Automatic cryo-EM particle selection for membrane proteins in spherical liposomes

Abstract

Random spherically constrained (RSC) single particle reconstruction is a method to obtain structures of membrane proteins embedded in lipid vesicles (liposomes). As in all single-particle cryo-EM methods, structure determination is greatly aided by reliable detection of protein “particles” in micrographs. After fitting and subtraction of the membrane density from a micrograph, normalized cross-correlation (NCC) and estimates of the particle signal amplitude are used to detect particles, using as references the projections of a 3D model. At each pixel position, the NCC is computed with only those references that are allowed by the geometric constraint of the particle’s embedding in the spherical vesicle membrane. We describe an efficient algorithm for computing this position-dependent correlation, and demonstrate its application to selection of membrane-protein particles, GluA2 glutamate receptors, which present very different views from different projection directions.

Introduction

Random Spherically Constrained (RSC) single particle reconstruction (Jiang et al., 2001, Wang and Sigworth, 2010) is a useful approach for studying the structures of membrane proteins in membrane environments. The proteins are reconstituted into spherical lipid vesicles (liposomes), which in turn are frozen in vitreous ice and imaged by electron cryomicroscopy (cryo-EM). As in all single-particle methods, the automatic “picking”, that is selection, of protein particles in micrographs is an important first step in three-dimensional structure determination. The embedding in spherical lipid vesicles presents both disadvantages and advantages. Vesicles are large (∼30 nm diameter) but ideally have only one or two protein particles embedded each one, yielding a low overall density of particles in a micrograph. This low density has made the problem of particle selection particularly important, as in our experience a typical 4 k × 4 k pixel micrograph contains only about 50 particles. This means that many micrographs must be taken and processed to obtain large datasets. Further, the low density of particles means that the relative density of “non-particles” such as frost balls or other contaminants is high. A further disadvantage is that, to avoid distortion of vesicles, the ice layer must be relatively thick, larger than the diameter of the vesicles; thus the high contrast that is observed with very thin ice layers in cryo-EM specimens cannot be exploited.

On the other hand, an advantage arises from the fact that no particles exist in regions between vesicles, and at a given position relative to the center of a vesicle an embedded particle presents a restricted set of views. We sought to design a particle-picking algorithm that efficiently exploits these geometric constraints.

A popular approach to automatic particle picking involves the search of a micrograph using one or more templates (reference images) using the local correlation function (Roseman, 2003, Zhu et al., 2004, Voss et al., 2009) sometimes combined with other criteria for improved detection (Chen and Grigorieff, 2007, Langlois et al., 2011). The local correlation function is also known in the image-processing literature as the normalized cross-correlation (NCC). The program described here computes the NCC, and another selection criterion derived from the NCC, using reference images that are projections of an initial 3D model for the particles to be discovered. Due to the geometric constraint of embedding a protein particle in a spherical vesicle, two of the three Euler angles of orientation of a particle can be determined, within a fourfold ambiguity, from the position of the particle’s projection in the micrograph. Here we adapt an eigenimage-expansion strategy for multiple-template searching (Sigworth, 2004) to exploit these constraints.

As a test case we consider the GluA2 glutamate receptor, a 400 kDa membrane protein. We simulate images using its known X-ray crystal structure (Sobolevsky et al., 2009), and search for particles in cryo-EM images of GluA2 reconstituted into lipid vesicles.

The following notation is used in this paper. An upper-case variable denotes a matrix or an image; a bold-face variable denotes a vector, while lower-case variable denotes a scalar. The squared norm or “power” of an image X having $n_p$ pixels with values $x_i$ $$is defined as

$${\left|X\right|}^2={\displaystyle \sum _{i=1}^{n_p}}{x}_i^2\text{,}$$

and $C\circ X$ denotes operator C operating on X.