Abstract
Cell differentiation is often associated with specific divisions and generations in a lineage tree. The presence of phenotypic noise, however, can make it difficult to observe such patterns. Using the group symmetry representation of a binary tree, it is shown how variation in a lineage can be compactly described by a set of natural variables each of which is labelled by the division at which a type of variation arises and the generation at which it is expressed. This harmonic analysis for a rooted tree provides a disciplined way to aggregate tree-structured data, improving the ability to identify differentiation patterns in noisy lineages. It also allows the proportion of variation of a phenotypic fate associated with each division to be estimated and compared to the proportion of variation expressed at each generation. The method has been applied to T-lymphocyte lineages tracked using time-lapse microscopy over several generations. For comparison, the analysis has been applied to C. elegans, a lineage with clear differentiation stages, and to a stationary branching process, which has none.
Footnotes
* This work was supported in part by Australian Research Council (ARC) grant FT140101104 to DGH, the National Health and Medical Research Council of Australia (NHMRC) Program Grant 1054618 to TPS, and NHMRC grants 620500 and APP1099140 and ARC grant FT0990405 to SMR. We thank Alan Rubin for suggesting we test our method on the C. elegans lineage.
MSC 2010 subject classifications: Primary 62H99; Secondary 62M99.