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A Single Sign-On Infrastructure for Science Gateways on a Use Case for Structural Bioinformatics
(2012)
Geometric morphometrics plays an important role in evolutionary studies. The state-of-the-art in this field are landmark-based methods. Since the landmarks usually need to be placed manually, only a limited number of landmarks are generally used to represent the shape of an anatomical structure. As a result, shape characteristics that cannot be properly represented by small sets of landmarks are disregarded.
In this study, we present a method that is free of this limitation. The method takes into account the whole shape of an anatomical structure, which is represented as a surface, hence the term ‘surface-based morphometrics’. Correspondence between two surfaces is established by defining a partitioning of the surfaces into homologous surface patches. The first step for the generation of a surface partitioning is to place landmarks on the surface. Subsequently, the landmarks are connected by curves lying on the surface. The curves, called ‘surface paths’, might either follow specific anatomical features or they can be geodesics, that is, shortest paths on the surface. One important requirement, however, is that the resulting surface path networks are topologically equivalent across all surfaces. Once the surface path networks have been defined, the surfaces are decomposed into patches according to the path networks.
This approach has several advantages. One of them is that we can discretize the surface by as many points as desired. Thus, even fine shape details can be resolved if this is of interest for the study. Since a point discretization is used, another advantage is that well-established analysis methods for landmark-based morphometrics can be utilized. Finally, the shapes can be easily morphed into one another, thereby greatly supporting the understanding of shape changes across all considered specimens.
To show the potential of the described method for evolutionary studies of biological specimens, we applied the method to the para-basisphenoid complex of the snake genus Eirenis. By using this anatomical structure as example, we present all the steps that are necessary for surface-based morphometrics, including the segmentation of the para-basisphenoid complex from micro-CT data sets. We also show some first results using statistical analysis as well as classification methods based on the presented technique.
The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schrödinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling.