVN activity as an effective HIV fusion inhibitor. Comparison of binding free energies averaged over snapshots from the solution and crystal simulations showed high promises in the use of the crystal matrix for acceleration of the conformational ensemble generation, the most time consuming step in MM/PB(GB)SA approach. Correlation between energy values based on solution versus crystal ensembles is 0.95 for both MM/PBSA and MM/GBSA methods.     

Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. The accuracy of ranking poses generated from docking

In molecular docking, it is challenging to develop a scoring function that is accurate to conduct high-throughput screenings. Most scoring functions implemented in popular docking software packages were developed with many approximations for computational efficiency, which sacrifices the accuracy of prediction. With advanced technology and powerful computational hardware nowadays, it is feasible to use rigorous scoring functions, such as molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) and molecular mechanics/generalized Born surface area (MM/GBSA) in molecular docking studies. Here, we systematically investigated the performance of MM/PBSA and MM/GBSA to identify the correct binding conformations and predict the binding free energies for 98 protein-ligand complexes. Comparison studies showed that MM/GBSA (69.4%) outperformed MM/PBSA (45.5%) and many popular scoring functions to identify the correct binding conformations. Moreover, we found that molecular dynamics simulations are necessary for some systems to identify the correct binding conformations. Based on our results, we proposed the guideline for MM/GBSA to predict the binding conformations. We then tested the performance of MM/GBSA and MM/PBSA to reproduce the binding free energies of the 98 protein-ligand complexes. The best prediction of MM/GBSA model with internal dielectric constant 2.0, produced a Spearman's correlation coefficient of 0.66, which is better than MM/PBSA (0.49) and almost all scoring functions used in molecular docking. In summary, MM/GBSA performs well for both binding pose predictions and binding free-energy estimations and is efficient to re-score the top-hit poses produced by other less-accurate scoring functions.     

Methodological aspects of QM/MM calculations: A case study on matrix metalloproteinase‐2

We address methodological issues in quantum mechanics/molecular mechanics (QM/MM) calculations on a zinc‐dependent enzyme. We focus on the first stage of peptide bond cleavage by matrix metalloproteinase‐2 (MMP‐2), that is, the nucleophilic attack of the zinc‐coordinating water molecule on the carbonyl carbon atom of the scissile fragment of the substrate. This step is accompanied by significant charge redistribution around the zinc cation, bond cleavage, and bond formation. We vary the size and initial geometry of the model system as well as the computational protocol to demonstrate the influence of these choices on the results obtained. We present QM/MM potential energy profiles for a set of snapshots randomly selected from QM/MM‐based molecular dynamics simulations and analyze the differences in the computed profiles in structural terms. Since the substrate in MMP‐2 is located on the protein surface, we investigate the influence of the thickness of the water layer around the enzyme on the QM/MM energy profile. Thin water layers (0–2 Å) give unrealistic results because of structural reorganizations in the active‐site region at the protein surface. A 12 Å water layer appears to be sufficient to capture the effect of the solvent; the corresponding QM/MM energy profile is very close to that obtained from QM/MM/SMBP calculations using the solvent macromolecular boundary potential (SMBP). We apply the optimized computational protocol to explain the origin of the different catalytic activity of the Glu116Asp mutant: the energy barrier for the first step is higher, which is rationalized on structural grounds. © 2016 Wiley Periodicals, Inc.     

A comparison of different initialization protocols to obtain statistically independent molecular dynamics simulations

We study how the results of molecular dynamics (MD) simulations are affected by various choices during the setup, e.g., the starting velocities, the solvation, the location of protons, the conformation of His, Asn, and Gln residues, the protonation and titration of His residues, and the treatment of alternative conformations. We estimate the binding affinity of ligands to four proteins calculated with the MM/GBSA method (molecular mechanics combined with a generalized Born and surface area solvation energy). For avidin and T4 lysozyme, all variations gave similar results within 2 kJ/mol. For factor Xa, differences in the solvation or in the selection of alternative conformations gave results that are significantly different from those of the other approaches by 4-6 kJ/mol, whereas for galectin-3, changes in the conformations, rotations, and protonation gave results that differed by 10 kJ/mol, but only if residues close to the binding site were modified. This shows that the results of MM/GBSA calculations are reasonably reproducible even if the MD simulations are set up with different software. Moreover, we show that the sampling of phase space can be enhanced by solvating the systems with different equilibrated water boxes, in addition to the common use of different starting velocities. If different conformations are available in the crystal structure, they should also be employed to enhance the sampling. Protonation, ionization, and conformations of Asn, Gln, and His may also be used to enhance sampling, but great effort should be spent to obtain as reliable predictions as possible close to the active site.     

Is inhibition process better described with MD(QM/MM) simulations? The case of urokinase type plasminogen activator inhibitors

Urokinase plasminogen activator (uPA) is an enzyme involved in cancer growth and metastasis. Therefore, the design of inhibitors of uPA is of high therapeutic value, and several chemical families have been explored, even if none has still emerged, emphasizing the need of a rationalized approach. This work represents a complete computational study of uPA complexed with five inhibitors, which present weak similarities. Molecular dynamics simulations in explicit solvent were conducted, and structural analyses, along with molecular mechanics (MM)/Poisson-Boltzmann surface area free energies estimations, yield precious structure-activity relationships of these inhibitors. Besides, we realized supplemental QM/MM computations that improved drastically the quality of our models providing original information on the hydrogen bonds and charge transfer effects, which are, most often, neglected in other studies. We suggest that these simulations and analyses could be reproduced for other systems involving protein/ligand molecular recognitions.     

Rapid prediction of solvation free energy. 3. Application to the SAMPL2 challenge

The SAMPL2 hydration free energy blind prediction challenge consisted of a data set of 41 molecules divided into three subsets: explanatory, obscure and investigatory, where experimental hydration free energies were given for the explanatory, withheld for the obscure, and not known for the investigatory molecules. We employed two solvation models for this challenge, a linear interaction energy (LIE) model based on explicit-water molecular dynamics simulations, and the first-shell hydration (FiSH) continuum model previously calibrated to mimic LIE data. On the 23 compounds from the obscure (blind) dataset, the prospectively submitted LIE and FiSH models provided predictions highly correlated with experimental hydration free energy data, with mean-unsigned-errors of 1.69 and 1.71 kcal/mol, respectively. We investigated several parameters that may affect the performance of these models, namely, the solute flexibility for the LIE explicit-solvent model, the solute partial charging method, and the incorporation of the difference in intramolecular energy between gas and solution phases for both models. We extended this analysis to the various chemical classes that can be formed within the SAMPL2 dataset. Our results strengthen previous findings on the excellent accuracy and transferability of the LIE explicit-solvent approach to predict transfer free energies across a wide spectrum of functional classes. Further, the current results on the SAMPL2 test dataset provide additional support for the FiSH continuum model as a fast yet accurate alternative to the LIE explicit-solvent model. Overall, both the LIE explicit-solvent model and the FiSH continuum solvation model show considerable improvement on the SAMPL2 data set over our previous continuum electrostatics-dispersion solvation model used in the SAMPL1 blind challenge.     

QM/MM–PB/SA scoring of the interaction strength between Akt kinase and apigenin analogues

Identification of small-molecule compounds that can bind specifically and stably to protein targets of biological interest is a challenge task in structure-based drug design. Traditionally, several fast approaches such as empirical scoring functions and free energy analysis have been widely used to fulfill for this purpose. In the current study, we raised the rigorous quantum mechanics/molecular mechanics in combination with semi-empirical Poisson–Boltzmann/surface area (QM/MM–PB/SA) as an efficient strategy to characterize the intermolecular interaction between Akt kinase and its small-molecule ligands, although this hybrid approach is computationally expensive as compared to those empirical methods. In a round of experimental activity reproduction test based on a set of known Akt–inhibitor complexes, QM/MM–PB/SA has been shown to perform much better than two widely used scoring functions as well as the sophisticated MM-PB/SA analysis with or without improvement by molecular dynamics (MD) simulations. Next, the QM/MM–PB/SA was employed to screen for strong Akt binders from an apigenin analogue set. Consequently, four compounds, namely apigenin, quercetin, gallocatechin and myricetin, were suggested to have high binding potency to Akt active site. A further kinase assay was conducted to determine the inhibitory activity of the four promising candidates against Akt kinase, resulting in IC₅₀ values of 38.4, 67.5, 157.1 and 25.5 nM, respectively.     

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.     

Analyzing the robustness of the MM/PBSA free energy calculation method: application to DNA conformational transitions

The ability to predict and characterize free energy differences associated with conformational equilibria or the binding of biomolecules is vital to understanding the molecular basis of many important biological functions. As biological studies focus on larger molecular complexes and properties of the genome, proteome, and interactome, the development and characterization of efficient methods for calculating free energy becomes increasingly essential. The aim of this study is to examine the robustness of the end-point free energy method termed the molecular mechanics Poisson-Boltzmann solvent accessible surface area (MM/PBSA) method. Specifically, applications of MM/PBSA to the conformational equilibria of nucleic acid (NA) systems are explored. This is achieved by comparing A to B form DNA conformational free energy differences calculated using MM/PBSA with corresponding free energy differences determined with a more rigorous and time-consuming umbrella sampling algorithm. In addition, the robustness of NA MM/PBSA calculations is also evaluated in terms of the sensitivity towards the choice of force field and the choice of solvent model used during conformational sampling. MM/PBSA calculations of the free energy difference between A-form and B-form DNA are shown to be in very close agreement with the PMF result determined using an umbrella sampling approach. Further, it is found that the MM/PBSA conformational free energy differences were also in agreement using either the CHARMM or AMBER force field. The influence of ionic strength on conformational stability was particularly insensitive to the choice of force field. Finally, it is also shown that the use of a generalized Born implicit solvent during conformational sampling results in free energy estimates that deviate slightly from those obtained using explicitly solvated MD simulations in these NA systems.     

How to obtain statistically converged MM/GBSA results

The molecular mechanics/generalized Born surface area (MM/GBSA) method has been investigated with the aim of achieving a statistical precision of 1 kJ/mol for the results. We studied the binding of seven biotin analogues to avidin, taking advantage of the fact that the protein is a tetramer with four independent binding sites, which should give the same estimated binding affinities. We show that it is not enough to use a single long simulation (10 ns), because the standard error of such a calculation underestimates the difference between the four binding sites. Instead, it is better to run several independent simulations and average the results. With such an approach, we obtain the same results for the four binding sites, and any desired precision can be obtained by running a proper number of simulations. We discuss how the simulations should be performed to optimize the use of computer time. The correlation time between the MM/GBSA energies is ～5 ps and an equilibration time of 100 ps is needed. For MM/GBSA, we recommend a sampling time of 20–200 ps for each separate simulation, depending on the protein. With 200 ps production time, 5–50 separate simulations are required to reach a statistical precision of 1 kJ/mol (800–8000 energy calculations or 1.5–15 ns total simulation time per ligand) for the seven avidin ligands. This is an order of magnitude more than what is normally used, but such a number of simulations is needed to obtain statistically valid results for the MM/GBSA method. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Structural and energetic insight into the interactions between the benzolactam inhibitors and tumor marker HSP90α

The heat shock protein 90α (HSP90α) provides a promising molecular target for cancer therapy. A series of novel benzolactam inhibitors exhibited distinct inhibitory activity for HSP90α. However, the structural basis for the impact of distinct R₁ substituent groups of nine benzolactam inhibitors on HSP90α binding affinities remains unknown. In this study, we carried out molecular docking, molecular dynamics (MD) simulations, and molecular mechanics and generalized Born/surface area (MM–GBSA) binding free energy calculations to address the differences. Molecular docking studies indicated that all nine compounds presented one conformation in the ATP-binding site of HSP90α N-terminal domain. MD simulations and subsequent MM–GBSA calculations revealed that the hydrophobic interactions between all compounds and HSP90α contributed the most to the binding affinity and a good linear correlation was obtained between the calculated and the experimental binding free energies (R = 0.88). The per residue decomposition revealed that the most remarkable differences of residue contributions were found in the residues Ala55, Ile96, and Leu107 defining a hydrophobic pocket for the R₁ group, consistent with the analysis of binding modes. This study may be helpful for the future design of novel HSP90α inhibitors.     

Predicting hydration free energies of polychlorinated aromatic compounds from the SAMPL-3 data set with FiSH and LIE models

Next-generation solvation models are devised to mimic the accuracy and generality of explicit solvation models at the speed of current popular implicit solvation models. One such method is the first-shell of hydration (FiSH) continuum model that was trained on hydration energetics from LIE calculations and molecular dynamics simulations in explicit solvent. Here we tested prospectively the FiSH model on the SAMPL-3 hydration data set that zooms in the effect of chlorination on solvation. We compare these FiSH predictions with those from retrospective LIE calculations. We find that neither FiSH nor LIE can reproduce well the absolute values and the trend of hydration free energies in the biphenyl and dioxin aromatic chlorination series. Some of the hypotheses behind this performance are discussed and tested. The LIE explicit-solvent model shows some improvement relative to the FiSH continuum model, and we correct a systematic deviation in the continuum van der Waals term of FiSH associated with aromatic Cl atom type.     

Binding free energy predictions of farnesoid X receptor (FXR) agonists using a linear interaction energy (LIE) approach with reliability estimation: application to the D3R Grand Challenge 2

Computational protein binding affinity prediction can play an important role in drug research but performing efficient and accurate binding free energy calculations is still challenging. In the context of phase 2 of the Drug Design Data Resource (D3R) Grand Challenge 2 we used our automated eTOX ALLIES approach to apply the (iterative) linear interaction energy (LIE) method and we evaluated its performance in predicting binding affinities for farnesoid X receptor (FXR) agonists. Efficiency was obtained by our pre-calibrated LIE models and molecular dynamics (MD) simulations at the nanosecond scale, while predictive accuracy was obtained for a small subset of compounds. Using our recently introduced reliability estimation metrics, we could classify predictions with higher confidence by featuring an applicability domain (AD) analysis in combination with protein–ligand interaction profiling. The outcomes of and agreement between our AD and interaction-profile analyses to distinguish and rationalize the performance of our predictions highlighted the relevance of sufficiently exploring protein–ligand interactions during training and it demonstrated the possibility to quantitatively and efficiently evaluate if this is achieved by using simulation data only.     

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.     

QM/MM-PBSA method to estimate free energies for reactions in proteins

We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.     

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.