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.
KeywordsElectron Tomography Surface Patch Tomographic Reconstruction Bundle Adjustment Fourier Integral Operator
Unable to display preview. Download preview PDF.
- Brand, M., Kang, K., Cooper, D.B.: Algebraic solution for the visual hull. In: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2004, vol. 1, pp. I–30–I–35 (2004)Google Scholar
- Cao, M., Zhang, H.B., Lu, Y., Nishi, R., Takaoka, A.: Formation and reduction of streak artefacts in electron tomography. Journal of Microscopy 239(1), 66–71 (2010)Google Scholar
- Duistermaat, J.J., Guillemin, V.W., Hörmander, L., Brüning, J.: Mathematics Past and Present: Fourier Integral Operators: Selected Classical Articles. Springer (1994)Google Scholar
- Greenleaf, A., Seeger, A.: Oscillatory and fourier integral operators with degenerate canonical relations, pp. 93–141. Publicacions Matematiques (2002)Google Scholar
- Guillemin, V.: On some results of gelfand in integral geometry. In: Proc. Symp. Pure Math., vol. 43, pp. 149–155 (1985)Google Scholar
- Hawkes, P.W.: Recent advances in electron optics and electron microscopy. Annales de la Foundation Louis de Broglie 29, 837–855 (2004)Google Scholar
- Heyden, A., Åström, K.: Euclidean reconstruction from almost uncalibrated cameras. In: Proceedings SSAB 1997 Swedish Symposium on Image Analysis, pp. 16–20. Swedish Society for Automated Image Analysis (1997)Google Scholar
- Hörmander, L.: The analysis of linear partial differential operators. In: The Analysis of Linear Partial Differential Operators. Springer, New York (1990)Google Scholar
- Institute For Computing in Science. In: Park city Workshop (2011), www.icis.anl.gov/programs/
- Machleidt, T., Robers, M., Hanson, G.T.: Protein labeling with flash and reash. Methods Mol. Biol. 356, 209–220 (2007)Google Scholar
- Palamodov, V.P.: A uniform reconstruction formula in integral geometry. arXiv:1111.6514v1 (2011)Google Scholar
- Phan, S., Lawrence, A.: Tomography of large format electron microscope tilt series: Image alignment and volume reconstr uction. In: CISP 2008: Congress on Image and Signal Processing, vol. 2, pp. 176–182 (May 2008)Google Scholar
- Phan, S., Lawrence, A., Molina, T., Lanman, J., Berlanga, M., Terada, M., Kulungowski, A., Obayashi, J., Ellisman, M.: Txbr montage reconstruction (submitted, 2012)Google Scholar
- Reimer, L., Kohl, H.: Transmission electron microscopy: physics of image formation. Springer (2008)Google Scholar
- Sharafutdinof, V.A.: Ray Transforms on Riemannian Manifolds. Lecture Notes. University of Washington, Seattle (1999)Google Scholar
- Wolf, L., Guttmann, M.: Artificial complex cells via the tropical semiring. In: CVPR (2007)Google Scholar