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.

中文翻译：

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突变积累如何取决于细胞谱系树的结构

多细胞生物体的所有细胞都是细胞分裂的产物，细胞分裂形成一棵二叉树，即所谓的细胞谱系树。由于细胞分裂伴随着复制错误，因此细胞谱系树的形状是体细胞进化（可能导致癌症）如何进行的关键决定因素。癌变需要一定数量的驱动突变的积累。通过将突变的积累映射到图论问题，我们提出了一种精确的数值方法来计算收集给定数量的突变的概率，并表明对于低突变率，可以用一个简单的分析公式来近似，该公式仅取决于谱系长度的分布，并且以最长的谱系为主。我们的结果对于理解自然选择如何塑造多细胞生物的细胞谱系树和抑制体细胞进化至关重要。