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Multicellular organisms often start life as a single cell. Subsequent cell division builds the body. Each mutational event during those developmental cell divisions carries forward to all descendant cells. The overall number of mutant cells in the body follows the Luria–Delbrück process. This article first reviews the basic quantitative principles by which one can understand the likely number of mutant cells and the variation in mutational burden between individuals. A recent Fréchet distribution approximation simplifies calculation of likelihoods and intuitive understanding of process. The second part of the article highlights consequences of somatic mutational mosaicism for understanding diseases such as cancer, neurodegeneration, and atherosclerosis.
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The number of neutral mutants in an expanding Luria-Delbrück population is approximately Fréchet
Background: A growing population of cells accumulates mutations. A single mutation early in the growth process carries forward to all descendant cells, causing the final population to have a lot of mutant cells. When the first mutation happens later in growth, the final population typically has fewer mutants. The number of mutant cells in the final population follows the Luria-Delbrück distribution. The mathematical form of the distribution is known only from its probability generating function. For larger populations of cells, one typically uses computer simulations to estimate the distribution. Methods: This article searches for a simple approximation of the Luria-Delbrück distribution, with an explicit mathematical form that can be used easily in calculations. Results: The Fréchet distribution provides a good approximation for the Luria-Delbrück distribution for neutral mutations, which do not cause a growth rate change relative to the original cells. Conclusions: The Fréchet distribution apparently provides a good match through its description of extreme value problems for multiplicative processes such as exponential growth.
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- Award ID(s):
- 1939423
- PAR ID:
- 10417673
- Date Published:
- Journal Name:
- F1000Research
- Volume:
- 11
- ISSN:
- 2046-1402
- Page Range / eLocation ID:
- 1254
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.12688/f1000research.127469.2
