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

Machine Learning;Algebraic Topology;Genomics;Quantitative Methods