## Extraction of Robust Voids and Pockets in Proteins

#### Raghavendra Sridharamurthy, Harish Doraiswamy, Siddharth Patel, Raghavan Varadarajan, and Vijay Natarajan

Voids and pockets in a protein refer to empty spaces that are enclosed by the protein molecule. Existing methods to compute, measure, and visualize the voids and pockets in a protein molecule are sensitive to inaccuracies in the empirically determined atomic radii. This paper presents a topological framework that enables robust computation and visualization of these structures. Given a fixed set of atoms, voids and pockets are represented as subsets of the weighted Delaunay triangulation of atom centers. A novel notion of $(\varepsilon,\pi)$-stable voids helps identify voids that are stable even after perturbing the atom radii by a small value. An efficient method is described to compute these stable voids for a given input pair of values $(\varepsilon,\pi)$.

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