A short overview of electron tomography Ozan ¨ Oktem ozan.oktem@sidec.com Sidec Technologies January 17, 2006 IMA Workshop: New Mathematics and Algorithms for 3-D Image Analysis, January 9-12, 2006
Outline The main application 1 The experimental setup 2 The forward model 3 Reconstruction methods 4 Open problems 5 Case studies 6
The structure determination problem The structure determination problem Recover the 3D structure of an individual molecule (e.g. a protein or a macromolecular assembly) at highest possible resolution in situ (in their cellular environment) or in vitro (in aqueous environment). X-ray crystallography and NMR are established methods. Major advantage: Atomic resolution. 1 Major disadvantage: Inability to study individual molecules in their 2 natural environment (in situ and in vitro). Electron tomography (ET) is an emerging technology. Major advantage: Enables study of individual molecules in their natural 1 environment (in situ and in vitro). Major disadvantage: Low resolution. 2
The structure determination problem The structure determination problem Recover the 3D structure of an individual molecule (e.g. a protein or a macromolecular assembly) at highest possible resolution in situ (in their cellular environment) or in vitro (in aqueous environment). X-ray crystallography and NMR are established methods. Major advantage: Atomic resolution. 1 Major disadvantage: Inability to study individual molecules in their 2 natural environment (in situ and in vitro). Electron tomography (ET) is an emerging technology. Major advantage: Enables study of individual molecules in their natural 1 environment (in situ and in vitro). Major disadvantage: Low resolution. 2
The structure determination problem The structure determination problem Recover the 3D structure of an individual molecule (e.g. a protein or a macromolecular assembly) at highest possible resolution in situ (in their cellular environment) or in vitro (in aqueous environment). X-ray crystallography and NMR are established methods. Major advantage: Atomic resolution. 1 Major disadvantage: Inability to study individual molecules in their 2 natural environment (in situ and in vitro). Electron tomography (ET) is an emerging technology. Major advantage: Enables study of individual molecules in their natural 1 environment (in situ and in vitro). Major disadvantage: Low resolution. 2
The transmission electron microscope (TEM) Field Emisson Gun (FEG) Electron beam First condenser lens Second condenser lens Condenser aperture Sample Objective lens Objective and selected area apertures First intermediate lens Second intermediate lens Projector lens Detector
Sample preparation and data collection scheme Sample preparation: Purpose is to enable thin (about 100 nm) fixed specimens while preserving the structure. In vitro samples: Flash-frozen in a millisecond. In situ samples: Chemically fixed, cryosectioned and immunolabeled (in order to find the molecule). Single axis tilting: The most common data collection scheme. ◮ Rotation around the tilt axis. The rotation angle is called the tilt angle and the angular range is usually from [ − 60 ◦ , 60 ◦ ]. ◮ Can reduce 3D reconstruction problem to a stack of 2D reconstruction problems.
Sample preparation and data collection scheme Sample preparation: Purpose is to enable thin (about 100 nm) fixed specimens while preserving the structure. In vitro samples: Flash-frozen in a millisecond. In situ samples: Chemically fixed, cryosectioned and immunolabeled (in order to find the molecule). Single axis tilting: The most common data collection scheme. ◮ Rotation around the tilt axis. The rotation angle is called the tilt angle and the angular range is usually from [ − 60 ◦ , 60 ◦ ]. ◮ Can reduce 3D reconstruction problem to a stack of 2D reconstruction problems.
Properties of TEM images of biological specimens Contrast depends on the atomic number. Biological specimens are composed of atoms of very low atomic number (carbon, hydrogen, nitrogen, phosphorus and sulphur). Main contrast mechanism is phase contrast which results from the quantum superposition of the electron wave and the interference caused by the optics rather than amplitude contrast. No quantum interference between components of the single electron wave function that originate from interaction with specimen in different quantum states, so a measured intensity is a superimposition of intensities. Electron wavelength for 300 keV is about 0 . 0197 ˚ A, sample thickness about 1000 ˚ A, and atomic resolution is about 1-2 ˚ A. Secondary structures (near atomic resolution) are visible when resolution is about 5-8 ˚ A. In any case, electron wavelength is not a limiting factor for the resolution.
Properties of TEM images of biological specimens Contrast depends on the atomic number. Biological specimens are composed of atoms of very low atomic number (carbon, hydrogen, nitrogen, phosphorus and sulphur). Main contrast mechanism is phase contrast which results from the quantum superposition of the electron wave and the interference caused by the optics rather than amplitude contrast. No quantum interference between components of the single electron wave function that originate from interaction with specimen in different quantum states, so a measured intensity is a superimposition of intensities. Electron wavelength for 300 keV is about 0 . 0197 ˚ A, sample thickness about 1000 ˚ A, and atomic resolution is about 1-2 ˚ A. Secondary structures (near atomic resolution) are visible when resolution is about 5-8 ˚ A. In any case, electron wavelength is not a limiting factor for the resolution.
Properties of TEM images of biological specimens Contrast depends on the atomic number. Biological specimens are composed of atoms of very low atomic number (carbon, hydrogen, nitrogen, phosphorus and sulphur). Main contrast mechanism is phase contrast which results from the quantum superposition of the electron wave and the interference caused by the optics rather than amplitude contrast. No quantum interference between components of the single electron wave function that originate from interaction with specimen in different quantum states, so a measured intensity is a superimposition of intensities. Electron wavelength for 300 keV is about 0 . 0197 ˚ A, sample thickness about 1000 ˚ A, and atomic resolution is about 1-2 ˚ A. Secondary structures (near atomic resolution) are visible when resolution is about 5-8 ˚ A. In any case, electron wavelength is not a limiting factor for the resolution.
Properties of TEM images of biological specimens Contrast depends on the atomic number. Biological specimens are composed of atoms of very low atomic number (carbon, hydrogen, nitrogen, phosphorus and sulphur). Main contrast mechanism is phase contrast which results from the quantum superposition of the electron wave and the interference caused by the optics rather than amplitude contrast. No quantum interference between components of the single electron wave function that originate from interaction with specimen in different quantum states, so a measured intensity is a superimposition of intensities. Electron wavelength for 300 keV is about 0 . 0197 ˚ A, sample thickness about 1000 ˚ A, and atomic resolution is about 1-2 ˚ A. Secondary structures (near atomic resolution) are visible when resolution is about 5-8 ˚ A. In any case, electron wavelength is not a limiting factor for the resolution.
The forward model Overview The forward model can be divided into the following parts. 1 Electron-specimen interaction. 2 Optics of the TEM. 3 The intensity and detector response.
Electron-specimen interaction Basic assumptions One electron in the specimen at a time. Average distance between two successive electrons much greater than the specimen thickness. Interaction is governed by the scalar Schr¨ odinger wave equation. Coloumb potential models elastic interaction, absorption potential models decrease in the flux of the non-scattered and elastically scattered electrons. Incident wave Ψ in is time harmonic and of the form Ψ in ( x , t ) := e − ik 2 � 2 m t u in ( x ) .
Electron-specimen interaction Basic assumptions One electron in the specimen at a time. Average distance between two successive electrons much greater than the specimen thickness. Interaction is governed by the scalar Schr¨ odinger wave equation. Coloumb potential models elastic interaction, absorption potential models decrease in the flux of the non-scattered and elastically scattered electrons. Incident wave Ψ in is time harmonic and of the form Ψ in ( x , t ) := e − ik 2 � 2 m t u in ( x ) .
Electron-specimen interaction Basic assumptions One electron in the specimen at a time. Average distance between two successive electrons much greater than the specimen thickness. Interaction is governed by the scalar Schr¨ odinger wave equation. Coloumb potential models elastic interaction, absorption potential models decrease in the flux of the non-scattered and elastically scattered electrons. Incident wave Ψ in is time harmonic and of the form Ψ in ( x , t ) := e − ik 2 � 2 m t u in ( x ) .
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