Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces

Diffusion MRI registration using orientation distribution functions

We propose a linear-elastic registration method to register diffusion-weighted MRI (DW-MRI) data sets by mapping their diffusion orientation distribution functions (ODFs). The ODFs were reconstructed using a q-ball imaging (QBI) technique to resolve intravoxel fiber crossing. The registration method is based on mapping the ODF maps represented by spherical harmonics which yield analytic solutions and reduce the computational complexity. ODF reorientation is required to maintain the consistency with transformed local fiber directions. The reorientation matrices are extracted from the local Jacobian and directly applied to the coefficients of spherical harmonics. The similarity cost of the registration is defined by the ODF shape distance calculated from the spherical harmonic coefficients. The transformation fields are regularized by linear elastic constraints. The proposed method was validated using both synthetic and real data sets. Experimental results show that the elastic registration improved the affine alignment by further reducing the ODF shape difference; reorientation during the registration produced registered ODF maps with more consistent principle directions compared to registrations without reorientation or simultaneous reorientation.

ParaFrag--an approach for surface-based similarity comparison of molecular fragments

A frequent task in computer-aided drug design is to identify novel chemotypes similar in activity but structurally different to a given reference structure. Here we report the development of a novel method for atom-independent similarity comparison of molecular fragments (substructures of drug-like molecules). The fragments are characterized by their local surface properties coded in the form of 3D pharmacophores. As surface properties, we used the electrostatic potential (MEP), the local ionization energy (IE(L)), local electron affinity (EA(L)) and local polarizability (POL) calculated on isodensity surfaces. A molecular fragment can then be represented by a minimal set of extremes for each surface property. We defined a tolerance sphere for each of these extremes, thus allowing us to assess the similarity of fragments in an analogous manner to classical pharmacophore comparison. As a first application of this method we focused on comparing rigid fragments suitable for scaffold hopping. A retrospective analysis of successful scaffold hopping reported for Factor Xa inhibitors [Wood MR et al (2006) J Med Chem 49:1231] showed that our method performs well where atom-based similarity metrics fail.

SHEF: a vHTS geometrical filter using coefficients of spherical harmonic molecular surfaces

SHEF (spherical harmonic coefficient filter), a geometrical matching procedure constituting a preliminary step in the virtual high throughput screening of large databases of small drug-like molecules, is demonstrated. This filter uses a description of both the binding site of the target and the ligand surfaces using spherical harmonic polynomial expansions. Using this representation, which is based on limited sets of spherical harmonic coefficients, considerably reduces the complexity of surface complementarity calculation. As a first test, 188 known protein-ligand complexes were used, and the results of docking the abstracted ligands into the bare proteins using SHEF were compared to the original X-ray structures. The ability of SHEF to retrieve known ligands "hidden" in a virtual library of 1,000 randomly selected drug-like compounds is also demonstrated.

Pattern recognition based on color-coded quantum mechanical surfaces for molecular alignment

A pattern recognition algorithm for the alignment of drug-like molecules has been implemented. The method is based on the calculation of quantum mechanical derived local properties defined on a molecular surface. This approach has been shown to be very useful in attempting to derive generalized, non-atom based representations of molecular structure. The visualization of these surfaces is described together with details of the methodology developed for their use in molecular overlay and similarity calculations. In addition, this paper also introduces an additional local property, the local curvature (C (L)), which can be used together with the quantum mechanical properties to describe the local shape. The method is exemplified using some problems representing common tasks encountered in molecular similarity.

Toward High Throughput 3D Virtual Screening Using Spherical Harmonic Surface Representations

Searching chemical databases for possible drug leads is often one of the main activities conducted during the early stages of a drug development project. This article shows that spherical harmonic molecular shape representations provide a powerful way to search and cluster small-molecule databases rapidly and accurately. Our clustering results show that chemically meaningful clusters may be obtained using only low order spherical harmonic expansions. Our database search results show that using low order spherical harmonic shape-based correlation techniques could provide a practical and efficient way to search very large 3D molecular databases, hence leading to a useful new approach for high throughput 3D virtual screening. The approach described is currently being extended to allow the rapid search and comparison of arbitrary combinations of molecular surface properties.

Tileable BTF

This paper presents a modular framework to efficiently apply the bidirectional texture functions (BTF) onto object surfaces. The basic building blocks are the BTF tiles. By constructing one set of BTF tiles, a wide variety of objects can be textured seamlessly without re-synthesizing the BTF. The proposed framework nicely decouples the surface appearance from the geometry. With this appearance-geometry decoupling, one can build a library of BTF tile sets to instantaneously dress and render various objects under variable lighting and viewing conditions. The core of our framework is a novel method for synthesizing seamless high-dimensional BTF tiles, that are difficult for existing synthesis techniques. Its key is to shorten the cutting paths and broaden the choices of samples so as to increase the chance of synthesizing seamless BTF tiles. To tackle the enormous data, the tile synthesis process is performed in compressed domain. This not just allows the handling of large BTF data during the synthesis, but also facilitates compact storage of the BTF in GPU memory during the rendering.

An extension of spherical harmonics to region-based rotationally invariant descriptors for molecular shape description and comparison

The use of spherical harmonics in the molecular sciences is widespread. They have been employed with success in, for instance, the crystallographic fast rotation function, small-angle scattering particle reconstruction, molecular surface visualisation, protein-protein docking, active site analysis and protein function prediction. An extension of the spherical harmonic expansion method is presented here that enables regions (bodies) rather than contours (surfaces) to be described and which lends itself favourably to the construction of rotationally invariant shape descriptors. This method introduces a radial term that extends the spherical harmonics to 3D polynomials. These polynomials maintain the advantages of the spherical harmonics (orthonormality, completeness, uniqueness and fast computation) but correct the drawbacks (contour based shape description and star-shape objects) and give rise to powerful invariant descriptors. We provide proof-of-principle examples illustrating the potential of this method for accurate object representation, an analysis of the descriptor classification power, and comparisons to other methods.

A novel surface registration algorithm with biomedical modeling applications

In this paper, we propose a novel surface matching algorithm for arbitrarily shaped but simply connected 3-D objects. The spherical harmonic (SPHARM) method is used to describe these 3-D objects, and a novel surface registration approach is presented. The proposed technique is applied to various applications of medical image analysis. The results are compared with those using the traditional method, in which the first-order ellipsoid is used for establishing surface correspondence and aligning objects. In these applications, our surface alignment method is demonstrated to be more accurate and flexible than the traditional approach. This is due in large part to the fact that a new surface parameterization is generated by a shortcut that employs a useful rotational property of spherical harmonic basis functions for a fast implementation. In order to achieve a suitable computational speed for practical applications, we propose a fast alignment algorithm that improves computational complexity of the new surface registration method from O(n3) to O(n2).

Shape variation in protein binding pockets and their ligands

A common assumption about the shape of protein binding pockets is that they are related to the shape of the small ligand molecules that can bind there. But to what extent is that assumption true? Here we use a recently developed shape matching method to compare the shapes of protein binding pockets to the shapes of their ligands. We find that pockets binding the same ligand show greater variation in their shapes than can be accounted for by the conformational variability of the ligand. This suggests that geometrical complementarity in general is not sufficient to drive molecular recognition. Nevertheless, we show when considering only shape and size that a significant proportion of the recognition power of a binding pocket for its ligand resides in its shape. Additionally, we observe a "buffer zone" or a region of free space between the ligand and protein, which results in binding pockets being on average three times larger than the ligand that they bind.

Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT)

This article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion-weighted magnetic resonance (MR) data. This novel approach utilizes the Fourier transform relationship between the water displacement probabilities and diffusion-attenuated MR signal expressed in spherical coordinates. The radial part of the Fourier integral is evaluated analytically under the assumption that MR signal attenuates exponentially. The values of the resulting functions are evaluated at a fixed distance away from the origin. The spherical harmonic transform of these functions yields the Laplace series coefficients of the probabilities on a sphere of fixed radius. Alternatively, probability values can be computed nonparametrically using Legendre polynomials. Orientation maps calculated from excised rat nervous tissue data demonstrate this technique's ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm. This proposed methodology has a trivial extension to multiexponential diffusion-weighted signal decay. The developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Fast orientation mapping from HARDI

This paper introduces a new, accurate and fast method for fiber orientation mapping using high angular resolution diffusion imaging (HARDI) data. The approach utilizes the Fourier relationship between the water displacement probabilities and diffusion attenuated magnetic resonance (MR) signal expressed in spherical coordinates. The Laplace series coefficients of the water displacement probabilities are evaluated at a fixed distance away from the origin. The computations take under one minute for most three-dimensional datasets. We present orientation maps computed from excised rat optic chiasm, brain and spinal cord images. The developed method will improve the reliability of tractography schemes and make it possible to correctly identify the neural connections between functionally connected regions of the nervous system.

Crystal structure of 3-chlorocatechol 1,2-dioxygenase key enzyme of a new modified ortho-pathway from the Gram-positive Rhodococcus opacus 1CP grown on 2-chlorophenol

The crystal structure of the 3-chlorocatechol 1,2-dioxygenase from the Gram-positive bacterium Rhodococcus opacus (erythropolis) 1CP, a Fe(III) ion-containing enzyme specialized in the aerobic biodegradation of 3-chloro- and methyl-substituted catechols, has been solved by molecular replacement techniques using the coordinates of 4-chlorocatechol 1,2-dioxygenase from the same organism (PDB code 1S9A) as a starting model and refined at 1.9 A resolution (R(free) 21.9%; R-factor 17.4%). The analysis of the structure and of the kinetic parameters for a series of different substrates, and the comparison with the corresponding data for the 4-chlorocatechol 1,2-dioxygenase isolated from the same bacterial strain, provides evidence of which active site residues are responsible for the observed differences in substrate specificity. Among the amino acid residues expected to interact with substrates, only three are altered Val53(Ala53), Tyr78(Phe78) and Ala221(Cys224) (3-chlorocatechol 1,2-dioxygenase(4-chlorocatechol 1,2-dioxygenase)), clearly identifying the substitutions influencing substrate selectivity in these enzymes. The crystallographic asymmetric unit contains eight subunits (corresponding to four dimers) that show heterogeneity in the conformation of a co-crystallized molecule bound to the catalytic non-heme iron(III) ion resembling a benzohydroxamate moiety, probably a result of the breakdown of recently discovered siderophores synthesized by Gram-positive bacteria. Several different modes of binding benzohydroxamate into the active site induce distinct conformations of the interacting protein ligands Tyr167 and Arg188, illustrating the plasticity of the active site origin of the more promiscuous substrate preferences of the present enzyme.

Targeting signal transducer and activator of transcription 3 with G-quartet oligonucleotides: a potential novel therapy for head and neck cancer

Signal transducer and activator of transcription 3 (Stat3) is a critical mediator of oncogenic signaling activated frequently in many types of human cancer where it contributes to tumor cell growth and resistance to apoptosis. Stat3 has been proposed as a promising target for anticancer drug discovery. Recently, we developed a series of G-quartet oligodeoxynucleotides (GQ-ODN) as novel and potent Stat3 inhibitors, which significantly suppressed the growth of prostate and breast tumors in nude mice. In the present study, we showed that GQ-ODN specifically inhibited DNA-binding activity of Stat3 as opposed to Stat1. Computer-based docking analysis revealed that GQ-ODN predominantly interacts with the SH2 domains of Stat3 homodimers to destabilize dimer formation and disrupt DNA-binding activity. We employed five regimens in the treatment of nude mice with tumors of head and neck squamous cell carcinoma (HNSCC): placebo, paclitaxel, GQ-ODN T40214, GQ-ODN T40231, and T40214 plus paclitaxel. The mean size of HNSCC tumors over 21 days only increased by 1.7-fold in T40214-treated mice and actually decreased by 35% in T40214 plus paclitaxel-treated mice whereas the mean size of HNSCC tumors increased 9.4-fold in placebo-treated mice in the same period. These findings show that GQ-ODN has potent activity against HNSCC tumor xenografts alone and in combination with paclitaxel.

Multipolar representation of protein structure

Background

That the structure determines the function of proteins is a central paradigm in biology. However, protein functions are more directly related to cooperative effects at the residue and multi-residue scales. As such, current representations based on atomic coordinates can be considered inadequate. Bridging the gap between atomic-level structure and overall protein-level functionality requires parameterizations of the protein structure (and other physicochemical properties) in a quasi-continuous range, from a simple collection of unrelated amino acids coordinates to the highly synergistic organization of the whole protein entity, from a microscopic view in which each atom is completely resolved to a "macroscopic" description such as the one encoded in the three-dimensional protein shape.

Results

Here we propose such a parameterization and study its relationship to the standard Euclidian description based on amino acid representative coordinates. The representation uses multipoles associated with residue Cα coordinates as shape descriptors. We demonstrate that the multipoles can be used for the quantitative description of the protein shape and for the comparison of protein structures at various levels of detail. Specifically, we construct a (dis)similarity measure in multipolar configuration space, and show how such a function can be used for the comparison of a pair of proteins. We then test the parameterization on a benchmark set of the protein kinase-like superfamily. We prove that, when the biologically relevant portions of the proteins are retained, it can robustly discriminate between the various families in the set in a way not possible through sequence or conventional structural representations alone. We then compare our representation with the Cartesian coordinate description and show that, as expected, the correlation with that representation increases as the level of detail, measured by the highest rank of multipoles used in the representation, approaches the dimensionality of the fold space.

Conclusion

The results described here demonstrate how a granular description of the protein structure can be achieved using multipolar coefficients. The description has the additional advantage of being immediately generalizable for any residue-specific property therefore providing a unitary framework for the study and comparison of the spatial profile of various protein properties.

Molecular shape and electrostatics in the encoding of relevant chemical information

We propose a molecule's chemistry can be hidden by representations of its shape and electrostatic field while retaining crucial, pharmaceutically relevant, information. Necessary, but not sufficient, to this proposition are the importance of shape and electrostatics to activity, the facility to easily represent, store and compare field properties, and knowledge of the density of possible drug-like molecules within a given radius of physical similarity. We provide methods and evidence to support the conclusion that a useful encoding is practical and propose tests for falsification.

An evaluation of spherical designs for molecular-like surfaces

The use of spherical harmonics in the molecular sciences is widespread. They have been employed with success in, for instance, the crystallographic fast rotation function, small-angle scattering particle reconstruction, molecular surface visualisation, protein-protein docking, active site analysis and protein function prediction. The calculation of spherical harmonic expansion coefficients requires integration over the full sphere and can be a computationally cumbersome and also numerically sensitive (with respect to the integration weights) procedure. It is shown here how the use of spherical t-designs and pre-computed near-equal weight integration layouts can significantly reduce the computational effort in the determination of spherical harmonic expansion coefficients for molecular surfaces, thus giving rise to a robust and highly efficient algorithm for the construction of molecular-like objects.

Modelling the structure of latexin–carboxypeptidase A complex based on chemical cross-linking and molecular docking

We have determined the three-dimensional structure of the protein complex between latexin and carboxypeptidase A using a combination of chemical cross-linking, mass spectrometry and molecular docking. The locations of three intermolecular cross-links were identified using mass spectrometry and these constraints were used in combination with a speed-optimised docking algorithm allowing us to evaluate more than 3 x 10(11) possible conformations. While cross-links represent only limited structural constraints, the combination of only three experimental cross-links with very basic molecular docking was sufficient to determine the complex structure. The crystal structure of the complex between latexin and carboxypeptidase A4 determined recently allowed us to assess the success of this structure determination approach. Our structure was shown to be within 4 A r.m.s. deviation of Calpha atoms of the crystal structure. The study demonstrates that cross-linking in combination with mass spectrometry can lead to efficient and accurate structural modelling of protein complexes.

Mechanism of Pyridine Protonation in Water Clusters of Increasing Size

This work presents a theoretical mechanistic study of the protonation of pyridine in water clusters, at the B3LYP/cc-pVDZ theory level. Clusters from one to five water molecules were used. Starting from previously determined structures, the reaction paths for the protonation process were identified. For complexes of pyridine with water clusters of up to three water molecules just one transition state (TS) links the solvated and protonated forms. It is found that the activation energy decreases with the number of water molecules. For complexes of four and five water molecules two transition states are found. For four water molecules, the first TS links the starting solvated structure with a new, less stable, solvated form through a concerted proton transfer between a ring of water molecules. The second TS links the new solvated structure to the protonated form. Thus, protonation is a two-step process. For the five water molecules cluster, the new solvated structure is more stable than the starting one. This structure exhibits two double hydrogen bonds involving the pyridinic nitrogen and several water molecules. The second TS links the new structure with the protonated form. Now the process occurs in one step. In all cases considered, the proton transfers involve an interconversion between covalent and hydrogen bonds. For four and five water molecules, the second TS is structurally and energetically very close to the protonated form. As evidenced by the vibration frequencies, this is due to a flat potential energy hypersurface in the direction of the reaction coordinate. Determination of DeltaG at 298.15 K and 1 atm shows that the protonation of pyridine needs at least four water molecules to be spontaneous. The complex with five water molecules exhibits a large DeltaG. This value yields a pKa of 2.35, relatively close to the reported 5.21 for pyridine in water.

Crystal Structure of the Hydroxyquinol 1,2-Dioxygenase from Nocardioides simplex 3E, a Key Enzyme Involved in Polychlorinated Aromatics Biodegradation

Hydroxyquinol 1,2-dioxygenase (1,2-HQD) catalyzes the ring cleavage of hydroxyquinol (1,2,4-trihydroxybenzene), a central intermediate in the degradation of aromatic compounds including a variety of particularly recalcitrant polychloro- and nitroaromatic pollutants. We report here the primary sequence determination and the analysis of the crystal structure of the 1,2-HQD from Nocardioides simplex 3E solved at 1.75 A resolution using the multiple wavelength anomalous dispersion of the two catalytic irons (1 Fe/293 amino acids). The catalytic Fe(III) coordination polyhedron composed by the side chains of Tyr164, Tyr197, His221, and His223 resembles that of the other known intradiol-cleaving dioxygenases, but several of the tertiary structure features are notably different. One of the most distinctive characteristics of the present structure is the extensive openings and consequent exposure to solvent of the upper part of the catalytic cavity arranged to favor the binding of hydroxyquinols but not catechols. A co-crystallized benzoate-like molecule is also found bound to the metal center forming a distinctive hydrogen bond network as observed previously also in 4-chlorocatechol 1,2-dioxygenase from Rhodococcus opacus 1CP. This is the first structure of an intradiol dioxygenase specialized in hydroxyquinol ring cleavage to be investigated in detail.

An Analytical, Variable Resolution, Complete Description of Static Molecules and Their Intermolecular Binding Properties

A fully analytical description of molecular shape, as defined by the shrink-wrap isodensity or solvent-excluded surfaces and local properties related to Coulomb, donor/acceptor, and polarizability (dispersion) interactions is described. The molecular surface and four local properties adequate for describing intermolecular interactions (the molecular electrostatic potential and the local ionization energy, electron affinity, and polarizability) are fitted to spherical-harmonic expansions, which provide a compact and information-rich description of the properties of the static molecule. The resolution of the description can be varied from isotropic to near atomistic detail by adjusting the order of the individual spherical-harmonic expansions. Examples are given to illustrate the effect of truncating the different spherical-harmonic approximations.

Real spherical harmonic expansion coefficients as 3D shape descriptors for protein binding pocket and ligand comparisons

MOTIVATION

An increasing number of protein structures are being determined for which no biochemical characterization is available. The analysis of protein structure and function assignment is becoming an unexpected challenge and a major bottleneck towards the goal of well-annotated genomes. As shape plays a crucial role in biomolecular recognition and function, the examination and development of shape description and comparison techniques is likely to be of prime importance for understanding protein structure-function relationships.

RESULTS

A novel technique is presented for the comparison of protein binding pockets. The method uses the coefficients of a real spherical harmonics expansion to describe the shape of a protein's binding pocket. Shape similarity is computed as the L2 distance in coefficient space. Such comparisons in several thousands per second can be carried out on a standard linux PC. Other properties such as the electrostatic potential fit seamlessly into the same framework. The method can also be used directly for describing the shape of proteins and other molecules.

AVAILABILITY

A limited version of the software for the real spherical harmonics expansion of a set of points in PDB format is freely available upon request from the authors. Binding pocket comparisons and ligand prediction will be made available through the protein structure annotation pipeline Profunc (written by Roman Laskowski) which will be accessible from the EBI website shortly.

Surface alignment of 3D spherical harmonic models: application to cardiac MRI analysis

The spherical harmonic (SPHARM) description is a powerful surface modeling technique that can model arbitrarily shaped but simply connected 3D objects and has been used in many applications in medical imaging. Previous SPHARM techniques use the first order ellipsoid for establishing surface correspondence and aligning objects. However, this first order information may not be sufficient in many cases; a more general method for establishing surface correspondence would be to minimize the mean squared distance between two corresponding surfaces. In this paper, a new surface matching algorithm is proposed for 3D SPHARM models to achieve this goal. This algorithm employs a useful rotational property of spherical harmonic basis functions for a fast implementation. Applications of medical image analysis (e.g., spatio-temporal modeling of heart shape changes) are used to demonstrate this approach. Theoretical proofs and experimental results show that our approach is an accurate and flexible surface correspondence alignment method.

Crystal structure of 4-chlorocatechol 1,2-dioxygenase from the chlorophenol-utilizing gram-positive Rhodococcus opacus 1CP

The crystal structure of the 4-chlorocatechol 1,2-dioxygenase from the Gram-positive bacterium Rhodococcus opacus (erythropolis) 1CP, a Fe(III) ion-containing enzyme involved in the aerobic biodegradation of chloroaromatic compounds, has been solved by multiple wavelength anomalous dispersion using the weak anomalous signal of the two catalytic irons (1 Fe/257 amino acids) and refined at a 2.5 A resolution (R(free) 28.7%; R factor 21.4%). The analysis of the structure and its comparison with the structure of catechol 1,2-dioxygenase from Acinetobacter calcoaceticus ADP1 (Ac 1,2-CTD) highlight significant differences between these enzymes. The general topology of the present enzyme comprises two catalytic domains (one for each subunit) related by a noncrystallographic 2-fold axis and separated by a common alpha-helical zipper motif consisting of five N-terminal helices from each subunit; furthermore the C-terminal tail is shortened significantly with respect to the known Ac 1,2-CTD. The presence of two phospholipids binding in a hydrophobic tunnel along the dimer axis is shown here to be a common feature for this class of enzyme. The active site cavity presents several dissimilarities with respect to the known catechol-cleaving enzyme. The catalytic nonheme iron(III) ion is bound to the side chains of Tyr-134, Tyr-169, His-194, and His-196, and a cocrystallized benzoate ion, bound to the metal center, reveals details on a novel mode of binding of bidentate inhibitors and a distinctive hydrogen bond network with the surrounding ligands. Among the amino acid residues expected to interact with substrates, several are different from the corresponding analogs of Ac 1,2-CTD: Asp-52, Ala-53, Gly-76, Phe-78, and Cys-224; in addition, regions of largely conserved amino acid residues in the catalytic cleft show different shapes resulting from several substantial backbone and side chain shifts. The present structure is the first of intradiol dioxygenases that specifically catalyze the cleavage of chlorocatechols, key intermediates in the aerobic catabolism of toxic chloroaromatics.

Method and algorithm of obtaining the molecular intrinsic characteristic contours (MICCs) of organic molecules

The molecular intrinsic characteristic contour (MICC) is defined as the set of all the classical turning points of electron movement in a molecule. Studies on the MICCs of some medium organic molecules, such as dimethylether, acetone, and some homologues of alkanes, alkenes, and alkynes, as well as the electron density distributions on the MICCs, are shown for the first time. Results show that the MICC is an intrinsic approach to shape and size of a molecule. Unlike the van der Waals hard-sphere model, the MICC is a smooth contour, and it has a clear physical meaning. Detailed investigations on the cross-sections of MICCs have provided a kind of important information about atomic size changing in the process of forming molecules. Studies on electron density distribution on the MICC not only provide a new insight into molecular shape, but also show that the electron density distribution on the boundary surface relates closely with molecular properties and reactivities. For the homologues of alkanes, Rout(H), Dmin, and Dmax (the minimum and maximum of electron density on the MICC), all have very good linear relationships with minus of the molecular ionization potential. This work may serve as a basis for exploring a new reactivity indicator of chemical reactions and for studying molecular shape properties of large organic and biological molecules.

Evaluation of protein docking predictions using Hex 3.1 in CAPRI rounds 1 and 2

This article describes and reviews our efforts using Hex 3.1 to predict the docking modes of the seven target protein-protein complexes presented in the CAPRI (Critical Assessment of Predicted Interactions) blind docking trial. For each target, the structure of at least one of the docking partners was given in its unbound form, and several of the targets involved large multimeric structures (e.g., Lactobacillus HPr kinase, hemagglutinin, bovine rotavirus VP6). Here we describe several enhancements to our original spherical polar Fourier docking correlation algorithm. For example, a novel surface sphere smothering algorithm is introduced to generate multiple local coordinate systems around the surface of a large receptor molecule, which may be used to define a small number of initial ligand-docking orientations distributed over the receptor surface. High-resolution spherical polar docking correlations are performed over the resulting receptor surface patches, and candidate docking solutions are refined by using a novel soft molecular mechanics energy minimization procedure. Overall, this approach identified two good solutions at rank 5 or less for two of the seven CAPRI complexes. Subsequent analysis of our results shows that Hex 3.1 is able to place good solutions within a list of <or=20 for four of the seven targets. This finding shows that useful in silico protein-protein docking predictions can now be made with increasing confidence, even for very large macromolecular complexes.

Protein-ligand recognition using spherical harmonic molecular surfaces: towards a fast and efficient filter for large virtual throughput screening

Molecular surfaces are important because surface-shape complementarity is often a necessary condition in protein-ligand interactions and docking studies. We have previously described a fast and efficient method to obtain triangulated surface-meshes by topologically mapping ellipsoids on molecular surfaces. In this paper, we present an extension of our work to spherical harmonic surfaces in order to approximate molecular surfaces of both ligands and receptor-cavities and to easily check the surface-shape complementarity. The method consists of (1) finding lobes and holes on both ligand and cavity surfaces using contour maps of radius functions with spherical harmonic expansions, (2) superposing the surfaces around a given binding site by minimizing the distance between their respective expansion coefficients. This docking procedure capabilities was demonstrated by application to 35 protein-ligand complexes of known crystal structures. The method can also be easily and efficiently used as a filter to detect in a large conformational sampling the possible conformations presenting good complementarity with the receptor site, and being, therefore, good candidates for further more elaborate docking studies. This "virtual screening" was demonstrated on the platelet thrombin receptor.