Identification of Convexity As a Common Structure Feature for Structures Generated for Two Short Peptides

Abstract This paper presents a simple 3D convex hull computational algorithm for detecting some common structural features in structures generated by a molecular dynamics simulation for two short flexible tachykinin peptides. In this algorithm, each atom in each generated structure is treated as a point in space. First, a triangulating procedure is used to triangulate a set of points (a structure). Then, the volume of a series of corresponding parallelepipeds formed for each of a triangular facet generated by the arbitrary selection of a fourth point from among the other points of the set is sorted. The frequency of atoms lying on the vertices of a series of hulls that have been computed for a group of structures generated with the same structural topology are analyzed by both a cluster and a principal components analytical method. We find that about 15% of the total atoms commonly lie on the vertices of the two series of hulls computed for structures generated with two different starting structures but which have the same structural topology. However, for structures generated with two different structural topologies, the possibility of the presence of these common vertices is only about 5%. When detectable, these common structural features may be treated as a set of correspondences in a program such as CoMFA for aligning structures generated for the two highly flexible peptides.

[1]  David G. Kirkpatrick,et al.  The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[2]  Robert F. Ling,et al.  Cluster analysis algorithms for data reduction and classification of objects , 1981 .

[3]  R. Cramer,et al.  Comparative molecular field analysis (CoMFA). 1. Effect of shape on binding of steroids to carrier proteins. , 1988, Journal of the American Chemical Society.

[4]  Yuichi Kato,et al.  A novel method for superimposing molecules and receptor mapping , 1987 .

[5]  Andrew C. Good,et al.  Utilization of Gaussian functions for the rapid evaluation of molecular similarity , 1992, J. Chem. Inf. Comput. Sci..

[6]  G Klebe,et al.  On the prediction of binding properties of drug molecules by comparative molecular field analysis. , 1993, Journal of medicinal chemistry.

[7]  B. Chazelle.  Editor's Foreword (Special Issue on the ACM Symposium). , 1989 .

[8]  Philip M. Dean,et al.  An exploration of a novel strategy for superposing several flexible molecules , 1993, J. Comput. Aided Mol. Des..

[9]  Herbert Edelsbrunner,et al.  An O(n log² h) Time Algorithm for the Three-Dimensional Convex Hull Problem , 1991, SIAM J. Comput..

[10]  B. Flury.  Common Principal Components and Related Multivariate Models , 1988 .

[11]  Michael Ian Shamos,et al.  Divide and Conquer for Linear Expected Time , 1978, Inf. Process. Lett..

[12]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[13]  T. O'donohue,et al.  Novel pharmacology of substance K-binding sites: a third type of tachykinin receptor. , 1984, Science.

[14]  Robert B. Hermann,et al.  OVID and SUPER: Two overlap programs for drug design , 1991, J. Comput. Aided Mol. Des..

[15]  Donald R. Chand,et al.  An Algorithm for Convex Polytopes , 1970, JACM.

[16]  J Tirado-Rives,et al.  Molecular dynamics simulations of the unfolding of an alpha-helical analogue of ribonuclease A S-peptide in water. , 1991, Biochemistry.

[17]  Matthew Clark,et al.  Comparative molecular field analysis (CoMFA). 2. Toward its use with 3D-structural databases , 1990 .

[18]  Peter Willett,et al.  Algorithms for the identification of three-dimensional maximal common substructures , 1987, J. Chem. Inf. Comput. Sci..

[19]  M. L. Connolly.  Solvent-accessible surfaces of proteins and nucleic acids. , 1983, Science.

[20]  H. Berendsen,et al.  ALGORITHMS FOR MACROMOLECULAR DYNAMICS AND CONSTRAINT DYNAMICS , 1977 .

[21]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[22]  Yvonne C. Martin,et al.  A fast new approach to pharmacophore mapping and its application to dopaminergic and benzodiazepine agonists , 1993, J. Comput. Aided Mol. Des..