On Bartlett's formulation of the Luria-Delbrück mutation model

Mathematical Biosciences

Volumn 215, Issue 1, 2008, Pages 48-54

  Zheng, Qi ^a  

^a TEXAS A AND M HEALTH SCIENCE CENTER   (United States)

Author keywords

Asymptotic analysis; Maximum likelihood principle; Mutant distribution; Mutation rate; Newton Raphson procedure; Probability generating function

Indexed keywords

DISTRIBUTION FUNCTIONS; DYNAMICS; ESTIMATION; EXPERIMENTS; MAXIMUM LIKELIHOOD ESTIMATION;

ASYMPTOTIC ANALYSIS; ASYMPTOTIC BEHAVIORS; CELL DYNAMICS; MATHEMATICAL DIFFICULTIES; MAXIMUM LIKELIHOOD PRINCIPLES; MAXIMUM-LIKELIHOOD PRINCIPLE; MUTANT DISTRIBUTION; MUTATION RATE; MUTATION RATES; NEWTON-RAPHSON PROCEDURE; PROBABILITY GENERATING FUNCTION; RESEARCH AND APPLICATION;

MATHEMATICAL MODELS;

ALGORITHM; COMPARATIVE STUDY; CYTOLOGY; ESTIMATION METHOD; EXPERIMENTAL STUDY; MODELING; MUTATION; NUMERICAL MODEL;

ALGORITHM; ARTICLE; MATHEMATICAL MODEL; MAXIMUM LIKELIHOOD METHOD; MICROORGANISM; MUTANT; MUTATION; NONHUMAN; PROBABILITY;

ALGORITHMS; GENETICS, MICROBIAL; MATHEMATICS; MODELS, GENETIC; MUTATION;

LURIA;

EID: 49849105116     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2008.05.005     Document Type: Article

References (31)

1. Angerer W.P. An explicit representation of the Luria-Delbrück distribution. J. Math. Biol. 42 (2001) 145
2. Armitage P. The statistical theory of bacterial populations subject to mutation. J. Roy. Stat. Soc. B 14 (1952) 1
3. Bartlett M.S. An Introduction to Stochastic Processes With Special Reference to Methods and Applications (1955), Cambridge University, London
4. Bartlett M.S. An Introduction to Stochastic Processes With Special Reference to Methods and Applications. second ed. (1966), Cambridge University, London
5. Bartlett M.S. An Introduction to Stochastic Processes With Special Reference to Methods and Applications. third ed. (1978), Cambridge University, Cambridge
6. Braun W. Bacterial Genetics. second ed. (1965), W.B. Saunders Company, Philadelphia
7. Cox D.R., and Miller H.D. The Theory of Stochastic Processes (1965), Chapman and Hall, London
8. Crump K.S., and Hoel D.G. Mathematical models for estimating mutation rates in cell populations. Biometrika 61 (1974) 237
9. Demerec M. Production of Staphylococcus strains resistant to various concentrations of penicillin. Proc. Natl. Acad. Sci. USA 31 (1945) 16
10. Drake J.W. A constant rate of spontaneous mutation in DNA-based microbes. Proc. Natl. Acad. Sci. USA 88 (1991) 7160
11. Kendal W.S., and Frost P. Pitfalls and practice of Luria-Delbrück fluctuation analysis: a review. Cancer Res. 48 (1988) 1060
12. Flajolet P., and Odlyzko A. Singularity analysis of generating functions. SIAM J. Discrete Math. 3 (1990) 216
13. Griffiths A.J.F., Miller J.H., Suzuki D.T., Lewontin R.C., and Gelbart W.M. An Introduction to Genetic Analysis. seventh ed. (2000), W.H. Freeman and Company, New York
14. Jones M.E., Thomas S.M., and Rogers A. Luria-Delbrück fluctuation experiments: design and analysis. Genetics 136 (1994) 1209
15. Kimmel M., and Axelrod D.E. Fluctuation test for two-stage mutations: application to gene amplification. Mutat. Res. 306 (1994) 45
16. Koch A.L. Mutation and growth rates from Luria-Delbrück fluctuation tests. Mutat. Res. 95 (1982) 129
17. Lea E.A., and Coulson C.A. The distribution of the numbers of mutants in bacterial populations. J. Genet. 49 (1949) 264
18. Luria S.E., and Delbrück M. Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28 (1943) 491
19. Ma W.T., Sandri G.vH., and Sarkar S. Analysis of the Luria and Delbrück distribution using discrete convolution powers. J. Appl. Probab. 29 (1992) 255
20. Mandelbrot B. A population birth-and-mutation process. I: Explicit distributions for the number of mutants in an old culture of bacteria. J. Appl. Probab. 11 (1974) 437
21. Oprea M., and Kepler T.B. Improved inference of mutation rates. II. Generalization of the Luria-Delbrück distribution for realistic cell-cycle time distributions. Theor. Popul. Biol. 59 (2001) 49
22. Pakes A.G. Remarks on the Luria-Delbrück distribution. J. Appl. Probab. 30 (1993) 991
23. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in C: The Art of Scientific Computing (1988), Cambridge University, New York
24. Rosche W.A., and Foster P.L. Determining mutation rates in bacterial populations. Methods 20 (2000) 4
25. Stewart F.M., Gordon D.M., and Levin B.R. Fluctuation analysis: the probability distribution of the number of mutants under different conditions. Genetics 124 (1990) 175
26. Wong R. Asymptotic Approximations of Integrals (1989), Academic, Boston
27. Zheng Q. On a compartmental analysis result. Math. Biosci. 130 (1995) 203
28. Zheng Q. Progress of a half century in the study of the Luria-Delbrück distribution. Math. Biosci. 162 (1999) 1
29. Zheng Q. New algorithms for Luria-Delbrück fluctuation analysis. Math. Biosci. 196 (2005) 198
30. Zheng Q. Update on estimation of mutation rates using data from fluctuation experiments. Genetics 171 (2005) 861
31. Zheng Q. On Haldane's formulation of Luria and Delbrück's mutation model. Math. Biosci. 209 (2007) 500