Prediction of binding poses to FXR using multi-targeted docking combined with molecular dynamics and enhanced sampling

Advanced molecular docking methods often aim at capturing the flexibility of the protein upon binding to the ligand. In this study, we investigate whether instead a simple rigid docking method can be applied, if combined with multiple target structures to model the backbone flexibility and molecular dynamics simulations to model the sidechain and ligand flexibility. The methods are tested for the binding of 35 ligands to FXR as part of the first stage of the Drug Design Data Resource (D3R) Grand Challenge 2 blind challenge. The results show that the multiple-target docking protocol performs surprisingly well, with correct poses found for 21 of the ligands. MD simulations started on the docked structures are remarkably stable, but show almost no tendency of refining the structure closer to the experimentally found binding pose. Reconnaissance metadynamics enhances the exploration of new binding poses, but additional collective variables involving the protein are needed to exploit the full potential of the method.     

Identification of ligands for RNA targets via structure-based virtual screening: HIV-1 TAR

Binding of the Tat protein to TAR RNA is necessary for viral replication of HIV-1. We screened the Available Chemicals Directory (ACD) to identify ligands to bind to a TAR RNA structure using a four-step docking procedure: rigid docking first, followed by three steps of flexible docking using a pseudobrownian Monte Carlo minimization in torsion angle space with progressively more detailed conformational sampling on a progressively smaller list of top-ranking compounds. To validate the procedure, we successfully docked ligands for five RNA complexes of known structure. For ranking ligands according to binding avidity, an empirical binding free energy function was developed which accounts, in particular, for solvation, isomerization free energy, and changes in conformational entropy. System-specific parameters for the function were derived on a training set of RNA/ligand complexes with known structure and affinity. To validate the free energy function, we screened the entire ACD for ligands for an RNA aptamer which binds l-arginine tightly. The native ligand ranked 17 out of ca. 153,000 compounds screened, i.e., the procedure is able to filter out >99.98% of the database and still retain the native ligand. Screening of the ACD for TAR ligands yielded a high rank for all known TAR ligands contained in the ACD and suggested several other potential TAR ligands. Eight of the highest ranking compounds not previously known to be ligands were assayed for inhibition of the Tat-TAR interaction, and two exhibited a CD₅₀ of ca. 1 M.     

Electroconductivity of Potassium Orthophosphate Modified by Four-Charged Cations

Solid solutions based on K₃PO₄ in systems K_{3 – 4x} E" _x PO₄ (E" = Si, Ti, Ge, Zr, Sn, Hf, Ce) are synthesized. The crystal structure, thermal behavior, and electroconduction of the synthesized solutions is studied. The narrowest single-phase regions take place in the systems where E" = Si, Ge (x 0.025), and the widest, in the system with Zr (x 0.125, at 700°C). Introducing Ti or Sn additives (x 0.05) and minimum quantities of Zr, Hf, or Ce (x = 0.025) into potassium orthophosphate leads to stabilization of highly-conductive -modification of K₃PO₄ at room temperature. Maximum values of potassium-cation conduction in all the systems studied correspond to regions of single-phase solid solutions based on K₃PO₄. The maximum electroconductivity (0.005 S cm^–1 at 300°C, 0.1 S cm^–1 at 700°C) and the smallest activation energies (32–35 kJ mol^–1) take place in the systems with Zr and Hf.     

A calorimetric investigation into copper–arginine and copper–alanine solid state interactions

Complexes of formula CuCl₂ · 2arg and CuCl₂ · 4ala (arg = arginine; ala = alanine) were prepared at room temperature by a solid state route. The metal–amino acid solid state interactions were studied by i.r. spectroscopy and solution calorimetry. For both complexes, participation of the carboxylate group as well as nitrogen in coordination are inferred, based on the i.r. data. For the copper–arginine compound, the calculated thermochemical parameters are: _rH_m = –114.9 ± 1.42 and _fH_m = –1608.3 ± 11.6 kJ mol^–1. For copper–alanine compound, a complete set of thermochemical parameters were calculated: _rH_m = –18.0 ± 0.9; _fH_m = –2490.4 ± 4.3; _DH_m = 597.2 ± 17.7; _MH_m = 771.9 ± 18.7; _gH_m = 627.1 ± 22.3 and D (Cu–L) = 156.8 ± 5.7 kJ mol^–1. Based on _rH_m and dissolution enthalpy values, a stronger intermolecular solid state interaction can be inferred for the arginine complex, than for the alanine one complex, probably due to the formation of intermolecular hydrogen bonds in the former.     

Efficient inclusion of receptor flexibility in grid-based protein-ligand docking

Accounting for receptor flexibility is an essential component of successful protein-ligand docking but still marks a major computational challenge. For many target molecules of pharmaceutical relevance, global backbone conformational changes are relevant during the ligand binding process. However, popular methods that represent the protein receptor molecule as a potential grid typically assume a rigid receptor structure during ligand-receptor docking. A new approach has been developed that combines inclusion of global receptor flexibility with the efficient potential grid representation of the receptor molecule. This is achieved using interpolation between grid representations of the receptor protein deformed in selected collective degrees of freedom. The method was tested on the docking of three ligands to apo protein kinase A (PKA), an enzyme that undergoes global structural changes upon inhibitor binding. Structural variants of PKA were generated along the softest normal mode of an elastic network representation of apo PKA. Inclusion of receptor deformability during docking resulted in a significantly improved docking performance compared with rigid PKA docking, thus allowing for systematic virtual screening applications at small additional computational cost.     

New approach to molecular docking and its application to virtual screening of chemical databases

This paper describes the validation of a molecular docking method and its application to virtual database screening. The code flexibly docks ligand molecules into rigid receptor structures using a tabu search methodology driven by an empirically derived function for estimating the binding affinity of a protein-ligand complex. The docking method has been tested on 70 ligand-receptor complexes for which the experimental binding affinity and binding geometry are known. The lowest energy geometry produced by the docking protocol is within 2.0 A root mean square of the experimental binding mode for 79% of the complexes. The method has been applied to the problem of virtual database screening to identify known ligands for thrombin, factor Xa, and the estrogen receptor. A database of 10,000 randomly chosen "druglike" molecules has been docked into the three receptor structures. In each case known receptor ligands were included in the study. The results showed good separation between the predicted binding affinities of the known ligand set and the database subset.     

slate: A method for the superposition of flexible ligands

A novel program for the superposition of flexible molecules, slate, is presented. It uses simulated annealing to minimise the difference between the distance matrices calculated from the hydrogen-bonding and aromatic-ring properties of two ligands. A method for generating a molecular stack using multiple pairwise matches is illustrated. These stacks are used by the program doh to predict the relative positions of receptor atoms that could form hydrogen bonds to two or more ligands in the dataset. The methodology has been applied to ligands binding to dihydrofolate reductase, thermolysin, H₃ histamine receptors, ₂ adrenoceptors and 5-HT_1D receptors. When there are sufficient numbers and diversity of molecules in the dataset, the prediction of receptor-atom positions is applicable to compound design.     

Temperature Dependence of Chloride Complexation for the Trivalent f-Elements

The influence of elevated temperatures on the formation of 1:1 chloro complexes for Eu³⁺ and Am³⁺ are reported. Using a solvent extraction technique, stability constants for the equilibrium M_(aq) ³⁺+Cl_(aq) ^– MCl_(aq) ²⁺ have been measured in the temperature range of 25–75 °C. Modest increases in ₁ are observed, and small positive enthalpies for these reactions are reported. These data are discussed in the context of previous reports for the trivalent lanthanide and actinide chloro systems.     

Theoretical analysis of magnetic and electric hyperfine interactions on 1H and 2H nuclei of bis(acetylacetonato) copper (II)

The INDO method has been used in calculating the tensors of hyperfine structure and the electric field gradient on the ¹H and ²H nuclei in Cu(acac)₂. The procedure used in calculating the magnetic resonance parameters (MRPs) is based on an accounting for one-center and two-center Coulomb integrals of dipole-dipole interaction. The influence of out-of-plane step distortion of the complex on the MRPs is examined critically.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 2, pp. 149–155, March–April, 1988.The authors wish to express their appreciation to P. V. Schastnev and S. A. Mustafaev for valuable discussion and for assistance in the work.     

Computational simulation of ligand docking to L-type pyruvate kinase subunit

Computational blind docking approach was used for mapping of possible binding sites in L-type pyruvate kinase subunit for peptides, RRASVA and the phosphorylated derivative RRAS(P_i)VA, which model the phosphorylatable N-terminal regulatory domain of the enzyme. In parallel, the same docking analysis was done for both substrates of this enzyme, phosphoenolpyruvate (PEP) and adenosine diphosphate (ADP), and for docking of fructose 1,6-bisphosphate (FBP), which is the allosteric activator of the enzyme. The binding properties of the entire surface of the protein were scanned and several possible binding sites were identified in domains A and C of the protein, while domain B revealed no docking sites for peptides or for substrates or the allosteric regulator. It was found that the docking sites of different ligands were partially overlapping, pointing to the possibility that some regulatory effects, observed in the case of L-type pyruvate kinase, may be caused by the competition of different ligands for the same binding sites.     

Very empirical treatment of solvation and entropy: a force field derived from Log Po/w

A non-covalent interaction force field model derived from the partition coefficient of 1-octanol/water solubility is described. This model, HINT for Hydropathic INTeractions, is shown to include, in very empirical and approximate terms, all components of biomolecular associations, including hydrogen bonding, Coulombic interactions, hydrophobic interactions, entropy and solvation/desolvation. Particular emphasis is placed on: (1) demonstrating the relationship between the total empirical HINT score and free energy of association, G _interaction; (2) showing that the HINT hydrophobic-polar interaction sub-score represents the energy cost of desolvation upon binding for interacting biomolecules; and (3) a new methodology for treating constrained water molecules as discrete independent small ligands. An example calculation is reported for dihydrofolate reductase (DHFR) bound with methotrexate (MTX). In that case the observed very tight binding, G _interaction–13.6 kcal mol^–1, is largely due to ten hydrogen bonds between the ligand and enzyme with estimated strength ranging between –0.4 and –2.3 kcal mol^–1. Four water molecules bridging between DHFR and MTX contribute an additional –1.7 kcal mol^–1 stability to the complex. The HINT estimate of the cost of desolvation is +13.9 kcal mol^–1.     

Effect of the rigidity and flexibility features of 2-pyridinyl or 8-quinolinyl based N-N chiral ligands on the stereochemical properties of [Pd(N-N)Cl2] complexes

The [Pd(N-N^∗)Cl₂] complexes have been obtained, as yellow solids, in almost quantitative yields; N-N^∗ indicate bidentate chiral ligands (S_a)-1, (S_a)-2, (S,S)-3, (R,R)-4, containing the rigid 2-pyridinyl or 8-quinolinyl building block skeleton and the C₂-symmetric chiral framework trans-2,5-dimethylpyrrolidinyl or (S)-(+)-2,2′-(2-azapropane-1,3-diyl)-1,1′-binaphthalene. The ligands pairs have the same C₂-symmetric chiral framework but different building block skeleton, beyond that for the basicity in the N-donor atoms, for rigidity and flexibility features. The N-N^∗ ligands act as chelating ligands leading a square planar geometry. The compounds [Pd(S,S-3)Cl₂] and [Pd(R,R-4)Cl₂] have been also characterised by X-ray diffraction. The rigidity and flexibility features of (S,S)-3 and (R,R)-4 ligands induce a different orientation of the trans-2,5-dimethylpyrrolidinyl moiety with respect to the pyridinyl and quinolinyl plane. This work shows that intrinsic rigidity and flexibility are not enough to define the ligand properties and to preview the effects that they induce on the reactivity of the metal complex.     

Enthalpy of dissociation of water at 325°C and LogK, ΔH, ΔS,and ΔC p values for the formation of NaOH(aq) from 250 to 325°C

The aqueous reactions H⁺+OH^–=H₂O at 325°C and Na⁺+OH^–= NaOH(aq) at 250–325°C, were studied using a flow calorimeter. Heats of mixing of aqueous NaOH and HCl solutions were measured at 325°C. The enthalpy of water formation (H=95.9 kJ-mol^–1, valid at 12.4 MPa and infinite dilution) was obtained at this temperature from the heat of mixing data but differs significantly from that calculated from the Marshall-Franck equation. This calorimetric H at 325°C was used in combination with literaturelog K and H values at lower temperatures to derive equations representinglog K, H, S, and C_p for the formation of water from 250 to 325°C. Heats of dilution of aqueous NaOH solutions were measured at 250, 275, 300, and 325°C. Log K, H, and S for the formation of NaOH(aq) were determined at these temperatures from the fits of the calculated and measured heats while C_p values were calculated from the variation of H with temperature. No previous experimental results have been reported for the formation of NaOH(aq). The isocoulombic reaction principle is tested using thelog K values obtained in this study. The plot oflog K vs. 1/T for the isocoulombic reaction NaOH(aq) +H⁺=H₂O+Na⁺ is approximately linear.Presented at the Second International Symposium on Chemistry in High Temperature Water, Provo, UT, August 1991.Taken in part from the Ph.D. Dissertation of Xuemin Chen, Brigham Young University, 1991.     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

A novel view of modelling interactions between synthetic and biological polymers via docking

Multipoint interactions between synthetic and natural polymers provide a promising platform for many topical applications, including therapeutic blockage of virus-specific targets. Docking may become a useful tool for modelling of such interactions. However, the rigid docking cannot be correctly applied to synthetic polymers with flexible chains. The application of flexible docking to these polymers as whole macromolecule ligands is also limited by too many possible conformations. We propose to solve this problem via stepwise flexible docking. Step 1 is docking of separate polymer components: (1) backbone units (BU), multi-repeated along the chain, and (2) side groups (SG) consisting of functionally active elements (SG _F ) and bridges (SG _B ) linking SG _F with BU. At this step, probable binding sites locations and binding energies for the components are scored. Step 2 is docking of component-integrating models: [BU] _m , SG = SG _F –SG _B , BU–SG, BU–BU(SG)–BU, BU(SG)–[BU] _m –BU(SG), and [BU _var (SG _var )] _m . Every modelling level yields new information, including how the linkage of various components influences on the ligand—target contacts positioning, orientation, and binding energy in step-by-step approximation to polymeric ligand motifs. Step 3 extrapolates the docking results to real-scale macromolecules. This approach has been demonstrated by studying the interactions between hetero-SG modified anionic polymers and the N-heptad repeat region tri-helix core of the human immunodeficiency virus type 1 (HIV-1) envelope glycoprotein gp41, the key mediator of HIV-1 fusion during virus entry. The docking results are compared to real polymeric compounds, acting as HIV-1 entry inhibitors in vitro. This study clarifies the optimal macromolecular design for the viral fusion inhibition and drug resistance prevention.     

CDOCKER and $$\lambda$$-dynamics for prospective prediction in D3R Grand Challenge 2

The opportunity to prospectively predict ligand bound poses and free energies of binding to the Farnesoid X Receptor in the D3R Grand Challenge 2 provided a useful exercise to evaluate CHARMM based docking (CDOCKER) and \(\lambda\)-dynamics methodologies for use in “real-world” applications in computer aided drug design. In addition to measuring their current performance, several recent methodological developments have been analyzed retrospectively to highlight best procedural practices in future applications. For pose prediction with CDOCKER, when the protein structure used for rigid receptor docking was close to the crystallographic holo structure, reliable poses were obtained. Benzimidazoles, with a known holo receptor structure, were successfully docked with an average RMSD of 0.97 \(\AA\). Other non-benzimidazole ligands displayed less accuracy largely because the receptor structures we chose for docking were too different from the experimental holo structures. However, retrospective analysis has shown that when these ligands were re-docked into their holo structures, the average RMSD dropped to 1.18 \(\AA\) for all ligands. When sulfonamides and spiros were docked with the apo structure, which agrees more with their holo structure than the structures we chose, five out of six ligands were correctly docked. These docking results emphasize the need for flexible receptor docking approaches. For \(\lambda\)-dynamics techniques, including multisite \(\lambda\)-dynamics (MS\(\lambda\)D), reasonable agreement with experiment was observed for the 33 ligands investigated; root mean square errors of 2.08 and 1.67 kcal/mol were obtained for free energy sets 1 and 2, respectively. Retrospectively, soft-core potentials, adaptive landscape flattening, and biasing potential replica exchange (BP-REX) algorithms were critical to model large substituent perturbations with sufficient precision and within restrictive timeframes, such as was required with participation in Grand Challenge 2. These developments, their associated benefits, and proposed procedures for their use in future applications are discussed.     

AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility

We describe the testing and release of AutoDock4 and the accompanying graphical user interface AutoDockTools. AutoDock4 incorporates limited flexibility in the receptor. Several tests are reported here, including a redocking experiment with 188 diverse ligand‐protein complexes and a cross‐docking experiment using flexible sidechains in 87 HIV protease complexes. We also report its utility in analysis of covalently bound ligands, using both a grid‐based docking method and a modification of the flexible sidechain technique. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Tensimetric investigation of the CrCl<Subscript>3</Subscript>—Cl<Subscript>2</Subscript> system in the temperature range of 600–1200 K

The sublimation pressure of chromium trichloride was measured by the static method with a quartz membrane-gauge manometer in the temperature range of 875–1230 K. An approximating equation for the sublimation pressure vs. temperature was found. The enthalpy (259.4±4 kJ mol^–1) and the entropy (224.2±3.5 J mol^–1 K^–1) of sublimation at 298 K were calculated. For the process 2 CrCl₃(g) + Cl₂(g) = 2 CrCl₄(g), the following values were obtained: _r H°₂₉₈ = –207.1±11.6 kJ mol^–1 and _r S°₂₉₈ = –173.6±10 5 J mol^–1 K^–1.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1561–1564, August, 2004.     

Hammerhead: fast,fully automated docking of flexible ligands to protein binding sites

Background: Molecular docking seeks to predict the geometry and affinity of the binding of a small molecule to a given protein of known structure. Rigid docking has long been used to screen databases of small molecules, because docking techniques that account for ligand flexibility have either been too slow or have required significant human intervention. Here we describe a docking algorithm, Hammerhead, which is a fast, automated tool to screen for the binding of flexible molecules to protein binding sites.Results: We used Hammerhead to successfully dock a variety of positive control ligands into their cognate proteins. The empirically tuned scoring function of the algorithm predicted binding affinities within 1.3 log units of the known affinities for these ligands. Conformations and alignments close to those determined crystallographically received the highest scores. We screened 80 000 compounds for binding to streptavidin, and biotin was predicted as the top-scoring ligand, with other known ligands included among the highest-scoring dockings. The screen ran in a few days on commonly available hardware.Conclusions: Hammerhead is suitable for screening large databases of flexible molecules for binding to a protein of known structure. It correctly docks a variety of known flexible ligands, and it spends an average of only a few seconds on each compound during a screen. The approach is completely automated, from the elucidation of protein binding sites, through the docking of molecules, to the final selection of compounds for assay.     

Convex-PL: a novel knowledge-based potential for protein-ligand interactions deduced from structural databases using convex optimization

We present a novel optimization approach to train a free-shape distance-dependent protein-ligand scoring function called Convex-PL. We do not impose any functional form of the scoring function. Instead, we decompose it into a polynomial basis and deduce the expansion coefficients from the structural knowledge base using a convex formulation of the optimization problem. Also, for the training set we do not generate false poses with molecular docking packages, but use constant RMSD rigid-body deformations of the ligands inside the binding pockets. This allows the obtained scoring function to be generally applicable to scoring of structural ensembles generated with different docking methods. We assess the Convex-PL scoring function using data from D3R Grand Challenge 2 submissions and the docking test of the CASF 2013 study. We demonstrate that our results outperform the other 20 methods previously assessed in CASF 2013. The method is available at http://team.inria.fr/nano-d/software/Convex-PL/.