Multiscale Methods for Signal Selection in Single-Cell Data.

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.

Quantitative study of developmental biology confirms Dickinsonia as a metazoan.

The late Ediacaran soft-bodied macroorganism Dickinsonia (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 Dickinsonia 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 Dickinsonia 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 Dickinsonia 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 Dickinsonia to the Metazoa, specifically the Eumetazoa plus Placozoa total group. Our findings have implications for the use of Dickinsonia in developmental debates surrounding the metazoan acquisition of axis specification and metamerism.