On the statistical analysis of single cell lineage trees

Abstract

Stem cells play a central role in the regeneration and repair of multicellular organisms. However, it remains far from trivial to reliably identify them. Despite decades of work, current techniques to isolate hematopoietic stem cells (HSCs) based on cell-surface markers only result in 50% purity, i.e. half of the sorted cells are not stem cells when functionally tested. Modern microscopy techniques allow us to follow single cells and their progeny for up to weeks in vitro, while recording the cell fates and lifetime of each individual cell. This cell tracking generates so-called lineage trees. Here, we propose statistical techniques to determine if the initial cell in a lineage tree was a HSC. We apply these techniques to murine hematopoietic lineage trees, revealing that 18% of the trees in our HSC dataset display a unique signature, and this signature is compatible with these trees having started from a true stem cell. Assuming 50% purity of HSC empirical datasets, this corresponds to a 0.35 power of the test, and the type-1-error is estimated to be 0.047. In summary, this study shows that statistical analysis of lineage trees could improve the classification of cells, which is currently done based on bio-markers only. Our statistical techniques are not limited to mammalian stem cell biology. Any type of single cell lineage trees, be it from bacteria, single cell eukaryotes, or single cells in a multicellular organism can be investigated. We expect this to contribute to a better understanding of the molecules influencing cellular dynamics at the single cell level.

Keywords: Bootstrap; Likelihood; Single cell analysis; Stem cells; Time lapse bioimaging.

Fig. 1

(A) Population purity of HSCs and MPPs. While the MPPs compartment consists of non-stem cells exclusively, the HSCs compartment is heterogeneous. (B) Example of a lineage tree. At each generation, dividing mother cells give rise to two daughter cells. The lifetime of the cells is linked to the length of the branches and time axis on the left. Cells that did not divide until the end of the observation time are labelled “Non-dividing”.

Fig. 2

Value of Λ for the empirical data (solid line) together with the bootstrap distributions (left panels) and simulated distributions (right panels). Dotted lines are .99 percentiles of the distributions.

Fig. 3

Each circle represents a tree T_EarlyMPP from EarlyMPP, each diamond represents a tree T_HSC from HSC. The x-axis displays $\Lambda (T,{\widehat{\theta }}_{\mathit{HSC}},{\widehat{\theta }}_{\mathit{EarlyMPP}}),$ seperated by the size of the tree via the y-axis. To the right of the dotted line are trees for which ${\widehat{\theta }}_{\mathit{HSC}}$ fits better than ${\widehat{\theta }}_{\mathit{EarlyMPP}},$ to the right of the dashed line are trees for which ${\widehat{\theta }}_{\mathit{HSC}}$ fits significantly better than ${\widehat{\theta }}_{\mathit{EarlyMPP}}$.