Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations

Free Energy Perturbation with Replica Exchange Molecular Dynamics (FEP/REMD) offers a powerful strategy to improve the convergence of free energy computations. In particular, it has been shown previously that a FEP/REMD scheme allowing random moves within an extended replica ensemble of thermodynamic coupling parameters "lambda" can improve the statistical convergence in calculations of absolute binding free energy of ligands to proteins [J. Chem. Theory Comput. 2009, 5, 2583]. In the present study, FEP/REMD is extended and combined with an accelerated MD simulations method based on Hamiltonian replica-exchange MD (H-REMD) to overcome the additional problems arising from the existence of kinetically trapped conformations within the protein receptor. In the combined strategy, each system with a given thermodynamic coupling factor lambda in the extended ensemble is further coupled with a set of replicas evolving on a biased energy surface with boosting potentials used to accelerate the inter-conversion among different rotameric states of the side chains in the neighborhood of the binding site. Exchanges are allowed to occur alternatively along the axes corresponding to the thermodynamic coupling parameter lambda and the boosting potential, in an extended dual array of coupled lambda- and H-REMD simulations. The method is implemented on the basis of new extensions to the REPDSTR module of the biomolecular simulation program CHARMM. As an illustrative example, the absolute binding free energy of p-xylene to the nonpolar cavity of the L99A mutant of T4 lysozyme was calculated. The tests demonstrate that the dual lambda-REMD and H-REMD simulation scheme greatly accelerates the configurational sampling of the rotameric states of the side chains around the binding pocket, thereby improving the convergence of the FEP computations.     

烷基芳基磺酸盐的分子动力学模拟与自由能微扰计算

为研究不同结构的表面活性剂分子在溶液中胶束化能力的差异, 采用分子动力学方法模拟三种烷基芳基磺酸盐在真空和水溶液环境下的结构与相互作用. 利用自由能微扰(FEP)方法计算了水合自由能, 发现与用传统热力学表面张力法测定自制的烷基芳基磺酸盐结果一致. 研究表明: 烷基芳基磺酸盐在水溶液中的胶束化过程是自发进行的, 随着分子结构中芳环向长烷基链中间位置移动, 胶束化能力和胶束稳定性均下降; 疏水基周围水分子的“冰山结构”会影响胶束的稳定性, 而水分子中氢键的生存周期是反映冰山结构变化的重要指标; 同时, 亲水基与水分子间形成氢键的数目会增强或减弱分子脱离胶束体的趋势, 从而影响胶束结构的稳定性.     

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations.     

关于副本交换分子动力学模拟复杂化学反应的研究

本文研究用温度副本交换分子动力学(T-REMD)和哈密顿副本交换分子动力学(H-REMD)方法模拟复杂化学反应的问题。使用具有不同活化能和反应能的简单置换反应模型,我们检验了上述两种方法用来预测反应平衡产物的效率和应用范围。T-REMD方法对具有适度活化能(约< 20 kcal·mol^-1)或者反应能量(< 3 kcal·mol^-1)的放热反应是有效的。由于在相空间的不完整采样,对于同时具有高活化能和反应能量的反应其模拟效率有严重障碍,并且对于吸热反应问题更为显着。另一方面,H-REMD对一系列具有不同活化能的反应能的模型表现出色,与T-REMD相比,H-REMD可以使用更少的副本获得优异的结果。     

DNA小沟结合药物DB818的分子动力学模拟和结合自由能分析

采用分子动力学模拟了DNA小沟结合芳香二脒药物DB818形成的复合物. 通过5 ns的模拟研究表明: DB818药物分子可紧密结合在DNA的AATTC小沟区域, 和双螺旋d[CGCGAATTCGCG]2形成稳定的复合物. 由于噻吩硫原子的弱电负性, 使DB818能够以更大的伸展程度与DNA的小沟结合, 形成更强的结合力. DB818苯并咪唑的氮原子能够与DNA 7位和19位T碱基上的氧原子形成两个稳定的氢键, 同时, DB818末端氨基氮原子分别与DNA 的20位T碱基的氧原子和9位C碱基的氧原子形成两个氢键. 另外, 运用MM_PBSA方法计算了DB293-DNA和DB818-DNA复合物的结合自由能, 计算结合能与实验值能较好的吻合, 通过比较其结合自由能, 从热力学能量角度说明了DB818有较大的熵值与较小的焓值贡献, 从而与DNA小沟结合的结合力比DB293强. 本文在分子水平上提供了DB818直接与双螺旋DNA相互作用的结构及复合物的动态变化情况, 为设计出更高生物活性的DNA小沟结合剂提供一定的理论依据.     

Computing Alchemical Free Energy Differences with Hamiltonian Replica Exchange Molecular Dynamics (H-REMD) Simulations

Alchemical free energy calculations play a very important role in the field of molecular modeling. Efforts have been made to improve the accuracy and precision of those calculations. One of the efforts is to employ a Hamiltonian replica exchange molecular dynamics (H-REMD) method to enhance conformational sampling. In this paper, we demonstrated that HREMD method not only improves convergence in alchemical free energy calculations but also can be used to compute free energy differences directly via the Free Energy Perturbation (FEP)algorithm. We show a direct mapping between the H-REMD and the usual FEP equations, which are then used directly to compute free energies. The H-REMD alchemical free energy calculation (Replica exchange Free Energy Perturbation, REFEP) was tested on predicting the pK(a) value of the buried Asp26 in thioredoxin. We compare the results of REFEP with TI and regular FEP simulations. REFEP calculations converged faster than those from TI and regular FEP simulations. The final predicted pK(a) value from the H-REMD simulation was also very accurate, only 0.4 pK(a) unit above the experimental value. Utilizing the REFEP algorithm significantly improves conformational sampling, and this in turn improves the convergence of alchemical free energy simulations.     

TATB基PBX结合能的分子动力学模拟

用分子动力学（MD）方法, 模拟计算了四种氟聚合物(聚偏二氟乙烯（PVDF）、聚三氟氯乙烯（PCTFE）、氟橡胶（F₂₃₁₁)、氟树脂(F₂₃₁₄))与TATB(1,3,5- 三氨基- 2,4,6- 三硝基苯)晶体的相互作用. 结果发现, 四种氟聚物与TATB的结合能大小排序为PVDF>F₂₃₁₁>F₂₃₁₄>PCTFE, 各氟聚物在TATB不同晶面上的结合能大小排序为(001)>(010)>(100), 结合能主要由分子间氢键决定.     

谷氨酰胺结合蛋白的分子动力学模拟和自由能计算

谷氨酰胺结合蛋白(Glutamine-binding protein, GlnBp)是大肠杆菌透性酶系统中一个细胞外液底物专一性结合蛋白, 对于细胞外液中谷氨酰胺(Gln)的运输和传递至关重要. 本文运用分子动力学(Molecular dynamics, MD)模拟采样, 考察了GlnBp关键残基与底物Gln之间的相互作用和GlnBp两条铰链的功能差别; 并采用MM-PBSA方法计算了GlnBp与底物Gln的结合自由能. 结果表明: Ph13, Phe50, Thr118和Ile69与底物Gln的范德华相互作用和Arg75, Thr70, Asp157, Gly68, Lys115, Ala67, His156与底物Gln的静电相互作用是结合Gln的主要推动力; 复合物的铰链区85～89柔性大, 对构象开合提供了结构基础; 而铰链区181～185柔性小, 其作用更多是在功能上把底物Gln限制在口袋中; 自由能预测值与实验值吻合. 本研究很好地解释了GlnBp结构与功能的关系, 为进一步了解GlnBp的开合及转运Gln的机制提供了重要的结构信息.     

多肽抑制剂抑制淀粉质多肽42构象转换的分子动力学模拟和结合自由能计算

应用分子动力学模拟和结合自由能计算方法研究了多肽抑制剂KLVFF、VVIA和LPFFD抑制淀粉质多肽42 (Aβ42)构象转换的分子机理. 结果表明, 三种多肽抑制剂均能够有效抑制Aβ42的二级结构由α-螺旋向β-折叠的构象转换. 另外, 多肽抑制剂降低了Aβ42分子内的疏水相互作用, 减少了多肽分子内远距离的接触, 有效抑制了Aβ42的疏水塌缩, 从而起到稳定其初始构象的作用. 这些抑制剂与Aβ42之间的疏水和静电相互作用(包括氢键)均有利于它们抑制Aβ42的构象转换. 此外, 抑制剂中的带电氨基酸残基可以增强其和Aβ42之间的静电相互作用(包括氢键), 并降低抑制剂之间的聚集, 从而大大增强对Aβ42构象转换的抑制能力. 但脯氨酸的引入会破坏多肽的线性结构, 从而大大降低其与Aβ42 之间的作用力. 上述分子模拟的结果揭示了多肽抑制剂KLVFF、VVIA和LPFFD抑制Aβ42构象转换的分子机理, 对于进一步合理设计Aβ的高效短肽抑制剂具有非常重要的理论指导意义.     

In Silico Study towards Repositioning of FDA-Approved Drug Candidates for Anticoronaviral Therapy: Molecular Docking,Molecular Dynamics and Binding Free Energy Calculations

The SARS-CoV-2 targets were evaluated for a set of FDA-approved drugs using a combination of drug repositioning and rigorous computational modeling methodologies such as molecular docking and molecular dynamics (MD) simulations followed by binding free energy calculations. Six FDA-approved drugs including, Ouabain, Digitoxin, Digoxin, Proscillaridin, Salinomycin and Niclosamide with promising anti-SARS-CoV-2 activity were screened in silico against four SARS-CoV-2 proteins—papain-like protease (PLpro), RNA-dependent RNA polymerase (RdRp), SARS-CoV-2 main protease (Mpro), and adaptor-associated kinase 1 (AAK1)—in an attempt to define their promising targets. The applied computational techniques suggest that all the tested drugs exhibited excellent binding patterns with higher scores and stable complexes compared to the native protein cocrystallized inhibitors. Ouabain was suggested to act as a dual inhibitor for both PLpro and Mpro enzymes, while Digitoxin bonded perfectly to RdRp. In addition, Salinomycin targeted PLpro. Particularly, Niclosamide was found to target AAK1 with greater affinity compared to the reference drug. Our study provides comprehensive molecular-level insights for identifying or designing novel anti-COVID-19 drugs.     

Discovery of Potential SARS-CoV-2M Protease Inhibitors by Virtual Screening,Molecular Dynamics,and Binding Free Energy Analyses

The severe acute respiratory syndrome coronavirus 2(SARS-CoV-2) gained tremendous attention due to its high infectivity and pathogenicity. The 3-chymotrypsin-like hydrolase protease(Mpro) of SARS-CoV-2 has been proven to be an important target for anti-SARS-CoV-2 activity. To better identify the drugs with potential in treating coronavirus disease 2019(COVID-19) caused by SARS-CoV-2 and according to the crystal structure of Mpro, we conducted a virtual screening of FDA-approved drugs and chemical agents that have entered clinical trials. As a result, 9 drug candidates with therapeutic potential for the treatment of COVID-19 and with good docking scores were identified to target SARS-CoV-2. Consequently, molecular dynamics(MD) simulation was performed to explore the dynamic interactions between the predicted drugs and Mpro. The binding mode during MD simulation showed that hydrogen bonding and hydrophobic interactions played an important role in the binding processes. Based on the binding free energy calculated by using MM/PBSA, Lopiravir, an inhibitor of human immunodeficiency virus(HIV) protease, is under investigation for the treatment of COVID-19 in combination with ritionavir, and it might inhibit Mpro effectively. Moreover, Ombitasvir, an inhibitor for non-structural protein 5 A of hepatitis C virus(HCV), has good inhibitory potency for Mpro. It is notable that the GS-6620 has a binding free energy, with respect to binding Mpro, comparable to that of ombitasvir. Our study suggests that ombitasvir and lopinavir are good drug candidates for the treatment of COVID-19, and that GS-6620 has good anti-SARS-CoV-2 activity.     

Statistical Analysis of Ion Mobility Spectrometry. I. Unbiased and Guided Replica-Exchange Molecular Dynamics

Achieving (bio)macromolecular structural assignment from the interpretation of ion mobility spectrometry (IMS) experiments requires successful comparison with computer modeling. Replica-exchange molecular dynamics simulations with suitable force fields not only offer a convenient framework to locate relevant conformations, especially in the case of multiple-funnel energy landscapes, but they are also well suited to statistical analyses. In the present paper, we discuss two extensions of the method used to improve its efficiency in the context of IMS. Two doubly-protonated polyalanines [RA₄XA₄K + 2H]²⁺ with X = V and D appear as favorable cases for which the calculated collision cross-section distributions naturally agree with the measurements, providing reliable candidate structures. For these compounds, a careful consideration of other order parameters based on the weighted histogram method resolves several otherwise hidden underlying conformational families. In the case of a much larger peptide exhibiting bistability, assignment is more difficult but could be achieved by guiding the sampling with an umbrella potential using the square gyration radius as the biasing coordinate. Applied to triply protonated bradykinine, the two presented methods indicate that different conformations compatible with the measurements are very close in energy.     

FKBP12蛋白与其抑制剂结合的分子动力学模拟和结合自由能计算

FKBP12 (FK506-binding protein-12)是一种具有神经保护和促神经再生作用的蛋白. 采用分子动力学模拟取样, 运用MM-GBSA方法计算了FKBP12和3个抑制剂(GPI-1046, 308和107)的绝对结合自由能, GPI-1046的结合能最小, 308小于107的结合能. 通过能量分解的方法考察了FKBP12蛋白的主要残基与抑制剂之间的相互作用和识别, 计算结果表明: 3个抑制剂具有相似的结合模式, Ile56和Tyr82主要表现为氢键作用, Tyr26, Phe46, Val55, Ile56, Trp59, Tyr82, Tyr87和Phe99形成疏水作用区. 计算结果和实验结果吻合.     

葡萄糖苷酶抑制剂作用机理的分子动力学模拟和自由能计算

含有锍离子的葡萄糖苷酶抑制剂如kotalanol (SK)和它除去磺酸基团后的衍生物(DSK), 是潜在的毒副作用较小的治疗II 型糖尿病的候选药物. α-葡萄糖苷酶抑制活性实验显示, DSK活性比SK略高, 而将二者环上的S原子替换成NH后(分别称为DSN和SN), DSN的活性要比SN高1500倍左右. 本文用分子动力学模拟, 结合自由能计算和自由能分解的方法对上述四个抑制剂的作用机理进行了研究. 研究结果表明活性的巨大差异是由NH基团取代效应和磺酸基团立体效应共同作用的结果, 由于N―C键长比S―C键长短, NH基团取代导致烷基链的翻转, 同时, 磺酸基团限制了链的翻转, 因此改变了抑制剂的结合模式. 计算结果与实验基本一致.本文的研究结果有助于进一步理解含锍离子的葡萄糖苷酶抑制剂的结合机理, 并为设计更有潜力的葡萄糖苷酶抑制剂提供了有价值的信息.     

Calculation of the Absolute Free Energy of Binding and Related Entropies with the HSMD-TI Method: The FKBP12-L8 Complex

The hypothetical scanning molecular dynamics (HSMD) method is used here for calculating the absolute free energy of binding, ΔA(0) of the complex of the protein FKBP12 with the ligand SB2 (also denoted L8) - a system that has been studied previously for comparing the performance of different methods. Our preliminary study suggests that considering long-range electrostatics is imperative even for a hydrophobic ligand such as L8. Therefore the system is modeled by the AMBER force field using Particle Mesh Ewald (PME). HSMD consists of three stages applied to both the ligand-solvent and ligand-protein systems. (1) A small set of system configurations (frames) is extracted from an MD trajectory. (2) The entropy of the ligand in each frame is calculated by a reconstruction procedure. (3) The contribution of water and protein to ΔA(0) is calculated for each frame by gradually increasing the ligand-environment interactions from zero to their full value using thermodynamic integration (TI). Unlike the conventional methods, the structure of the ligand is kept fixed during TI, and HSMD is thus free from the end-point problem encountered with the double annihilation method (DAM); therefore, the need for applying restraints is avoided. Furthermore, unlike the conventional methods, the entropy of the ligand and water is obtained directly as a byproduct of the simulation. In this paper, in addition to the difference in the internal entropies of the ligand in the two environments, we calculate for the first time the external entropy of the ligand, which provides a measure for the size of the active site. We obtain ΔA(0) = -10.7 ±1.0 as compared to the experimental values -10.9 and -10.6 kcal/mol. However, a protein/water system treated by periodic boundary conditions grows significantly with increasing protein size and the computation of ΔA(0) would become expensive by all methods. Therefore, we also apply HSMD to FKBP12-L8 described by the GSBP/SSBP model of Roux's group (implemented in the software CHARMM) where only part of the protein and water around the active site are considered and long-range electrostatic effects are taken into account. For comparison this model was also treated by the double decoupling method (DDM). The two methods have led to comparable results for ΔA(0) which are somewhat lower than the experimental value. The ligand was found to be more confined in the active site described by GSBP/SSBP than by PME where its entropy in solvent is larger than in the active site by 1.7 and by 5.5 kcal/mol, respectively.     

激酶ABL与肉豆蔻酰位点小分子作用机理的分子动力学模拟及自由能计算

采用分子动力学方法研究激酶ABL 与ATP 位点小分子imatinib、P16 及变构位点小分子STJ、MS7、MS9、3YY、MYR等的结合, 并用GBSA (generalized Born surface area)方法将结合自由能分解到各残基. 自由能计算结果表明, 小分子STJ、MS7、MS9 有利于imatinib 与ABL 结合; 小分子STJ、MS7、MS9 与激酶ABL的结合自由能接近, 绝对值均大于ABL 与3YY、MYR 的结合自由能. 能量分解表明, ABL 残基ILE502、VAL506、LEU510与STJ和MYR的相互作用是αI 螺旋处于弯曲状态的重要原因. 模拟过程中ABL肉豆蔻酰口袋残基均方根偏差(RMSD)变化值表明, STJ等小分子抑制剂与ABL结合后降低了肉豆蔻酰口袋残基的柔性.     

应用L-J(12/6)势能模型对Fe2+水化作用的分子动力学模拟

本文首先优化出Fe²⁺和水分子相互作用的Lennard-Jones(12/6)势能模型中的2个参数：ε_IW=0.180 kcal·mol^-1和σ_IW=0.2885 nm。然后在298.15 K和573 K 温度条件下，用这个势能模型去运行Fe²⁺极稀水溶液系统的分子动力学模拟。模拟的结果显示，Fe²⁺的第一和第二水化壳层的结构和动力学性质与实验的，以及其他势能模型模拟出的结果一致。模拟的同时获得了关于RWK2水分子模型内部结构变化的新信息。此外，模拟揭示了温度变化对Fe²⁺水化结构和动力学性质的影响。     

Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses,a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses

We propose a free energy calculation method for receptor–ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host–guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein–ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.     

Alchemical Grid Dock (AlGDock): Binding Free Energy Calculations between Flexible Ligands and Rigid Receptors

Alchemical Grid Dock (AlGDock) is open-source software designed to compute the binding potential of mean force—the binding free energy between a flexible ligand and a rigid receptor—for a small organic ligand and a biological macromolecule. Multiple BPMFs can be used to rigorously compute binding affinities between flexible partners. AlGDock uses replica exchange between thermodynamic states at different temperatures and receptor–ligand interaction strengths. Receptor–ligand interaction energies are represented by interpolating precomputed grids. Thermodynamic states are adaptively initialized and adjusted on-the-fly to maintain adequate replica exchange rates. In demonstrative calculations, when the bound ligand is treated as fully solvated, AlGDock estimates BPMFs with a precision within 4 kT in 65% and within 8 kT for 91% of systems. It correctly identifies the native binding pose in 83% of simulations. Performance is sometimes limited by subtle differences in the important configuration space of sampled and targeted thermodynamic states. © 2019 Wiley Periodicals, Inc.