Identification of convexity as a common structure feature for structures generated for two short peptides
Introduction
Matching flexible molecules is one of the most complicated problems in drug design, since many equivalent matches may be found for different conformations (Dean, 1993; Marshall, 1993; Itai et al., 1993). In general, several conformations of low energy are first obtained and then an efficient superposition method is used to match the molecules (Perkins and Dean, 1993). It is extremely difficult to match peptides which are all structurally related and highly flexible and have many functional groups (Marshall, 1993; Perkins and Dean, 1993). If the 3D structure of the corresponding binding pocket is known, the flexibility problem may be dealt with by docking a peptide for which several conformations have been generated (Klebe and Abraham, 1993). Recently, methods for aligning molecules according to their surfaces and field properties have been proposed (Cramer III et al., 1988; Kato et al., 1987). These approaches do not require predefined correspondences in terms of “pharmacophoric groups” (Cramer III et al., 1988; Kato et al., 1987). The matching process is purely combinatory in nature and only geometrical correspondences between atoms serving the same putative function are considered, e.g. a hydrophobic group, a hydrogen-bond acceptor or a donor functional group (Cramer III et al., 1988; Kato et al., 1987). Brint and Willett (1987) have described a clique detection method based on interatomic distances as the best method for rapidly matching “cliques” (corresponding points or sites) in an input and reference “graph” (molecule or connection table). Based on this clique-detection technique, Martin et al. (1993) have developed a program called DISCO (DIStance COmparisons) to match molecules of low-energy conformations generated. Since surface-exposed functional groups of a ligand are more likely to be “seen” by a receptor, approaches that concentrate on mapping and comparing common surfaces and field properties derived from these groups are better suited for aligning structures (Hermann and Herron, 1991; Good et al., 1992; Clark et al., 1990). This report presents an algorithm for computing a 3D convex hull and detecting some common structural features of structures generated for two short tachykinin peptides. These features are the exposed functional groups on the vertices of a convex hull computed for each structure generated.
In computational geometry, finding efficient convex hull algorithms is an intensively studied problem (Kirkpatrick and Raimund, 1986; Chand and Kapur, 1970; Bentley and Shamos, 1978; Preparata and Shamos, 1985; Clarkson and Shor, 1989; Edelsbrunner and Shi, 1991). In addition to the gift-wrapping method of Chand and Kapur (1970), other known 3D convex hull algorithms are, (a) the divide-and-conquer algorithm of Bentley and Shamos (1978), (b) the beneath–beyond method of Kallay (Preparata and Shamos, 1985), (c) the randomized and output-sensitive algorithm of Clarkson and Shor (1989), and (d) the marriage before conquest algorithm of Edelsbrunner and Shi (1991). Our convex hull calculation is based on the structures of two tachykinin peptides generated by the AMBER 4.0 program (Pearlman et al., 1991). Although the only difference in the sequences of these two peptides is at the C-terminal residue, the binding activities with the NK-1 receptor differ substantially (Buck et al., 1984). To deal with the flexibility problem, two structures are randomly generated for each peptide. Each structure is solvated in a box of water molecules and then subjected to 70 picosecond (PS) of molecular dynamics (MD) simulation using the AMBER 4.0 program (Pearlman et al., 1991). Longer in vacuo MD simulation runs for some selected structures at 1000 K are also performed. To compute the convex hull, each atom in each structure extracted from a MD simulation run is treated as a point. Then, a triangulating procedure is applied to the point set generated for each structure. Each generated triangular facet can form a parallelepiped with a fourth point arbitrarily selected from among the other points. A convex hull facet is identified as the one for which the magnitude of the volume of all the corresponding parallelepipeds calculated are all negative or positive. The structure and composition of vertices of each computed convex hull are further analyzed by both a cluster and a principal components (PC) analytical algorithm. We find that although the shapes of convex hulls computed for structures generated for the two peptides differ significantly, a certain number of vertices are composed of the same atoms that have been identified in the group of convex hull computed for the peptides. Some of these “common” vertices are heterologous hydrogen atoms, but others may be hydrophobic. These common vertices may be used to assign correspondences in programs such as CoMFA (Cramer III et al., 1988) for aligning structures generated for the two peptides.
Section snippets
Material and methods
The amino acid sequences of the above tachykinin peptides studied, namely, substance P (SP) and [Pro11]-SP are as follows:The binding activities of peptides SP and [Pro11]-SP with the NK-1 receptor were determined to be 0.64 and 420 nm, respectively (Buck et al., 1984). Using standard AMBER LINK-EDIT-PARM operation procedures, two random structures were generated composed of united atoms
Results and discussion
A convex hull computed for a complicated molecule can distinguish atoms inside the hull or on the vertices. The 3D convex hull is conventionally computed by the gift-wrapping method of Chand and Kapur (1970). The overall complexity of this method in the worst-case is dependent on Nd/2+1+Nd/2 log N, where N is the number of points in a point set and d is the dimensionality of the set in space (Avis and Bhattacharya, 1983). However, this method requires a series of steps to discover an initial
Acknowledgements
We thank Dr C. Y. Tang of the Computer Science Department, NTHU, for discussions on the design of the convex hull computation algorithm. This work was supported in part by a grant from the National Science Council, ROC (NSC85-2311-B007-026).
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