Assessment of distributions for fitting lag times of individual cells in bacterial populations

Modeling the Effects of the Preculture Temperature on the Lag Phase of Listeria monocytogenes at 25°C

In predictive microbiology, the study of the microbial lag phase, i.e., the time needed for bacteria to adapt to a new environment before multiplying, has received a great deal of attention in the research literature. The microbial lag phase is more difficult to estimate than the specific growth rate because the lag phase is impacted by the previous and actual growth environments. In this study, the growth of Listeria monocytogenes preincubated at 0, 5, 10, and 15°C and subsequently grown at 25°C was investigated at the single-cell and population levels. The population lag phase of L. monocytogenes was obtained by fitting the Baranyi model, and the single-cell lag time was estimated by the time to detection method. The lag phase at the single-cell and population levels of L. monocytogenes presented a downward trend as the preculture temperature ranged from 0 to 15°C. The population lag phase of L. monocytogenes was lower than the single-cell lag time at the same preculture temperature. In addition, except for the zero-lag distribution at a preculture temperature of 15°C, all the single-cell lag time distributions of L. monocytogenes followed a Weibull distribution under all preculture temperatures. The preculture temperature had a significant impact on the rapid variation in the single-cell lag time distribution. Thus, the influence of preculture temperature on the lag phase needs to be quantitatively analyzed for better assessment of microbiological risk.

The importance of lag time extension in determining bacterial resistance to antibiotics

It is widely appreciated that widespread antibiotic resistance has significantly reduced the utility of today's antibiotics. Many antibiotics now fail to cure infectious diseases, although they are classified as effective bactericidal agents based on antibiotic susceptibility tests. Here, via kinetic growth assays, we evaluated the effects of 12 commonly used antibiotics on the lag phase of a range of pure environmental isolates and of sludge bacterial communities with a high diversity. We show that an extended lag phase offers bacteria survival advantages and promotes regrowth upon the removal of antibiotics. By utilizing both lag phase extension and IC50, the killing efficiency of an antibiotic on a strain or a community can be easily revealed. Interestingly, for several strains of relevance to endemic nosocomial infections (e.g. Acinetobacter sp. and Pseudomonas aeruginosa) and the diverse sludge communities, tetracycline and quinolone antibiotics are most likely to be resisted via extended lag phase. This discovery is significant from a clinical point view since underestimation of bacteria resistance can lead to the recurrence of diseases.

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".

Assessing the survival of Listeria monocytogenes in a domestic freezer by analyzing subsequent growth at 30°C using a novel reference method

Listeria monocytogenes is a serious pathogen capable of extensive survival under frozen storage. Using optical density and multiple initial inocula in multiple identically prepared microtiter plates, the effect of storage time at -22°C on the subsequent growth at 30°C of the organism when defrosted was studied using a technique that compared the growth (through time to detection) of a test plate (previously frozen) with that of an identically prepared control plate, analyzed at the start of the experiment. Experiments were carried out using tryptic soy broth (TSB) or TSB supplemented with 3% salt. Plates were stored and frozen for up to 6 months (10 days, 20 days, 2 months, and 6 months). As storage time increased, there was only a small relative increase in the lag and the variance in the time to detection observed. When compared with storage in 3% salt TSB, which reduced the specific growth rate relative to growth in standard TSB, there were only marginally greater increases in lag and data variance. After 6 months storage in 3% salt TSB, there were some indications of inactivation (observed as small reductions of the initial optical density (equal to 1 × 10(9) CFU/ml) equivalent to a 50% inactivation. The method and the analyses suggest that this technique could allow easy examination of the effect of frozen storage on given cultures, with respect to the effects of pH, water activity, and also the effect of preservatives commonly used as extra hurdles in foods.

Mass and density measurements of live and dead Gram-negative and Gram-positive bacterial populations

Monitoring cell growth and measuring physical features of food-borne pathogenic bacteria are important for better understanding the conditions under which these organisms survive and proliferate. To address this challenge, buoyant masses of live and dead Escherichia coli O157:H7 and Listeria innocua were measured using Archimedes, a commercially available suspended microchannel resonator (SMR). Cell growth was monitored with Archimedes by observing increased cell concentration and buoyant mass values of live growing bacteria. These growth data were compared to optical density measurements obtained with a Bioscreen system. We observed buoyant mass measurements with Archimedes at cell concentrations between 10(5) and 10(8) cells/ml, while growth was not observed with optical density measurements until the concentration was 10(7) cells/ml. Buoyant mass measurements of live and dead cells with and without exposure to hydrogen peroxide stress were also compared; live cells generally had a larger buoyant mass than dead cells. Additionally, buoyant mass measurements were used to determine cell density and total mass for both live and dead cells. Dead E. coli cells were found to have a larger density and smaller total mass than live E. coli cells. In contrast, density was the same for both live and dead L. innocua cells, while the total mass was greater for live than for dead cells. These results contribute to the ongoing challenge to further develop existing technologies used to observe cell populations at low concentrations and to measure unique physical features of cells that may be useful for developing future diagnostics.

Quantitative phenotypic analysis of multistress response in Zygosaccharomyces rouxii complex

Zygosaccharomyces rouxii complex comprises three yeasts clusters sourced from sugar- and salt-rich environments: haploid Zygosaccharomyces rouxii, diploid Zygosaccharomyces sapae and allodiploid/aneuploid strains of uncertain taxonomic affiliations. These yeasts have been characterized with respect to gene copy number variation, karyotype variability and change in ploidy, but functional diversity in stress responses has not been explored yet. Here, we quantitatively analysed the stress response variation in seven strains of the Z. rouxii complex by modelling growth variables via model and model-free fitting methods. Based on the spline fit as most reliable modelling method, we resolved different interstrain responses to 15 environmental perturbations. Compared with Z. rouxii CBS 732(T) and Z. sapae strains ABT301(T) and ABT601, allodiploid strain ATCC 42981 and aneuploid strains CBS 4837 and CBS 4838 displayed higher multistress resistance and better performance in glycerol respiration even in the presence of copper. μ-based logarithmic phenotypic index highlighted that ABT601 is a slow-growing strain insensitive to stress, whereas ABT301(T) grows fast on rich medium and is sensitive to suboptimal conditions. Overall, the differences in stress response could imply different adaptation mechanisms to sugar- and salt-rich niches. The obtained phenotypic profiling contributes to provide quantitative insights for elucidating the adaptive mechanisms to stress in halo- and osmo-tolerant Zygosaccharomyces yeasts.

Alternative approach to modeling bacterial lag time, using logistic regression as a function of time, temperature, pH, and sodium chloride concentration

The objective of this study was to develop a probabilistic model to predict the end of lag time (λ) during the growth of Bacillus cereus vegetative cells as a function of temperature, pH, and salt concentration using logistic regression. The developed λ model was subsequently combined with a logistic differential equation to simulate bacterial numbers over time. To develop a novel model for λ, we determined whether bacterial growth had begun, i.e., whether λ had ended, at each time point during the growth kinetics. The growth of B. cereus was evaluated by optical density (OD) measurements in culture media for various pHs (5.5 ∼ 7.0) and salt concentrations (0.5 ∼ 2.0%) at static temperatures (10 ∼ 20°C). The probability of the end of λ was modeled using dichotomous judgments obtained at each OD measurement point concerning whether a significant increase had been observed. The probability of the end of λ was described as a function of time, temperature, pH, and salt concentration and showed a high goodness of fit. The λ model was validated with independent data sets of B. cereus growth in culture media and foods, indicating acceptable performance. Furthermore, the λ model, in combination with a logistic differential equation, enabled a simulation of the population of B. cereus in various foods over time at static and/or fluctuating temperatures with high accuracy. Thus, this newly developed modeling procedure enables the description of λ using observable environmental parameters without any conceptual assumptions and the simulation of bacterial numbers over time with the use of a logistic differential equation.

Population heterogeneity of Lactobacillus plantarum WCFS1 microcolonies in response to and recovery from acid stress

Within an isogenic microbial population in a homogenous environment, individual bacteria can still exhibit differences in phenotype. Phenotypic heterogeneity can facilitate the survival of subpopulations under stress. As the gram-positive bacterium Lactobacillus plantarum grows, it acidifies the growth medium to a low pH. We have examined the growth of L. plantarum microcolonies after rapid pH downshift (pH 2 to 4), which prevents growth in liquid culture. This acidification was achieved by transferring cells from liquid broth onto a porous ceramic support, placed on a base of low-pH MRS medium solidified using Gelrite. We found a subpopulation of cells that displayed phenotypic heterogeneity and continued to grow at pH 3, which resulted in microcolonies dominated by viable but elongated (filamentous) cells lacking septation, as determined by scanning electron microscopy and staining cell membranes with the lipophilic dye FM4-64. Recovery of pH-stressed cells from these colonies was studied by inoculation onto MRS-Gelrite-covered slides at pH 6.5, and outgrowth was monitored by microscopy. The heterogeneity of the population, calculated from the microcolony areas, decreased with recovery from pH 3 over a period of a few hours. Filamentous cells did not have an advantage in outgrowth during recovery. Specific regions within single filamentous cells were more able to form rapidly dividing cells, i.e., there was heterogeneity even within single recovering cells.

Influence of environmental stress on distributions of times to first division in Escherichia coli populations, as determined by digital-image analysis of individual cells

The distributions of times to first cell division were determined for populations of Escherichia coli stationary-phase cells inoculated onto agar media. This was accomplished by using automated analysis of digital images of individual cells growing on agar and calculation of the "box area ratio." Using approximately 300 cells per experiment, the mean time to first division and standard deviation for cells grown in liquid medium at 37 degrees C and inoculated on agar and incubated at 20 degrees C were determined as 3.0 h and 0.7 h, respectively. Distributions were observed to tail toward the higher values, but no definitive model distribution was identified. Both preinoculation stress by heating cultures at 50 degrees C and postinoculation stress by growth in the presence of higher concentrations of NaCl increased mean times to first division. Both stresses also resulted in an increase in the spread of the distributions that was proportional to the mean division time, the coefficient of variation being constant at approximately 0.2 in all cases. The "relative division time," which is the time to first division for individual cells expressed in terms of the cell size doubling time, was used as measure of the "work to be done" to prepare for cell division. Relative division times were greater for heat-stressed cells than for those growing under osmotic stress.

Quantitative analysis of population heterogeneity of the adaptive salt stress response and growth capacity of Bacillus cereus ATCC 14579

Bacterial populations can display heterogeneity with respect to both the adaptive stress response and growth capacity of individual cells. The growth dynamics of Bacillus cereus ATCC 14579 during mild and severe salt stress exposure were investigated for the population as a whole in liquid culture. To quantitatively assess the population heterogeneity of the stress response and growth capacity at a single-cell level, a direct imaging method was applied to monitor cells from the initial inoculum to the microcolony stage. Highly porous Anopore strips were used as a support for the culturing and imaging of microcolonies at different time points. The growth kinetics of cells grown in liquid culture were comparable to those of microcolonies grown upon Anopore strips, even in the presence of mild and severe salt stress. Exposure to mild salt stress resulted in growth that was characterized by a remarkably low variability of microcolony sizes, and the distributions of the log(10)-transformed microcolony areas could be fitted by the normal distribution. Under severe salt stress conditions, the microcolony sizes were highly heterogeneous, and this was apparently caused by the presence of both a nongrowing and growing population. After discriminating these two subpopulations, it was shown that the variability of microcolony sizes of the growing population was comparable to that of non-salt-stressed and mildly salt-stressed populations. Quantification of population heterogeneity during stress exposure may contribute to an optimized application of preservation factors for controlling growth of spoilage and pathogenic bacteria to ensure the quality and safety of minimally processed foods.

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.

Modeling individual cell lag time distributions for Listeria monocytogenes

The food industry faces two paradoxical demands: on the one hand, foods need to be microbiologically safe for consumption and on the other hand, consumers want fresh, minimally processed foods. To meet these demands, more insight into the mechanisms of microbial growth is needed, which includes, among others, the microbial lag phase. This is the time needed by bacterial cells to adapt to a new environment (for example, after food product contamination) before starting an exponential growth regime. Since food products are often contaminated with low amounts of pathogenic microorganisms, it is important to know the distribution of these individual cell lag times to make accurate predictions concerning food safety. More precisely, cells with the shortest lag times (i.e., appearing in the left tail of the distribution) are largely decisive for the outgrowth of the population. In this study, an integrated modeling approach is proposed and applied to an existing data set of individual cell lag time measurements of Listeria monocytogenes. In a first step, a logistic modeling approach is applied to predict the fraction of zero-lag cells (which start growing immediately) as a function of temperature, pH, and water activity. For the nonzero-lag cells, the mean and variance of the lag time distribution are modeled with a hyperbolic-type model structure. This mean and variance allow identification of the parameters of a two-parameter Weibull distribution, representing the nonzero-lag cell lag time distribution. The integration of the developed models allows prediction of a global distribution of individual cell lag times for any combination of environmental conditions in the interpolation domain of the original temperature, pH, and water activity settings. The global fitting quality of the model is quantified using several measures indicating that the model gives accurate predictions, erring slightly on the fail-safe side when predicting the shortest lag times.

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.