Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape

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.