Travel depth, a new shape descriptor for macromolecules: application to ligand binding.

Depth is a term frequently applied to the shape and surface of macromolecules, describing for example the grooves in DNA, the shape of an enzyme active site, or the binding site for a small molecule in a protein. Yet depth is a difficult property to define rigorously in a macromolecule, and few computational tools exist to quantify this notion, to visualize it, or analyze the results. We present our notion of travel depth, simply put the physical distance a solvent molecule would have to travel from a surface point to a suitably defined reference surface. To define the reference surface, we use the limiting form of the molecular surface with increasing probe size: the convex hull. We then present a fast, robust approximation algorithm to compute travel depth to every surface point. The travel depth is useful because it works for pockets of any size and complexity. It also works for two interesting special cases. First, it works on the grooves in DNA, which are unbounded in one direction. Second, it works on the case of tunnels, that is pockets that have no "bottom", but go through the entire macromolecule. Our algorithm makes it straightforward to quantify discussions of depth when analyzing structures. High-throughput analysis of macromolecule depth is also enabled by our algorithm. This is demonstrated by analyzing a database of protein-small molecule binding pockets, and the distribution of bound magnesium ions in RNA structures. These analyses show significant, but subtle effects of depth on ligand binding localization and strength.