Three Dimensional Electron Microscopy/Initial model

Initial Modeling

Initial modeling is the process of using aligned and characterized electron microscopy images to produce a 3D reconstruction of the imaged particle. However, because each image is only a 2D projection of a 3D structure, it can often be quite difficult to determine the actual 3D structure of the original particle. To counteract this problem, researchers turn to the projection slice theorem: for any 3D object, the Fourier transform of each 2D projection it casts is a slice of the Fourier transform of the original 3D object. Thus, if enough 2D projections are obtained, the Fourier transform of the 3D object can be entirely reconstructed, and the original 3D object modeled in space by taking the inverse Fourier transform.

There are a number of common techniques used for initial modeling, some of which are described below.

Use of Generic Shapes

Information on generic structures of molecules can be useful for initial model formation. Using generic shapes like spheres, cubes etc. of molecules can help provide a starting point to obtain a detailed structure using a technique that has better resolution. It can often be easier to start with a generic shape and work towards a high-resolution model than to start from nothing and attempt to generate the model de novo. However, this method can introduce significant bias if the starting shape chosen is not an accurate representation of the actual structure of the molecule.

Use of Pre-existing Structures

Previously solved 3D structures are stored either in the Electron Microscopy Data Bank (EMDB) or the Protein Data Bank (PDB). 3D structures of biomolecules derived using electron microscopy are deposited in EMDB. EMDB’s for U.S, Japan, UK and Asia all act independently under their own protocols. Similarly, protein structures derived using X-ray crystallography, NMR, electron microscopy etc. are deposited at the Protein Data Bank (PDB). Approximately 90% structures submitted to PDB are derived using X-ray crystallography. The PDB contains the X, Y and Z coordinates for several protein structures.

New structures can be assessed against previous structures which helps validate the new structure in some capacity. When attempting to compile an initial model, a lower-resolution pre-existing structure is often used, so that any higher-resolution details are filled in by the obtained data in an attempt to avoid bias in the final structure. A structure can be taken from either the EMDBs or the PDB and blurred and then used to fill in the details of the new structure. For example in a research study while placing the protein and RNA structures into the 50S ribosomal subunit, the researchers used previously solved generic RNA-duplex and RNA tetraloops to position the density map of the 50S subunit . Thus, lower resolution data can be combined with new high resolution data to facilitate better interpretation.

Common Lines Method

Two projection views of a molecule intersecting at a common line in Fourier space.

The common lines method is a technique used to obtain an initial model by taking advantage of the points at which different projections of a structure intersect in Fourier space. The creation of initial 3D models from 2D images acquired from single-particle electron microscopy indisputably relies on data obtained from different views of the molecule of interest. The central feature of the common lines method is the definitive relationship of the center section, 1D, in Fourier space of 2D image views in noise free space

To obtain an initial 3D model reconstruction using the common lines method all particles are compared to one another in attempt to identify angular relationships. Since there are common lines for all particles the central section of the 2D Fourier transform can be determined by comparing the center section of the Fourier transform of all particles to one another. However, since the common lines method relies heavily on the identification of the shared 1D lines, the method is extremely hindered by noisy raw images. As a rule, the use of common lines on noisy raw images is error prone . In addition to limitations related to signal-to-noise ratios, the common lines method cannot be used to identify the handedness of a molecule.

Random Conical Tilt

Depicts RCT projections producing missing cone.

Random Conical Tilt (RCT) requires that two images be taken of the same set of particles – one at a high tilt angle (usually around 60°), and the other at no tilt (0°) . This results in two views of each particle within the sampling area that are physically related. The rotation angle of the molecule in the untilted image provides one angle for reconstruction, the angle of the specimen holder another, and the tilted images are used to construct the initial model . These images can also be characterized and separated into distinct groups corresponding to different orientations of the imaged particles, resolving much of the uncertainty in samples of heterogeneous orientations .

However, RCT also has several limitations. The copper grid on which the sample sits limits the maximum angle to which the specimen can be tilted, and because the paired images are not orthogonal, there is a significant amount of missing data – the “missing cone” . In addition, because two images of the same sample area are required, the sample is exposed to a much larger dose of radiation. The tilted image is usually taken first, and thus the images with the least radiation damage are used to reconstruct the image , but the alignment data must necessarily suffer, because it is taken from the second, untilted image . This problem is more apparent when the samples are in vitreous ice (cryoEM) – both because the higher electron density of a negative stain serves to protect the sample particles from damage from the electron beam, and because the first dose of radiation can often melt the ice, causing the particles to drift between the first and second images. The vitreous ice of cryoEM samples is also often preserved by the use of a small carboy of liquid nitrogen on the end of the sample holder, and any movement of this carboy (such as that required to tilt the sample holder within the microscope) can cause the liquid nitrogen to boil, thus shaking the sample holder and reducing the resolution of the resulting images.

Orthogonal Tilt Reconstruction

Orthogonal Tilt Reconstruction (OTR) works in much the same way as RCT, with the exception that the paired images taken are at 90° angles to one another. Taking images at 0° and 90° is impossible, due to the physical dimensions of the sample holder (as mentioned previously), so OTR circumvents this problem by taking images at 45° and -45° . The use of orthogonal images means that the entirety of the structure is sampled in Fourier space, thus eliminating the “missing cone” of RCT – this is its main advantage. However, it does still share the other limitations of RCT, as it still requires exposing a sample area to two doses of radiation and still requires physical movement of the sample holder.

OTR also has a unique limitation – it only works if the particles being imaged do not have a preferred orientation at 0° ; in other words, OTR works only for those particles that randomly assume all possible orientations on the sample area. For any particles which have a tendency to orient themselves in a certain way, OTR is not a viable reconstruction method.

Tomography

Tomography is again similar to both RCT and OTR, except that many more images are taken, at various angular orientations . Again, the rotation angles are limited by the physical dimensions of the sample holder, meaning that some of the structure cannot be sampled – but unlike the “missing cone” of RCT, tomography results in a “missing wedge” . Multiple rotation sets can be combined, however, to produce a complete initial model. Because many more images are required, though, the dosage of each image must be lowered dramatically to avoid radiation damage to the sample. Tomography thus requires a balancing act - maximizing the number of images that can be collected while still ensuring that each image is exposed to enough radiation to produce sufficient contrast for alignment .

Particle drift becomes a more significant problem in tomography, because there are so many more images in which the position of each particle must be determined. Thus, it is often beneficial to add markers of high electron-density to the particles, which will show up as constant dark spots in every image and can be used to track any motion of their associated particles in each image.