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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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Estimating the transfer rates of bacterial plasmids with an adapted Luria–Delbrück fluctuation analysis
To increase our basic understanding of the ecology and evolution of conjugative plasmids, we need reliable estimates of their rate of transfer between bacterial cells. Current assays to measure transfer rate are based on deterministic modeling frameworks. However, some cell numbers in these assays can be very small, making estimates that rely on these numbers prone to noise. Here, we take a different approach to estimate plasmid transfer rate, which explicitly embraces this noise. Inspired by the classic fluctuation analysis of Luria and Delbrück, our method is grounded in a stochastic modeling framework. In addition to capturing the random nature of plasmid conjugation, our new methodology, the Luria–Delbrück method (“LDM”), can be used on a diverse set of bacterial systems, including cases for which current approaches are inaccurate. A notable example involves plasmid transfer between different strains or species where the rate that one type of cell donates the plasmid is not equal to the rate at which the other cell type donates. Asymmetry in these rates has the potential to bias or constrain current transfer estimates, thereby limiting our capabilities for estimating transfer in microbial communities. In contrast, the LDM overcomes obstacles of traditional methods by avoiding restrictive assumptions about growth and transfer rates for each population within the assay. Using stochastic simulations and experiments, we show that the LDM has high accuracy and precision for estimation of transfer rates compared to the most widely used methods, which can produce estimates that differ from the LDM estimate by orders of magnitude.
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- PAR ID:
- 10392608
- Editor(s):
- Shou, Wenying
- Date Published:
- Journal Name:
- PLOS Biology
- Volume:
- 20
- Issue:
- 7
- ISSN:
- 1545-7885
- Page Range / eLocation ID:
- e3001732
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1371/journal.pbio.3001732
