Representing thermal vibrations and uncertainty in molecular surfaces

The previous methods to compute smooth molecular surface assumed that each atom in a molecule has a fixed position without thermal motion or uncertainty. In real world, the position of an atom in a molecule is fuzzy because of its uncertainty in protein structure determination and thermal energy of the atom. In this paper, we propose a method to compute smooth molecular surface for fuzzy atoms. The Gaussian distribution is used for modeling the fuzziness of each atom, and a p-probability sphere is computed for each atom with a certain confidence level. The smooth molecular surface with fuzzy atoms is computed efficiently from extended-radius p-probability spheres. We have implemented a program for visualizing three-dimensional molecular structures including the smooth molecular surface with fuzzy atoms using multi-layered transparent surfaces, where the surface of each layer has a different confidence level and the transparency associated with the confidence level.