Two implications of common models of microbial growth

Abstract

Analysis of a generalised growth equation shows that both the maximum growth rate of a microbial culture and the duration of the lag phase are related to each other and to the maximum growth. Similar relationships apply to growth expressions, such as the logistic and Gompertz models, that are special cases of the generalised model. Moreover, the same relationships are observed qualitatively in measurements of the growth of Salmonella species. These results may allow the characterisation of microbial growth with fewer parameters than is usually the case and imply the likelihood of a fundamental physiological interdependence between maximum growth rate, the duration of the lag time and the maximum growth. References

• Malthus, T., An Essay on the Principle of Population, as it Affects the Future Improvement of Society with Remarks on the Speculations of Mr. Godwin, M. Condorcet, and Other Writers, J. Johnson, 1798.
• Marusic, M. and Bajzer, Z., Generalized two-parameter equation of growth, J. Math. Anal. Appl., 179, 1993, 446--462. doi:10.1006/jmaa.1993.1361.
• Marusic, M., Bajzer, Z., Vuk-Pavolic, S. and Freyer, J. P., Tumor growth in vivo and as multicellular spheroids compared by mathematical models, Bull. Math. Biol., 56, 1994, 617--631. doi:10.1007/BF02460714.
• Redfield, R. J., Is quorum sensing a side effect of diffusion sensing?, Trends Microbiol., 10, 2002, 365--370. doi:10.1016/S0966-842X(02)02400-9.
• R Core Development Team, R: a package for statistical computing, R Foundation for Statistical Computing, 2006. http://www.r-project.org.
• Russell, J. B. and Cook, G. M., Energetics of bacterial growth: balance of anabolic and catabolic reactions, Microbiol. Rev., 59, 1995, 48--62. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=239354.
• Turner, M. E., Jr, Bradley, E. L., Jr, Kirk, K. A. and Pruitt, K. M., A theory of growth, Math. Biosci., 29, 1976, 367--373. doi:10.1016/0025-5564(76)90112-7.
• Savageau, M. A., Growth equations---a general equation and a survey os special cases, Math. Biosci., 48, 1980, 267--278. doi:10.1016/0025-5564(80)90061-9.
• Verhulst, P.-F., Notice sur la loi que la population suit dans son accroissement, Corresp. Math. Physique, 10, 1838, 113--121. http://www.google.com.au/books?id=NTgDAAAAQAAJ&printsec=frontcover&dq=editions:0X2PwfU_YZepVwHW.
• Winsor, C. P., The Gompertz curve as a growth curve. Proc. Natl Acad. Sci. USA, 18, 1932, 1--8. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1076153.
• Anonymous, Combase. http://www.combase.cc.
• Zweitering, M. H., Jongenburger, I., Rombouts, F. M. and van't Riet, K., Modeling of the bacterial growth curve, Appl. Environ. Microbiol., 56, 1990, 1875--1881. http://intl-aem.asm.org/cgi/content/abstract/56/6/1875.
• Baranyi, J. and Tamplin, M. L., ComBase: a common database on microbial responses to food environments, J. Food Protect., 67, 2004, 1967--1971. http://apt.allenpress.com/aptonline/?request=get-abstract&issn=0362-028X&volume=067&issue=09&page=1967.
• Buchanan, R. L. and Cygnarowicz, M. L., A mathematical approach toward defining and calculating the duration of the lag phase, Food Microbiol., 7, 1990, 237--240. doi:10.1016/0740-0020(90)90029-H.
• Gompertz, B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Phil. Trans R. Soc. Lond., 115, 1825, 513--585. doi:10.1098/rstl.1825.0026.