Limitations of the linear and the projection approximations in three-dimensional transmission electron microscopy of fully hydrated proteins.
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.
Royal Institute of Technology, School of Technology and Health, Handen, Sweden.|Department of Biosciences and Nutrition, Karolinska Institutet, Huddinge, Sweden.
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PJ
Koeck
Department of Biosciences and Nutrition, Karolinska Institutet, Huddinge, Sweden.
A
A
Karshikoff
D021621:Imaging, Three-Dimensional / Q000379:methods*; D046529:Microscopy, Electron, Transmission / Q000379:methods*; D008962:Models, Theoretical; D011506:Proteins / Q000737:chemistry* / Q000648:ultrastructure*
D011506:Proteins
Cryo transmission electron microscopy; defocus gradient; linear imaging; multislice simulation; phase contrast transfer function; projection approximation; resolution; weak phase and amplitude object approximation