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The absence of a conventional association between the cell-cell cohabitationand its emergent dynamics into cliques during development has hindered ourunderstanding of how cell populations proliferate, differentiate, and compete,i.e. the cell ecology. With the recent advancement of the single-cellRNA-sequencing (RNA-seq), we can potentially describe such a link byconstructing network graphs that characterize the similarity of the geneexpression profiles of the cell-specific transcriptional programs, andanalyzing these graphs systematically using the summary statistics informed bythe algebraic topology. We propose the single-cell topological simplicialanalysis (scTSA). Applying this approach to the single-cell gene expressionprofiles from local networks of cells in different developmental stages withdifferent outcomes reveals a previously unseen topology of cellular ecology.These networks contain an abundance of cliques of single-cell profiles boundinto cavities that guide the emergence of more complicated habitation forms. Wevisualize these ecological patterns with topological simplicial architecturesof these networks, compared with the null models. Benchmarked on thesingle-cell RNA-seq data of zebrafish embryogenesis spanning 38,731 cells, 25cell types and 12 time steps, our approach highlights the gastrulation as themost critical stage, consistent with consensus in developmental biology. As anonlinear, model-independent, and unsupervised framework, our approach can alsobe applied to tracing multi-scale cell lineage, identifying critical stages, orcreating pseudo-time series.

Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomics