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During cell division, kinetochore microtubules (KMTs) provide a physical linkage between the chromosomes and the rest of the spindle. KMTs in mammalian cells are organized into bundles, so-called kinetochore-fibers (k-fibers), but the ultrastructure of these fibers is currently not well characterized. Here we show by large-scale electron tomography that each k-fiber in HeLa cells in metaphase is composed of approximately nine KMTs, only half of which reach the spindle pole. Our comprehensive reconstructions allowed us to analyze the three-dimensional (3D) morphology of k-fibers and their surrounding MTs in detail. We found that k-fibers exhibit remarkable variation in circumference and KMT density along their length, with the pole-proximal side showing a broadening. Extending our structural analysis then to other MTs in the spindle, we further observed that the association of KMTs with non-KMTs predominantly occurs in the spindle pole regions. Our 3D reconstructions have implications for KMT growth and k-fiber self-organization models as covered in a parallel publication applying complementary live-cell imaging in combination with biophysical modeling (Conway et al., 2022). Finally, we also introduce a new visualization tool allowing an interactive display of our 3D spindle data that will serve as a resource for further structural studies on mitosis in human cells.
A Soft-Correspondence Approach to Shape-based Disease Grading with Graph Convolutional Networks
(2022)
Shape analysis provides principled means for understanding anatomical structures from medical images. The underlying notions of shape spaces, however, come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of soft correspondences. In particular, we present a graph-based learning approach for morphometric classification of disease states that is based on a generalized notion of shape correspondences in terms of functional maps. We demonstrate the performance of the derived classifier on the open-access ADNI database for differentiating normal controls and subjects with Alzheimer’s disease. Notably, our experiment shows that our approach can improve over state-of-the-art from geometric deep learning.
Background: Despite recent advances in cellular cryo-electron tomography (CET), developing automated tools for macromolecule identification in submolecular resolution remains challenging due to the lack of annotated data and high structural complexities. To date, the extent of the deep learning methods constructed for this problem is limited to conventional Convolutional Neural Networks (CNNs). Identifying macromolecules of different types and sizes is a tedious and time-consuming task. In this paper, we employ a capsule-based architecture to automate the task of macro- molecule identification, that we refer to as 3D-UCaps. In particular, the architecture is composed of three components: feature extractor, capsule encoder, and CNN decoder. The feature extractor converts voxel intensities of input sub-tomograms to activities of local features. The encoder is a 3D Capsule Network (CapsNet) that takes local features to generate a low-dimensional representation of the input. Then, a 3D CNN decoder reconstructs the sub-tomograms from the given representation by upsampling.
Results: We performed binary and multi-class localization and identification tasks on synthetic and experimental data. We observed that the 3D-UNet and the 3D-UCaps had an F1−score mostly above 60% and 70%, respectively, on the test data. In both network architectures, we observed degradation of at least 40% in the F1-score when identifying very small particles (PDB entry 3GL1) compared to a large particle (PDB entry 4D8Q). In the multi-class identification task of experimental data, 3D-UCaps had an F1-score of 91% on the test data in contrast to 64% of the 3D-UNet. The better F1-score of 3D-UCaps compared to 3D-UNet is obtained by a higher precision score. We speculate this to be due to the capsule network employed in the encoder. To study the effect of the CapsNet-based encoder architecture further, we performed an ablation study and perceived that the F1-score is boosted as network depth is increased which
is in contrast to the previously reported results for the 3D-UNet. To present a reproducible work, source code, trained models, data as well as visualization results are made publicly available.
Conclusion: Quantitative and qualitative results show that 3D-UCaps successfully perform various downstream tasks including identification and localization of macro- molecules and can at least compete with CNN architectures for this task. Given that the capsule layers extract both the existence probability and the orientation of the molecules, this architecture has the potential to lead to representations of the data that are better interpretable than those of 3D-UNet.
Our ability to grasp and understand complex phenomena is essentially based on recognizing structures and relating these to each other. For example, any meteorological description of a weather condition and explanation of its evolution recurs to meteorological structures, such as convection and circulation structures, cloud fields and rain fronts. All of these are spatiotemporal structures, defined by time-dependent patterns in the underlying fields. Typically, such a structure is defined by a verbal description that corresponds to the more or less uniform, often somewhat vague mental images of the experts.
However, a precise, formal definition of the structures or, more generally, concepts is often desirable, e.g., to enable automated data analysis or the development of phenomenological models. Here, we present a systematic approach and an interactive tool to obtain formal definitions of spatiotemporal structures. The tool enables experts to evaluate and compare different structure definitions on the basis of data sets with time-dependent fields that contain the respective structure. Since structure definitions are typically parameterized, an essential part is to identify parameter ranges that lead to desired structures in all time steps. In addition, it is important to allow a quantitative assessment of the resulting structures simultaneously. We demonstrate the use of the tool by applying it to two meteorological examples: finding structure definitions for vortex cores and center lines of temporarily evolving tropical cyclones.
Ideally, structure definitions should be objective and applicable to as many data sets as possible. However, finding such definitions, e.g., for the common atmospheric structures in meteorology, can only be a long-term goal. The proposed procedure, together with the presented tool, is just a first systematic approach aiming at facilitating this long and arduous way.
The analysis of brain networks is central to neurobiological research. In this context the following tasks often arise: (1) understand the cellular composition of a reconstructed neural tissue volume to determine the nodes of the brain network; (2) quantify connectivity features statistically; and (3) compare these to predictions of mathematical models. We present a framework for interactive, visually supported accomplishment of these tasks. Its central component, the stratification matrix viewer, allows users to visualize the distribution of cellular and/or connectional properties of neurons at different levels of aggregation. We demonstrate its use in four case studies analyzing neural network data from the rat barrel cortex and human temporal cortex.
3D shapes provide substantially more information than 2D images. However, the acquisition of 3D shapes is sometimes very difficult or even impossible in comparison with acquiring 2D images, making it necessary to derive the 3D shape from 2D images. Although this is, in general, a mathematically ill-posed problem, it might be solved by constraining the problem formulation using prior information. Here, we present a new approach based on Kendall’s shape space to reconstruct 3D shapes from single monocular 2D images. The work is motivated by an application to study the feeding behavior of the basking shark, an endangered species whose massive size and mobility render 3D shape data nearly impossible to obtain, hampering understanding of their feeding behaviors and ecology. 2D images of these animals in feeding position, however, are readily available. We compare our approach with state-of-the-art shape-based approaches both on human stick models and on shark head skeletons. Using a small set of training shapes, we show that the Kendall shape space approach is substantially more robust than previous methods and always results in plausible shapes. This is essential for the motivating application in which specimens are rare and therefore only few training shapes are available.
Polyp-Cavity Segmentation of Cold-Water Corals guided by Ambient Occlusion and Ambient Curvature
(2022)
The segmentation of cavities in three-dimensional images of arbitrary objects is a difficult problem since the cavities are usually connected to the outside of the object without any difference in image intensity. Hence, the information whether a voxel belongs to a cavity or the outside needs to be derived from the ambient space. If a voxel is enclosed by object material, it is very likely that this voxel belongs to a cavity. However, there are dense structures where a voxel might still belong to the outside even though it is surrounded to a large degree by the object. This is, for example, the case for coral colonies. Therefore, additional information needs to be considered to distinguish between those cases. In this paper, we introduce the notion of ambient curvature, present an efficient way to compute it, and use it to segment coral polyp cavities by integrating it into the ambient occlusion framework. Moreover, we combine the ambient curvature with other ambient information in a Gaussian mixture model, trained from a few user scribbles, resulting in a significantly improved cavity segmentation. We showcase the superiority of our approach using four coral colonies of very different morphological types. While in this paper we restrict ourselves to coral data, we believe that the concept of ambient curvature is also useful for other data. Furthermore, our approach is not restricted to curvature but can be easily extended to exploit any properties given on an object's surface, thereby adjusting it to specific applications.
The remarkably complex skeletal systems of the sea stars (Echinodermata, Asteroidea), consisting of hundreds to thousands of individual elements (ossicles), have intrigued investigators for more than 150 years. While the general features and structural diversity of isolated asteroid ossicles have been well documented in the literature, the task of mapping the spatial organization of these constituent skeletal elements in a whole-animal context represents an incredibly laborious process, and as such, has remained largely unexplored.
To address this unmet need, particularly in the context of understanding structure-function relationships in these complex skeletal systems, we present an integrated approach that combines micro-computed tomography, semi-automated ossicle segmentation, data visualization tools, and the production of additively manufactured tangible models to reveal biologically relevant structural data that can be rapidly analyzed in an intuitive manner.
In the present study, we demonstrate this high-throughput workflow by segmenting and analyzing entire skeletal systems of the giant knobby star, Pisaster giganteus, at four different stages of growth. The in-depth analysis, presented herein, provides a fundamental understanding of the three-dimensional skeletal architecture of the sea star body wall, the process of skeletal maturation during growth, and the relationship between skeletal organization and morphological characteristics of individual ossicles.
The widespread implementation of this approach for investigating other species, subspecies, and growth series has the potential to fundamentally improve our understanding of asteroid skeletal architecture and biodiversity in relation to mobility, feeding habits, and environmental specialization in this fascinating group of echinoderms.
Data are often subject to some degree of uncertainty, whether aleatory or epistemic. This applies both to experimental data acquired with sensors as well as to simulation data. Displaying these data and their uncertainty faithfully is crucial for gaining knowledge. Specifically, the effective communication of the uncertainty can influence the interpretation of the data and the user’s trust in the visualization. However, uncertainty-aware visualization has gotten little attention in molecular visualization. When using the established molecular representations, the physicochemical attributes of the molecular data usually already occupy the common visual channels like shape, size, and color. Consequently, to encode uncertainty information, we need to open up another channel by using feature lines. Even though various line variables have been proposed for uncertainty visualizations, they have so far been primarily used for two-dimensional data and there has been little perceptual evaluation. Thus, we conducted two perceptual studies to determine the suitability of the line variables blur, dashing, grayscale, sketchiness, and width for distinguishing several values in molecular visualizations. While our work was motivated by uncertainty visualization, our techniques and study results also apply to other types of scalar data.