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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 ( eig i ) 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. [ABSTRACT FROM AUTHOR]

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.

We introduce the notion of multiscale covariance tensor fields (CTF) associated with Euclidean random variables as a gateway to the shape of their distributions. Multiscale CTFs quantify variation of the data about every point in the data landscape at all spatial scales, unlike the usual covariance tensor that only quantifies global variation about the mean. Empirical forms of localized covariance previously have been used in data analysis and visualization, for example, in local principal component analysis, but we develop a framework for the systematic treatment of theoretical questions and mathematical analysis of computational models. We prove strong stability theorems with respect to the Wasserstein distance between probability measures, obtain consistency results for estimators, as well as bounds on the rate of convergence of empirical CTFs. These results show that CTFs are robust to sampling, noise and outliers. We provide numerous illustrations of how CTFs let us extract shape from data and also apply CTFs to manifold clustering, the problem of categorizing data points according to their noisy membership in a collection of possibly intersecting smooth submanifolds of Euclidean space. We prove that the proposed manifold clustering method is stable and carry out several experiments to illustrate the method. [ABSTRACT FROM AUTHOR]

Pseudomonas aeruginosa (P.a) is one of the most critical antibiotic resistant bacteria in the world and is the most prevalent pathogen in cystic fibrosis (CF), causing chronic lung infections that are considered one of the major causes of mortality in CF patients. Although several studies have contributed to understanding P.a within-host adaptive evolution at a genomic level, it is still difficult to establish direct relationships between the observed mutations, expression of clinically relevant phenotypes, and clinical outcomes. Here, we performed a comparative untargeted LC/HRMS-based metabolomics analysis of sequential isolates from chronically infected CF patients to obtain a functional view of P.a adaptation. Metabolic profiles were integrated with expression of bacterial phenotypes and clinical measurements following multiscale analysis methods. Our results highlighted significant associations between P.a “metabotypes”, expression of antibiotic resistance and virulence phenotypes, and frequency of clinical exacerbations, thus identifying promising biomarkers and therapeutic targets for difficult-to-treat P.a infections

Heart failure (HF) is a complex syndrome which can be the exit of different etiologies which lead to a common clinical picture. Treatment outcome is modest and new insights into pathophysiology are needed to improve effectively diagnosis, prognosis, and therapy. As a complex disease, it can really benefit from the new approach provided by molecular medicine where information about the cell program can deeply change the patient management. The comprehension of molecular mechanisms relies on new technologies which are able to provide data at the different levels of the cell workflow. A proper processing of these data is as essential as the generation of data itself, together with an integrative approach able to exploit observations at different scales, starting from the molecular levels up to an effective assessment of phenotype with cardiovascular and systemic parameters. In this paper, evidences concerning current understanding of HF, passing from one scale to another, are reported, to underline how functional genomics and systems biology perspective, fostered by the combination of biotechnologies and bioinformatic methods, may transform the concepts of diagnosis and, consequently, of treatment, toward the fulfillment of the invoked patient-specific medicine. [ABSTRACT FROM PUBLISHER]

Pseudomonas aeruginosa (P.a) is one of the most critical antibiotic resistant bacteria in the world and is the most prevalent pathogen in cystic fibrosis (CF), causing chronic lung infections that are considered one of the major causes of mortality in CF patients. Although several studies have contributed to understanding P.a within-host adaptive evolution at a genomic level, it is still difficult to establish direct relationships between the observed mutations, expression of clinically relevant phenotypes, and clinical outcomes. Here, we performed a comparative untargeted LC/HRMS-based metabolomics analysis of sequential isolates from chronically infected CF patients to obtain a functional view of P.a adaptation. Metabolic profiles were integrated with expression of bacterial phenotypes and clinical measurements following multiscale analysis methods. Our results highlighted significant associations between P.a "metabotypes", expression of antibiotic resistance and virulence phenotypes, and frequency of clinical exacerbations, thus identifying promising biomarkers and therapeutic targets for difficult-to-treat P.a infections [ABSTRACT FROM AUTHOR]