A combined discrete-continuous model describing the lag phase of Listeria monocytogenes.

Food microbiologists generally use continuous sigmoidal functions such as the empirical Gompertz equation to obtain the kinetic parameters specific growth rate (mu) and lag phase duration (lambda) from bacterial growth curves. This approach yields reliable information on mu; however, values for lambda are difficult to determine accurately due, in part, to our poor understanding of the physiological events taking place during adaptation of cells to new environments. Existing models also assume a homogeneous population of cells, thus there is a need to develop discrete event models which can account for the behavior of individual cells. Time to detection (t(d)) values were determined for Listeria monocytogenes using an automated turbidimetric instrument, and used to calculate mu. Mean individual cell lag times (tL) were calculated as the difference between the observed t(d) and the theoretical value estimated using mu. Variability in tL for individual cells in replicate wells was estimated using serial dilutions. A discrete stochastic model was applied to the individual cells, and combined with a deterministic population-level growth model. This discrete-continuous model incorporating tL and the variability in tL (expressed as standard deviation; S.D.(L)) predicted a reduced variability between wells with increased number of cells per well, in agreement with experimental findings. By combining the discrete adaptation step with a continuous growth function it was possible to generate a model which accurately described the transition from lag to exponential phase. This new model may serve as a useful tool for describing individual cell behavior, and thus increasing our knowledge of events occurring during the lag phase.

[1]  C. Bourgeois,et al.  Modélisation des effets du pH, de l'acide lactique, du glycérol et du NaCl sur la croissance des cellules végétatives de Clostridium tyrobutyricum en milieu de culture , 1995 .

[2]  T. A. Roberts,et al.  Predicting microbial growth: growth responses of salmonellae in a laboratory medium as affected by pH, sodium chloride and storage temperature. , 1988, International journal of food microbiology.

[3]  V. Grimm Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future? , 1999 .

[4]  J. Hudson Comparison of response surface models for Listeria monocytogenes strains under aerobic conditions , 1994 .

[5]  T. Ross,et al.  Development of a predictive model to describe the effects of temperature and water activity on the growth of spoilage pseudomonads. , 1997, International journal of food microbiology.

[6]  J P Flandrois,et al.  A model describing the relationship between lag time and mild temperature increase duration. , 1997, International journal of food microbiology.

[7]  B. Hills,et al.  A new model for bacterial growth in heterogeneous systems. , 1994, Journal of theoretical biology.

[8]  B. P. Hills,et al.  Multi-compartment kinetic models for injury, resuscitation, induced lag and growth in bacterial cell populations , 1995 .

[9]  T. Ross,et al.  Development and evaluation of a predictive model for the effect of temperature and water activity on the growth rate of Vibrio parahaemolyticus. , 1997, International journal of food microbiology.

[10]  J Baranyi,et al.  Mathematics of predictive food microbiology. , 1995, International journal of food microbiology.

[11]  Baranyi Comparison of Stochastic and Deterministic Concepts of Bacterial Lag. , 1998, Journal of theoretical biology.

[12]  Tom Ross,et al.  Predictive Microbiology : Theory and Application , 1993 .

[13]  J. Baranyi Simple is good as long as it is enough , 1997 .

[14]  C. Pin,et al.  Predictive models as means to quantify the interactions of spoilage organisms. , 1998, International journal of food microbiology.

[15]  W. Garthright,et al.  The three-phase linear model of bacterial growth: a response , 1997 .

[16]  P Dalgaard,et al.  Estimation of bacterial growth rates from turbidimetric and viable count data. , 1994, International journal of food microbiology.

[17]  H. Lappin-Scott,et al.  The use of an automated growth analyser to measure recovery times of single heat‐injured Salmonella cells , 1997, Journal of applied microbiology.

[18]  D. Thuault,et al.  Modelling Bacillus cereus growth. , 1997, International journal of food microbiology.

[19]  Paul Tobback,et al.  Modelling the influence of temperature and carbon dioxide upon the growth of Pseudomonas fluorescens , 1993 .

[20]  J. Hudson,et al.  COMPARISON OF LAG TIMES OBTAINED FROM OPTICAL DENSITY AND VIABLE COUNT DATA FOR A STRAIN OF PSEUDOMONAS FRAGI , 1994 .

[21]  J Baranyi,et al.  A dynamic approach to predicting bacterial growth in food. , 1994, International journal of food microbiology.

[22]  R. C. Whiting,et al.  When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves , 1997 .

[23]  W. Garthright Refinements in the prediction of microbial growth curves , 1991 .

[24]  R. Mckellar,et al.  A heterogeneous population model for the analysis of bacterial growth kinetics. , 1997, International journal of food microbiology.

[25]  C. Pin,et al.  Estimating Bacterial Growth Parameters by Means of Detection Times , 1999, Applied and Environmental Microbiology.

[26]  A. Łomnicki Individual-based models and the individual-based approach to population ecology , 1999 .