Limitations of the linear and the projection approximations in three‐dimensional transmission electron microscopy of fully hydrated proteins

• Published in: Journal of microscopy (Oxford) 2015-09, Vol.259 (3), p.197-209
• Main Authors: KOECK, P.J.B., KARSHIKOFF, A.
• Format: Article
• Language: English
• Subjects: Cryo transmission electron microscopy; defocus gradient; Electron microscopes; Imaging, Three-Dimensional - methods; linear imaging; Medicin och hälsovetenskap; Microscopy, Electron, Transmission - methods; Models, Theoretical; multislice simulation; phase contrast transfer function; projection approximation; Proteins - chemistry; Proteins - ultrastructure; resolution; Transmission electron microscopy; weak phase and amplitude object approximation
• ISSN: 0022-2720; 1365-2818; 1365-2818
• DOI: 10.1111/jmi.12253

Summary We establish expressions for the linear and quadratic terms in the series expansion of the phase and the phase and amplitude object description of imaging thin specimens by transmission electron microscopy. Based on these expressions we simulate the corresponding contributions to images of unstained protein complexes of varying thickness and arrive at an estimate for how much each term contributes to the contrast of the image. From this we can estimate a maximum specimen thickness for which the weak phase and the weak amplitude and phase object approximation (and therefore linear imaging) is still reasonably accurate. When discussing thick specimens it is also necessary to consider limitations due to describing the image as a filtered projection of the specimen, since the different layers of the specimen are not imaged with the same defocus value. We therefore compared simulations based on the projection approximation with the more accurate multislice model of image formation. However, we find that the errors due to nonlinear image contributions are greater than those due to the defocus gradient for the defocus values chosen for the simulations. Finally, we study how the discussed nonlinear image contributions and the defocus gradient affect the quality of three‐dimensional reconstructions. We find that three‐dimensional reconstructions reach high resolution when at the same time exhibiting localized systematic structural errors. Non‐Technical Cryo transmission electron microscopy and three‐dimensional reconstruction can be used to determine a three‐dimensional model of a protein molecule. In the mathematical methods used for three‐dimensional reconstruction assumptions are made about a linear relationship between the images recorded in the electron microscope and the objects being imaged. In this paper we investigate with computer simulations at what specimen thickness these assumptions start breaking down and what sort of errors can be expected in the three‐dimensional reconstructions when the assumptions are not valid anymore.