Cancer Risk and the Somatic Cell-lineage Tree

All the cells of an organism are the product of cell divisions organized into a single binary tree. This somatic cell-lineage tree is not uniform in the sense that its lineages have different lengths. As cell divisions are accompanied by replication errors, longer cell lineages are more prone to the accumulation of mutations and, thereby, to somatic evolution, which can potentially lead to the development of cancer. By mapping the accumulation of driver mutations along a somatic cell-lineage tree into a graph theoretical problem, we have been able to derive an analytical formula for the probability of carcinogenesis in an arbitrary cell-lineage tree with a given rate of driver mutations per cell division. The result is consistent with epidemiological data and highlights the significance of the longest cell lineages. We also show how tissues can minimize the length of their longest lineages through differentiation hierarchies.