| dc.description.abstracteng | Structural biology is the study of the assembly of proteins and protein complexes. These proteins and protein complexes are small units in the cell of a living being. In order to sustain life they take care of biochemical processes, e.g. growth. Their operating principle depends on the assembly of the protein. One of the techniques to visualize the structure of a protein complex is electron cryo-microscopy (cryo-EM). The goal of cryo-EM is to achieve atomic resolution for the protein complex structure. For this purpose, thousands of rapidly frozen protein complexes are imaged with the Transmission Electron Microscope (TEM).
During image processing, called single particle analysis (SPA), the protein complexes are identified on the micrograph, averaged and reconstructed to a 3D density map of that protein complex. The averaging and reconstructing steps are iteratively repeated to resolve protein complex up to atomic resolution. State-of-the-art is to split cryo-EM data into two subsets to ensure an independent refinement of the images, the gold-standard refinement.
The raw single particle projection images are very noisy and therefore, lack a good ratio between the power of the signal produced by the protein complex and the power of the noise. This is called Signal-to-Noise-Ratio (SNR). The noise is a random process describing all the factors that distort the signal. The ratio has a great impact on the image processing quality and further on the reconstructed protein complex structure.
In general, the theoretical instrument resolution determines the smallest distance between two point sources, which are distinguishable within the object. The resolution of the TEM depends on the imaging source, here electrons, the quality of the lenses and the mechanical stability. A second definition for the term resolution is the point, respectively sine, resolution. It defines the point (resp. sine), where the smallest detail (the highest spatial frequency) is resolved. In cryo-EM, it is estimated by the Fourier Shell Correlation (FSC). The FSC is the correlation between two reconstructed maps of the identical protein complex in Fourier space. If the FSC drops below a specific threshold, the resolution of the protein complex is defined by the corresponding spatial frequency. The FSC is used as a resolution criterion for reconstructed protein structures in cryo-EM. However, the FSC is only a correlation, which measures the relation between two variables. In spite of the usage
of the FSC as a resolution criterion, it does not measure chemical features corresponding to a certain resolution number. The correlation is not equal to the causality and hence, does not measure the accuracy of the reconstructed density map. Furthermore, in SPA cryo-EM, the correlation is influenced by the structural maps and its properties. The noise affects the refinement of the raw projection images. After each iteration step of the refinement, the FSC measures the current resolution of the half maps. Even though it is assumed that the noise in cryo-EM data is uncorrelated, it has been shown that noise influences the FSC due to the statistical behavior. As a result, the FSC has a tendency to overestimate the resolution. Furthermore, there exists no other validation tool in cryo-EM.
One advantage of the single particle cryo-EM visualization is the acquisitions of the
image phases. However, the protein complex is a weak-phase-object (WPO) which means that it is too small to generate a sufficient phase contrast. During image acquisition a defocus is introduced to enhance the phase contrast. The raw data is negatively affected by these aberrations. As a result the raw single particle images need to be corrected for these defects. The Contrast Transfer Function (CTF) describes the defocus and other aberrations of the TEM encountered in the recorded data. A CTF miscorrection of the cryo-EM data leads to a defect of the 3D protein structure. Furthermore, the algorithms for the alignment and the classification of cryo-EM data is capable to fit noise into signal. Two experiments were executed to show the effect of a reference map on the projection images. The low SNR in the cryo-EM data makes it difficult to distinguish between noise and signal. Both algorithms are biased towards the reference model and overfit the reconstructed signal.
In this thesis, three experiments are carried out to demonstrate the noise influence on
image processing algorithms and the resulting misinterpretation of the data. Moreover,
the noise and the model-bias influence the computation of the FSC. The FSC fails to
detect the resolution of the reconstructed cryo-EM data. In all three experiments, the FSC overestimated the resolution.
Due to the failure of the FSC other resolution measurements are needed. A validation
approach based on a residual distance between the detected signal and the reconstructed signal was derived in the thesis. The algorithm introduced a ratio called Quality-Spectral Signal-to-Noise-Ratio (QSSNR) which defines a ratio the power of the reconstructed signal and the power of the residual between the recorded image and the re-projection image of the reconstructed protein complex map. Based on statistical assumptions there exists a general relationship between the FSC and the Spectral Signal-to-Noise-Ratio (SSNR). With this connection the Fourier Ring Correlation of projections (FRC of projections) was computed based on the QSSNR. The method was tested for synthetic and experimental data. | de |