Shape modeling and matching in identifying 3D protein structures

In this paper, we describe a novel geometric approach in the process of recovering 3D protein structures from scalar volumes. The input to our method is a sequence of αα-helices that make up a protein, and a low-resolution protein density volume where possible locations of αα-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of synthetic and authentic inputs, the shape-modeling approach is capable of identifying helix correspondences in noise-abundant volumes at high accuracy with minimal or no user intervention.