Semi-automatic stitching of filamentous structures in image stacks from serial-section electron tomography.

We present a software-assisted workflow for the alignment and matching of filamentous structures across a three-dimensional (3D) stack of serial images. This is achieved by combining automatic methods, visual validation, and interactive correction. After the computation of an initial automatic matching, the user can continuously improve the result by interactively correcting landmarks or matches of filaments. Supported by a visual quality assessment of regions that have been already inspected, this allows a trade-off between quality and manual labour. The software tool was developed in an interdisciplinary collaboration between computer scientists and cell biologists to investigate cell division by quantitative 3D analysis of microtubules (MTs) in both mitotic and meiotic spindles. For this, each spindle is cut into a series of semi-thick physical sections, of which electron tomograms are acquired. The serial tomograms are then stitched and non-rigidly aligned to allow tracing and connecting of MTs across tomogram boundaries. In practice, automatic stitching alone provides only an incomplete solution, because large physical distortions and a low signal-to-noise ratio often cause experimental difficulties. To derive 3D models of spindles despite dealing with imperfect data related to sample preparation and subsequent data collection, semi-automatic validation and correction is required to remove stitching mistakes. However, due to the large number of MTs in spindles (up to 30k) and their resulting dense spatial arrangement, a naive inspection of each MT is too time-consuming. Furthermore, an interactive visualisation of the full image stack is hampered by the size of the data (up to 100 GB). Here, we present a specialised, interactive, semi-automatic solution that considers all requirements for large-scale stitching of filamentous structures in serial-section image stacks. To the best of our knowledge, it is the only currently available tool which is able to process data of the type and size presented here. The key to our solution is a careful design of the visualisation and interaction tools for each processing step to guarantee real-time response, and an optimised workflow that efficiently guides the user through datasets. The final solution presented here is the result of an iterative process with tight feedback loops between the involved computer scientists and cell biologists. LAY DESCRIPTION: Electron tomography of biological samples is used for a three-dimensional (3D) reconstruction of filamentous structures, such as microtubules (MTs) in mitotic and meiotic spindles. Large-scale electron tomography can be applied to increase the reconstructed volume for the visualisation of full spindles. For this, each spindle is cut into a series of semi-thick physical sections, from which electron tomograms are acquired. The serial tomograms are then stitched and non-rigidly aligned to allow tracing and connecting of MTs across tomogram boundaries. Previously, we presented fully automatic approaches for this 3D reconstruction pipeline. However, large volumes often suffer from imperfections (ie physical distortions) caused by the image acquisition process, making it difficult to apply fully automatic approaches for matching and stitching of numerous tomograms. Therefore, we developed an interactive, semi-automatic solution that considers all requirements for large-scale stitching of microtubules in image stacks of consecutive sections. We achieved this by combining automatic methods, visual validation and interactive error correction, thus allowing the user to continuously improve the result by interactively correcting landmarks or matches of filaments. We present large-scale reconstructions of spindles in which the automatic workflow failed and where different steps of manual corrections were needed. Our approach is also applicable to other biological samples showing 3D distributions of MTs in a number of different cellular contexts.

Microtubule reorganization during female meiosis in C. elegans.

Most female meiotic spindles undergo striking morphological changes while transitioning from metaphase to anaphase. The ultra-structure of meiotic spindles, and how changes to this structure correlate with such dramatic spindle rearrangements remains largely unknown. To address this, we applied light microscopy, large-scale electron tomography and mathematical modeling of female meiotic Caenorhabditis elegans spindles. Combining these approaches, we find that meiotic spindles are dynamic arrays of short microtubules that turn over within seconds. The results show that the metaphase to anaphase transition correlates with an increase in microtubule numbers and a decrease in their average length. Detailed analysis of the tomographic data revealed that the microtubule length changes significantly during the metaphase-to-anaphase transition. This effect is most pronounced for microtubules located within 150 nm of the chromosome surface. To understand the mechanisms that drive this transition, we developed a mathematical model for the microtubule length distribution that considers microtubule growth, catastrophe, and severing. Using Bayesian inference to compare model predictions and data, we find that microtubule turn-over is the major driver of the spindle reorganizations. Our data suggest that in metaphase only a minor fraction of microtubules, those closest to the chromosomes, are severed. The large majority of microtubules, which are not in close contact with chromosomes, do not undergo severing. Instead, their length distribution is fully explained by growth and catastrophe. This suggests that the most prominent drivers of spindle rearrangements are changes in nucleation and catastrophe rate. In addition, we provide evidence that microtubule severing is dependent on katanin.

Male meiotic spindle features that efficiently segregate paired and lagging chromosomes.

Chromosome segregation during male meiosis is tailored to rapidly generate multitudes of sperm. Little is known about mechanisms that efficiently partition chromosomes to produce sperm. Using live imaging and tomographic reconstructions of spermatocyte meiotic spindles in Caenorhabditis elegans, we find the lagging X chromosome, a distinctive feature of anaphase I in C. elegans males, is due to lack of chromosome pairing. The unpaired chromosome remains tethered to centrosomes by lengthening kinetochore microtubules, which are under tension, suggesting that a 'tug of war' reliably resolves lagging. We find spermatocytes exhibit simultaneous pole-to-chromosome shortening (anaphase A) and pole-to-pole elongation (anaphase B). Electron tomography unexpectedly revealed spermatocyte anaphase A does not stem solely from kinetochore microtubule shortening. Instead, movement of autosomes is largely driven by distance change between chromosomes, microtubules, and centrosomes upon tension release during anaphase. Overall, we define novel features that segregate both lagging and paired chromosomes for optimal sperm production.

Interactive Visualization of RNA and DNA Structures.

The analysis and visualization of nucleic acids (RNA and DNA) is playing an increasingly important role due to their fundamental importance for all forms of life and the growing number of known 3D structures of such molecules. The great complexity of these structures, in particular, those of RNA, demands interactive visualization to get deeper insights into the relationship between the 2D secondary structure motifs and their 3D tertiary structures. Over the last decades, a lot of research in molecular visualization has focused on the visual exploration of protein structures while nucleic acids have only been marginally addressed. In contrast to proteins, which are composed of amino acids, the ingredients of nucleic acids are nucleotides. They form structuring patterns that differ from those of proteins and, hence, also require different visualization and exploration techniques. In order to support interactive exploration of nucleic acids, the computation of secondary structure motifs as well as their visualization in 2D and 3D must be fast. Therefore, in this paper, we focus on the performance of both the computation and visualization of nucleic acid structure. We present a ray casting-based visualization of RNA and DNA secondary and tertiary structures, which enables for the first time real-time visualization of even large molecular dynamics trajectories. Furthermore, we provide a detailed description of all important aspects to visualize nucleic acid secondary and tertiary structures. With this, we close an important gap in molecular visualization.

A Switch in Microtubule Orientation during C. elegans Meiosis.

In oocytes of many organisms, meiotic spindles form in the absence of centrosomes [1-5]. Such female meiotic spindles have a pointed appearance in metaphase with microtubules focused at acentrosomal spindle poles. At anaphase, the microtubules of acentrosomal spindles then transition to an inter-chromosomal array, while the spindle poles disappear. This transition is currently not understood. Previous studies have focused on this inter-chromosomal microtubule array and proposed a pushing model to drive chromosome segregation [6, 7]. This model includes an end-on orientation of microtubules with chromosomes. Alternatively, chromosomes were thought to associate along bundles of microtubules [8, 9]. Starting with metaphase, this second model proposed a pure lateral chromosome-to-microtubule association up to the final meiotic stages of anaphase. Here, we applied large-scale electron tomography [10] of staged C. elegans oocytes in meiosis to analyze the orientation of microtubules in respect to chromosomes. We show that microtubules at metaphase I are primarily oriented laterally to the chromosomes and that microtubules switch to an end-on orientation during progression through anaphase. We further show that this switch in microtubule orientation involves a kinesin-13 microtubule depolymerase, KLP-7, which removes laterally associated microtubules around chromosomes. From this, we conclude that both lateral and end-on modes of microtubule-to-chromosome orientations are successively used in C. elegans oocytes to segregate meiotic chromosomes.

Quantification of three-dimensional spindle architecture.

Mitotic and meiotic spindles are microtubule-based structures to faithfully segregate chromosomes. Electron tomography is currently the method of choice to analyze the three-dimensional (3D) architecture of both types of spindles. Over the years, we have developed methods and software for automatic segmentation and stitching of microtubules in serial sections for large-scale reconstructions. 3D reconstruction of microtubules, however, is only the first step toward biological insight. The second step is the analysis of the structural data to derive measurable spindle properties. Here, we present a comprehensive set of techniques to quantify spindle parameters. These techniques provide quantitative analyses of specific microtubule classes and are applicable to a variety of tomographic reconstructions of spindles from different organisms.

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network.

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.

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory.

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.

Ligand Excluded Surface: A New Type of Molecular Surface.

The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes - including visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.

Exploring cavity dynamics in biomolecular systems.

BACKGROUND: The internal cavities of proteins are dynamic structures and their dynamics may be associated with conformational changes which are required for the functioning of the protein. In order to study the dynamics of these internal protein cavities, appropriate tools are required that allow rapid identification of the cavities as well as assessment of their time-dependent structures. RESULTS: In this paper, we present such a tool and give results that illustrate the applicability for the analysis of molecular dynamics trajectories. Our algorithm consists of a pre-processing step where the structure of the cavity is computed from the Voronoi diagram of the van der Waals spheres based on coordinate sets from the molecular dynamics trajectory. The pre-processing step is followed by an interactive stage, where the user can compute, select and visualize the dynamic cavities. Importantly, the tool we discuss here allows the user to analyze the time-dependent changes of the components of the cavity structure. An overview of the cavity dynamics is derived by rendering the dynamic cavities in a single image that gives the cavity surface colored according to its time-dependent dynamics. CONCLUSION: The Voronoi-based approach used here enables the user to perform accurate computations of the geometry of the internal cavities in biomolecules. For the first time, it is possible to compute dynamic molecular paths that have a user-defined minimum constriction size. To illustrate the usefulness of the tool for understanding protein dynamics, we probe the dynamic structure of internal cavities in the bacteriorhodopsin proton pump.

Voronoi-based extraction and visualization of molecular paths.

Visual analysis is widely used to study the behavior of molecules. Of particular interest are the analysis of molecular interactions and the investigation of binding sites. For large molecules, however, it is difficult to detect possible binding sites and paths leading to these sites by pure visual inspection. In this paper, we present new methods for the computation and visualization of potential molecular paths. Using a novel filtering method, we extract the significant paths from the Voronoi diagram of spheres. For the interactive visualization of molecules and their paths, we present several methods using deferred shading and other state-of-the-art techniques. To allow for a fast overview of reachable regions of the molecule, we illuminate the molecular surface using a large number of light sources placed on the extracted paths. We also provide a method to compute the extension surface of selected paths and visualize it using the skin surface. Furthermore, we use the extension surface to clip the molecule to allow easy visual tracking of even deeply buried paths. The methods are applied to several proteins to demonstrate their usefulness.