A mathematical model for mechanotransduction at the early steps of suture formation

Growth and patterning of craniofacial sutures are subjected to the effects of mechanical stress. Mechanotransduction processes occurring at the margins of the sutures are not precisely understood. Here, we propose a simple theoretical model based on the orientation of collagen fibres within the suture in response to local stress. We demonstrate that fibre alignment generates an instability leading to the emergence of interdigitations. We confirm the appearance of this instability both analytically and numerically. To support our model, we use histology and synchrotron x-ray microtomography and reveal the fine structure of fibres within the sutural mesenchyme and their insertion into the bone. Furthermore, using a mouse model with impaired mechanotransduction, we show that the architecture of sutures is disturbed when forces are not interpreted properly. Finally, by studying the structure of sutures in the mouse, the rat, an actinopterygian (\emph{Polypterus bichir}) and a placoderm (\emph{Compagopiscis croucheri}), we show that bone deposition patterns during dermal bone growth are conserved within jawed vertebrates. In total, these results support the role of mechanical constraints in the growth and patterning of craniofacial sutures, a process that was probably effective at the emergence of gnathostomes, and provide new directions for the understanding of normal and pathological suture fusion

A comparison of flare forecasting methods. II. Benchmarks, metrics and performance results for operational solar flare forecasting systems

YesSolar flares are extremely energetic phenomena in our Solar System. Their impulsive, often drastic radiative increases, in particular at short wavelengths, bring immediate impacts that motivate solar physics and space weather research to understand solar flares to the point of being able to forecast them. As data and algorithms improve dramatically, questions must be asked concerning how well the forecasting performs; crucially, we must ask how to rigorously measure performance in order to critically gauge any improvements. Building upon earlier-developed methodology (Barnes et al. 2016, Paper I), international representatives of regional warning centers and research facilities assembled in 2017 at the Institute for Space-Earth Environmental Research, Nagoya University, Japan to – for the first time – directly compare the performance of operational solar flare forecasting methods. Multiple quantitative evaluation metrics are employed, with focus and discussion on evaluation methodologies given the restrictions of operational forecasting. Numerous methods performed consistently above the “no skill” level, although which method scored top marks is decisively a function of flare event definition and the metric used; there was no single winner. Following in this paper series we ask why the performances differ by examining implementation details (Leka et al. 2019, Paper III), and then we present a novel analysis method to evaluate temporal patterns of forecasting errors in (Park et al. 2019, Paper IV). With these works, this team presents a well-defined and robust methodology for evaluating solar flare forecasting methods in both research and operational frameworks, and today’s performance benchmarks against which improvements and new methods may be compared

Edar/Eda interactions regulate enamel knot formation in tooth morphogenesis.

tabby and downless mutant mice have apparently identical defects in teeth, hair and sweat glands. Recently, genes responsible for these spontaneous mutations have been identified. downless (Dl) encodes Edar, a novel member of the tumour necrosis factor (TNF) receptor family, containing the characteristic extracellular cysteine rich fold, a single transmembrane region and a death homology domain close to the C terminus. tabby (Ta) encodes ectodysplasin-A (Eda) a type II membrane protein of the TNF ligand family containing an internal collagen-like domain. As predicted by the similarity in adult mutant phenotype and the structure of the proteins, we demonstrate that Eda and Edar specifically interact in vitro. We have compared the expression pattern of Dl and Ta in mouse development, taking the tooth as our model system, and find that they are not expressed in adjacent cells as would have been expected. Teeth develop by a well recorded series of epithelial-mesenchymal interactions, similar to those in hair follicle and sweat gland development, the structures found to be defective in tabby and downless mice. We have analysed the downless mutant teeth in detail, and have traced the defect in cusp morphology back to initial defects in the structure of the tooth enamel knot at E13. Significantly, the defect is distinct from that of the tabby mutant. In the tabby mutant, there is a recognisable but small enamel knot, whereas in the downless mutant the knot is absent, but enamel knot cells are organised into a different shape, the enamel rope, showing altered expression of signalling factors (Shh, Fgf4, Bmp4 and Wnt10b). By adding a soluble form of Edar to tooth germs, we were able to mimic the tabby enamel knot phenotype, demonstrating the involvement of endogenous Eda in tooth development. We could not, however, reproduce the downless phenotype, suggesting the existence of yet another ligand or receptor, or of ligand-independent activation mechanisms for Edar. Changes in the structure of the enamel knot signalling centre in downless tooth germs provide functional data directly linking the enamel knot with tooth cusp morphogenesis. We also show that the Lef1 pathway, thought to be involved in these mutants, functions independently in a parallel pathway