The Poisson Distribution Is Applied to Improve the Estimation of Individual Cell and Micropopulation Lag Phases

Abstract

Many articles dealing with individual cell lag phase determination assume that growth, when observed, comes from one cell. This assumption is not in agreement with the Poisson distribution, which uses the probability of growth in a sample to predict how many samples contain one, two, or some other number of cells. This article analyses and compares different approaches to improve the accuracy of lag phase estimation of individual cells and micropopulations. It argues that if the highest initial load, as predicted by the Poisson distribution, is assigned to the sample with the shortest lag phase, the second highest to the sample with the second shortest lag phase and so on, the resulting lag phase distributions would be more accurate. This study also proposes the use of a robust test, permutation test, to compare lag phase distributions obtained in different situations.

Share and Cite:

J. Juan Aguirre, C. Bravo, J. A. Ordóñez and G. García de Fernando, "The Poisson Distribution Is Applied to Improve the Estimation of Individual Cell and Micropopulation Lag Phases," Advances in Microbiology, Vol. 2 No. 2, 2012, pp. 146-161. doi: 10.4236/aim.2012.22020.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] P. J. Stephens, J. A. Joynson, K. W. Davies, R. Holbrook, H. M. Lappin-Scott and T. J. Humphrey, “The Use of an Automated Growth Analyser to Measure Recovery Times of Single Heat-Injured Salmonella Cells,” Journal of Applied Microbiology, Vol. 83, No. 4, 1997, pp. 445-455. doi:10.1046/j.1365-2672.1997.00255.x
[2] K. Francois, F. Devlieghere, A. R. Standaert, A. H. Geeraerd, J. F. Van Impe and J. Debevere, “Modelling the Individual Cell Lag Phase. Isolating Single Cells: Protocol Development,” Letter of Applied Microbiology, Vol. 37, No. 1, 2003, pp. 26-30. doi:10.1046/j.1472-765X.2003.01340.x
[3] A. Metris, S. M. George, M. W. Peck and J. Baranyi, “Distribution of Turbidity Detection Times Produced by Single Cell-Generated Bacterial Populations,” Journal of Microbiological Methods, Vol. 55, No. 3, 2003, pp. 821-827. doi:10.1016/j.mimet.2003.08.006
[4] A. Elfwing, Y. LeMarc, J. Baranyi and A. Ballagi, “Observing Growth and Division of Large Numbers of Individual Bacteria by Image Analysis,” Applied and Environmental Microbiology, Vol. 70, No. 2, 2004, pp. 675-678. doi:10.1128/AEM.70.2.675-678.2004
[5] L. Guillier, P. Pardon and J.C. Augustin, “Influence of Stress on Individual Lag Time Distributions of Listeria monocytogenes,” Applied and Environmental Microbiology, Vol. 71, No. 6, 2005, pp. 2940-2948. doi:10.1128/AEM.71.6.2940-2948.2005
[6] M. D'Arrigo, G. D. Garcia de Fernando, R. Velasco de Diego, J. A. Ordonez, S. M. George and C. Pin, “Indirect Measurement of the Lag Time Distribution of Single Cells of Listeria innocua in Food,” Applied and Environmental Microbiology, Vol. 72, No. 4, 2006, pp. 2533-2538. doi:10.1128/AEM.72.4.2533-2538.2006
[7] C. Pin and J. Baranyi, “Kinetics of Single Cells: Observation and Modeling of a Stochastic Process,” Applied and Environmental Microbiology, Vol. 72, No. 3, 2006, pp. 2163-2169. doi:10.1128/AEM.72.3.2163-2169.2006
[8] G. W. Niven, J. S. Morton, T. Fuks and B. M. Mackey, “Influence of Environmental Stress on Distributions of Times to First Division in Escherichia coli Populations, as Determined by Digital-Image Analysis of Individual Cells,” Applied and Environmental Microbiology, Vol. 74, No. 12, 2008, pp. 3757-3763. doi:10.1128/AEM.02551-07
[9] J. S. Aguirre, M. R. Rodriguez and G. D. Garcia de Fernando, “Effects of Electron Beam Irradiation on the Variability in Survivor Number and Duration of Lag Phase of Four Food-Borne Organisms,” International Journal of Food Microbiology. Vol. 149, No. 3, 2011, pp. 236-246. doi:10.1016/j.ijfoodmicro.2011.07.003
[10] I. A. Swinnen, K. Bernaerts, E. J. Dens, A. H. Geeraerd and J. F. Van Impe, “Predictive Modelling of the Microbial Lag Phase: A Review,” International Journal of Food Microbiology. Vol. 94, No. 2, 2004, pp. 137-159. doi:10.1016/j.ijfoodmicro.2004.01.006
[11] J. P. Smelt, G. D. Otten and A. P. Bos, “Modelling the Effect Of Sublethal Injury on the Distribution of the Lag Times of Individual Cells of Lactobacillus plantarum,” International Journal of Food Microbiology, Vol. 73, No. 2-3, 2002, pp. 207-212.
[12] A. Metris, S. M. George and J. Baranyi, “Use of Optical Density Detection Times to Assess the Effect of Acetic Acid on Single-Cell Kinetics,” Applied and Environmental Microbiology, Vol. 72, No. 10, 2006, pp. 6674-6679. doi:10.1128/AEM.00914-06
[13] BACANOVA, “Final Report on the European Project QLRT-2000-01145: Optimisation of Safe Food Processing Methods Based on Accurate Characterisation of Bacterial Lag Time Using Analysis of Variance Techniquesm,” BACANOVA Consortium, European Commission, Brussels, 2005.
[14] J. Baranyi and C. Pin, “Estimating Bacterial Growth Parameters by Means of Detection Times,” Applied and Environmental Microbiology, Vol. 65, No. 2, 1999, pp. 732-736.
[15] R. C. McKellar and K. Knight, “A Combined Discrete-Continuous Model Describing the Lag Phase of Listeria monocytogenes,” International Journal of Food Microbiology, Vol. 54, No. 3, 2000, pp. 171-180. doi:10.1016/S0168-1605(99)00204-4
[16] T. P. Robinson, O. O. Aboaba, A. Kaloti, M. J. Ocio, J. Baranyi and B. M. Mackey, “The Effect of Inoculum Size on the Lag Phase of Listeria monocytogenes,” International Journal of Food Microbiology, Vol. 70, No. 1-2, 2001, pp. 163-173. doi:10.1016/S0168-1605(01)00541-4
[17] R. C. McKellar and A. Hawke, “Assessment of Distributions for Fitting Lag Times of Individual Cells in Bacterial Populations,” International Journal of Food Microbiology, Vol. 106, No. 2, 2006, pp. 169-175. doi:10.1016/j.ijfoodmicro.2005.06.018
[18] J. Baranyi, S. M. George and Z. Kutalik, “Parameter Estimation for the Distribution of Single Cell Lag Times,” Journal of Theoretical Biology, Vol. 259, No. 1, 2009, pp. 24-30. doi:10.1016/j.jtbi.2009.03.023
[19] I. Espejo, F. Fernández, M. A. López, M. Mu?oz, A. M. Rodríguez, A. Sánchez and C. Valero, “Estadística Descriptiva y Probabilidad,” 3rd Edition, U.d.C., Cadiz, 2006. http://knuth.uca.es/repos/l_edyp/pdf/-febrero06/lib_edyp.apendices.pdf
[20] T. Hesterberg, D. S. Moore, S. Monaghan, A. Clipson, R. Epstein and G. P. McCabe, “Bootstrap Methods and Permutation Tests,” In: W. H. McCabe, Ed., Introduction to the Practice of Statistics (5th Edition), Freeman & Co., New York, 2005, pp. 14.1-14.70.
[21] S. Holm, “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of Statistics, Vol. 6, 1979, pp. 65-70.
[22] H. Abdi, “Bonferroni and Sidák Corrections for Multiple Comparisons,” In: C. S. Neil Salkind, Ed., Encyclopedia of Measurement and Statistics, Dallas, Thousand Oaks, 2007, pp. 103-107.
[23] R Version 2.72, “Language and Environment for Statistical Computing,” The R Foundation for Statistical Computing, 2008.
[24] C. Pin and J. Baranyi, “Single-Cell and Population Lag Times as a Function of Cell Age,” Applied and Environmental Microbiology, Vol. 74, No. 8, 2008, pp. 2534-2536. doi:10.1128/AEM.02402-07

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.