The Combined Focal Cross Entropy and Dice Loss Function for Segmentation of Protein Secondary Structures from Cryo-EM 3D Density maps

Although cryo-electron microscopy (cryo-EM) has been successfully used to derive atomic structures for many proteins, it is still challenging to derive atomic structure when the resolution of cryo-EM density maps is in the medium resolution range such as 5-10 A. Although multiple neural networks have been proposed for the problem of secondary structure detection from cryo-EM 3D images, loss functions used in the existing networks are primarily based on cross entropy loss (CE). In order to study the behavior of various loss functions in the secondary structure detection problem, we investigated five loss functions and compared their performances. Using a U-net architecture in DeepSSETracer and a test set of 65 protein chains of atomic structures and their corresponding cryo-EM density component maps, we found that the combined function with focal cross entropy loss (FCE) and Dice loss (DL) provides the best overall detection of secondary structures. In particular, the combined loss function has a significant enhancement of an overall F
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score of 6.7% when compared to CE in detection of $\beta-$sheet voxels that are generally much harder to be detected accurately than for helix voxels. Our work shows the potential of designing effective loss functions to enhance the detection of hard cases in the segmentation of secondary structure problem.