Similarity and complementarity of molecular shapes: Applicability of a topological analysis approach

Developments based on a topological analysis approach of electron density maps are presented and applied to two different fields: the interpretation of electron density maps of proteins and the description of shape 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 (points where the gradient of the density vanishes, i.e., peaks and passes), is generated using the program ORCRIT. On one hand, the interpretation of protein electron density maps is based on similarity evaluations between graphs of critical points and known structures. So far, the method has been applied to 3 Angstrom resolution maps for the recognition of secondary structure motifs using a procedure relevant to expert systems in artificial intelligence. Satisfying matches between critical point graphs and their corresponding protein structure depict the ability of the topological analysis to catch the essential secondary structural features in electron density maps. On the other hand, mapping the accessible volume of a host molecule is achieved by representing the peaks as ellipsoids with axes related to local curvature of the electron density function. Related energies of the interacting species can also be estimated. A qualitative comparison is made between the results generated by the topological analysis and energy values obtained by conventional molecular mechanics calculations. A positive comparison and a close complementarity between cyclodextrin and ligands shows that the topological analysis method gives a good representation of the electron density function.