Classical detection theory and the cryo-EM particle selection problem
Introduction
The identification of individual particles in micrographs is a bottleneck in the high resolution determination of protein structures by electron cryomicroscopy (Nicholson and Glaeser, 2001). There are two goals that must be satisfied by a successful implementation of automatic particle picking. The first is to detect individual particle images in the presence of random noise. This is a problem that is equivalent to the classical problem of detecting symbols in a noisy communication channel. The second goal is to distinguish true particle images from artifacts or images of corrupted particles. This is a more difficult problem because in general its solution requires both information about the desired particles and also information about the characteristics of non-particles.
In this paper an implementation of automatic particle picking is based on the classical “matched filter” or “correlation detector” method. The prerequisite is that some sort of 3D density map of the particle is already available; projections of this map are used to derive references for the detector. In the past, correlation-based schemes using a single reference (Frank and Wagenknecht, 1984; Lata et al., 1995) or a representative set of references (Ludtke et al., 1999; Roseman, 2003; Stoschek and Hegerl, 1997; Wong et al., 2003) have been presented. The approach followed here uses the classical matched filter rather than the modern statistical techniques employed by Stoschek and Hegerl (1997) and by Wong et al. (2003). The main difference from previous work is that the spectrum of the background noise of a micrograph is standardized through the application of a pre-whitening filter. With this standardization, the frequency of finding “false particles” can be estimated, and a statistic for discriminating “true” particles has a known distribution. Also described here is a method to reduce the computational burden of using many references, employing principal component analysis (PCA). A closely related application of PCA is described by Ogura and Sato (2003) for their particle picker that is based on a neural network.
Section snippets
The particle detection problem
To illustrate the algorithms described here, the results will be given with reference to an annotated keyhole limpet hemocyanin (KLH) dataset (Zhu et al., 2003) available at http://ami.Scripps.edu/prtl_data. This dataset consists of 82 micrographs, each 2k × 2k pixels in size, with the pixel size being 2.2 Å. For the processing described here the high-defocus “Exposure 2” micrographs were used, and binning of pixels was employed to increase the pixel size to 8.8 Å. The images show “side” views and
The particle discrimination problem
The correlation detector does not discriminate well between true particles and other objects: any image motif that provides a sufficiently large inner product will be counted as a particle. Stoschek and Hegerl (1997) have demonstrated a correlation detector that can discriminate well among different types of particles. However, in the present case where the objects to be discriminated against cannot be specified, what is needed instead is a test of similarity of the observed image to one of the
Discussion
Described here is an automatic particle selection algorithm that shows good performance on a simple dataset having an excellent signal-to-noise ratio. Its performance on more challenging datasets has not been tested, but there is hope that some of the underlying principles—a standardized noise model, a fast algorithm for multiple correlations, and a discrimination statistic t with a predictable distribution—may be combined with other approaches to yield a truly robust automatic particle
Acknowledgements
I am grateful to Shirley Wang (Yale College) for assistance in programming. I also thank Professors Peter Schultheiss (Yale), Eric Hansen (Thayer School of Engineering, Dartmouth College), and Marshall Bern (Palo Alto Research Center) for advice and discussions. The data used here were provided by the National Resource for Automated Molecular Microscopy (supported by National Center for Research Resources Grant No. RR17573). The author’s work was supported by NIH Grant No. NS21501.
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