Protein structure and function are largely specified by the distribution of different atoms and residues relative to the core and surface of the molecule. Relative depths of atoms therefore are key attributions that have been widely used in protein structure modeling and function annotation. However, accurate calculation of depth is time consuming. Here, we developed an algorithm which uses Euclidean distance transform (EDT) to convert the target protein structure into a 3D gray-scale image, where depths of atoms in the protein can be conveniently and precisely derived from the minimum distance of the pixels to the surface of the protein. We tested the proposed EDT-based method on a set of 261 non-redundant protein structures, which shows that the method is 2.6 times faster than the widely used method proposed by Chakravarty and Varadarajan. Depth values by EDT method are highly accurate with a Pearson’s correlation coefficient ≈1 compared to the calculations from exhaustive search. To explore the usefulness of the method in protein structure prediction, we add the calculated residue depth to the scoring function of the state of the art, profile–profile alignment based fold-recognition program, which shows an additional 3% improvement in the TM-score of the alignments. The data demonstrate that the EDT-based depth calculation program can be used as an efficient tool to assist protein structure analysis and structure-based function annotation.
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