Applying linear interaction energy method for binding affinity calculations of podophyllotoxin analogues with tubulin using continuum solvent model and prediction of cytotoxic activity

Podophyllotoxin and its analogues have important therapeutic value in the treatment of cancer, due to their ability to induce apoptosis in cancer cells in a proliferation-independent manner. These ligands bind to colchicine binding site of tubulin near the α- and β-tubulin interface and interfere with tubulin polymerization. The binding free energies of podophyllotoxin-based inhibitors of tubulin were computed using a linear interaction energy (LIE) method with a surface generalized Born (SGB) continuum solvation model. A training set of 76 podophyllotoxin analogues was used to build a binding affinity model for estimating the free energy of binding for 36 inhibitors (test set) with diverse structural modifications. The average root mean square error (RMSE) between the experimental and predicted binding free energy values was 0.56 kcal/mol which is comparable to the level of accuracy achieved by the most accurate methods, such as free energy perturbation (FEP) or thermodynamic integration (TI). The squared correlation coefficient between experimental and SGB–LIE estimates for the free energy for the test set compounds is also significant (R² = 0.733). On the basis of the analysis of the binding energy, we propose that the three-dimensional conformation of the A, B, C and D rings is important for interaction with tubulin. On the basis of this insight, 12 analogues of varying ring modification were taken, tested with LIE methodology and then validated with their experimental potencies of tubulin polymerization inhibition. Low levels of RMSE for the majority of inhibitors establish the structure-based LIE method as an efficient tool for generating more potent and specific inhibitors of tubulin by testing rationally designed lead compounds based on podophyllotoxin derivatization.     

Applying linear interaction energy method for binding affinity calculations of podophyllotoxin analogues with tubulin using continuum solvent model and prediction of cytotoxic activity

Podophyllotoxin and its analogues have important therapeutic value in the treatment of cancer, due to their ability to induce apoptosis in cancer cells in a proliferation-independent manner. These ligands bind to colchicine binding site of tubulin near the α- and β-tubulin interface and interfere with tubulin polymerization. The binding free energies of podophyllotoxin-based inhibitors of tubulin were computed using a linear interaction energy (LIE) method with a surface generalized Born (SGB) continuum solvation model. A training set of 76 podophyllotoxin analogues was used to build a binding affinity model for estimating the free energy of binding for 36 inhibitors (test set) with diverse structural modifications. The average root mean square error (RMSE) between the experimental and predicted binding free energy values was 0.56 kcal/mol which is comparable to the level of accuracy achieved by the most accurate methods, such as free energy perturbation (FEP) or thermodynamic integration (TI). The squared correlation coefficient between experimental and SGB–LIE estimates for the free energy for the test set compounds is also significant (R² = 0.733). On the basis of the analysis of the binding energy, we propose that the three-dimensional conformation of the A, B, C and D rings is important for interaction with tubulin. On the basis of this insight, 12 analogues of varying ring modification were taken, tested with LIE methodology and then validated with their experimental potencies of tubulin polymerization inhibition. Low levels of RMSE for the majority of inhibitors establish the structure-based LIE method as an efficient tool for generating more potent and specific inhibitors of tubulin by testing rationally designed lead compounds based on podophyllotoxin derivatization.     

Computational determination of binding structures and free energies of glucose 6-phosphate dehydrogenase with novel steroid inhibitors

Glucose 6-phosphate dehydrogenase (G6PD), the first and the rate-limiting enzyme in the pentose phosphate pathway (PPP), catalyzes the oxidation of G6P to 6-phosphogluconolactone and the reduction of NADP⁺ to NADPH. Its key role in cancer promotes the development of a potent and selective inhibitor that might increase cancer cell death when combined with radiotherapy. In the present study, we investigated the detailed binding modes and binding free energies for G6PD interacting with a promising series of recently developed inhibitors, i.e., the steroid derivatives, by performing molecular docking, molecular dynamics (MD) simulations, and binding free energy calculations. The docking indicates that the inhibitors occupy the binding sites of both G6P and NADP⁺. The calculated binding free energies on the basis of the MD-simulated enzyme–inhibitor complexes are in good agreement with the experimental activity data for all of the examined inhibitors. The valuable insights into the detailed enzyme–inhibitor binding including the important intermolecular interactions, e.g., the hydrogen bond interaction and the hydrophobic interaction, have been provided. The computational results provide new insights into future rational design of more potent inhibitors of G6PD as a treatment for cancer.     

6-巯基嘌呤质子转移异构化的量子化学计算研究

采用密度泛函B3LYP方法,在6-311G(d,p)基组水平上对6-巯基嘌呤质子转移引起的硫酮式与硫醇式互变异构反应机理进行了计算研究,获得了互变异构过程的反应焓、活化能、活化吉布斯自由能和质子转移反应的速率常数等参数。计算结果表明,6-巯基嘌呤无论是孤立分子还是一水合物,其硫酮式TP2是最稳定的异构体。计算结果同已有实验结果相符。由硫酮式通过分子内质子转移向硫醇式异构化找到4条反应通道(P1,P2,P3,P4),各通道的活化能分别为114.0,133.9,128.0,95.1 kJ·mol~(-1)。当水分子参与反应以双质子转移机理异构化时,活化能垒显著降低,各通道的活化能依次降为51.2,63.0,70.5,42.8 kJ·mol~(-1),可见,水助催化有利于硫酮式向硫醇式转变。计算结果还表明,氢键的强弱对TP2一水合物的稳定性会有一定的影响。     

Molecular insights into inclusion complexes of mansonone E and H enantiomers with various β-cyclodextrins

The structural dynamics and stability of inclusion complexes of mansonone E (ME) and H (MH) including their stereoisomers with various βCDs (methylated- and hydroxypropylated-βCDs) were investigated by classical molecular dynamics (MD) simulations and binding free energy calculations. The simulation results revealed that mansonones are able to form inclusion complexes with βCDs. The guest molecules are not completely inserted into the host cavity, their preferably positions are nearby the secondary rim with the oxane ring dipping into the hydrophobic inner cavity. The encapsulation process leads to a higher rigidity of the βCDs enhancing the intramolecular hydrogen bond formation ability and decreasing the chance of glucopyranose rotation. According to the MM-PBSA binding free energy calculation, all considered inclusion complexes are stable and the binding energies are mainly caused by van der Waals interactions. Moreover, the free energy calculations showed significant differences in the complexation energies for the stereoisomers, which could enable the separation of the isomers by analytical techniques for further pharmaceutical applications.     

Study of the interaction of Huperzia saururus Lycopodium alkaloids with the acetylcholinesterase enzyme

In the present study, we describe and compare the binding modes of three Lycopodium alkaloids (sauroine, 6-hydroxylycopodine and sauroxine; isolated from Huperzia saururus) and huperzine A with the enzyme acetylcholinesterase. Refinement and rescoring of the docking poses (obtained with different programs) with an all atom force field helped to improve the quality of the protein–ligand complexes. Molecular dynamics simulations were performed to investigate the complexes and the alkaloid's binding modes. The combination of the latter two methodologies indicated that binding in the active site is favored for the active compounds. On the other hand, similar binding energies in both the active and the peripheral sites were obtained for sauroine, thus explaining its experimentally determined lack of activity. MM-GBSA predicted the order of binding energies in agreement with the experimental IC₅₀ values.     

Could MM-GBSA be accurate enough for calculation of absolute protein/ligand binding free energies?

Implicit solvation methods such as MM-GBSA, when applied to evaluating protein/ligand binding free energies, are widely believed to be accurate only for the estimation of relative binding free energies for a congeneric series of ligands. In this work, we show that the MM-GBSA flavor of Prime 3.0, VSGB-2.0, with a variable dielectric model and a novel energy function, could be approaching the accuracy required for evaluating absolute binding free energies, albeit, through a linear regression fit. The data-set used for validation includes 106 protein–ligand complexes that were carefully selected to control for variability in the affinity data as well as error in the modeled complexes. Through systematic analysis, we also quantify the degradation in the R² of fit between experimental and calculated values with either greater variability in the affinity data or an increase in error in the modeled protein/ligand complexes. Limitations for its application in drug discovery are discussed along with the identification of areas for future development.     

Linear interaction energy models for β-secretase (BACE) inhibitors: Role of van der Waals,electrostatic, and continuum-solvation terms

Computing the binding affinity of a protein–ligand complex is one of the most fundamental and difficult tasks in computer-aided drug design. Many approaches for computing binding affinities can be classified as linear interaction energy (LIE) models as they rely on some type of linear fit of computed interaction energies between ligand and protein. We have examined the computed interaction energies of a series of β-secretase (BACE) inhibitors in terms of van der Waals, coulombic, and continuum-solvation contributions to ligand binding. We have also systematically examined the effect of different protonation states of the protein and ligands. We find that the binding affinities are relatively insensitive to the protonation state of the protein when neutral ligands are considered. Inclusion of charged ligands leads to large deviations in the coulomb, solvation, and even van der Waals terms. The latter is due to increased repulsive van der Waals interactions in the complex due to the strong coulomb attraction found between oppositely charged functional groups in the protein and ligand. In general, we find that the best models are obtained when the protein is judiciously charged (e.g. Asp32⁻, Arg235⁺) and the potentially charged ligands are treated as neutral.     

Linear interaction energy models for beta-secretase (BACE) inhibitors: Role of van der Waals, electrostatic, and continuum-solvation terms

Computing the binding affinity of a protein–ligand complex is one of the most fundamental and difficult tasks in computer-aided drug design. Many approaches for computing binding affinities can be classified as linear interaction energy (LIE) models as they rely on some type of linear fit of computed interaction energies between ligand and protein. We have examined the computed interaction energies of a series of β-secretase (BACE) inhibitors in terms of van der Waals, coulombic, and continuum-solvation contributions to ligand binding. We have also systematically examined the effect of different protonation states of the protein and ligands. We find that the binding affinities are relatively insensitive to the protonation state of the protein when neutral ligands are considered. Inclusion of charged ligands leads to large deviations in the coulomb, solvation, and even van der Waals terms. The latter is due to increased repulsive van der Waals interactions in the complex due to the strong coulomb attraction found between oppositely charged functional groups in the protein and ligand. In general, we find that the best models are obtained when the protein is judiciously charged (e.g. Asp32⁻, Arg235⁺) and the potentially charged ligands are treated as neutral.     

Conformational analysis of alkali metal complexes of anionic species of aspartic acid, their interconversion and deprotonation: a DFT investigation

Gas-phase geometry-optimized structures of aspartate complexes of anionic species (Hasp(-)) with lithium, sodium and potassium metal cations and transition-state structures for their interconversions were obtained using the density functional theory computations at the B3LYP/6-311++G(d,p) level of theory. The metal ion affinities of Hasp(-) species and deprotonation energies of [Hasp-M] complexes, M=Li+, Na+ and K+, and their conformers were obtained. Relative energies of the [Hasp-M] complex conformers, reaction energies, thermodynamic properties, rate and equilibrium constants of their complexation are reported. Binding energies of the most stable complexes with Li+, Na+ and K+ are -168.53, -133.34 and -117.68kcal/mol, respectively. The most stable complex conformer as a tri-coordinated form for aspartate complex with Li(+) and bi-coordinated form for aspartate complexes with Na+ and K+ were found.     

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87–0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82–0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10 kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65–0.99 and 0.76–0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953–0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes.     

Insight into the structural mechanism for PKBα allosteric inhibition by molecular dynamics simulations and free energy calculations

Protein kinase B (PKB/Akt) is an attractive target for the treatment of tumor. Unlike PKB's ATP-competitive inhibitors, its allosteric inhibitors can maintain PKB's inactive state via its binding in a pocket between PH domain and kinase domain, which specifically inhibit PKB by preventing the phosphorylations of Thr308 and Ser473. In the present studies, MD simulations were performed on three allosteric inhibitors with different inhibitory potencies (IC₅₀) to investigate the interaction modes between the inhibitors and PKBα. MM/GB(PB)SA were further applied to calculate the binding free energies of these inhibitors binding to PKBα. The computed binding free energies were consistent with the ranking of their experimental bioactivities. The key residues of PKBα interacting with the allosteric inhibitor were further discussed by analyzing the different interaction modes of these three inhibitors binding to PKBα and by calculating binding free energy contributions of corresponding residues around the binding pocket. The structural requirements were then summarized for the allosteric inhibitor binding to PKBα. A possible structural mechanism of PKBα inhibition induced by the binding of allosteric inhibitor was formulated. The current studies indicate that there should be an optimum balance between the van der Waals and total electrostatic interactions for further designing of PKBα allosteric inhibitors.     

Binding affinity models for Falcipain inhibition based on the Linear Interaction Energy method

The high rate of drug resistance as well as the complex biochemical process of the parasite reproduction cycle makes development of new drugs for malaria a very important but challenging task. Falcipain 2 (FL2) and Falcipain 3 (FL3) are the major cysteine protease enzymes that play a central role in providing essential amino acids for the parasite’s protein biosynthesis through the hemoglobin hydrolysis process. Selective inhibition of these enzymes is considered as a promising chemotherapeutic target. In the present investigation, the highly efficient linear interaction energy (LIE) method has been parameterized for binding affinity predictions and assessed with a set of 244 compounds for FL2 and FL3 inhibition. The results revealed that the van der Waals energy is very important for ligands binding to Falcipain proteins and that, overall, the electrostatic energy contribution is minor. The best models obtained for FL2 and FL3 give root mean square errors (RMSE) of 1.82 and 1.33 kcal/mol respectively, for the test set. In this study, we also investigate how the choice of initial protein-ligand confirmation (pose) impacts the overall quality of the LIE models. Moreover, the transferability of LIE parameters is further discussed.     

Conformational and energy evaluations of novel peptides binding to dengue virus envelope protein

Effective novel peptide inhibitors which targeted the domain III of the dengue envelope (E) protein by blocking dengue virus (DENV) entry into target cells, were identified. The binding affinities of these peptides towards E-protein were evaluated by using a combination of docking and explicit solvent molecular dynamics (MD) simulation methods. The interactions of these complexes were further investigated by using the Molecular Mechanics-Poisson Boltzmann Surface Area (MMPBSA) and Molecular Mechanics Generalized Born Surface Area (MMGBSA) methods. Free energy calculations of the peptides interacting with the E-protein demonstrated that van der Waals (vdW) and electrostatic interactions were the main driving forces stabilizing the complexes. Interestingly, calculated binding free energies showed good agreement with the experimental dissociation constant (K_d) values. Our results also demonstrated that specific residues might play a crucial role in the effective binding interactions. Thus, this study has demonstrated that a combination of docking and molecular dynamics simulations can accelerate the identification process of peptides as potential inhibitors of dengue virus entry into host cells.     

Theoretical studies on the interactions of XIAP-BIR3 domain with bicyclic and tricyclic core monovalent Smac mimetics

X-linked IAP can bind caspase-9 and inhibit its activity. Mitochondrial protein Smac/DIABLO can also interact with XIAP and relieve the inhibition on caspase-9 to induce apoptosis. A series of artificial Smac mimetics have been used to mimic the Smac N-terminal tetrapeptide AVPI to bind to XIAP-BIR3, but these structural diverse mimetics exhibited distinct binding affinities. To get an insight into the binding nature and optimize the structures, molecular docking and dynamics simulations were used to study the binding of XIAP-BIR3 with three groups of Smac mimetics. The docking results reveal that these Smac mimetics anchored on the surface groove of XIAP-BIR3 and superimposed well with AVPI. The modifications on the seven-membered ring of bicyclic core segment do not strengthen the binding affinity, while a benzyl introduced to the five-membered ring is favorable to the binding. Molecular dynamics simulations on three typical systems show that these complexes are very stable. Hydrogen bonds between the bicyclic core segment and Thr308 play critical roles in maintaining the stability of complex. The binding free energies calculated by MM_PBSA method are consistent with the experimental results.     

A reduce package for determining lie symmetries of ordinary and partial differential equations

Title of program: LIE0,LIE1,LIE2,LIE3,LIE4 Catalogue number: AAZB Program obtainable form: CPC Program library, Queen's University in Belfast, N. Ireland (see application form in this issue) Computer: Siemens 7.760 Operating system: BS 2000 Programming language used: LISP High speed storage required: depends on the problem, minimum about 400 000 bytes No. of bits in a word: 32 Number of cards in combined program and test deck: 200     

Enhanced stability of a naringenin/2,6-dimethyl β-cyclodextrin inclusion complex: Molecular dynamics and free energy calculations based on MM- and QM-PBSA/GBSA

The structure, dynamic behavior and binding affinity of the inclusion complexes between naringenin and the two cyclodextrins (CDs), β-CD and its 2,6-dimethyl derivative (DM-β-CD), were theoretically studied by multiple molecular dynamics simulations and free energy calculations. Naringenin most likely prefers to bind with CDs through the phenyl ring. Although a lower hydrogen bond formation of naringenin with the 3-hydroxyl group of DM-β-CD (relative to β-CD) was observed, the higher cavity could encapsulate almost the whole naringenin molecule. In contrast for the naringenin/β-CD complex, the phenyl ring feasibly passed through the primary rim resulting in the chromone ring binding inside instead. MM-PBSA/GBSA and QM-PBSA/GBSA binding free energies strongly suggested a greater stability of the naringenin/DM-β-CD inclusion complex. Van der Waals force played an important role as the key guest–host interaction for the complexation between naringenin and each cyclodextrin.     

Cation-pi interaction in potassium-polyene complexes and the fate of potassium ion: a theoretical study

Ab initio studies have been done at B3LYP/6-31G* level of theory to determine the structural changes on the substitution of potassium to odd-numbered all-trans conjugated polyenes ranging from C(5) to C(13). The results show that potassium is always positioned in the form of K(+) above an odd carbon other than the terminal carbons and that the stablest structural isomer is the one with K(+) lying above the central odd carbon. If a central odd carbon does not exist (as in C(11)-system), then K(+) will be positioned above the odd carbon nearest to the central carbon to achieve maximum stability. The difference in the binding energies of the isomers is generally small and it becomes insignificantly small as the carbon chain length increases so that under suitable conditions K(+) ion may be made to move between the ends of the polyene. The metal-polyene complexes are seen to have a considerably reduced HOMO-LUMO gap. Further, the interaction of potassium with the polyene not only caused a total rearrangement of the bond lengths, bond angles and dihedral angles, but also induced a bend (warping) to the polyenic fragment that pockets K(+). The structural changes and stability of the metal-polyene complexes are explained in terms of electrostatic interaction and cation-pi cloud interaction.