Extraction, quantification and visualization of protein pockets

Molecular surfaces of proteins and other biomolecules, while modeled as smooth analytic interfaces separating the molecule from solvent, often contain a number of pockets, holes and interconnected tunnels with many openings (mouths), aka molecular features in contact with the solvent. Several of these molecular features are biochemically significant as pockets are often active sites for ligand binding or enzymatic reactions, and tunnels are often solvent ion conductance zones. Since pockets or holes or tunnels share similar surface feature visavis their openings (mouths), we shall sometimes refer to these molecular features collectively as generalized pockets or pockets. In this paper we focus on elucidating all these pocket features of a protein (from its atomistic description), via a simple and practical geometric algorithm. We use a two-step level set marching method to compute a volumetric pocket function phi P(x) as the result of an outward and backward propagation. The regions inside pockets can be represented as phi P(x) > 0 and pocket boundaries are computed as the level set phi P(x) = epsilon , where epsilon > 0 is a small number. The pocket function phi P(x) can be computed efficiently by fast distance transforms. This volumetric representation allows pockets to be analyzed quantitatively and visualized with various techniques. Such feature analysis and quantitative visualization are also generalizable to many other classes of smooth and analytic free-form surfaces or interface boundaries.