How mutation accumulation depends on the structure of the cell lineage tree

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.