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With biomedical sciences quickly outgrowing many other application areas in terms of data generation, there is a unique opportunity for life sciences to become one of the greatest beneficiaries of research in machine learning and AI, and also inspire foundational developments in it.

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. In this review, we illustrate this on three problems related to networks: network models for relational data, causal structure discovery, and phylogenetics. For each problem, we give an overview of recent results in algebraic statistics, with emphasis on the statistical achievements made possible by these tools and their practical relevance for applications to other scientific disciplines.

Introduction:A fundamental hallmark of cancer is that tumor cells repurpose the tissue microenvironment to promote their own survival. An increased understanding of these mechanisms may lead to improved microenvironment-directed therapies, particularly in lymphoid malignancies. In classic Hodgkin lymphoma (cHL), the rare malignant Hodgkin Reed Sternberg (HRS) cells are surrounded by a CD4+ T-cell and macrophage-rich inflammatory infiltrate. Recent multiplexed immunofluorescence studies suggest that the micron-scale niche around HRS cells is composed of distinct populations of PD-L1+ macrophages and CD4+ T cells, including regulatory CTLA4+ and LAG3+ subsets (Carey et al. Blood 2017, Patel et al. Blood 2019 and Aoki et al. Cancer Discov 2020). However, the topography of the intact tumor microenvironment of cHL requires further definition. Recent single-cell RNA sequencing studies have led to important insights into the biology of cHL; however, they do not adequately capture myeloid cells, fibroblasts, and HRS cells, likely due to the relative fragility of these cells in conventional tissue dissociation protocols. In this study, we use tandem single nucleus and spatially resolved RNA sequencing to systematically dissect the pro-tumorigenic cellular niche of cHL to define potentially targetable microenvironmental dependencies.

Abnormalities in nuclear and chromatin organization are hallmarks of many diseases including cancer. In this review, we highlight our understanding of how the cellular microenvironment regulates nuclear morphology and, with it, the spatial organization of chromosomes and genes, resulting in cell type-specific genomic programs. We also discuss the molecular basis for maintaining nuclear and genomic integrity and how alterations in nuclear mechanotransduction pathways result in various diseases. Finally, we highlight the importance of digital pathology based on nuclear morphometric features combined with single-cell genomics for early cancer diagnostics.

It is well established that cells sense chemical signals from their local microenvironment and transduce them to the nucleus to regulate gene expression programmes. Although a number of experiments have shown that mechanical cues can also modulate gene expression, the underlying mechanisms are far from clear. Nevertheless, we are now beginning to understand how mechanical cues are transduced to the nucleus and how they influence nuclear mechanics, genome organization and transcription. In particular, recent progress in super-resolution imaging, in genome-wide application of RNA sequencing, chromatin immunoprecipitation and chromosome conformation capture and in theoretical modelling of 3D genome organization enables the exploration of the relationship between cell mechanics, 3D chromatin configurations and transcription, thereby shedding new light on how mechanical forces regulate gene expression.

A combination of experiments and ellipsoid packing models elucidate the critical role of cell geometry in the 3D organization of chromosomes and gene expression. The results show that transcription-dependent chromosome positions, their orientations, and their relative intermingling depend on cell mechanical constraints.

ABSTRACTCell geometry is tightly coupled to gene expression patterns within the tissue microenvironment. This perspective synthesizes evidence that the 3D organization of chromosomes is a critical intermediate for geometric control of genomic programs. Using a combination of experiments and modeling we outline approaches to decipher the mechano-genomic code that governs cellular homeostasis and reprogramming.

The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-)faithfulness with respect to a hypergraph is introduced. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. It is proven that strong-faithfulness defined in terms of interaction parameters ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association. [ABSTRACT FROM AUTHOR]

Coronaviruses employ various nuclear signalling mechanisms for their propagation. Here we link replication of coronaviruses, including SARS-CoV-2, the coronavirus disease 2019 (COVID-19)-causing virus, with cytoskeleton-dependent signalling and 3D genome organization. This link could provide novel insights into the high coronavirus pathogenicity in certain cellular states, particularly those associated with ageing.