Identifying Components in 3D Density Maps of Protein Nanomachines by Multi-scale Segmentation

Abstract

Segmentation of density maps obtained using cryo-electron microscopy (cryo-EM) is a challenging task, and is typically accomplished by time-intensive interactive methods. The goal of segmentation is to identify the regions inside the density map that correspond to individual components. We present a multi-scale segmentation method for accomplishing this task that requires very little user interaction. The method uses the concept of scale space, which is created by convolution of the input density map with a Gaussian filter. The latter process smoothes the density map. The standard deviation of the Gaussian filter is varied, with smaller values corresponding to finer scales and larger values to coarser scales. Each of the maps at different scales is segmented using the watershed method, which is very efficient, completely automatic, and does not require the specification of seed points. Some detail is lost in the smoothing process. A sharpening process reintroduces detail into the segmentation at the coarsest scale by using the segmentations at the finer scales. We apply the method to simulated density maps, where the exact segmentation (or ground truth) is known, and rigorously evaluate the accuracy of the resulting segmentations.

Fig. 1

Illustration of the S³ method, including smoothing, segmentation, and sharpening operations. The input density map and the smoothed density maps are shown on the left by iso-surfaces. The segmentations are illustrated by smoothed surfaces that enclose each region.

Fig. 2

Three simulated density maps of nanomachines that the S³ method was applied to. The resulting segmentations visually match the ground truth very well.

Fig. 3

Average segmentation accuracies for 4 density maps. The accuracy for each protein component is computed using (1), and an average is then calculated over all the proteins in each density map. This average is plotted at all the scales considered. The scale where σ = 0 refers to the input density map. The average highest attainable accuracy given the segmentation of a density map at each scale is plotted in red.