Cancer Risk and the Somatic 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 one of the key determinants of how somatic evolution, which can potentially lead to cancer, proceeds. Cancer initiation usually requires the accumulation of a certain number of driver mutations. By mapping the accumulation of driver mutations into a graph theoretical problem, we show that in leading order of the mutation rate the probability of collecting a given number of driver mutations depends only on the distribution of the lineage lengths (irrespective of any other details of the cell lineage tree), and we derive a simple analytical formula for this probability. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms in order to reduce their lifetime risk of cancer. In particular, our results highlight the significance of the longest cell lineages. Our analytical formula also provides a tool to quantify cancer susceptibility in theoretical models of tissue development and maintenance, as well as for empirical data on cell linage trees. Significance StatementA series of cell divisions starting from a single cell produce and maintain tissues of multicellular organisms. Somatic evolution, including the development of cancer, takes place along the cell lineage tree traced out by these cell divisions. A fundamental question in cancer research is how the lifetime risk of cancer depends on the properties of an arbitrary cell lineage tree. Here we show that for small mutation rates (which is the case in reality) the distribution of the lineage lengths alone determines cancer risk, and that this risk can be described by a simple analytical formula. Our results have far-reaching implications not only for cancer research, but also for evolutionary biology in general.