Supplementary Table 1, Figures 1-3 from EphB4 Promotes Site-Specific Metastatic Tumor Cell Dissemination by Interacting with Endothelial Cell–Expressed EphrinB2
Supplementary Figures S1-S3 from CD44 Variant Isoforms Promote Metastasis Formation by a Tumor Cell-Matrix Cross-talk That Supports Adhesion and Apoptosis Resistance
In recent years, Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) has emerged as a flexible method that enables semi-automated volume ultrastructural imaging. We present a toolset for adherent cells that enables tracking and finding cells, previously identified in light microscopy (LM), in the FIB-SEM, along with the automatic acquisition of high-resolution volume datasets. We detect the underlying grid pattern in both modalities (LM and EM), to identify common reference points. A combination of computer vision techniques enables complete automation of the workflow. This includes setting the coincidence point of both ion and electron beams, automated evaluation of the image quality and constantly tracking the sample position with the microscope's field of view reducing or even eliminating operator supervision. We show the ability to target the regions of interest in EM within 5 µm accuracy while iterating between different targets and implementing unattended data acquisition. Our results demonstrate that executing volume acquisition in multiple locations autonomously is possible in EM.
Cryo-electron tomography (cryo-ET) is a groundbreaking technology for 3D visualisation and analysis of biomolecules in the context of cellular structures. It allows structural investigations of single proteins as well as their spatial arrangements within the cell. Cryo-tomograms provide a snapshot of the complex, heterogeneous and transient subcellular environment. Due to the excellent structure preservation in amorphous ice, it is possible to study interactions and spatial relationships of proteins in their native state without interference caused by chemical fixatives or contrasting agents. With the introduction of focused ion beam (FIB) technology, the preparation of cellular samples for electron tomography has become much easier and faster. The latest generation of integrated FIB and scanning electron microscopy (SEM) instruments (dual beam microscopes), specifically designed for cryo-applications, provides advances in automation, imaging and the preparation of high-pressure frozen bulk samples using cryo-lift-out technology. In addition, correlative cryo-fluorescence microscopy provides cellular targeting information through integrated software and hardware interfaces. The rapid advances, based on the combination of correlative cryo-microscopy, cryo-FIB and cryo-ET, have already led to a wealth of new insights into cellular processes and provided new 3D image data of the cell. Here we introduce our recent developments within the cryo-tomography workflow, and we discuss the challenges that lie ahead. LAY DESCRIPTION: This article describes our recent developments for the cryo-electron tomography (cryo-ET) workflow. Cryo-ET offers superior structural preservation and provides 3D snapshots of the interior of vitrified cells at molecular resolution. Before a cellular sample can be imaged by cryo-ET, it must be made accessible for transmission electron microscopy. This is achieved by preparing a 200-300 nm thin cryo-lamella from the cellular sample using a cryo-focused ion beam (cryo-FIB) microscope. Cryo-correlative light and electron microscopy (cryo-CLEM) is used within the workflow to guide the cryo-lamella preparation to the cellular areas of interest. We cover a basic introduction of the cryo-ET workflow and show new developments for cryo-CLEM, which facilitate the connection between the cryo-light microscope and the cryo-FIB. Next, we present our progress in cryo-FIB software automation to streamline cryo-lamella preparation. In the final section we demonstrate how the cryo-FIB can be used for 3D imaging and how bulk-frozen cellular samples (obtained by high-pressure freezing) can be processed using the newly developed cryo-lift-out technology.
Intermediate filaments (IFs) are principal components of the cytoskeleton, a dynamic integrated system of structural proteins that provides the functional architecture of metazoan cells. They are major contributors to the elasticity of cells and tissues due to their high mechanical stability and intrinsic flexibility. The basic building block for the assembly of IFs is a rod-like, 60-nm-long tetrameric complex made from two antiparallel, half-staggered coiled coils. In low ionic strength, tetramers form stable complexes that rapidly assemble into filaments upon raising the ionic strength. The first assembly products, "frozen" by instantaneous chemical fixation and viewed by electron microscopy, are 60-nm-long "unit-length" filaments (ULFs) that apparently form by lateral in-register association of tetramers. ULFs are the active elements of IF growth, undergoing longitudinal end-to-end annealing with one another and with growing filaments. Originally, we have employed quantitative time-lapse atomic force and electron microscopy to analyze the kinetics of vimentin-filament assembly starting from a few seconds to several hours. To obtain detailed quantitative insight into the productive reactions that drive ULF formation, we now introduce a "stopped-flow" approach in combination with static light-scattering measurements. Thereby, we determine the basic rate constants for lateral assembly of tetramers to ULFs. Processing of the recorded data by a global fitting procedure enables us to describe the hierarchical steps of IF formation. Specifically, we propose that tetramers are consumed within milliseconds to yield octamers that are obligatory intermediates toward ULF formation. Although the interaction of tetramers is diffusion controlled, it is strongly driven by their geometry to mediate effective subunit targeting. Importantly, our model conclusively reflects the previously described occurrence of polymorphic ULF and mature filaments in terms of their number of tetramers per cross section.
Journal Article Array Tomography and Beam Deceleration – High-Throughput Imaging with the ZEISS GeminiSEM using Atlas 5 and Beam Deceleration Get access Angert Isabel, Angert Isabel Carl Zeiss Microscopy GmbH, Jena Germany Search for other works by this author on: Oxford Academic Google Scholar Kirmse Robert, Kirmse Robert Carl Zeiss Microscopy GmbH, Jena Germany Search for other works by this author on: Oxford Academic Google Scholar Marlene Thaler, Marlene Thaler Carl Zeiss Microscopy GmbH, Jena Germany Search for other works by this author on: Oxford Academic Google Scholar Kirk Czymmek Kirk Czymmek Carl Zeiss Microscopy GmbH, Jena Germany Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 22, Issue S3, 1 July 2016, Pages 28–29, https://doi.org/10.1017/S1431927616000994 Published: 25 July 2016
Studying the fine details of biological cells and tissues not only requires a microscope which can attain high resolution images, but also a sample preparation technique that preserves the structures in a close-to-life or near-native state. Rapid-freezing techniques allow to maintain the high water content of cells and immobilize the sample in a near-native state for cryo-imaging by fluorescence, electron or X-ray microscopy. A major limitation for correlative cryo-fluorescence microscopy is the current unavailability of cryo-immersion optics that could yield a higher numerical aperture. Combining ZEISS LSM 880 with Airyscan and cryo-fluorescent imaging utilizing the Linkam CMS 196 cryo-stage allows to obtain a significant increase in resolution and signal-to-noise (SNR) compared to standard confocal images under cryoconditions. ZEISS Airyscan, with its novel confocal detection scheme, enables the user to record high-quality cryofluorescence data even without immersion optics. Cryo-Preparation of cells Biological objects such as cells are primarily composed of carbon compounds and up to 70 percent water. Studying the fine details of cells and tissues in their native aqueous Figure 1 Growing cells on electron microscopy grids. Various kinds of eukaryotic cells can be cultured on gold specimen supports for electron micro scopy. Gold is preferred over copper in order to prevent cytotoxic effects by copper ions. The cells adhere to a carbon support film covering the whole gold EM mesh grid. environment not only requires a microscope which can attain high resolution images, but also a sample preparation technique that rules out the possibility of any structural changes. Vitrification is a cryo-preparation technique which allows to maintain the high water content of cells, by freezing them to a temperature of app. -190° C within a matter of milliseconds [1]. This fast-freezing process prevents the water molecules from crystallizing and forms a glass-like layer of amorphous ice that preserves cellular structures in a near-native state.
The investigation of vitrified biological specimens (i.e. samples that are plunge or high pressure frozen) enables the visualization of cellular ultrastructure in a near native fully hydrated state, unadulterated by harmful preparation methods. Here, we focus on two recent cryo imaging modalities and discuss their impact on cryo correlative workflows. First, we present confocal cryo fluorescence microscopy, utilizing a novel confocal detector scheme with improved signal to noise ratio (SNR) and resolution. Second, we show volume imaging of multicellular specimens by cryo focused ion beam scanning electron microscopy (FIB/SEM). Confocal laser scanning microscopes (LSM) are renowned for their optical sectioning capability, a feature enabled by utilizing a pinhole that rejects out of focus light. Closing the pinhole improves lateral resolution, but also causes less light to reach the detector leading to reduced signal to noise ratios. In cryo fluorescence microscopy, the situation is aggravated by the fact that currently no immersion optics are available and consequently only numerical apertures below NA 1 are possible. Here we combined Airyscan, a novel detector module (available for ZEISS LSM 780, 800 and 880) together with a cryo correlative stage (Linkam CMS 196) for cryo fluorescent imaging of vitrified cells prepared on electron microscopy grids (Figure 1a). The Airyscan detection module allows the spatially resolved detection of fluorescence light otherwise rejected by the pinhole in a standard confocal system. We show that under cryo conditions even without immersion optics a significant increase in resolution and SNR can be obtained with Airyscan compared to standard confocal images (Figure 1 b&c). In FIB/SEM tomography three‐dimensional volumetric data from biological specimens is obtained by sequentially removing material with the ion beam and imaging the milled block faces by scanning with the electron beam. Only recently, it has been shown that this imaging method can be applied also to frozen hydrated specimens [1]. Cryo FIB/SEM tomography allows the mapping of large multicellular specimens in the near native state and is particularly suited to analyze samples that require remaining hydrated. We demonstrate this approach by imaging the cryo immobilized specimens (e.g. mouse optic nerve) (Figure 2). Both methods by themselves promise significant advantages for biomedical research by being able to investigate biological specimens in the near native fully hydrated state. Yet correlating both imaging modalities, LSM and FIB/SEM of vitrified samples, has the potential to provide even deeper insights into biological context. In contrast to correlative workflows using resin embedded samples, cryo imaging workflows do not have to find the optimal balance between preserving cellular ultrastructure and maintaining the functional integrity of fluorophores. Moreover, major mechanisms leading to irreversible bleaching of fluorescent molecules are suppressed at cryo temperatures [2]. The correlation between cryo light and electron microscopy data will greatly benefit from an increase in resolution in fluorescence imaging. Cryo Airyscan is a first step in that direction and can deliver three‐dimensional optical sectioning data that can be used to reliably target cellular structures in a FIB/SEM microscope, before the structural context is explored by cryo FIB/SEM tomography.
Correlative microscopy combines information from light and electron microscopy (LM and EM) into one comprehensive dataset. The “Shuttle & Find” interface from Zeiss was the first easy to use solution for imaging one and the same sample region in different microscopes, i.e. from widefield or confocal LSMs to environmental or field emission SEMs (FE-SEM). However, Shuttle & Find is limited to 2D applications. Correlative Array Tomography (CAT) is a correlative volumetric microscopy method on a high-throughput basis. Ordered arrays of ultrathin, resin-embedded serial sections can be imaged with different microscopical modalities. Serial sections are prepared using an ultramicrotome and for correlative array tomography, sections were stained for imaging with a widefield microscope and a scanning electron microscope. CAT is a non-destructive method that allows multiple investigations of the same sample and even multiple successive fluorescent staining procedures [1]. Multiple staining cycles of a large number of antigens or the use of different fluorescent proteins followed by the ultrastructural investigation in a SEM enables the analysis of functional and structural information in the same context. The software module “ ZEN Correlative Array Tomography” enables an easy and efficient workflow from LM (e.g. fluorescence) to FE-SEM or vice versa. The first step after inserting the sample into one microscope (LM or SEM) is to perform a quick calibration to establish a coordinate system. Subsequently the software guides the user through an automated process to recognize the ribbons of serial section. Regions of interest (ROI) can then be selected in one section and these ROIs are then automatically duplicated to all other recognized section. Once this process is completed image acquisition of all ROIs is performed automatically by the software thus generating a 3D volume stack from the serial sections. In the second step the sample along with the acquired data is transferred to next microscope (LM to SEM or vice versa). After the initial calibration of the coordinates the subsequent information on section and ROI position can be loaded and re-used for a fast set-up of the imaging parameters. Again, the microscope will then automatically acquire all images at the same regions that were already investigated. Finally a correlative 3D dataset can be created by first aligning both LM and SEM image stack separately. Afterwards the user correlates both volumes by identifying the same four reference points in both dataset thus obtaining a full 3D correlative volume.
Charting and understanding the full wiring diagram of complex neuronal structures such as the central nervous system or the brain (Connectomics) is one of the big remaining challenges in life sciences. Although at first it appears nearly impossible to map out a full diagram of, e.g., a mouse brain with sufficient resolution to identify each and every connection between neurons, recent technological advances move such an ambitious undertaking into the realms of possibility without spending decades at a microscope. However there are still many challenges to address in order to pave the way for fast and systematic neurobiological understanding of whole networks. These challenges range from a more robust and reproducible sample preparation to automated image data acquisition, more efficient data storage strategies and powerful data analysis tools. Here we will review novel imaging techniques developed for the challenge of mapping out the full connectome of a nervous system, brain or eye to name just a few examples. The imaging techniques reviewed cover light sheet illumination methods, single and multi-beam scanning electron microscopy, and we will briefly mention the possible combination of both light and electron microscopy. In particular we will review 'clearing' and in vivo methods that can be performed with light sheet fluroescence microscopes such as the ZEISS Lightsheet Z.1. We will then focus on scanning electron microscopy with single and multi-beam instruments including methods such as serial blockface imaging and array tomography methods.
Cryo-electron microscopy is expanding its scope from macromolecules towards much larger and more complex cellular specimens such as organelles, cells and entire tissues. While isolated macromolecular specimens are typically composed of only very few different components that may be recognized by their shape, size or state of polymerization, cellular specimens combine large numbers of proteinaceous structures as well as nucleic acids and lipid arrays. Consequently, an unambiguous identification of these structures within the context of a whole cell may create a very difficult challenge. On plastic-embedded specimens, or Tokuyasu sections (Tokuyasu, 1980), epitopes that are exposed at the surface can be tagged by antibodies. However, vitrified sections have to be kept at strict cryo-conditions (below -140 °C) and therefore do not allow any post-sectioning treatment of the specimens other than data acquisition in the microscope. Hence, the labels have to be placed into the specimen before freezing. Here we report on the application of a small metal-clustering protein, metallothionein (MTH), as a clonable label capable of clustering metal atoms into a high-density particle with high spatial resolution. We tested MTH as a label for kinesin-decorated microtubules (MTs) as well as the building blocks of desmin intermediate filaments (IFs).
Membrane Type-1 Matrix Metalloproteinase (MT1-MMP, MMP-14) is regarded as the prototype of a membrane- tethered protease. It drives fundamental biological processes ranging from embryogenesis to cancer metastasis. The proteolytic cleavage of proteins by MT1-MMP can rapidly alter the biophysical properties of a cell’s microenvironment. Cell’s must thus be able to sense and react to these alterations and transduce these effectively in biochemical signals and cell responses. Although many cells react as acutely to such physical stimuli as they do to chemical ones, the regulatory effects of these have been less extensively explored. In order to investigate a possible interdependency of proteolytic matrix cleavage by MT1-MMP and the generation and sensing of force by cells, a model system was established which exploits the properties of a matrix array of parallel collagen-I fibers. The resulting an-isotropy of the matrix with high tensile strength along the fibers and high mobility perpendicular to it allows the convenient detection of bundling and cleavage of the collagen fibers, as well as spreading and durotaxis of the cells. In summary, we have demonstrated that cell adhesion, force generation, and force sensing are vital for the regulation of MT1-MMP for efficient cleavage of collagen-I.
It is becoming increasingly evident that the micromechanics of cells and their environment determine cell fate and function as much as soluble molecular factors do. We hypothesized that extracellular matrix proteolysis by membrane type 1 matrix metalloproteinase (MT1-MMP) depends on adhesion, force generation and rigidity sensing of the cell. Melanoma cells (MV3 clone) stably transfected with MT1-MMP, or the empty vector as a control, served as the model system. α2β1 integrins (cell adhesion), actin and myosin II (force generation and rigidity sensing) were blocked by their corresponding inhibitors (α2β1 integrin antibodies, Cytochalasin D, blebbistatin). A novel, anisotropic matrix array of parallel, fluorescently labeled collagen-I fibrils was used. Cleavage and bundling of the collagen-I fibrils, and spreading and durotaxis of the cells on this matrix array could be readily discerned and quantified by a combined set-up for fluorescence and atomic force microscopy. In short, expression of the protease resulted in the generation of structural matrix defects, clearly indicated by gaps in the collagen lattice and loose fiber bundles. This key feature of matrix remodeling depended essentially on the functionality of α2β1 integrin, the actin filament network and myosin II motor activity. Interference with any of these negatively impacted matrix cleavage and three-dimensional matrix entanglement of cells.
Abstract The tyrosine kinase receptor EphB4 interacts with its ephrinB2 ligand to act as a bidirectional signaling system that mediates adhesion, migration, and guidance by controlling attractive and repulsive activities. Recent findings have shown that hematopoietic cells expressing EphB4 exert adhesive functions towards endothelial cells expressing ephrinB2. We therefore hypothesized that EphB4/ephrinB2 interactions may be involved in the preferential adhesion of EphB4-expressing tumor cells to ephrinB2-expressing endothelial cells. Screening of a panel of human tumor cell lines identified EphB4 expression in nearly all analyzed tumor cell lines. Human A375 melanoma cells engineered to express either full-length EphB4 or truncated EphB4 variants which lack the cytoplasmic catalytic domain (ΔC-EphB4) adhered preferentially to ephrinB2-expressing endothelial cells. Force spectroscopy by atomic force microscopy confirmed, on the single cell level, the rapid and direct adhesive interaction between EphB4 and ephrinB2. Tumor cell trafficking experiments in vivo using sensitive luciferase detection techniques revealed significantly more EphB4-expressing A375 cells but not ΔC-EphB4–expressing or mock-transduced control cells in the lungs, the liver, and the kidneys. Correspondingly, ephrinB2 expression was detected in the microvessels of these organs. The specificity of the EphB4-mediated tumor homing phenotype was validated by blocking the EphB4/ephrinB2 interaction with soluble EphB4-Fc. Taken together, these experiments identify adhesive EphB4/ephrinB2 interactions between tumor cells and endothelial cells as a mechanism for the site-specific metastatic dissemination of tumor cells. Mol Cancer Res; 8(10); 1297–309. ©2010 AACR.
Intermediate filaments (IFs) assembled in vitro from recombinantly expressed proteins have a diameter of 8-12 nm and can reach several micrometers in length. IFs assemble from a soluble pool of subunits, tetramers in the case of vimentin. Upon salt addition, the subunits form first unit length filaments (ULFs) within seconds and then assembly proceeds further by end-to-end fusion of ULFs and short filaments. So far, IF subunits have mainly been observed by electron microscopy of glycerol sprayed and rotary metal shadowed specimens. Due to the shear forces during spraying the IF subunits appear generally as straight thin rods. In this study, we used atomic force microscopy (AFM), cryo-electron microscopy (cryo-EM) combined with molecular modeling to investigate the conformation of the subunits of vimentin, desmin and keratin K5/K14 IFs in various conditions. Due to their anisotropic shape the subunits are difficult to image at high resolution by cryo-EM. In order to enhance contrast we used a cryo-negative staining approach. The subunits were clearly identified as thin, slightly curved rods. However the staining agent also forced the subunits to aggregate into two-dimensional networks of dot-like structures. To test this conformational change further, we imaged dried unfixed subunits on mica by AFM revealing a mixture of extended and dot-like conformations. The use of divalent ions such as calcium and magnesium, as well as glutaraldehyde exposure favored compact conformations over elongated ones. These experimental results as well as coarse-grained molecular dynamics simulations of a vimentin tetramer highlight the plasticity of IF subunits.
Together with microtubules and actin filaments (F-actin), intermediate filaments (IFs) form the cytoskeleton of metazoan cells. However, unlike the other two entities that are extremely conserved, IFs are much more diverse and are grouped into five different families. In contrast to microtubules and F-actin, IFs do not exhibit a polarity, which may be the reason that no molecular motors travel along them. The molecular structure of IFs is less well resolved than that of the other cytoskeletal systems. This is partially due to their functional variability, tissue-specific expression, and their intrinsic structural properties. IFs are composed mostly of relatively smooth protofibrils formed by antiparallel arranged alpha-helical coiled-coil bundles flanked by small globular domains at either end. These features make them difficult to study by various electron microscopy methods or atomic force microscopy (AFM). Furthermore, the elongated shape of monomeric or dimeric IF units interferes with the formation of highly ordered three-dimensional (3-D) crystals suitable for atomic resolution crystallography. So far, most of the data we currently have on IF macromolecular structures come from electron microscopy of negatively stained samples, and fragmented alpha-helical coiled-coil units solved by X-ray diffraction. In addition, AFM allows the observation of the dynamic states of IFs in solution and delivers a new view into the assembly properties of IFs. Here, we discuss the applicability of cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) for the field. Both methods are strongly related and have only recently been applied to ifs. However, cryo-EM revealed distinct new features within IFs that have not been seen before, and cryo-ET adds a 3-D view of IFs revealing the path and number of protofilaments within the various IF assemblies.
Abstract CD44 designates a large family of proteins with a considerable structural and functional diversity, which are generated from one gene by alternative splicing. As such, the overexpression of CD44 variant isoform (CD44v) has been causally related to the metastatic spread of cancer cells. To study the underlying mechanism, stable knockdown clones with deletion of exon v7 containing CD44 isoforms (CD44vkd) of the highly metastatic rat adenocarcinoma line BSp73ASML (ASMLwt) were established. ASML-CD44vkd clones hardly form lung metastases after intrafootpad application and the metastatic load in lymph nodes is significantly reduced. Rescuing, albeit at a reduced level, CD44v expression in ASML-CD44vkd cells (ASML-CD44vrsc) restores the metastatic potential. The following major differences in ASMLwt, ASML-CD44vkd, and ASML-CD44vrsc clones were observed: (a) ASMLwt cells produce and assemble a matrix in a CD44v-dependent manner, which supports integrin-mediated adhesion and favors survival. This feature is lost in the ASML-CD44vkd cells. (b) CD44v cross-linking initiates phosphatidylinositol 3-kinase/Akt activation in ASMLwt cells. Accordingly, apoptosis resistance is strikingly reduced in ASML-CD44vkd cells. The capacity to generate an adhesive matrix but not apoptosis resistance is restored in ASML-CD44vrsc cells. These data argue for a 2-fold effect of CD44v on metastasis formation: CD44v-mediated matrix formation is crucial for the settlement and growth at a secondary site, whereas apoptosis resistance supports the efficacy of metastasis formation. (Mol Cancer Res 2009;7(2):168–79)
Nanomechanical properties of filamentous biopolymers, such as the persistence length, may be determined from two-dimensional images of molecules immobilized on surfaces. For a single filament in solution, two principal adsorption scenarios are possible. Both scenarios depend primarily on the interaction strength between the filament and the support: i) For interactions in the range of the thermal energy, the filament can freely equilibrate on the surface during adsorption; ii) For interactions much stronger than the thermal energy, the filament will be captured by the surface without having equilibrated. Such a 'trapping' mechanism leads to more condensed filament images and hence to a smaller value for the apparent persistence length. To understand the capture mechanism in more detail we have performed Brownian dynamics simulations of relatively short filaments by taking the two extreme scenarios into account. We then compared these 'ideal' adsorption scenarios with observed images of immobilized vimentin intermediate filaments on different surfaces. We found a good agreement between the contours of the deposited vimentin filaments on mica ('ideal' trapping) and on glass ('ideal' equilibrated) with our simulations. Based on these data, we have developed a strategy to reliably extract the persistence length of short worm-like chain fragments or network forming filaments with unknown polymer-surface interactions.
The salt-induced in vitro assembly of cytoplasmic intermediate filament (IF) proteins such as vimentin is characterized by a very rapid lateral association of soluble tetrameric subunits into 60-nm-long full-width "unit-length" filaments (ULFs). We have demonstrated for this prototype IF protein that filament elongation occurs by the longitudinal annealing of ULFs into short IFs. These IFs further longitudinally anneal and thus constitute a progressively elongating filament population that over time yields filaments of several microm in length. Previously, we provided a mathematical model for the kinetics of the assembly process based on the average length distribution of filaments as determined by time-lapse electron and atomic force microscopy. Thereby, we were able to substantiate the concept that end-to-end-annealing of both ULFs and short filaments is obligatory for the formation of long IFs (Kirmse, R.; Portet, S.; Mücke, N. Aebi, U.; Herrmann, H.; Langowski, J. J. Biol. Chem. 2007, 282, 18563-18572). As the next step in understanding the mechanics of IF formation, we have expanded our mathematical model to describe the quantitative aspects of IF assembly by taking into account geometry constraints as well as the diffusion properties of rodlike linear aggregates. Thereby, we have developed a robust model for the time-dependent filament length distribution of IFs under standard conditions.
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