A reliable extraction of filament data from microscopic images is of high interest in the analysis of acto-myosin structures as early morphological markers in mechanically guided differentiation of human mesenchymal stem cells and the understanding of the underlying fiber arrangement processes. In this paper, we propose the filament sensor (FS), a fast and robust processing sequence which detects and records location, orientation, length, and width for each single filament of an image, and thus allows for the above described analysis. The extraction of these features has previously not been possible with existing methods. We evaluate the performance of the proposed FS in terms of accuracy and speed in comparison to three existing methods with respect to their limited output. Further, we provide a benchmark dataset of real cell images along with filaments manually marked by a human expert as well as simulated benchmark images. The FS clearly outperforms existing methods in terms of computational runtime and filament extraction accuracy. The implementation of the FS and the benchmark database are available as open source.

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produces a variety of non-winding, non-dense descriptors. This is achieved by deforming tori into spheres and then using a variant of the recently developed principle nested spheres analysis. This PCA analysis involves a step of small sphere fitting and we provide an improved test to avoid overfitting. However, deforming tori into spheres creates singularities. We introduce a data-adaptive pre-clustering technique to keep the singularities away from the data. For the frequently encountered case that the residual variance around the PCA main component is small, we use a post-mode hunting technique for more fine-grained clustering. Thus in general, there are three successive interrelated key steps of torus-PCA in practice: pre-clustering, deformation, and post-mode hunting. We illustrate our method with two recently studied RNA structure (tori) data sets: one is a small RNA data set which is established as the benchmark for PCA and we validate our method through this data. Another is a large RNA data set (containing the small RNA data set) for which we show that our method provides interpretable principal components as well as giving further insight into its structure.

The (CLT) central limit theorems for generalized Fréchet means (data descriptors assuming values in stratified spaces, such as intrinsic means, geodesics, etc.) on manifolds from the literature are only valid if a certain empirical process of Hessians of the Fréchet function converges suitably, as in the proof of the prototypical BP-CLT (Bhattacharya and Patrangenaru (2005)). This is not valid in many realistic scenarios and we provide for a new very general CLT. In particular this includes scenarios where, in a suitable chart, the sample mean fluctuates asymptotically at a scale n α with exponents α < 1/2 with a non-normal distribution. As the BP-CLT yields only fluctuations that are, rescaled with n 1/2 , asymptotically normal, just as the classical CLT for random vectors, these lower rates, somewhat loosely called smeariness, had to date been observed only on the circle (Hotz and Huckemann (2015)). We make the concept of smeariness on manifolds precise, give an example for two-smeariness on spheres of arbitrary dimension, and show that smeariness, although "almost never" occurring, may have serious statistical implications on a continuum of sample scenarios nearby. In fact, this effect increases with dimension, striking in particular in high dimension low sample size scenarios.

X-ray diffraction from biomolecular assemblies is a powerful technique which can provide structural information about complex architectures such as the locomotor systems underlying muscle contraction. However, in its conventional form, macromolecular diffraction averages over large ensembles. Progress in x-ray optics has now enabled to probe structures on sub-cellular scales, with the beam confined to a distinct organelle. Here, we use scanning small angle x-ray scattering (scanning SAXS) to probe the diffraction from cytoskeleton networks in cardiac tissue cells. In particular, we focus on actin-myosin composites, which we identify as the dominating contribution to the anisotropic diffraction patterns, by correlation with optical fluorescence microscopy. To this end, we use a principal component analysis approach to quantify direction, degree of orientation, nematic order, and the second moment of the scattering distribution in each scan point. We compare the fiber orientation from micrographs of fluorescently labeled actin fibers to the structure orientation of the x-ray dataset and thus correlate signals of two different measurements: the native electron density distribution of the local probing area versus specifically labeled constituents of the sample. Further, we develop a robust and automated fitting approach based on a power law expansion, in order to describe the local structure factor in each scan point over a broad range of the momentum transfer q r . Finally, we demonstrate how the methodology shown for freeze dried cells in the first part of the paper can be translated to alive cell recordings.Recent progress in x-ray optics has now overcome this barrier, enabling hard x-ray spot sizes in the submicron range [24], well suited to record structural data within precise locations of a single cell. X-rays even in the multi-keV regime required for diffraction studies can nowadays be focussed by a variety of optical elements, including diffractive optics such as Fresnel zone plates [25], compound refractive lenses [26-28] and elliptical Kirkpatrick-Baez (KB) mirrors [29][30][31][32]. Similar to earlier scanning diffraction work on biomaterials such as wood and bone [33][34][35][36][37][38], we can hence now combine high resolution in reciprocal space with at least moderate resolution in real space. Scanning small angle x-ray scattering (scanning SAXS) experiments requiring a sample environment for biological cells are typically not compatible with the ultimate small spot sizes of 10 nm and below, as presented in [31,39,40], but values in the range of 80-300 nm are feasible, in particular in terms of the working distance, and readily allow structure factors to be assigned to different cellular compartments. Presently, feasibility of cellular scanning SAXS has been demonstrated for a variety of biological cells, ranging from bacterial cells D. radiodurans [6] to eukaryotes such as the amoeba D. discoideum [10], adenoma cells [7-9, 41], and human mesenchymal stem cells (hMSC) [11].Beyond these previous proof-...

Blood platelets are the key cellular players in blood clotting and thus of great biomedical importance. While spreading at the site of injury, they reorganize their cytoskeleton within minutes and assume a flat appearance. As platelets possess no nucleus, many standard methods for visualizing cytoskeletal components by means of fluorescence tags fail. Here we employ silicon-rhodamine actin and tubulin probes for imaging these important proteins in a time-resolved manner. We find two distinct timescales for platelet spread area development and for cytoskeletal reorganization, indicating that although cell spreading is most likely associated with actin polymerization at the cell edges, distinct, stress-fiber-like actin structures within the cell, which may be involved in the generation of contractile forces, form on their own timescale. Following microtubule dynamics allows us to distinguish the role of myosin, microtubules and actin during early spreading.