State-of-the-art and perspectives of geometric and implicit modeling for molecular surfaces

This paper reviews state-of-the-art methods and presents new perspectives of implicit modeling, together with their relations with Constructive-Solid-Geometry, for the computation and analysis of molecular surfaces. The link between implicit modeling techniques and the generation of molecular surfaces is possible thanks to the representation of the molecule as the iso-surface of an implicit function and to the definition of the solvent-accessible/solvent-excluded surfaces as the union/intersection of atoms. We also review methods that consider the position of each atom as a probability distribution and introduce new representations of molecular surfaces based on the uncertainty and thermal vibration of the atoms. Finally, the specialization of implicit modeling techniques to molecular surfaces allows us to analyze geometric/topological properties of molecules;to address molecular docking through the identification of cavities; and to combine surface-based and volume-based information through the implicit representation of the electron density map.