Albert Lawrence

High-performance electron tomography of complex biological specimens.

We have evaluated reconstruction methods using smooth basis functions in the electron tomography of complex biological specimens. In particular, we have investigated series expansion methods, with special emphasis on parallel computation. Among the methods investigated, the component averaging techniques have proven to be most efficient and have generally shown fast convergence rates. The use of smooth basis functions provides the reconstruction algorithms with an implicit regularization mechanism, very appropriate for noisy conditions. Furthermore, we have applied high-performance computing (HPC) techniques to address the computational requirements demanded by the reconstruction of large volumes. One of the standard techniques in parallel computing, domain decomposition, has yielded an effective computational algorithm which hides the latencies due to interprocessor communication. We present comparisons with weighted back-projection (WBP), one of the standard reconstruction methods in the areas of computational demand and reconstruction quality under noisy conditions. These techniques yield better results, according to objective measures of quality, than the weighted backprojection techniques after a very few iterations. As a consequence, the combination of efficient iterative algorithms and HPC techniques has proven to be well suited to the reconstruction of large biological specimens in electron tomography, yielding solutions in reasonable computation times.

Alignment of Cryo-Electron Tomography Datasets

Data acquisition of cryo-electron tomography (CET) samples described in previous chapters involves relatively imprecise mechanical motions: the tilt series has shifts, rotations, and several other distortions between projections. Alignment is the procedure of correcting for these effects in each image and requires the estimation of a projection model that describes how points from the sample in three-dimensions are projected to generate two-dimensional images. This estimation is enabled by finding corresponding common features between images. This chapter reviews several software packages that perform alignment and reconstruction tasks completely automatically (or with minimal user intervention) in two main scenarios: using gold fiducial markers as high contrast features or using relevant biological structures present in the image (marker-free). In particular, we emphasize the key decision points in the process that users should focus on in order to obtain high-resolution reconstructions.

TxBR montage reconstruction for large field electron tomography

Electron tomography (ET) has been proven an essential technique for imaging the structure of cells beyond the range of the light microscope down to the molecular level. Large-field high-resolution views of biological specimens span more than four orders of magnitude in spatial scale, and, as a consequence, are rather difficult to generate directly. Various techniques have been developed towards generating those views, from increasing the sensor array size to implementing serial sectioning and montaging. Datasets and reconstructions obtained by the latter techniques generate multiple three-dimensional (3D) reconstructions, that need to be combined together to provide all the multiscale information. In this work, we show how to implement montages within TxBR, a tomographic reconstruction software package. This work involves some new application of mathematical concepts related to volume preserving transformations and issues of gauge ambiguity, which are essential problems arising from the nature of the observation in an electron microscope. The purpose of TxBR is to handle those issues as generally as possible in order to correct for most distortions in the 3D reconstructions and allow for a seamless recombination of ET montages.

Tomography of Large Format Electron Microscope Tilt Series: Image Alignment and Volume Reconstruction

Image alignment is a critical step in obtaining high quality reconstructions. Bundle adjustment, based on a general projective model, combined with calculation of the envelope of backprojected tangents to a surface of revolution around the rotation axis establish the parameters of the projection maps, rotation angles and axis of rotation. Subsequent regression techniques may be used to calculate higher order polynomial corrections to the projection maps, and can compensate for curvilinear trajectories through the object, sample warping, and optical aberration. Backprojection from properly filtered images along the nominal electron trajectories yields high quality 3D reconstructions. We report here on recent extensions to the electron microscope tomography code, TxBR. In addition we discuss the basis for this code in the theory of Fourier integral operators.

Electron tomography and multiscale biology

Electron tomography (ET) is an emerging technology for the three dimensional imaging of cellular ultrastructure. In combination with other techniques, it can provide three dimensional reconstructions of protein assemblies, correlate 3D structures with functional investigations at the light microscope level and provide structural information which extends the findings of genomics and molecular biology. Realistic physical details are essential for the task of modeling over many spatial scales. While the electron microscope resolution can be as low as a fraction of a nm, a typical 3D reconstruction may just cover 1/1015 of the volume of an optical microscope reconstruction. In order to bridge the gap between those two approaches, the available spatial range of an ET reconstruction has been expanded by various techniques. Large sensor arrays and wide-field camera assemblies have increased the field dimensions by a factor of ten over the past decade, and new techniques for serial tomography and montaging make possible the assembly of many three-dimensional reconstructions. The number of tomographic volumes necessary to incorporate an average cell down to the protein assembly level is of the order 104, and given the imaging and algorithm requirements, the computational problem lays well in the exascale range. Tomographic reconstruction can be made parallel to a very high degree, and their associated algorithms can be mapped to the simplified processors comprising, for example, a graphics processor unit. Programming this on a GPU board yields a large speedup, but we expect that many more orders of magnitude improvement in computational capabilities will still be required in the coming decade. Exascale computing will raise a new set of problems, associated with component energy requirements (cost per operation and costs of data transfer) and heat dissipation issues. As energy per operation is driven down, reliability decreases, which in turn raises difficult problems in validation of computer models (is the algorithmic approach faithful to physical reality), and verification of codes (is the computation reliably correct and replicable). Leaving aside the hardware issues, many of these problems will require new mathematical and algorithmic approaches, including, potentially, a re-evaluation of the Turing model of computation.

The application of energy-filtered electron microscopy to tomography of thick, selectively stained biological samples.

Publisher Summary This chapter describes the use of energy-filtered electron microscopy (EM) to enhance contrast and reduce the chromatic aberration in the imaging of thick, selectively stained specimens. For thick specimens, the resolution of electron microscopy is severely limited by chromatic aberration that results from the inability of current electron lenses to deal uniformly with beam electrons that have a distribution of energies as a result of inelastic scattering in the samples. The chapter describes a technique of automated, most-probable loss (MPL) tomography. It shows that for thick, selectively stained biological specimens, this method produces a dramatic increase in the resolution of the projected images. These improvements are particularly evident at the large tilt angles required to improve tomographic resolution in the z-direction. In addition, MPL tomography effectively increases the usable thickness of selectively stained samples that can be imaged at a given accelerating voltage by improving resolution relative to unfiltered transmission electron microscopy (TEM).

3D reconstruction of biological structures: automated procedures for alignment and reconstruction of multiple tilt series in electron tomography

Transmission electron microscopy allows the collection of multiple views of specimens and their computerized three-dimensional reconstruction and analysis with electron tomography. Here we describe development of methods for automated multi-tilt data acquisition, tilt-series processing, and alignment which allow assembly of electron tomographic data from a greater number of tilt series, yielding enhanced data quality and increasing contrast associated with weakly stained structures. This scheme facilitates visualization of nanometer scale details of fine structure in volumes taken from plastic-embedded samples of biological specimens in all dimensions. As heavy metal-contrasted plastic-embedded samples are less sensitive to the overall dose rather than the electron dose rate, an optimal resampling of the reconstruction space can be achieved by accumulating lower dose electron micrographs of the same area over a wider range of specimen orientations. The computerized multiple tilt series collection scheme is implemented together with automated advanced procedures making collection, image alignment, and processing of multi-tilt tomography data a seamless process. We demonstrate high-quality reconstructions from samples of well-described biological structures. These include the giant Mimivirus and clathrin-coated vesicles, imaged in situ in their normal intracellular contexts. Examples are provided from samples of cultured cells prepared by high-pressure freezing and freeze-substitution as well as by chemical fixation before epoxy resin embedding.

Iterative Methods in Large Field Electron Microscope Tomography

Electron tomography (ET) is a powerful technology allowing the three-dimensional (3D) imaging of cellular ultrastructure. These structures are reconstructed from a set of micrographs taken at different sample orientations, the final volume being the solution of a general inverse problem. Two different approaches are used in this context: iterative methods and filtered backprojection. Iterative methods are known to provide high-resolution 3D reconstructions for ET under noisy and incomplete data conditions. However, all previous implementations have been restricted to the straight-line projection models. This is not accurate since electron trajectories in electron microscopes do not follow the straight-line optics assumed for X-rays, and biological samples may warp as a result of being exposed to an electron beam. Compensation for curvilinear trajectories, nonlinear electron optics, and sample warping constitutes a major advance in large-field ET and has made possible resolution down to the molecular level...

Serial reconstruction and montaging from large-field electron microscope tomograms

Electron microscope tomography [1] has been proven as an essential technique for imaging the structure of cells beyond the range of the light microscope down to the molecular level. However, because of the extreme difference in spatial scales, there is a large gap to be bridged between light and electron microscopy. Various techniques have been developed, including increasing size of the sensor arrays, serial sectioning and montaging. Data sets and reconstructions obtained by the latter techniques generate many 3D reconstructions that need to be glued together to provide information at a larger spatial scale. However, during the course of data acquisition, thin slices may become warped in optical and electron microscope preparations. We review some procedures for de-warping sections and reassembling them into larger reconstructions, and present some data from electron microscopy.

3D reconstruction from electron microscope images with TxBR

Tomographic reconstruction from large format electron microscope requires special procedures to handle geometric distortions arising from electron optics as opposed to light-ray optics. In particular, electrons travel in curvilinear paths through the sample and defocus and other aberrations can be more severe. We report on a software package, TxBR, which solves the inverse problem associated with a generalized ray transform. We also review the prospects for automated alignment, and discuss possible approaches.