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Single-cell sequencing data consists of a point cloud where the points are cells, with coordinates RNA expression levels in each gene. Since the tissue is destroyed by the sequencing procedure, the dynamics of gene expression must be inferred from the structure and geometry of the point cloud. In this talk, we will build a biological interpretation of the one-dimensional cohomology classes in hallmark gene subsets as models for transient biological processes. Such processes include the cell-cycle, but more generally model homeostatic negative feedback loops. Our procedure uses persistent cohomology to identify features, and integration of differential forms to estimate the cascade of genes associated with the underlying dynamics of gene expression.
This is joint work with Markus Youssef and Tâm Nguyen at EPFL.