Inheritance entropy: A model-independent method to probe the hereditary structure of cell lineage trees

Quantifying the impact of hereditary transmission within lineage trees remains a fundamental challenge universal to a wide array of biological domains. Here, we introduce the new concept of inheritance entropy, a quantity designed to gauge the hereditary structure of inactive cells across a lineage. We measure this entropy in 32 human stem cell clonal colonies, obtained from high-definition single-cell lineage tracing experiments, and show that in the greatest majority of clones the entropy is decisively smaller than that of the corresponding nonhereditary ensemble, hence proving that variations in the proliferative power of stem cell lineages are determined by hereditary epigenetic factors that regulate cell-cycle exit. The method can also be employed to locate the specific node of the tree where a mutation in the probability of inactivity occurs, together with a determination of the lag between the mutation ultimately leading to inactivity and its actual expression. This framework can be used to assess in a robust, simple and model-agnostic way the hereditary origin of differential growth in any type of lineage trees.