Sebastian Lück

Three-dimensional analysis of intermediate filament networks using SEM tomography

We identified tomographic reconstruction of a scanning electron microscopy tilt series recording the secondary electron signal as a well‐suited method to generate high‐contrast three‐dimensional data of intermediate filament (IF) networks in pancreatic cancer cells. Although the tilt series does not strictly conform to the projection requirement of tomographic reconstruction, this approach is possible due to specific properties of the detergent‐extracted samples. We introduce an algorithm to extract the graph structure of the IF networks from the tomograms based on image analysis tools. This allows a high‐resolution analysis of network morphology, which is known to control the mechanical response of the cells to large‐scale deformations. Statistical analysis of the extracted network graphs is used to investigate principles of structural network organization which can be linked to the regulation of cell elasticity.

Novel electron tomographic methods to study the morphology of keratin filament networks.

The three-dimensional (3D) keratin filament network of pancreatic carcinoma cells was investigated with different electron microscopical approaches. Semithin sections of high-pressure frozen and freeze substituted cells were analyzed with scanning transmission electron microscope (STEM) tomography. Preservation of subcellular structures was excellent, and keratin filaments could be observed; however, it was impossible to three-dimensionally track the individual filaments. To obtain a better signal-to-noise ratio in transmission mode, we observed ultrathin sections of high-pressure frozen and freeze substituted samples with low-voltage (30 kV) STEM. Contrast was improved compared to 300 kV, and individual filaments could be observed. The filament network of samples prepared by detergent extraction was imaged by high-resolution scanning electron microscopy (SEM) with very good signal-to-noise ratio using the secondary electron signal and the 3D structure could be elucidated by SEM tomography. In freeze-dried samples it was possible to discern between keratin filaments and actin filaments because the helical arrangement of actin subunits in the F-actin could be resolved. When comparing the network structures of the differently prepared samples, we found no obvious differences in filament length and branching, indicating that the intermediate filament network is less susceptible to preparation artifacts than the actin network.

Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells. They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of piecewise-deterministic Markov processes to the modeling of keratin network formation with high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors. Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, is modulated by lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic � 2 -goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean-square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable �-mixing condition on the underlying stationary marked point process which can be checked for a number of Poissonbased models and, in particular, in the case of geostatistical marking. Our method needs a central limit theorem for �-mixing random fields which is proved by extending Bernstein’s blocking technique to non-cubic index sets and seems to be of interest in its own right. By large-scale model-based simulations the performance of our test is studied in dependence of the model parameters which determine the range of spatial correlations.

Modeling chondrocyte patterns by elliptical cluster processes.

Superficial zone chondrocytes (CHs) of human joints are spatially organized in distinct horizontal patterns. Among other factors, the type of spatial CH organization within a given articular surface depends on whether the cartilage has been derived from an intact joint or the joint is affected by osteoarthritis (OA). Furthermore, specific variations of the type of spatial organization are associated with particular states of OA. This association may prove relevant for early disease recognition based on a quantitative structural characterization of CH patterns. Therefore, we present a point process model describing the distinct morphology of CH patterns within the articular surface of intact human cartilage. This reference model for intact CH organization can be seen as a first step towards a model-based statistical diagnostic tool. Model parameters are fitted to fluorescence microscopy data by a novel statistical methodology utilizing tools from cluster and principal component analysis. This way, the complex morphology of surface CH patters is represented by a relatively small number of model parameters. We validate the point process model by comparing biologically relevant structural characteristics between the fitted model and data derived from photomicrographs of the human articular surface using techniques from spatial statistics.

Missing wedge computed tomography by iterative algorithm DIRECTT

A strategy to mitigate typical reconstruction artefacts in missing wedge computed tomography is presented. These artefacts appear as elongations of reconstructed details along the mean direction (i.e. the symmetry centre of the projections). Although absent in standard computed tomography applications, they are most prominent in advanced electron tomography and also in special topics of X‐ray and neutron tomography under restricted geometric boundary conditions. We investigate the performance of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm to reduce the directional artefacts in standard procedures. In order to be sensitive to the anisotropic nature of missing wedge artefacts, we investigate isotropic substructures of metal foam as well as circular disc models. Comparison is drawn to filtered backprojection and algebraic techniques. Reference is made to reconstructions of complete data sets. For the purpose of assessing the reconstruction quality, Fourier transforms are employed to visualize the missing wedge directly. Deficient reconstructions of disc models are evaluated by a length‐weighted kernel density estimation, which yields the probabilities of boundary orientations. The DIRECTT results are assessed at different signal‐to‐noise ratios by means of local and integral evaluation parameters.

Three-dimensional analysis of the intermediate filament network using SEM-tomography

Pancreatic cancer is characterized by its early infiltration of adjacent tissue. There is a correlation between the keratin filament network structure and the migration ability of cells [1]. In earlier papers we quantitatively investigated two-dimensional images of the three-dimensional keratin network [2]. It is the goal of our ongoing research to expand these studies to three-dimensional datasets. We investigated, therefore, intermediate filaments from detergent-extracted cells by SEM-tomography.

Reduzierung von Missing-Wedge-Artefakten der CT mit DIRECTT

Kurzfassung Typische „Missing Wedge“(MW)-Artefakte in Rekonstruktionen der Computertomografie können mit dem iterativen DIRECTT-Algorithmus (Direkte iterative Rekonstruktion computertomografischer Trajektorien) unterdrückt werden. Die durch fehlende Projektionswinkel bedingten MW-Restriktionen betreffen bisher nur Sonderapplikationen der Röntgen- und Neutronentomografie, müssen in der Nanometer auflösenden Elektronentomografie jedoch als Standard akzeptiert werden. Die MW-Artefakte werden besonders effektiv mit einer spezifischen DIRECTT-Prozedur partiell diskreter Zwischenlösungen beseitigt. Für die Beurteilung der Abbildungsqualität werden Rekonstruktionen von vollständigen und unvollständigen Mess- und Modell-Datensätzen erzeugt und mit Ergebnissen anderer Algorithmen (gefilterte Rückprojektion (FBP) und ART-Methoden) verglichen. Die Fourier-Transformierten der Rekonstruktionen demonstrieren die erfolgreiche Ergänzung der fehlenden Information im MW-Bereich. Die quantitative Bewertung der lokalen Rekonstruktionsqualität mit Methoden der räumlichen Statistik ergibt auch für unterschiedliche Signal-Rausch-Verhältnisse signifikante Vorteile gegenüber FBP und ART.