Cryo-electron microscopy (cryo-EM) has recently emerged as a prominent biophysical method for macromolecular structure determination. Many research efforts have been devoted to produce cryo-EM images, density maps, at near-atomic resolution. Despite many advances in technology, the resolution of the generated density maps may not be sufficiently adequate and informative to directly construct the atomic structure of proteins. At medium-resolution (∼4-10Å), secondary structure elements (α-helices and β-sheets) are discernable, whereas finding the correspondence of secondary structure elements detected in the density map with those on the sequence remains a challenging problem. In this paper, an automatic framework is proposed to solve α-helix correspondence problem in three-dimensional space. Through modeling of the sequence with the aid of a novel strategy, the α-helix correspondence problem is initially transformed into a complete weighted bipartite graph matching problem. An innovative correlation-based scoring function based on a well-known and robust statistical method is proposed for weighting the graph. Moreover, two local optimization algorithms, which are Greedy and Improved Greedy algorithms, have been presented to find α-helix correspondence. A widely used data set including 16 reconstructed and 4 experimental cryo-EM maps were chosen to verify the accuracy and reliability of the proposed automatic method. The experimental results demonstrate that the automatic method is highly efficient (86.25% accuracy), robust (11.3% error rate), fast (∼1.4 seconds), and works independently from cryo-EM skeleton.

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