SIMILARITY AND COMPLEMENTARITY OF MOLECULAR SHAPES - APPLICABILITY OFA TOPOLOGICAL ANALYSIS APPROACH

Developments based on a topological analysis approach of electron dens ity maps are presented and applied to two different fields: the interp retation of electron density maps of proteins and the description of s hape complementarity between a cyclodextrin host and a guest molecule. A global representation of the electron density distribution, through the location, identification and linkage of its critical points (poin ts where the gradient of the density vanishes, i.e., peaks and passes) , is generated using the program ORCRIT. On one hand, the interpretati on of protein electron density maps is based on similarity evaluations between graphs of critical points and known structures. So far, the m ethod has been applied to 3 Angstrom resolution maps for the recogniti on of secondary structure motifs using a procedure relevant to expert systems in artificial intelligence. Satisfying matches between critica l point graphs and their corresponding protein structure depict the ab ility of the topological analysis to catch the essential secondary str uctural features in electron density maps. On the other hand, mapping the accessible volume of a host molecule is achieved by representing t he peaks as ellipsoids with axes related to local curvature of the ele ctron density function. Related energies of the interacting species ca n also be estimated. A qualitative comparison is made between the resu lts generated by the topological analysis and energy values obtained b y conventional molecular mechanics calculations. A positive comparison and a close complementarity between cyclodextrin and ligands shows th at the topological analysis method gives a good representation of the electron density function.