Development of a global stochastic model relating the distribution of individual cell and population physiological states

Effect of storage temperature on the lag time of Geobacillus stearothermophilus individual spores

The lag times (λ) of Geobacillus stearothermophilus single spores were studied at different storage temperatures ranging from 45 to 59 °C using the Bioscreen C method. A significant variability of λ was observed among individual spores at all temperatures tested. The storage temperature affected both the position and the spread of the λ distributions. The minimum mean value of λ (i.e. 10.87 h) was observed at 55 °C, while moving away from this temperature resulted in an increase for both the mean and standard deviation of λ. A Cardinal Model with Inflection (CMI) was fitted to the reverse mean λ, and the estimated values for the cardinal parameters T_min, T_max, T_opt and the optimum mean λ of G. stearothermophilus were found to be 38.1, 64.2, 53.6 °C and 10.3 h, respectively. To interpret the observations, a probabilistic growth model for G. stearothermophilus individual spores, taking into account λ variability, was developed. The model describes the growth of a population, initially consisting of N₀ spores, over time as the sum of cells in each of the N₀ imminent subpopulations originating from a single spore. Growth simulations for different initial contamination levels showed that for low N₀ the number of cells in the population at any time is highly variable. An increase in N₀ to levels exceeding 100 spores results in a significant decrease of the above variability and a shorter λ of the population. Considering that the number of G. stearothermophilus surviving spores in the final product is usually very low, the data provided in this work can be used to evaluate the probability distribution of the time-to-spoilage and enable decision-making based on the "acceptable level of risk".

Influence of stress on single-cell lag time and growth probability for Listeria monocytogenes in half Fraser broth

The impacts of 12 common food industry stresses on the single-cell growth probability and single-cell lag time distribution of Listeria monocytogenes were determined in half Fraser broth, the primary enrichment broth of the International Organization for Standardization detection method. First, it was determined that the ability of a cell to multiply in half Fraser broth is conditioned by its history (the probability for a cell to multiply can be decreased to 0.05), meaning that, depending on the stress in question, the risk of false-negative samples can be very high. Second, it was established that when cells are injured, the single-cell lag times increase in mean and in variability and that this increase represents a true risk of not reaching the detection threshold of the method in the enrichment broth. No relationship was observed between the impact on single-cell lag times and that on growth probabilities. These results emphasize the importance of taking into account the physiological state of the cells when evaluating the performance of methods to detect pathogens in food.

Predictive model for survival and growth of Salmonella typhimurium DT104 on chicken skin during temperature abuse

To better predict risk of Salmonella infection from chicken subjected to temperature abuse, a study was undertaken to develop a predictive model for survival and growth of Salmonella Typhimurium DT104 on chicken skin with native flora. For model development, chicken skin portions (2.14 cm2) were inoculated with 0.85 log of Salmonella Typhimurium DT104 (ATCC 700408) and then stored at 5 to 50 degrees C for 8 h. Kinetic data from the storage trials were fit to a primary model to determine lag time (lamda), specific growth rate (micrro), and the 95% prediction interval (PI). Secondary models for lamda, mu, and PI as a function of storage temperature were developed and then combined with the primary model to create a tertiary model. Performance of the tertiary model was evaluated against dependent data, independent data for interpolation, and independent data for extrapolation to kosher chicken skin by using an acceptable prediction zone from -1 (fail-safe) to 0.5 (fail-dangerous) log per skin portion. Survival of Salmonella Typhimurium DT104 on chicken skin was observed during 8 h of storage at 5 to 20 degrees C and at 50 degrees C, whereas growth was observed from 25 to 45 degrees C and was optimal at 40 degrees C with a lamda of 2.5 h and a mu of 1.1 log/h. Variation of pathogen growth, as assessed by PI, increased in a nonlinear manner as a function of temperature and was greater for growth conditions than no-growth conditions. The percentage of acceptable prediction errors was 82.6% for dependent data, 83.7% for independent data for interpolation, and 81.6% for independent data for extrapolation to kosher skin, which all exceeded the performance criterion of 70% acceptable predictions. Thus, it was concluded that the tertiary model provided valid predictions for survival and growth of Salmonella Typhimurium DT104 from a low initial dose on both nonkosher and kosher chicken skin with native flora.

Effect of the population heterogeneity on growth behavior and its estimation

Different types of the Logistic model are constructed based on a simple assumption that the microbial populations are all composed of homogeneous members and consequently, the condition of design for the initial value of these models has to be rather limited in the case of N(t(0))=N(0). Therefore, these models cannot distinguish the dynamic behavior of the populations possessing the same N(0) from heterogeneous phases. In fact, only a certain ratio of the cells in a population is dividing at any moment during growth progress, termed as theta, and thus, dN/dt not only depends on N, but also on theta. So theta is a necessary element for the condition design of the initial value. Unfortunately, this idea has long been neglected in widely used growth models. However, combining together the two factors (N(0) and theta) into the initial value often leads to the complexity in the mathematical solution. This difficulty can be overcome by using instantaneous rates (V(inst)) to express growth progress. Previous studies in our laboratory suggested that the V(inst) curve of the bacterial populations all showed a Guassian function shape and thus, the different growth phases can be reasonably distinguished. In the present study, the Gaussian distribution function was transformed approximately into an analytical form (Y(i)=alpha(e)[-0.5(x(i)-x(0)/b)(2)]) that can be conveniently used to evaluate the growth parameters and in this way the intrinsic growth behavior of a bacterial species growing in heterogeneous phases can be estimated. In addition, a new method has been proposed, in this case, the lag period and the double time for a bacterial population can also be reasonably evaluated. This approach proposed could thus be expected to reveal important insight of bacterial population growth. Some aspects in modeling population growth are also discussed.

Effect of sub-lethal heating and growth temperature on expression of the ribosomal RNA rrnB P(2) promoter during the lag phase of Pseudomonas fluorescens

Current models for the lag phase of food-borne pathogens are limited by our poor understanding of the physiological changes taking place as bacterial cells prepare for exponential growth. In a previous paper in this series, a strain of Pseudomonas fluorescens containing the Tn7-luxCDABE gene cassette regulated by the rRNA promoter rrnB P(2) was used to measure the influence of starvation on the lag phase duration (LPD(OD)) and growth rate (R(OD)). rrnB P(2) promoter activity increased exponentially during the lag phase, and was characterized by lag (LPD(Exp)) and rate (R(Exp)) parameters. In the present study, this work was expanded to include the influence of growth temperature (10 to 30 degrees C) and exposure to sub-lethal heating at 47 degrees C. With these additional datasets, the LPD(Exp) was often more pronounced than had been noted with starvation, so the original exponential association model (EXP) was compared to logistic and Gompertz (GOM) models. Based on root mean square error, the GOM model gave the better fit for some of the sub-lethal heating and growth temperature datasets; however, the EXP model was assessed as best overall. Increased growth temperature and decreased time of sub-lethal heating produced significant decreases in LPD(OD) and LPD(Exp) and increases in R(OD) and R(Exp). The results suggest that different stressors have differential effects on gene expression and subsequent growth.

Modelling the individual cell lag time distributions of Listeria monocytogenes as a function of the physiological state and the growth conditions

The individual cell lag time distributions of Listeria monocytogenes were characterized for 54 combinations of 22 initial physiological states, 18 growth conditions, and 11 strains. The individual cell lag times were deduced from the times for cultures issued from individual cells to reach an optical density threshold. The extreme value type II distribution with a shape parameter set to 5 was shown effective to describe the 54 observed distributions. The theoretical distributions of individual lag times were thus predictable from the observed means and standard deviations of cell lag times. More interestingly, relationships were proposed to predict the mean and the standard deviation of individual cell lag times from population lag times observed with high initial concentration experiments. The observed relations are consistent with the constancy of the product of the growth rate by the lag time at the cell level for a given physiological state when growth conditions are varying. This product, k, is thus representative of the cell physiological state. The proposed models allow the prediction of individual cell lag time distributions of L. monocytogenes in different growth conditions. We also observed that, whatever the stress encountered and the strains used, the coefficient of variation of the distributions of k was quite constant. These results could be used to describe the variability of the behaviour of few cells of L. monocyotgenes contaminating foods and stressed in the environment of food industry or by food processing.

Effect of environmental stresses on the mean and distribution of individual cell lag times of Escherichia coli O157:H7

The effect of starvation, heat or acid stress on duration of individual cell lag time (tau) and standard deviation (SD) of tau was investigated using Escherichia coli O157:H7. Cells were stressed by exposure to acid (pH 3.5), heat (50 degrees C), or starvation in either glucose-free mineral medium (MOPS), tryptic soy broth (TSB) or Luria broth (LB). Stressed cells were then diluted into wells of a Bioscreen plate to obtain single cells per well. Replicate time to detection (td) values were obtained using the Bioscreen and used to calculate the tau and SD. Significant (P< or =0.05) increases in tau over untreated controls were found for the following treatments: 14 days in acid; 2 h of heating; 3 days starvation in MOPS; and 2 days starvation in either TSB or LB. The largest increase in tau was >2-fold from 2.5 to 5.6 h observed with the heat treatment. MOPS starvation was more detrimental to the cells than was acid treatment over the same time period. A significant increase in SD was found with 21 days acid treatment, and 2 days starvation in either TSB or LB. No significant increase in SD was found for MOPS starvation or heat treatment. Lognormal, Gamma, ExtremeValue and Weibull distributions were fitted to the tau data using BestFit. The results suggest that the Lognormal distribution is suitable for fitting tau data from either stressed or unstressed cells.