12 March 2002 Representing thermal vibrations and uncertainty in molecular surfaces
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The smooth molecular surface is defined as the surface which an external probe sphere touches as it is rolled over the spherical atoms of a molecule. 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 an extended-radius p-probability sphere is computed for each atom with a certain confidence level. An extended-radius p-probability sphere is defined for atom i as the smallest sphere containing the atom i with a probability p. The fuzzy molecular surface is defined as a collection of molecular surfaces constructed from extended-radius p-probability spheres for each probability p. We have implemented a program for visualizing three-dimensional molecular structures including the fuzzy molecular surface using multi-layered transparent surfaces, where the surface of each layer has a different confidence level and the transparency associated with the confidence level.
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Chang Ha Lee, Chang Ha Lee, Amitabh Varshney, Amitabh Varshney, } "Representing thermal vibrations and uncertainty in molecular surfaces", Proc. SPIE 4665, Visualization and Data Analysis 2002, (12 March 2002); doi: 10.1117/12.458813; https://doi.org/10.1117/12.458813

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