A Discrete Geometry Method for Atom Depth Computation in Complex Molecular Systems

The field of structural biology is rapidly advancing thanks to significant improvements in X-ray crystallography, nuclear magnetic resonance (NMR), cryo-electron microscopy, and bioinformatics. The identification of structural descriptors allows for the correlation of functional properties with characteristics such as accessible molecular surfaces, volumes, and binding sites. Atom depth has been recognized as an additional structural feature that links protein structures to their folding and functional properties. In the case of proteins, the atom depth is typically defined as the distance between the atom and the nearest surface point or nearby water molecule. In this paper, we propose a discrete geometry method to calculate the depth index with an alternative approach that takes into account the local molecular shape of the protein. To compute atom depth indices, we measure the volume of the intersection between the molecule and a sphere with an appropriate reference radius, centered on the atom for which we want to quantify the depth. We validate our method on proteins of diverse shapes and sizes and compare it with metrics based on the distance to the nearest water molecule from bulk solvent to demonstrate its effectiveness.