Eleanor J. Gardiner

RASCAL: Calculation of Graph Similarity using Maximum Common Edge Subgraphs

A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection.

Protein docking using a genetic algorithm

A genetic algorithm (GA) for protein–protein docking is described, in which the proteins are represented by dot surfaces calculated using the Connolly program. The GA is used to move the surface of one protein relative to the other to locate the area of greatest surface complementarity between the two. Surface dots are deemed complementary if their normals are opposed, their Connolly shape type is complementary, and their hydrogen bonding or hydrophobic potential is fulfilled. Overlap of the protein interiors is penalized. The GA is tested on 34 large protein–protein complexes where one or both proteins has been crystallized separately. Parameters are established for which 30 of the complexes have at least one near‐native solution ranked in the top 100. We have also successfully reassembled a 1,400‐residue heptamer based on the top‐ranking GA solution obtained when docking two bound subunits. Proteins 2001;44:44–56.

Clique-detection algorithms for matching three-dimensional molecular structures.

The representation of chemical and biological molecules by means of graphs permits the use of a maximum common subgraph (MCS) isomorphism algorithm to identify the structural relationships existing between pairs of such molecular graphs. Clique detection provides an efficient way of implementing MCS detection, and this article reports a comparison of several different clique-detection algorithms when used for this purpose. Experiments with both small molecules and proteins demonstrate that the most efficient of these particular applications, which typically involve correspondence graphs with low edge densities, is the algorithm described by Carraghan and Pardalos. This is shown to be two to three times faster than the Bron-Kerbosch algorithm that has been used previously for MCS applications in chemistry and biology. However, the latter algorithm enables all substructures common to a pair of molecules to be identified, and not just the largest ones, as with the other algorithms considered here. The two algorithms can usefully be combined to increase the efficiency of database-searching systems that use the MCS as a measure of structural similarity.

Effectiveness of 2D fingerprints for scaffold hopping

BACKGROUND It has been suggested that similarity searching using 2D fingerprints may not be suitable for scaffold hopping. METHODS This article reports a detailed evaluation of the effectiveness of six common types of 2D fingerprints when they are used for scaffold-hopping similarity searches of the Molecular Design Limited Drug Data Report database, World of Molecular Bioactivity database and Maximum Unbiased Validation database. RESULTS The results demonstrate that 2D fingerprints can be used for scaffold hopping, with novel scaffolds being identified in nearly every search that was carried out. The degree of enrichment depends on the structural diversity of the actives that are being sought, with the greatest enrichments often being obtained using the extended connectivity fingerprint encoding a circular substructure of diameter four bonds (ECFP4) fingerprint. CONCLUSION 2D fingerprints provide a simple and computationally efficient way of identifying novel chemotypes in lead-discovery programs.

Graph-theoretic techniques for macromolecular docking

We propose a solution to the problem of docking two macromolecules. We represent each of two proteins as a set of potential hydrogen bond donors and acceptors and use a clique-detection algorithm to find maximally complementary sets of donor/acceptor pairs. Preliminary results are presented which demonstrate the feasibility of the method.

Further development of reduced graphs for identifying bioactive compounds

Reduced graphs provide summary representations of chemical structures. Here, a variety of different types of reduced graphs are compared in similarity searches. The reduced graphs are found to give comparable performance to Daylight fingerprints in terms of the number of active compounds retrieved. However, no one type of reduced graph is found to be consistently superior across a variety of different data sets. Consequently, a representative set of reduced graphs was chosen and used together with Daylight fingerprints in data fusion experiments. The results show improved performance in 10 out of 11 data sets compared to using Daylight fingerprints alone. Finally, the potential of using reduced graphs to build SAR models is demonstrated using recursive partitioning. An SAR model consistent with a published model is found following just two splits in the decision tree.

Representing clusters using a maximum common edge substructure algorithm applied to reduced graphs and molecular graphs

Chemical databases are routinely clustered, with the aim of grouping molecules which share similar structural features. Ideally, medicinal chemists are then able to browse a few representatives of the cluster in order to interpret the shared activity of the cluster members. However, when molecules are clustered using fingerprints, it may be difficult to decipher the structural commonalities which are present. Here, we seek to represent a cluster by means of a maximum common substructure based on the shared functionality of the cluster members. Previously, we have used reduced graphs, where each node corresponds to a generalized functional group, as topological molecular descriptors for virtual screening. In this work, we precluster a database using any clustering method. We then represent the molecules in a cluster as reduced graphs. By repeated application of a maximum common edge substructure (MCES) algorithm, we obtain one or more reduced graph cluster representatives. The sparsity of the reduced graphs means that the MCES calculations can be performed in real time. The reduced graph cluster representatives are readily interpretable in terms of functional activity and can be mapped directly back to the molecules to which they correspond, giving the chemist a rapid means of assessing potential activities contained within the cluster. Clusters of interest are then subject to a detailed R-group analysis using the same iterated MCES algorithm applied to the molecular graphs.

SPRITE and ASSAM: web servers for side chain 3D-motif searching in protein structures

Similarities in the 3D patterns of amino acid side chains can provide insights into their function despite the absence of any detectable sequence or fold similarities. Search for protein sites (SPRITE) and amino acid pattern search for substructures and motifs (ASSAM) are graph theoretical programs that can search for 3D amino side chain matches in protein structures, by representing the amino acid side chains as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graphs nodes while the edges are the inter-pseudo-atomic distances. Both programs require the input file to be in the PDB format. The objective of using SPRITE is to identify matches of side chains in a query structure to patterns with characterized function. In contrast, a 3D pattern of interest can be searched for existing occurrences in available PDB structures using ASSAM. Both programs are freely accessible without any login requirement. SPRITE is available at http://mfrlab.org/grafss/sprite/ while ASSAM can be accessed at http://mfrlab.org/grafss/assam/.

Structural mechanics of DNA wrapping in the nucleosome.

Experimental X-ray crystal structures and a database of calculated structural parameters of DNA octamers were used in combination to analyse the mechanics of DNA bending in the nucleosome core complex. The 1kx5 X-ray crystal structure of the nucleosome core complex was used to determine the relationship between local structure at the base-step level and the global superhelical conformation observed for nucleosome-bound DNA. The superhelix is characterised by a large curvature (597 degrees) in one plane and very little curvature (10 degrees) in the orthogonal plane. Analysis of the curvature at the level of 10-step segments shows that there is a uniform curvature of 30 degrees per helical turn throughout most of the structure but that there are two sharper kinks of 50 degrees at +/-2 helical turns from the central dyad base pair. The curvature is due almost entirely to the base-step parameter roll. There are large periodic variations in roll, which are in phase with the helical twist and account for 500 degrees of the total curvature. Although variations in the other base-step parameters perturb the local path of the DNA, they make minimal contributions to the total curvature. This implies that DNA bending in the nucleosome is achieved using the roll-slide-twist degree of freedom previously identified as the major degree of freedom in naked DNA oligomers. The energetics of bending into a nucleosome-bound conformation were therefore analysed using a database of structural parameters that we have previously developed for naked DNA oligomers. The minimum energy roll, the roll flexibility force constant and the maximum and minimum accessible roll values were obtained for each base step in the relevant octanucleotide context to account for the effects of conformational coupling that vary with sequence context. The distribution of base-step roll values and corresponding strain energy required to bend DNA into the nucleosome-bound conformation defined by the 1kx5 structure were obtained by applying a constant bending moment. When a single bending moment was applied to the entire sequence, the local details of the calculated structure did not match the experiment. However, when local 10-step bending moments were applied separately, the calculated structure showed excellent agreement with experiment. This implies that the protein applies variable bending forces along the DNA to maintain the superhelical path required for nucleosome wrapping. In particular, the 50 degrees kinks are constraints imposed by the protein rather than a feature of the 1kx5 DNA sequence. The kinks coincide with a relatively flexible region of the sequence, and this is probably a prerequisite for high-affinity nucleosome binding, but the bending strain energy is significantly higher at these points than for the rest of the sequence. In the most rigid regions of the sequence, a higher strain energy is also required to achieve the standard 30 degrees curvature per helical turn. We conclude that matching of the DNA sequence to the local roll periodicity required to achieve bending, together with the increased flexibility required at the kinks, determines the sequence selectivity of DNA wrapping in the nucleosome.

GAPDOCK: a Genetic Algorithm Approach to Protein Docking in CAPRI round 1.

As part of the first Critical Assessment of PRotein Interactions, round 1, we predict the structure of two protein–protein complexes, by using a genetic algorithm, GAPDOCK, in combination with surface complementarity, buried surface area, biochemical information, and human intervention. Among the five models submitted for target 1, HPr phosphocarrier protein (B. subtilis) and the hexameric HPr kinase (L. lactis), the best correctly predicts 17 of 52 interprotein contacts, whereas for target 2, bovine rotavirus VP6 protein‐monoclonal antibody, the best model predicts 27 of 52 correct contacts. Given the difficult nature of the targets, these predictions are very encouraging and compare well with those obtained by other methods. Nevertheless, it is clear that there is a need for improved methods for distinguishing between “correct” and “plausible but incorrect” complexes. Proteins 2003;52:10–14.