No abstract

The late Ediacaran soft-bodied macroorganism (age range approx. 560-550 Ma) has often been interpreted as an early animal, and is increasingly invoked in debate on the evolutionary assembly of eumetazoan body plans. However, conclusive positive evidence in support of such a phylogenetic affinity has not been forthcoming. Here we subject a collection of specimens interpreted to represent multiple ontogenetic stages to a novel, quantitative method for studying growth and development in organisms with an iterative body plan. Our study demonstrates that grew via pre-terminal 'deltoidal' insertion and inflation of constructional units, followed by a later inflation-dominated phase of growth. This growth model is contrary to the widely held assumption that grew via terminal addition of units at the end of the organism bearing the smallest units. When considered alongside morphological and behavioural attributes, our developmental data phylogenetically constrain to the Metazoa, specifically the Eumetazoa plus Placozoa total group. Our findings have implications for the use of in developmental debates surrounding the metazoan acquisition of axis specification and metamerism.

Treatment of severe COVID-19 is currently limited by clinical heterogeneity and incomplete understanding of potentially druggable immune mediators of disease. To advance this, we present a comprehensive multi-omic blood atlas in patients with varying COVID-19 severity and compare with influenza, sepsis and healthy volunteers. We identify immune signatures and correlates of host response. Hallmarks of disease severity revealed cells, their inflammatory mediators and networks as potential therapeutic targets, including progenitor cells and specific myeloid and lymphocyte subsets, features of the immune repertoire, acute phase response, metabolism and coagulation. Persisting immune activation involving AP-1/p38MAPK was a specific feature of COVID-19. The plasma proteome enabled sub-phenotyping into patient clusters, predictive of severity and outcome. Tensor and matrix decomposition of the overall dataset revealed feature groupings linked with disease severity and specificity. Our systems-based integrative approach and blood atlas will inform future drug development, clinical trial design and personalised medicine approaches for COVID-19.

It is well-known that odd-dimensional manifolds have Euler characteristic zero. Furthemore orientable manifolds have an even Euler characteristic unless the dimension is a multiple of 4. We prove here a generalisation of these statements: a k-orientable manifold (or more generally Poincaré complex) has even Euler characteristic unless the dimension is a multiple of 2 k+1 , where we call a manifold k-orientable if the i th Stiefel-Whitney class vanishes for all 0 < i < 2 k (k ≥ 0). More generally, we show that for a k-orientable manifold the Wu classes v l vanish for all l that are not a multiple of 2 k . For k = 0, 1, 2, 3, korientable manifolds with odd Euler characteristic exist in all dimensions 2 k+1 m, but whether there exist a 4-orientable manifold with an odd Euler characteristic is an open question.

Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores (eigi) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them.