Open Access

Biological armors derive their mechanical integrity in part from their geometric architectures, often involving tessellations: individual structural elements tiled together to form surface shells. The carapace of boxfish, for example, is comprised of mineralized polygonal plates, called scutes, arranged in a complex geometric pattern and nearly completely encasing the body. In contrast to artificial armors, the boxfish exoskeleton grows with the fish; the relationship between the tessellation and the gross structure of the armor is therefore critical to sustained protection throughout growth. To clarify whether or how the boxfish tessellation is maintained or altered with age, we quantify architectural aspects of the tessellated carapace of the longhorn cowfish Lactoria cornuta through ontogeny (across nearly an order of magnitude in standard length) and in a high-throughput fashion, using high-resolution microCT data and segmentation algorithms to characterize the hundreds of scutes that cover each individual. We show that carapace growth is canalized with little variability across individuals: rather than continually adding scutes to enlarge the carapace surface, the number of scutes is surprisingly constant, with scutes increasing in volume, thickness, and especially width with age. As cowfish and their scutes grow, scutes become comparatively thinner, with the scutes at the edges (weak points in a boxy architecture) being some of the thickest and most reinforced in younger animals and thinning most slowly across ontogeny. In contrast, smaller scutes with more variable curvature were found in the limited areas of more complex topology (e.g. around fin insertions, mouth, and anus). Measurements of Gaussian and mean curvature illustrate that cowfish are essentially tessellated boxes throughout life: predominantly zero curvature surfaces comprised of mostly flat scutes, and with scutes with sharp bends used sparingly to form box edges. Since growth of a curved, tiled surface with a fixed number of tiles would require tile restructuring to accommodate the surface’s changing radius of curvature, our results therefore illustrate a previously unappreciated advantage of the odd boxfish morphology: by having predominantly flat surfaces, it is the box-like body form that in fact permits a relatively straightforward growth system of this tessellated architecture (i.e. where material is added to scute edges). Our characterization of the ontogeny and maintenance of the carapace tessellation provides insights into the potentially conflicting mechanical, geometric and developmental constraints of this species, but also perspectives into natural strategies for constructing mutable tiled architectures.

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.

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neural networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a single rule to fit the empirical data, SBI considers many parametrizations of a wiring rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rules and relies on machine learning methods to estimate a probability distribution (the `posterior distribution over rule parameters conditioned on the data') that characterizes all data-compatible rules. We demonstrate how to apply SBI in connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.

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.