Single particle analysis
Encyclopedia
Single Particle Analysis is a group of related of computerized image processing techniques used to analyze images from transmission electron microscopy (TEM). These methods were developed to improve and extend the information obtainable from TEM images of particulate samples, typically proteins or other large biological entities such as virus
es. Individual images of stained or unstained particles are very noisy, and so hard to interpret. Combining several digitized images of similar particles together gives an image with stronger and more easily interpretable features. An extension of this technique uses single particle methods to build up a three dimensional reconstruction of the particle. Using cryo-electron microscopy
it is now possible to generate reconstructions with sub-nanometer resolution
and near-atomic resolution in the case of highly symmetric viruses.
and vitreous ice-embedded cryo-EM
samples. Single particle analysis methods are, in general, reliant on the sample being homogeneous, although techniques for dealing with conformational heterogeneity are being developed.
Images (micrographs) collected on film are digitized using high-quality scanners, although increasingly electron microscopes have built-in CCD
detectors coupled to a phosphorescent layer. The image processing is carried out using specialized software programs, often run on multi-processor computer clusters. Depending on the sample or the desired results, various steps of two- or three-dimensional processing can be done.
.
However, a micrograph often contains particles in multiple different orientations and/or conformations, and so to get more representative image averages, a method is required to group similar particle images together into multiple sets. This is normally carried out using one of several data analysis and image classification algorithms, such as multi-variate statistical analysis
and hierarchical ascendant classification, or K-means classification.
Often data sets of tens of thousands of particle images are used, and to reach an optimal solution an iterative procedure of alignment and classification is used, whereby strong image averages produced by classification are used as reference images for a subsequent alignment of the whole data set.
information in the images, which can affect the results of the alignment and classification procedures. This is particularly useful in negative stain
images. The algorithms make use of fast Fourier transforms (FFT), often employing gaussian shaped soft-edged masks in reciprocal space to suppress certain frequency ranges. High-pass filters remove low spatial frequencies (such as ramp or gradient effects), leaving the higher frequencies intact. Low-pass filters remove high spatial frequency features and have a blurring effect on fine details.
. This, along with features inherent in the microscope's lens system, creates blurring of the collected images visible as a point spread function
. The combined effects of the imaging conditions are known as the Contrast transfer function
(CTF), and can be approximated mathematically as a function in reciprocal space. Specialized image processing techniques such as phase flipping and amplitude correction/wiener filtering can (at least partially) correct for the CTF, and allow high resolution reconstructions.
Before a reconstruction can be made, the orientation of the object in each image needs to be estimated. Several methods have been developed to work out the relative Euler angles
of each image. Some are based on common lines (common 1D projections and sinograms
), others use iterative projection matching algorithms. The latter uses a simple starting model and compares the experimental images to projections of the model to bootstrap towards a solution.
Methods are also available for making 3D reconstructions of helical samples, taking advantage of the helical symmetry. Both real space methods (treating sections of the helix as single particles) and reciprocal space methods (using diffraction patterns) have been used.
) of each particle is known from the tilt geometry.
3D reconstructions from random conical tilt suffer from missing information resulting from a restricted range of orientations. Known as the missing cone (due to the shape in reciprocal space), this causes distortions in the 3D maps. However, the missing cone problem can often be overcome by combining several tilt reconstructions. Tilt methods are best suited to negatively stained samples, and can be used for particles that adsorb to the carbon support film in preferred orientations. The phenomenon known as charging or beam-induced movement makes collecting high-tilt images of samples in vitreous ice challenging.
Virus
A virus is a small infectious agent that can replicate only inside the living cells of organisms. Viruses infect all types of organisms, from animals and plants to bacteria and archaea...
es. Individual images of stained or unstained particles are very noisy, and so hard to interpret. Combining several digitized images of similar particles together gives an image with stronger and more easily interpretable features. An extension of this technique uses single particle methods to build up a three dimensional reconstruction of the particle. Using cryo-electron microscopy
Cryo-electron microscopy
Cryo-electron microscopy , or electron cryomicroscopy, is a form of transmission electron microscopy where the sample is studied at cryogenic temperatures...
it is now possible to generate reconstructions with sub-nanometer resolution
Resolution (electron density)
Resolution in terms of electron density is a measure of the resolvability in the electron density map of a molecule. In X-ray crystallography, resolution is the highest resolvable peak in the diffraction pattern...
and near-atomic resolution in the case of highly symmetric viruses.
Techniques
Single particle analysis can be done on both negatively stainedNegative stain
Negative staining is an established method, often used in diagnostic microscopy, for contrasting a thin specimen with an optically opaque fluid....
and vitreous ice-embedded cryo-EM
Cryo-electron microscopy
Cryo-electron microscopy , or electron cryomicroscopy, is a form of transmission electron microscopy where the sample is studied at cryogenic temperatures...
samples. Single particle analysis methods are, in general, reliant on the sample being homogeneous, although techniques for dealing with conformational heterogeneity are being developed.
Images (micrographs) collected on film are digitized using high-quality scanners, although increasingly electron microscopes have built-in CCD
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
detectors coupled to a phosphorescent layer. The image processing is carried out using specialized software programs, often run on multi-processor computer clusters. Depending on the sample or the desired results, various steps of two- or three-dimensional processing can be done.
Alignment and Classification
Biological samples, and especially samples embedded in thin vitreous ice, are highly radiation sensitive, thus only low electron doses can be used to image the sample. This low dose, as well as variations in the metal stain used (if used) means images have high noise relative to the signal given by the particle being observed. By aligning several similar images to each other so they are in register and then averaging them, an image with higher signal to noise ratio can be obtained. As the noise is mostly randomly distributed and the underlying image features constant, by averaging the intensity of each pixel over several images only the constant features are reinforced. Typically, the optimal alignment (a translation and an in-plane rotation) to map one image onto another is calculated by cross-correlationCross-correlation
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long-duration signal for a shorter, known feature...
.
However, a micrograph often contains particles in multiple different orientations and/or conformations, and so to get more representative image averages, a method is required to group similar particle images together into multiple sets. This is normally carried out using one of several data analysis and image classification algorithms, such as multi-variate statistical analysis
Multivariate statistics
Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one statistical variable. The application of multivariate statistics is multivariate analysis...
and hierarchical ascendant classification, or K-means classification.
Often data sets of tens of thousands of particle images are used, and to reach an optimal solution an iterative procedure of alignment and classification is used, whereby strong image averages produced by classification are used as reference images for a subsequent alignment of the whole data set.
Image Filtering
Image filtering (band pass filtering) is often used to reduce the influence of high and/or low spatial frequencySpatial frequency
In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is...
information in the images, which can affect the results of the alignment and classification procedures. This is particularly useful in negative stain
Negative stain
Negative staining is an established method, often used in diagnostic microscopy, for contrasting a thin specimen with an optically opaque fluid....
images. The algorithms make use of fast Fourier transforms (FFT), often employing gaussian shaped soft-edged masks in reciprocal space to suppress certain frequency ranges. High-pass filters remove low spatial frequencies (such as ramp or gradient effects), leaving the higher frequencies intact. Low-pass filters remove high spatial frequency features and have a blurring effect on fine details.
Contrast Transfer Function
Due to the nature of image formation in the electron microscope, bright-field TEM images are obtained using significant underfocusFocus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
. This, along with features inherent in the microscope's lens system, creates blurring of the collected images visible as a point spread function
Point spread function
The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response, the PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob...
. The combined effects of the imaging conditions are known as the Contrast transfer function
Contrast transfer function
The contrast transfer function is a type of optical transfer function that affects images collected in an transmission electron microscope. The contrast transfer function must be corrected in the images in order to obtain high resolution structures in three-dimensional electron microscopy,...
(CTF), and can be approximated mathematically as a function in reciprocal space. Specialized image processing techniques such as phase flipping and amplitude correction/wiener filtering can (at least partially) correct for the CTF, and allow high resolution reconstructions.
Three dimensional reconstruction
Transmission electron microscopy images are projections of the object showing the distribution of density through the object, similar to medical X-rays. By making use of the projection slice theorem a three dimensional reconstruction of the object can be generated by combining many images (2D projections) of the object taken from a range of viewing angles. Proteins in vitreous ice usually adopt a random distribution of orientations, allowing an isotropic reconstruction. Filtered back projection is a commonly used method of generating 3D reconstructions in single particle analysis, although many alternative algorithms exist.Before a reconstruction can be made, the orientation of the object in each image needs to be estimated. Several methods have been developed to work out the relative Euler angles
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required...
of each image. Some are based on common lines (common 1D projections and sinograms
Radon transform
thumb|right|Radon transform of the [[indicator function]] of two squares shown in the image below. Lighter regions indicate larger function values. Black indicates zero.thumb|right|Original function is equal to one on the white region and zero on the dark region....
), others use iterative projection matching algorithms. The latter uses a simple starting model and compares the experimental images to projections of the model to bootstrap towards a solution.
Methods are also available for making 3D reconstructions of helical samples, taking advantage of the helical symmetry. Both real space methods (treating sections of the helix as single particles) and reciprocal space methods (using diffraction patterns) have been used.
Tilt Methods
The specimen stage of the microscope can be tilted (typically along a single axis), allowing the single particle technique known as random conical tilt. An area of the specimen is imaged at both zero and at high angle (~60-70 degrees) tilts, or in the case of the related method of orthogonal tilt reconstruction, +45 and -45 degrees. Pairs of particles corresponding to the same object at two different tilts (tilt pairs) are selected, and by following the parameters used in subsequent alignment and classification steps a three dimensional reconstruction can be generated relatively easily. This is because the viewing angle (defined as three Euler anglesEuler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required...
) of each particle is known from the tilt geometry.
3D reconstructions from random conical tilt suffer from missing information resulting from a restricted range of orientations. Known as the missing cone (due to the shape in reciprocal space), this causes distortions in the 3D maps. However, the missing cone problem can often be overcome by combining several tilt reconstructions. Tilt methods are best suited to negatively stained samples, and can be used for particles that adsorb to the carbon support film in preferred orientations. The phenomenon known as charging or beam-induced movement makes collecting high-tilt images of samples in vitreous ice challenging.
Map Visualization and Fitting
Various software programs are available that allow viewing the 3D maps. These often enable the user to manually dock in protein coordinates (structures from X-ray crystallography or NMR) of subunits into the electron density. Several programs can also fit subunits computationally.Examples
- Important information on protein synthesis, ligand binding and RNA interaction can be obtained using this novel technique at medium resolutions of 7.5 to 25Å.
- Methanococcus maripaludis chaperonin, reconstructed to 0.43 nanometer resolution. This bacterial protein complex is a machine for folding other proteins, which get trapped within the shell.
- Fatty acid synthase from yeast at 0.59 nanometer resolution. This huge enzyme complex is responsible for building the long chain fatty acids essential for cellular life.
- A 0.33 nanometer reconstruction of Aquareovirus. These viruses infect fish and other aquatic animals. The reconstruction has high enough resolution to have amino acid side chain densities easily visible.