## Volumetric Constraints in 3D Tomography Applied to Electron Microscopy (2002)

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Citations: | 4 - 1 self |

### BibTeX

@MISC{Marabini02volumetricconstraints,

author = {R. Marabini and G. T. Herman and C.O.S. Sorzano and J.M. Carazo},

title = {Volumetric Constraints in 3D Tomography Applied to Electron Microscopy},

year = {2002}

}

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### Abstract

D Electron Microscopy aims at the reconstruction of density volumes corresponding to the mass distribution of macromolecules imaged with an electron microscope. There are many factors limiting the resolution achievable when this technique is applied to biomolecules: microscope transfer function, molecule flexibility, lack of projections from certain directions, unknown angular distribution, image noise, etc. In this communication we propose the use of aprioriinformation such as particle symmetry, occupied volume, known surface, density nonnegativity and similarity to a known volume in order to improve the quality of the reconstruction. When a series expansion of the reconstructed volume is done, all these constraints are expressed as a set of equations which the expansion coefficients must satisfy. In this work, this equation set is specified and the effect of each one on the reconstruction of a realistic phantom is explored.

### Citations

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(Show Context)
Citation Context .... Similarity to a known volume It is known that the reconstruction algorithm based on ART tends to minimize the least squares distance between the iterative solution at each stage and the initial one =-=[9]-=-. Usually a zero valued initial volume is provided as starting point to the iterative algorithm expressing the uncertainty about the correct reconstructed volume and trying to minimize the variance of... |

159 | Three-Dimensional Electron Microscopy of Macromolecular Assemblies - Frank - 1996 |

56 |
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(Show Context)
Citation Context ...m which assume that a volume f ¢ r£ can be expressed as a linear combination of a set of basis funtions b ¢ r£ properly placed in the space. For this work spherically symmetric functions termed bl=-=obs [6] are used-=- as basis functions. f ¢ ¤ ∑ r£ xi ¦ b i ¢ § ri£ r Both, the blobs shape and their spatial distribution are fixed and the unknows are the coefficients xi. These coefficients xi are related to... |

28 |
Fully 3D reconstruction in electron microscopy
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(Show Context)
Citation Context ...gía” of Spain. 0-7803-7584-X/02/$17.00 ©2002 IEEE 641 C.O.S. Sorzano, J.M. Carazo † Centro Nacional de Biotecnología-CSIC Campus Universidad Autónoma de Madrid 28049 Madrid Spain algorithm, AR=-=T+blobs [5], -=-is specially suitable for dealing with them. 2. MATERIALS AND METHODS ART with blobs is a series-expansion algorithm which assume that a volume f ¢ r£ can be expressed as a linear combination of a s... |

27 |
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Citation Context ...macromolecules due to the wide range of specimens that can be addressed, as well as the increasing resolutions achieved currently (50S and 70S subunits of E. Coli’s ribosome at 7.5 ˚A [1] and 11.5 =-=˚A [2] res-=-pectively, Semliki Forest virus’ capsid at 9 ˚A[3], and GroEL at 11.5 ˚A[4]). However, these high-resolution studies usually need a large number of projection images. In this work, we propose the ... |

23 |
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(Show Context)
Citation Context ... can be addressed, as well as the increasing resolutions achieved currently (50S and 70S subunits of E. Coli’s ribosome at 7.5 ˚A [1] and 11.5 ˚A [2] respectively, Semliki Forest virus’ capsid a=-=t 9 ˚A[3],-=- and GroEL at 11.5 ˚A[4]). However, these high-resolution studies usually need a large number of projection images. In this work, we propose the incorporation of aprioriinformation into the reconstru... |

17 |
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(Show Context)
Citation Context ...eded to impose this constraint. Known surface There exist experimental microscopy techniques producing the image of the surface of a protein such as Metal Shadowing [7] or the Atomic Force Microscopy =-=[8]-=-. Furthermore, nonlinear image processing methods like thresholding, segmentation, and mathematical morphology can provide an approximation of the reconstruction volume. The information carried by suc... |

16 |
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(Show Context)
Citation Context ...l as the increasing resolutions achieved currently (50S and 70S subunits of E. Coli’s ribosome at 7.5 ˚A [1] and 11.5 ˚A [2] respectively, Semliki Forest virus’ capsid at 9 ˚A[3], and GroEL at =-=11.5 ˚A[4]-=-). However, these high-resolution studies usually need a large number of projection images. In this work, we propose the incorporation of aprioriinformation into the reconstruction process in a non-li... |

6 |
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(Show Context)
Citation Context ...lution and KV is the support where this solution is defined. 3. RESULTS To test the efficacy of the proposed constraints 500 projection images were simulated from an atomic model of bacteriorhodopsin =-=[10]-=- (see Figure 1 left). The collection geometry simulates that obtained in random conical tilt [11, Chap. 5]. A signal to noise ratio of 1/3 was simulated. Figure 1 shows an isosurface rendering account... |

5 |
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(Show Context)
Citation Context ...e volumetric constraints are not needed to impose this constraint. Known surface There exist experimental microscopy techniques producing the image of the surface of a protein such as Metal Shadowing =-=[7]-=- or the Atomic Force Microscopy [8]. Furthermore, nonlinear image processing methods like thresholding, segmentation, and mathematical morphology can provide an approximation of the reconstruction vol... |

4 |
The 3D arrangement of the 23
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(Show Context)
Citation Context ...s of biological macromolecules due to the wide range of specimens that can be addressed, as well as the increasing resolutions achieved currently (50S and 70S subunits of E. Coli’s ribosome at 7.5 �=-=�A [1] and -=-11.5 ˚A [2] respectively, Semliki Forest virus’ capsid at 9 ˚A[3], and GroEL at 11.5 ˚A[4]). However, these high-resolution studies usually need a large number of projection images. In this work,... |