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Comparing mutation rates under the Luria–Delbrück protocol

Abstract

Comparison of microbial mutation rates under the Luria–Delbrück protocol is a routine laboratory task. However, execution of this important task has been hampered by the lack of proper statistical methods. Visual inspection or improper use of the t test and the Mann–Whitney test can impair the quality of genetic research. This paper proposes a unified framework for constructing likelihood ratio tests that overcome three important obstacles to the proper comparison of microbial mutation rates. Specifically, algorithms for likelihood ratio tests have been devised that allow for partial plating, differential growth rates and unequal terminal cell population sizes. The new algorithms were assessed by computer simulations. In addition, a strategy for multiple comparison was illustrated by reanalyzing the experimental data from a study of bacterial resistance against tuberculosis antibiotics.

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References

  1. Agresti A (2007) An introduction to categorical data analysis, 2nd edn. Wiley-Interscience, Hoboken

    Book  Google Scholar 

  2. Bachmann H, Starrenburg MJC, Molenaar D, Kleerebezem M, van Hylckama Vlieg JET (2012) Microbial domestication signatures of Lactococcus lactis can be reproduced by experimental evolution. Genome Res 22:115–124

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  3. Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B 57:289–300

    Google Scholar 

  4. Boe L, Tolker-Nielsen T, Eegholm K-M, Spliid H, Vrang A (1994) Fluctuation analysis of mutations to nalidixic acid resistance in Escherichia coli. J Bacteriol 176:2781–2787

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Bolz NJ, Lenhart JS, Weindorf SC, Simmons LA (2012) Residues in the n-terminal domain of MutL required for mismatch repair in Bacillus subtilis. J Bacteriol 194:5361–5367

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  6. Cifone MA, Fidler IJ (1981) Increasing metastatic potential is associated with increasing genetic instability of clones isolated from murine neoplasms. Proc Natl Acad Sci 78:6949–6952

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  7. Crane GJ, Thomas SM, Jones ME (1996) A modified Luria–Delbrück fluctuation assay for estimating and comparing mutation rates. Mutat Res 354:171–182

    Article  PubMed  Google Scholar 

  8. Csörgő B, Fehér T, Tímár E, Blattner FR, Pósfai G (2012) Low-mutation-rate, reduced-genome Escherichia coli: an improved host for faithful maintenance of engineered genetic constructs. Microb Cell Fact 11:11

    Article  PubMed  PubMed Central  Google Scholar 

  9. Fehér T, Cseh F, Umenhoffer K, Karcagi I, Pósfai G (2006) Characterization of cycA mutants of Escherichia coli: an assay for measuring in vivo mutation rates. Mutat Res 595:184–190

    Article  PubMed  Google Scholar 

  10. Flohr RCE, Blom CJ, Rainey PB, Beaumont HJE (2013) Founder niche constrains evolutionary adaptive radiation. Proc Natl Acad Sci USA 110:20663–20668

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  11. Ford CB, Shah RR, Meada MK, Gagneux S, Murray MB, Cohen T, Johnston JC, Gardy J, Lipsitch M, Fortune SM (2013) Mycobacterium tuberculosis mutation rate estimates from different lineages predict substantial differences in the emergence of drug-resistant tuberculosis. Nat Genet 45:784–790

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  12. Jones ME, Thomas SM, Rogers A (1994) Luria–Delbrück fluctuation experiments: design and analysis. Genetics 136:1209–1216

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Lea EA, Coulson CA (1949) The distribution of the numbers of mutants in bacterial populations. J Genet 49:264–285

    CAS  Article  PubMed  Google Scholar 

  14. Luria SE (1984) A slot machine, a broken test tube: an autobiography. Harper & Row, New York

    Google Scholar 

  15. Luria SE, Delbrück M (1943) Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28:491–511

    CAS  PubMed  PubMed Central  Google Scholar 

  16. Ma WT, Sandri G vH, Sarkar S (1992) Analysis of the Luria and Delbrück distribution using discrete convolution powers. J Appl Prob 29:255–267

    Article  Google Scholar 

  17. MaGrath M, van Pittius NCG, van Helden PD, Warren RM, Warner DF (2014) Mutation rate and the emergence of drug resistance in Mycobacterium tuberculosis. J Antimicrob Chemother 69:292–302

    Article  Google Scholar 

  18. Monti MR, Miguel V, Borgogno MV, Argaraña CE (2012) Functional analysis of the interaction between the mismatch repair protein MutS and the replication processivity factor \(\beta\) clamp in Pseudomonas aeruginosa. DNA Repair 11:463–469

    CAS  Article  PubMed  Google Scholar 

  19. Painter KL, Strange E, Parkhill J, Bamford KB, Armstrong-James D (2015) Staphylococcus aureus adapts to oxidative stress by producing \({\rm H}_{2} {\rm O}_{2}\)-resistant small-colony variants via the SOS response. Infect Immun 83:1830–1844

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  20. Rajanna C, Quellette G, Rashid M, Zemla A, Karavis M, Zhou C, Revazishvili T, Redmond B, McNew L, Bakanidze L, Imnadze P, Rivers B, Skowronski EW, O’Connell KP, Sulkvelidze A, Gibbons HS (2013) A strain of Yersinia pestis with a mutator phenotype from the republic of georgia. FEMS Microbiol Lett 343:113–120

    CAS  Article  PubMed  Google Scholar 

  21. Rosche WA, Foster PL (2000) Determining mutation rates in bacterial populations. Methods 20:4–17

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  22. Sabatinos SA, Mastro TL, Green MD, Forsburg SL (2013) A mammalian-like DNA damage response of fission yeast to nucleoside analogs. Genetics 193:143–157

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  23. Sánchez A, Sharma S, Rozenzhak S, Roguev A, Krogan NJ, Chabes A, Russell P (2012) Replication fork collapse and genome instability in a deoxycytidylate deaminase mutant. Mol Cell Biol 32:4445–4454

    Article  PubMed  PubMed Central  Google Scholar 

  24. Sarkar S, Ma WT, Sandri G vH (1992) On fluctuation analysis: a new, simple and efficient method for computing the expected number of mutants. Genetica 85:173–179

    CAS  Article  PubMed  Google Scholar 

  25. Schenker N, Gentleman JF (2001) On judging the significance of differences by examining overlap between confidence intervals. Am Stat 55:182–186

    Article  Google Scholar 

  26. Shockley AH, Doo DW, Rodriguez GP, Crouse GF (2013) Oxidative damage and mutagenesis in Saccharomyces cerevisiae: genetic studies of pathways affecting replication fidelity of 8-oxoguanine. Genetics 195:359–367

    Article  PubMed  PubMed Central  Google Scholar 

  27. Stewart FM (1991) Fluctuation analysis: the effect of plating efficiency. Genetica 84:51–55

    CAS  Article  PubMed  Google Scholar 

  28. Walsh BW, Boltz SA, Wessel SR, Schroeder JW, Keck JL, Simmons LA (2014) RecD2 helicase limits replication fork stress in Bacillus subtilis. J Bacteriol 196:1359–1368

    Article  PubMed  PubMed Central  Google Scholar 

  29. Werngren J, Hoffner SE (2003) Drug-susceptible Mycobacterium tuberculosis Beijing genotype does not develop mutation-conferred resistance to rifampin at an elevated rate. J Clin Microbiol 41:1520–1524

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  30. Wielgoss S, Barrick JE, Tenaillon O, Wiser MJ, Dittma WJ, Cruveiller S, Chane-Woon-Ming B, Médigue C, Lenski RE (2013) Mutation rate dynamics in a bacterial population reflect tension between adaptation and genetic load. Proc Natl Acad Sci USA 110:222–227

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  31. Zheng Q (1999) Progress of a half century in the study of the Luria–Delbrück distribution. Math Biosci 162:1–32

    CAS  Article  PubMed  Google Scholar 

  32. Zheng Q (2005) New algorithms for Luria–Delbrück fluctuation analysis. Math Biosci 196:198–214

    Article  PubMed  Google Scholar 

  33. Zheng Q (2008) A note on plating efficiency in fluctuation experiments. Math Biosci 216:150–153

    Article  PubMed  Google Scholar 

  34. Zheng Q (2015a) Methods for comparing mutation rates using fluctuation assay data. Mutat Res Fundam Mol Mech Mutagen 777:20–22

    CAS  Article  Google Scholar 

  35. Zheng Q (2015b) A new practical guide to the Luria–Delbrück protocol. Mutat Res Fundam Mol Mech Mutagen 781:7–13

    CAS  Article  Google Scholar 

  36. Zheng Q (2016) rSalvador 1.5: an R tool for the Luria–Delbrück fluctuation assay. http://eeeeeric.github.io/rSalvador

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Acknowledgments

My special appreciation goes to J. Werngren who explained to me minute experimental details with extraordinary patience. I also own a debt to two conscientious reviewers whose detailed comments substantially improved the presentation of the material in this manuscript. Part of the reported investigation relied heavily on an IBM iDataPlex cluster and an IBM NeXtScale cluster, managed by Texas A&M University Supercomputing Facility.

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Correspondence to Qi Zheng.

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Zheng, Q. Comparing mutation rates under the Luria–Delbrück protocol. Genetica 144, 351–359 (2016). https://doi.org/10.1007/s10709-016-9904-3

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Keywords

  • Fluctuation experiment
  • Likelihood ratio test
  • Plating efficiency
  • Relative fitness
  • Antibiotic resistance