Statistical Inference in Cell Lineage Trees

Abstract

New approaches to lineage tracking allow the study of cell differentiation over many generations of cells during development in multicellular organisms. Understanding the variability observed in these lineage trees requires new statistical methods. Whereas invariant cell lineages, such as that for the nematode Caenorhabditis elegans, can be described using a lineage map, defined as the fixed pattern of phenotypes overlaid onto the binary tree structure, the variability of cell lineages from higher organisms makes it impossible to draw a single lineage map. Here, we introduce lineage variability maps which describe the pattern of second-order variation throughout the lineage tree. These maps can be undirected graphs of the partial correlations between every lineal position or directed graphs showing the dynamics of bifurcated patterns in each subtree. By using the symmetry invariance of a binary tree to develop a generalized spectral analysis for cell lineages, we show how to infer these graphical models for lineages of any depth from sample sizes of only a few pedigrees. When tested on pedigrees from C. elegans expressing a marker for pharyngeal differentiation potential, the maps recover essential features of the known lineage map. When applied to highly-variable pedigrees monitoring cell size in T lymphocytes, the maps show how most of the phenotype is set by the founder naive T cell. Lineage variability maps thus elevate the concept of the lineage map to the population level, addressing questions about the potency and dynamics of cell lineages and providing a way to quantify the progressive restriction of cell fate with increasing depth in the tree.\n\nAuthor summaryMulticellular organisms develop from a single fertilized egg by sequential cell divisions. The progeny from these divisions adopt different traits that are transmitted and modified through many generations. By tracking how cell traits change with each successive cell division throughout the family, or lineage, tree, it has been possible to understand where and how these modifications are controlled at the single-cell level, thereby addressing questions about, for example, the developmental origin of tissues, the sources of differentiation in immune cells, or the relationship between primary tumors and metastases. Such lineages often show large variability, with apparently identical founder cells giving rise to different patterns of descendants. Fundamental scientific questions, such as about the range of possible cell types a cell can give rise to, are often about this variability. To characterize this variation, and thus understand the lineage at the population level, we introduce lineage variability maps. Using data from worm and mammalian cell lineages we show how these maps provide quantifiable answers to questions about any developing lineage, such as the potency of founder cells and the progressive restriction of cell fate at each stage in the tree.