Treatment of small deformations of polyhedral shapes of functional group distributions in biomolecules

Polyhedral models of the distribution of the essential functional groups (t he EFG polyhedra) within biomolecules provide simple tools for the study of small deformations affecting the mutual positioning of functional groups. In general, the relative locations of various functional groups may have an important role in determining the biochemical activities of biomolecules; the mere presence of functional sours is of ten insufficient to ensure a gi ven biochemical effect linked to the functional group. Accessibility and th e possibility of geometrically constrained, concerted action of several fun ctional groups are of major importance in many instances. Often, small mole cular deformations have a crucial role. Ln order to describe small deformat ions of biomolecules, two polyhedral deformation approaches are implemented for the entire electron density. The repositioning of essential functional groups generates a typically nonlinear deformation of the electron density that can be modeled by a nonlinear deformation of the entire three-dimensi onal space. These nonlinear deformations reproduce exactly the new location s of the reference points of the essential functional groups, and approxima te the electron density of the new EFG polyhedron using either of two simpl e algorithms, the dimension expansion-reduction (DER) or the weighted affin e transformation (WAT) algorithm. The adaptation of these two techniques to deformations defined in terms of the large scale EFG features of biomolecu les is described. (C) 2000 John Wiley & Sons, Inc.