Harmonic modes as variables to approximately account for receptor flexibility in ligand–receptor docking simulations: Application to DNA minor groove ligand complex

An approach to approximately account for receptor flexibility in ligand–receptor docking simulations is described and applied to a DNA/Hoechst 33258 analogue complex. Harmonic modes corresponding to eigenvectors with small eigenvalues of the Hessian matrix of the potential energy function were used as independent variables to describe receptor flexibility. For the DNA minor groove ligand case most of the conformational difference between an energy minimized free DNA and ligand-bound structure could be assigned to 5–40 harmonic receptor modes with small eigenvalues. During docking, deformations of the DNA receptor structure in the subset of harmonic modes were limited using a simple penalty function that avoided the summation over all intrareceptor atom pairs. Significant improvement of the sterical fit between ligand and receptor was found upon relaxation of the DNA in the subset of harmonic modes after docking of the ligand at the position found in the known crystal structure. In addition, the harmonic mode relaxation resulted in DNA structures that were more similar to the energy minimized ligand-bound form. Although harmonic mode relaxation also leads to improved sterical fit for other ligand placements, the placement as observed in the crystal structure could still be identified as the site with the most favorable sterical interactions. Because relaxation in the harmonic modes is orders of magnitude faster than conventional energy minimization using all atom coordinates as independent variables, the approach might be useful as a preselection tool to recognize ligand binding sites accessible only upon small conformational changes of the receptor. The harmonic mode relaxed structures can only be considered as approximate structures because deformation of the receptor in the harmonic modes can lead to small perturbations of the stereochemical geometry of the molecule. Energy minimization of preselected ligand–DNA docking candidates in all atom coordinates is required to reduce these deviations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 287–300, 1999     

Modeling loop backbone flexibility in receptor‐ligand docking simulations

The relevance of receptor conformational change during ligand binding is well documented for many pharmaceutically relevant receptors, but is still not fully accounted for in in silico docking methods. While there has been significant progress in treatment of receptor side chain flexibility sampling of backbone flexibility remains challenging because the conformational space expands dramatically and the scoring function must balance protein–protein and protein–ligand contributions. Here, we investigate an efficient multistage backbone reconstruction algorithm for large loop regions in the receptor and demonstrate that treatment of backbone receptor flexibility significantly improves binding mode prediction starting from apo structures and in cross docking simulations. For three different kinase receptors in which large flexible loops reconstruct upon ligand binding, we demonstrate that treatment of backbone flexibility results in accurate models of the complexes in simulations starting from the apo structure. At the example of the DFG‐motif in the p38 kinase, we also show how loop reconstruction can be used to model allosteric binding. Our approach thus paves the way to treat the complex process of receptor reconstruction upon ligand binding in docking simulations and may help to design new ligands with high specificity by exploitation of allosteric mechanisms. © 2012 Wiley Periodicals, Inc.     

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.     

Exploring hierarchical refinement techniques for induced fit docking with protein and ligand flexibility

We present a series of molecular‐mechanics‐based protein refinement methods, including two novel ones, applied as part of an induced fit docking procedure. The methods used include minimization; protein and ligand sidechain prediction; a hierarchical ligand placement procedure similar to a‐priori protein loop predictions; and a minimized Monte Carlo approach using normal mode analysis as a move step. The results clearly indicate the importance of a proper opening of the active site backbone, which might not be accomplished when the ligand degrees of freedom are prioritized. The most accurate method consisted of the minimized Monte Carlo procedure designed to open the active site followed by a hierarchical optimization of the sidechain packing around a mobile flexible ligand. The methods have been used on a series of 88 protein‐ligand complexes including both cross‐docking and apo‐docking members resulting in complex conformations determined to within 2.0 Å heavy‐atom RMSD in 75% of cases where the protein backbone rearrangement upon binding is less than 1.0 Å α‐carbon RMSD. We also demonstrate that physics‐based all‐atom potentials can be more accurate than docking‐style potentials when complexes are sufficiently refined. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

On the applicability of elastic network normal modes in small-molecule docking

Incorporating backbone flexibility into protein-ligand docking is still a challenging problem. In protein-protein docking, normal mode analysis (NMA) has become increasingly popular as it can be used to describe the collective motions of a biological system, but the question of whether NMA can also be useful in predicting the conformational changes observed upon small-molecule binding has only been addressed in a few case studies. Here, we describe a large-scale study on the applicability of NMA for protein-ligand docking using 433 apo/holo pairs of the Astex data sets. On the basis of sets of the first normal modes from the apo structure, we first generated for each paired holo structure a set of conformations that optimally reproduce its C(α) trace with respect to the underlying normal mode subspace. Using AutoDock, GOLD, and FlexX we then docked the original ligands into these conformations to assess how the docking performance depends on the number of modes used to reproduce the holo structure. The results of our study indicate that, even for such a best-case scenario, the use of normal mode analysis in small-molecule docking is restricted and that a general rule on how many modes to use does not seem to exist or at least is not easy to find.     

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     

Expanded interaction fingerprint method for analyzing ligand binding modes in docking and structure-based drug design

An expanded interaction fingerprint method has been developed for analyzing the binding modes of ligands in docking and structure-based design methods. Taking the basic premise of representing a ligand in terms of a binary string that denotes its interactions with a target protein, we have expanded the method to include additional interaction-specific information. By considering the hydrogen-bonding strength and/or accessibility of the hydrogen bonding groups within a binding site as well as their geometric arrangement we aim to provide a better representation of a ligand-protein interaction. These expanded methods have been applied to the postprocessing of binding poses generated in a docking study for 220 different proteins and to the analysis of ligands generated by an automated ligand-generation algorithm for the anthrax oedema factor. In the docking study, the application of the interaction fingerprint method as a postprocessing tool resulted in an increased success rate in identifying the crystallographic binding mode. In the analysis of the ligands generated for the anthrax oedema factor, the incorporation of additional interaction-specific information resulted in a more intuitive and comprehensive analysis of automated ligand-generation output.     

Ligand-biased ensemble receptor docking (LigBEnD): a hybrid ligand/receptor structure-based approach

Ligand docking to flexible protein molecules can be efficiently carried out through ensemble docking to multiple protein conformations, either from experimental X-ray structures or from in silico simulations. The success of ensemble docking often requires the careful selection of complementary protein conformations, through docking and scoring of known co-crystallized ligands. False positives, in which a ligand in a wrong pose achieves a better docking score than that of native pose, arise as additional protein conformations are added. In the current study, we developed a new ligand-biased ensemble receptor docking method and composite scoring function which combine the use of ligand-based atomic property field (APF) method with receptor structure-based docking. This method helps us to correctly dock 30 out of 36 ligands presented by the D3R docking challenge. For the six mis-docked ligands, the cognate receptor structures prove to be too different from the 40 available experimental Pocketome conformations used for docking and could be identified only by receptor sampling beyond experimentally explored conformational subspace.     

Flexible ligand docking without parameter adjustment across four ligand–receptor complexes

Understanding molecular recognition is one of the fundamental problems in molecular biology. Computationally, molecular recognition is formulated as a docking problem. Ideally, a molecular docking algorithm should be computationally efficient, provide reasonably thorough search of conformational space, obtain solutions with reasonable consistency, and not require parameter adjustments. With these goals in mind, we developed DIVALI (Docking wIth eVolutionary AlgorIthms), a program which efficiently and reliably searches for the possible binding modes of a ligand within a fixed receptor. We use an AMBER-type potential function and search for good ligand conformations using a genetic algorithm (GA). We apply our system to study the docking of both rigid and flexible ligands in four different complexes. Our results indicate that it is possible to find diverse binding modes, including structures like the crystal structure, all with comparable potential function values. To achieve this, certain modifications to the standard GA recipe are essential. © 1995 John Wiley & Sons, Inc.     

Maximum common binding modes (MCBM): consensus docking scoring using multiple ligand information and interaction fingerprints

Improving the scoring functions for small molecule-protein docking is a highly challenging task in current computational drug design. Here we present a novel consensus scoring concept for the prediction of binding modes for multiple known active ligands. Similar ligands are generally believed to bind to their receptor in a similar fashion. The presumption of our approach was that the true binding modes of similar ligands should be more similar to each other compared to false positive binding modes. The number of conserved (consensus) interactions between similar ligands was used as a docking score. Patterns of interactions were modeled using ligand receptor interaction fingerprints. Our approach was evaluated for four different data sets of known cocrystal structures (CDK-2, dihydrofolate reductase, HIV-1 protease, and thrombin). Docking poses were generated with FlexX and rescored by our approach. For comparison the CScore scoring functions from Sybyl were used, and consensus scores were calculated thereof. Our approach performed better than individual scoring functions and was comparable to consensus scoring. Analysis of the distribution of docking poses by self-organizing maps (SOM) and interaction fingerprints confirmed that clusters of docking poses composed of multiple ligands were preferentially observed near the native binding mode. Being conceptually unrelated to commonly used docking scoring functions our approach provides a powerful method to complement and improve computational docking experiments.     

Geometrically feasible binding modes of a flexible ligand molecule at the receptor site

A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.     

Network dimensionality and ligand flexibility in lanthanide terephthalate hydrates

Various lanthanide open framework materials incorporating the terephthalate (TP) entity were prepared using hydrothermal synthesis methods at a moderate temperature of 170 °C. The compounds Nd₂(TP)₃(H₂O)₄(1), Er₂(TP)₃(H₂O)₄(2), Yb₂(TP)₃(H₂O)₂(3), Yb₂(TP)₃(H₂O)₆(4), and Yb₂(TP)₃(H₂O)₈·2H₂O (5), were characterized by single crystal structural analysis and FT-IR spectroscopy. While compounds 1 and 2 have been reported before on the basis of powder X-ray diffraction, the structural characterization of any ytterbium terephthalate species is unprecedented. Compounds 1-5 crystallize in triclinic settings with space group P-1. The compounds are compared with their previously reported Er and Tb-counterparts and the reduction of the dimensionality of the resulting networks from 3D over 2D to 1D with increasing level of hydration is discussed. Compounds 1, 2, and 3 with the lowest water content assemble in three-dimensional network lattices. Compounds 4 and 5, however, form 2D layered systems and 1D rod like chains, respectively, which are held together by hydrogen bonds originating from coordinating H₂O. The crystal lattices of the 3D networks experience higher levels of tension as can be seen by increasing out-of-plane torsion with regard to the terephthalate carboxylate groups. Moreover, there seems to be a correlation between the level of strain on the aromatic ligands and the reduction of the number of carboxylate oxygen atoms that are part of the coordination polyhedra.     

FDS: flexible ligand and receptor docking with a continuum solvent model and soft-core energy function

The docking of flexible small molecule ligands to large flexible protein targets is addressed in this article using a two-stage simulation-based method. The methodology presented is a hybrid approach where the first component is a dock of the ligand to the protein binding site, based on deriving sets of simultaneously satisfied intermolecular hydrogen bonds using graph theory and a recursive distance geometry algorithm. The output structures are reduced in number by cluster analysis based on distance similarities. These structures are submitted to a modified Monte Carlo algorithm using the AMBER-AA molecular mechanics force field with the Generalized Born/Surface Area (GB/SA) continuum model. This solvent model is not only less expensive than an explicit representation, but also yields increased sampling. Sampling is also increased using a rotamer library to direct some of the protein side-chain movements along with large dihedral moves. Finally, a softening function for the nonbonded force field terms is used, enabling the potential energy function to be slowly turned on throughout the course of the simulation. The docking procedure is optimized, and the results are presented for a single complex of the arabinose binding protein. It was found that for a rigid receptor model, the X-ray binding geometry was reproduced and uniquely identified based on the associated potential energy. However, when side-chain flexibility was included, although the X-ray structure was identified, it was one of three possible binding geometries that were energetically indistinguishable. These results suggest that on relaxing the constraint on receptor flexibility, the docking energy hypersurface changes from being funnel-like to rugged. A further 14 complexes were then examined using the optimized protocol. For each complex the docking methodology was tested for a fully flexible ligand, both with and without protein side-chain flexibility. For the rigid protein docking, 13 out of the 15 test cases were able to find the experimental binding mode; this number was reduced to 11 for the flexible protein docking. However, of these 11, in the majority of cases the experimental binding mode was not uniquely identified, but was present in a cluster of low energy structures that were energetically indistinguishable. These results not only support the presence of a rugged docking energy hypersurface, but also suggest that it may be necessary to consider the possibility of more than one binding conformation during ligand optimization.     

Structural diversity through ligand flexibility: two novel metal-organic nets via ligand-to-ligand cross-linking of "paddlewheels"

Solvothermal reaction of a partially flexible ligand, H(4)L, and Cu(NO(3))(2)·2.5H(2)O afforded two cross-linked Kagomé lattices of formula [Cu(2)(L)](n): an acs net sustained by novel trigonal prismatic supermolecular building blocks (SBBs) and the first example of a partially pillared Kagomé net.     

A hybrid method of molecular dynamics and harmonic dynamics for docking of flexible ligand to flexible receptor

We have developed a new docking method to consider receptor flexibility, a hybrid method of molecular dynamics and harmonic dynamics. The global motions of the whole receptor were approximately introduced into those of the receptor in the docking simulation as harmonic dynamics. On the other hand, the local flexibility of the side chains was also considered by conventional molecular dynamics. We confirmed that this new method can reproduce the fluctuations of the whole receptor by making a comparison of the directions and amplitudes of the global fluctuations. Then this method was applied to the docking of HIV-1 protease and its ligand. As a result, we observed a docking process where the ligand enters into the binding pocket well, which implies that this method is effective enough to reproduce a molecular complex formation.     

Approaches to solving the rigid receptor problem by identifying a minimal set of flexible residues during ligand docking

BACKGROUND: Using fixed receptor sites derived from high-resolution crystal structures in structure-based drug design does not properly account for ligand-induced enzyme conformational change and imparts a bias into the discovery and design of novel ligands. We sought to facilitate the design of improved drug leads by defining residues most likely to change conformation, and then defining a minimal manifold of possible conformations of a target site for drug design based on a small number of identified flexible residues. RESULTS: The crystal structure of thymidylate synthase from an important pathogenic target Pneumocystis carinii (PcTS) bound to its substrate and the inhibitor, BW1843U89, is reported here and reveals a new conformation with respect to the structure of PcTS bound to substrate and the more conventional antifolate inhibitor, CB3717. We developed an algorithm for determining which residues provide 'soft spots' in the protein, regions where conformational adaptation suggests possible modifications for a drug lead that may yield higher affinity. Remodeling the active site of thymidylate synthase with new conformations for only three residues that were identified with this algorithm yields scores for ligands that are compatible with experimental kinetic data. CONCLUSIONS: Based on the examination of many protein/ligand complexes, we develop an algorithm (SOFTSPOTS) for identifying regions of a protein target that are more likely to accommodate plastically to regions of a drug molecule. Using these indicators we develop a second algorithm (PLASTIC) that provides a minimal manifold of possible conformations of a protein target for drug design, reducing the bias in structure-based drug design imparted by structures of enzymes co-crystallized with inhibitors.     

Knowing when to give up: early-rejection stratagems in ligand docking

Virtual screening is an important resource in the drug discovery community, of which protein–ligand docking is a significant part. Much software has been developed for this purpose, largely by biochemists and those in related disciplines, who pursue ever more accurate representations of molecular interactions. The resulting tools, however, are very processor-intensive. This paper describes some initial results from a project to review computational chemistry techniques for docking from a non-chemistry standpoint. An abstract blueprint for protein–ligand docking using empirical scoring functions is suggested, and this is used to discuss potential improvements. By introducing computer science tactics such as lazy function evaluation, dramatic increases to throughput can and have been realized using a real-world docking program. Naturally, they can be extended to any system that approximately corresponds to the architecture outlined.     

On-chip electrochemical detection of CdS quantum dots using normal and multiple recycling flow through modes

A flexible hybrid polydimethylsiloxane (PDMS)-polycarbonate (PC) microfluidic chip with integrated screen printed electrodes (SPE) was fabricated and applied for electrochemical quantum dots (QDs) detection. The developed device combines the advantages of flexible microfluidic chips, such as their low cost, the possibility to be disposable and amenable to mass production, with the advantages of electrochemistry for its facility of integration and the possibility to miniaturize the analytical device. Due to the interest in biosensing applications in general and particularly the great demand for labelling alternatives in affinity biosensors, the electrochemistry of cadmium sulfide quantum dots (CdS QDs) is evaluated. Square wave anodic stripping voltammetry (SWASV) is the technique used due to its sensitivity and low detection limits that can be achieved. The electrochemical as well as the microfluidic parameters of the developed system are optimized. The detection of CdS QDs in the range between 50 to 8000 ng mL(-1) with a sensitivity of 0.0009 μA/(ng mL(-1)) has been achieved. In addition to the single in-chip flow through measurements, the design of a recirculation system with the aim of achieving lower detection limits using reduced volumes (25 μL) of sample was proposed as a proof-of-concept.     

Bending dynamics of acetylene: new modes born in bifurcations of normal modes

Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C2H2. An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.     

Dispersion of normal modes in cis 1,4 polybutadiene

Among the synthetic polymers of commercial potential, poly-butadiene is an important rubbery material and it encompasses the bulk elastomers in use. To the best of our knowledge, a complete normal coordinate analysis with full phonon dispersion curves for cis 1,4 polybutadiene (CPBD) have not been reported so far. In the present communication, we report a complete normal coordinate analysis with full dispersion curves, density-of-states and calculation of heat capacity. The normal coordinate analysis has been carried out using the Urey-Bradley force field and the Wilson's GF matrix method as modified by Higgs. A comparison has been made with trans 1,4 polybutadiene (TPBD). The prominent features of the dispersion curves like crossing over and regions of zero-slope away from the zone centre are discussed. To check the validity of the force field used and the assignments, normal mode calculations are also performed for unsaturated C-deuterated and fully deuterated CPBD.