@article{4011,
  abstract     = {The size and shape of macromolecules such as proteins and nucleic acids play an important role in their functions. Prior efforts to quantify these properties have been based on various discretization or tessellation procedures involving analytical or numerical computations. In this article, we present an analytically exact method for computing the metric properties of macromolecules based on the alpha shape theory. This method uses the duality between alpha complex and the weighted Voronoi decomposition of a molecule. We describe the intuitive ideas and concepts behind the alpha shape theory and the algorithm for computing areas and volumes of macromolecules. We apply our method to compute areas and volumes of a number of protein systems. We also discuss several difficulties commonly encountered in molecular shape computations and outline methods to overcome these problems. (C) 1998 Wiley-Liss, Inc.},
  author       = {Liang, Jie and Edelsbrunner, Herbert and Fu, Ping and Sudhakar, Pamidighantam and Subramaniam, Shankar},
  issn         = {0887-3585},
  journal      = {Proteins: Structure, Function and Bioinformatics},
  number       = {1},
  pages        = {1 -- 17},
  publisher    = {Wiley-Blackwell},
  title        = {{Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape}},
  doi          = {10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O},
  volume       = {33},
  year         = {1998},
}

@article{4012,
  abstract     = {The structures of proteins are well-packed, yet they contain numerous cavities which play key roles in accommodating small molecules, or enabling conformational changes. From high-resolution structures it is possible to identify these cavities. We have developed a precise algorithm based on alpha shapes for measuring space-filling-based molecular models (such as van der Waals, solvent accessible, and molecular surface descriptions). We applied this method for accurate computation of the surface area and volume of cavities in several proteins. In addition, all of the atoms/residues Lining the cavities are identified, We use this method to study the structure and the stability of proteins, as well as to locate cavities that could contain structural water molecules in the proton transport pathway in the membrane protein bacteriorhodopsin.},
  author       = {Liang, Jie and Edelsbrunner, Herbert and Fu, Ping and Sudhakar, Pamidighantam and Subramaniam, Shankar},
  issn         = {0887-3585},
  journal      = {Proteins: Structure, Function and Bioinformatics},
  number       = {1},
  pages        = {18 -- 29},
  publisher    = {Wiley-Blackwell},
  title        = {{Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins}},
  doi          = {10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H},
  volume       = {33},
  year         = {1998},
}