New determinations and simplified representations of macromolecular surfaces

Abstract Several new methods or improvements of older algorithms determining the different pieces of molecular surface are presented. Their improvement in time and their complexity are discussed. Only the indexes of the atoms on which the pieces are relying are, in fact, determined, since their explicit representation from these numbers varies according to the 3D capabilities of the graphic workstation (dots, grid, etc.), and this generation is not C.P.U. consuming. To have a simplified representation of the surface of macromolecules, a polyhedron with planar triangular faces is then introduced: Each concave triangular surface piece is replaced with planar triangles relying on its three atomic centers, while saddle-shaped rectangles and convex pieces are wholly ignored. A minimal data structure of the polyhedron is then proposed, which contains only topological informations, since no coordinates have been generated. If the atomic radius is then considered to be constant (independent of atomic type), the surface of a set of N points is now defined by the choice of a subset with a topology. This choice is controlled by a parameter of rugosity (the atomic radius). Contrary to Voronoi polyhedrons partition, which gives a topology for a set of N points, our approach gives a topology only for the exterior points of this set. A few applications of this very simple definition of molecular surface are then discussed: the 3D interactive manipulation of macromolecules, the steric intermolecular recognition, and the determination of local and global properties of the surface.