Fitting of random tessellation models to keratin filament networks

Characterization of squamous cell carcinomas of the head and neck using methods of spatial statistics

In the present study, 53 cases of squamous cell carcinomas of the head and neck were characterized by a quantitative histological texture analysis based on principles of spatial statistics. A planar tessellation of the epithelial tumour component was generated by a skeletonization algorithm. The size distribution of the virtual cells of this planar tessellation, and the size distribution of the profiles of the tumour cell nuclei were estimated in terms of area and boundary length. The intensity, the reduced second moment function (K-function) and the pair correlation function of the point process of the centroids of the profiles of the tumour cell nuclei were also estimated. For both purposes, it is necessary to correct for edge effects, which we consider in this paper in some detail. Specifically, the point patterns of the tumour cell nuclei were considered as realizations of a point process, where the points exist only in the epithelial tumour component (the permitted phase) and not in the stroma (the forbidden phase). The methods allow to characterize each individual tumour by a series of summary statistics. The total set of cases was then partitioned into two groups: 19 cases without lymph node metastases (pN0), and 34 nodal positive cases (pN1 or pN2). Statistical analysis showed no significant differences between the intensities, the mean K-functions and the mean pair correlation functions of the tumour cell nucleus profiles of the two groups. However, there were some significant differences between the sizes of the virtual cells and of the nucleus profiles of the nodal negative cases as compared to the nodal positive cases. In a logistic regression analysis, one of the quantitative nuclear size variables (mean nuclear area) was found to be a significant predictor of lymph node metastasis, in addition to tumour stage. The study shows the potential of methods of spatial statistics for objective quantitative grading of squamous cell carcinomas of the head and neck, and provides an example for modelling histological point patterns as realizations of planar point processes occupying a reference phase which is only a partial component of the total tissue.

Modeling the self-organization property of keratin intermediate filaments

Keratin intermediate filaments (IFs) fulfill an important function of structural support in epithelial cells. The necessary mechanical attributes require that IFs be organized into a crosslinked network and accordingly, keratin IFs are typically organized into large bundles in surface epithelia. For IFs comprised of keratins 5 and 14 (K5, K14), found in basal keratinocytes of epidermis, bundling can be self-driven through interactions between K14's carboxy-terminal tail domain and two regions in the central α-helical rod domain of K5. Here, we exploit theoretical principles and computational modeling to investigate how such cis-acting determinants best promote IF crosslinking. We develop a simple model where keratin IFs are treated as rigid rods to apply Brownian dynamics simulation. Our findings suggest that long-range interactions between IFs are required to initiate the formation of bundlelike configurations, while tail domain-mediated binding events act to stabilize them. Our model explains the differences observed in the mechanical properties of wild-type versus disease-causing, defective IF networks. This effort extends the notion that the structural support function of keratin IFs necessitates a combination of intrinsic and extrinsic determinants, and makes specific predictions about the mechanisms involved in the formation of crosslinked keratin networks in vivo.

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.

Measuring the nanomechanical properties of cancer cells by digital pulsed force mode imaging

In this paper, we demonstrate that the digital pulsed force mode data can distinguish two cancer cell lines (HeLa, Panc) by their mechanical properties. The live cells were imaged in buffer solution. The digital pulsed force mode measured 175 force-distance curves per second which, due to the speed of the measurement, were distorted by the viscous drag in the buffer. We show that this drag force causes a sinusoidal addition to the force-distance curves. By subtracting the viscous drag effect one obtains standard force-distance curves. The force-distance curves are then evaluated to extract key data on the curves, such as adhesion energies, local stiffness or the width of the hysteresis loop. These data are then correlated to classify the force-distance curves. We show examples based on the width of the hysteresis loop and the adhesion energies. Outliers in this classification scheme are points where, potentially, interesting new physics or different physics might happen. Based on classification schemes adapted to experimental settings, we propose that the digital pulsed force mode is a tool to evaluate the time evolution of the mechanical response of cells.