title: Simultaneous determination of sample thickness, tilt, and electron mean free path using tomographic tilt images based on Beer-Lambert law.
abstract: Cryo-electron tomography (cryo-ET) is an emerging technique that can elucidate the architecture of macromolecular complexes and cellular ultrastructure in a near-native state. Some important sample parameters, such as thickness and tilt, are needed for 3-D reconstruction. However, these parameters can currently only be determined using trial 3-D reconstructions. Accurate electron mean free path plays a significant role in modeling image formation process essential for simulation of electron microscopy images and model-based iterative 3-D reconstruction methods; however, their values are voltage and sample dependent and have only been experimentally measured for a limited number of sample conditions. Here, we report a computational method, tomoThickness, based on the Beer-Lambert law, to simultaneously determine the sample thickness, tilt and electron inelastic mean free path by solving an overdetermined nonlinear least square optimization problem utilizing the strong constraints of tilt relationships. The method has been extensively tested with both stained and cryo datasets. The fitted electron mean free paths are consistent with reported experimental measurements. The accurate thickness estimation eliminates the need for a generous assignment of Z-dimension size of the tomogram. Interestingly, we have also found that nearly all samples are a few degrees tilted relative to the electron beam. Compensation of the intrinsic sample tilt can result in horizontal structure and reduced Z-dimension of tomograms. Our fast, pre-reconstruction method can thus provide important sample parameters that can help improve performance of tomographic reconstruction of a wide range of samples.
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.
authors.forename: Rui
authors.initials: R
authors.lastname: Yan
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.
authors.forename: Thomas J
authors.initials: TJ
authors.lastname: Edwards
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.
authors.forename: Logan M
authors.initials: LM
authors.lastname: Pankratz
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Kuhn
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.
authors.forename: Jason K
authors.initials: JK
authors.lastname: Lanman
authors.affiliation: Department of Pathology and Laboratory Medicine, University of Texas Health Science Center, Houston, TX 77030, USA.
authors.forename: Jun
authors.initials: J
authors.lastname: Liu
authors.affiliation: Markey Center for Structural Biology, Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA. Electronic address: jiang12@purdue.edu.
authors.forename: Wen
authors.initials: W
authors.lastname: Jiang
mesh_terms: D000818:Animals; D002460:Cell Line; D006224:Cricetinae; D020285:Cryoelectron Microscopy / Q000379:methods*; D004330:Drosophila / Q000821:virology; D055032:Electron Microscope Tomography / Q000379:methods*; D005347:Fibroblasts / Q000821:virology; D021621:Imaging, Three-Dimensional / Q000379:methods*; D046911:Macromolecular Substances / Q000032:analysis; D030381:Nodaviridae; D012845:Sindbis Virus
chemical_list: D046911:Macromolecular Substances
keywords: Electron tomography; Inelastic scattering; Mean free path; Nonlinear least square optimization