A. Métris

Use of Optical Density Detection Times To Assess the Effect of Acetic Acid on Single-Cell Kinetics

ABSTRACT The growth of Listeria innocua at different acetic acid concentrations (0 to 2,000 ppm) was monitored by optical density measurements in a Bioscreen (Labsystems, Vantaa, Finland). The generated populations came from low inocula that were obtained by serial dilution. A new method to estimate both the growth rate and the lag time of single cells from the detection times (time to reach an optical density of 0.11) was developed. It assumes that the single-cell lag times follow a gamma distribution and takes into account the randomness of the inoculation level. (The initial cell number per well was assumed to follow a Poisson distribution.) In this way, relatively small numbers of replicates are sufficient to obtain a robust estimation of the distribution of single-cell lag times. The results were validated with plate count experiments. It was found that logarithms of both the growth rates and of population lag times increased linearly with the acetic acid concentration. The logarithm of the scale parameter of the gamma distribution of the single-cell lag times also increased linearly with the acetic acid concentration irrespective of the phase of the inoculum.

Modeling the Variability of Single-Cell Lag Times for Listeria innocua Populations after Sublethal and Lethal Heat Treatments

ABSTRACT Optical density measurements were used to estimate the effect of heat treatments on the single-cell lag times of Listeria innocua fitted to a shifted gamma distribution. The single-cell lag time was subdivided into repair time (the shift of the distribution assumed to be uniform for all cells) and adjustment time (varying randomly from cell to cell). After heat treatments in which all of the cells recovered (sublethal), the repair time and the mean and the variance of the single-cell adjustment time increased with the severity of the treatment. When the heat treatments resulted in a loss of viability (lethal), the repair time of the survivors increased with the decimal reduction of the cell numbers independently of the temperature, while the mean and variance of the single-cell adjustment times remained the same irrespective of the heat treatment. Based on these observations and modeling of the effect of time and temperature of the heat treatment, we propose that the severity of a heat treatment can be characterized by the repair time of the cells whether the heat treatment is lethal or not, an extension of the F value concept for sublethal heat treatments. In addition, the repair time could be interpreted as the extent or degree of injury with a multiple-hit lethality model. Another implication of these results is that the distribution of the time for cells to reach unacceptable numbers in food is not affected by the time-temperature combination resulting in a given decimal reduction.

Lag Phase of Salmonella enterica under Osmotic Stress Conditions

ABSTRACT Salmonella enterica serovar Typhimurium was grown at salt concentrations ranging from 0.5 to 7.5% in minimal medium with and without added osmoprotectant and in a rich medium. In minimal medium, the cells showed an initial decline period, and consequently the definition of the lag time of the resultant log count curve was revised. The model of Baranyi and Roberts (Int. J. Food Microbiol. 23:277-294, 1994) was modified to take into account the initial decline period, based on the assumption that the log count curve of the total population was the sum of a dying and a surviving-then-growing subpopulation. The lag time was defined as the lag of the surviving subpopulation. It was modeled by means of a parameter quantifying the biochemical work the surviving cells carry out during this phase, the “work to be done.” The logarithms of the maximum specific growth rates as a function of the water activity in the three media differed only by additive constants, which gave a theoretical basis for bias factors characterizing the relationships between different media. Models for the lag and the “work to be done” as a function of the water activity showed similar properties, but in rich medium above 5% salt concentrations, the data showed a maximum for this work. An accurate description of the lag time is important to avoid food wastage, which is an issue of increasing significance in the food industry, while maintaining food safety standards.

Lag phase of Salmonella under osmotic stress

ABSTRACT Salmonella enterica serovar Typhimurium was grown at salt concentrations ranging from 0.5 to 7.5% in minimal medium with and without added osmoprotectant and in a rich medium. In minimal medium, the cells showed an initial decline period, and consequently the definition of the lag time of the resultant log count curve was revised. The model of Baranyi and Roberts (Int. J. Food Microbiol. 23:277-294, 1994) was modified to take into account the initial decline period, based on the assumption that the log count curve of the total population was the sum of a dying and a surviving-then-growing subpopulation. The lag time was defined as the lag of the surviving subpopulation. It was modeled by means of a parameter quantifying the biochemical work the surviving cells carry out during this phase, the “work to be done.” The logarithms of the maximum specific growth rates as a function of the water activity in the three media differed only by additive constants, which gave a theoretical basis for bias factors characterizing the relationships between different media. Models for the lag and the “work to be done” as a function of the water activity showed similar properties, but in rich medium above 5% salt concentrations, the data showed a maximum for this work. An accurate description of the lag time is important to avoid food wastage, which is an issue of increasing significance in the food industry, while maintaining food safety standards.

Modelling osmotic stress by Flux Balance Analysis at the genomic scale

Predictive microbiology for food safety is still primarily based on empirical models describing the effect of the environmental conditions of the food on the kinetics of the growth of foodborne pathogens. One way to make these models more mechanistic is to use systems biology methods such as Flux Balance Analysis (FBA). FBA consists of evaluating the possible fluxes through the metabolic reactions taking place in a cell. Using this method, the specific growth rate of Escherichia coli can be predicted by assuming, as an objective function, that the cells maximise their biomass production during balanced growth. Whilst this works under favourable environmental conditions, our simulations show that this objective function is not sufficient to explain the decrease of the growth rate due to osmotic stress. One feature of the FBA models is that the parameters and objective function in general refer to chemostat experiments where the carbon source is the main limiting factor. This may be relevant to some foods where the carbon to nitrogen balance is limiting but, in general, it is the physico-chemical conditions which are the most stringent. We therefore need to examine the effect of such constraints on the fluxes and/or modify the objective function, or to elaborate the metabolic model by taking into account other functional levels of the cell in order to develop mechanistic predictive models for osmotic stress conditions.

Physiological state of single cells of Listeria innocua in organic acids

The growth of Listeria innocua in three organic acids was monitored by optical density measurements in a Bioscreen C automatic plate reader (Labsystems, Finland). The method described by Metris et al. [Metris, A., George, S.M., Baranyi, J., 2006. Use of optical density detection times to assess the effect of acetic acid on single-cell kinetics. Applied and Environmental Microbiology 72, 6674-6679.], was used to estimate both the growth rate and the lag time of single cells. It was found that the logarithm of both the growth rates and the population lag times increased linearly with sorbic acid concentration in the same way as previously described with acetic acid but the relationship was not linear with lactic acid. Of the three acids tested, sorbic was the most inhibitory for an equivalent undissociated acid concentration. The effect of lactic acid was dependent on both the growth phase of the inoculum and the inoculum concentration.

Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens

Addition of salt to food is one of the most ancient and most common methods of food preservation. However, little is known of how bacterial cells adapt to such conditions. We propose to use piecewise linear approximations to model the regulatory adaptation of Escherichiacoli to osmotic stress. We apply the method to eight selected genes representing the functions known to be at play during osmotic adaptation. The network is centred on the general stress response factor, sigma S, and also includes a module representing the catabolic repressor CRP-cAMP. Glutamate, potassium and supercoiling are combined to represent the intracellular regulatory signal during osmotic stress induced by salt. The output is a module where growth is represented by the concentration of stable RNAs and the transcription of the osmotic gene osmY. The time course of gene expression of transport of osmoprotectant represented by the symporter proP and of the osmY is successfully reproduced by the network. The behaviour of the rpoS mutant predicted by the model is in agreement with experimental data. We discuss the application of the model to food-borne pathogens such as Salmonella; although the genes considered have orthologs, it seems that supercoiling is not regulated in the same way. The model is limited to a few selected genes, but the regulatory interactions are numerous and span different time scales. In addition, they seem to be condition specific: the links that are important during the transition from exponential to stationary phase are not all needed during osmotic stress. This model is one of the first steps towards modelling adaptation to stress in food safety and has scope to be extended to other genes and pathways, other stresses relevant to the food industry, and food-borne pathogens. The method offers a good compromise between systems of ordinary differential equations, which would be unmanageable because of the size of the system and for which insufficient data are available, and the more abstract Boolean methods.

Bacterial economics: adaptation to stress conditions via stage-wise changes in the response mechanism.

Common features of microbial adaptation are analysed with mathematical models and extended to stress conditions when the bacterial population declines before growing again. A parallel is drawn between bacterial and human communities in terms of non-mutation-based adaptation (acclimation) to stress. For a case study, the behaviour of Escherichia coli under osmotic stress, is detailed. It is suggested that stress modelling adaptation should be the focus of further developments in predictive food microbiology.

Integrated Kinetic and Probabilistic Modeling of the Growth Potential of Bacterial Populations

ABSTRACT When bacteria are exposed to osmotic stress, some cells recover and grow, while others die or are unculturable. This leads to a viable count growth curve where the cell number decreases before the onset of the exponential growth phase. From such curves, it is impossible to estimate what proportion of the initial cells generates the growth because it leads to an ill-conditioned numerical problem. Here, we applied a combination of experimental and statistical methods, based on optical density measurements, to infer both the probability of growth and the maximum specific growth rate of the culture. We quantified the growth potential of a bacterial population as a quantity composed from the probability of growth and the “suitability” of the growing subpopulation to the new environment. We found that, for all three laboratory media studied, the probability of growth decreased while the “work to be done” by the growing subpopulation (defined as the negative logarithm of their suitability parameter) increased with NaCl concentration. The results suggest that the effect of medium on the probability of growth could be described by a simple shift parameter, a differential NaCl concentration that can be accounted for by the change in the medium composition. Finally, we highlighted the need for further understanding of the effect of the osmoprotectant glycine betaine on metabolism.

Data for the qualitative modeling of the osmotic stress response to NaCl in Escherichia coli

Qualitative modeling approaches allow to provide a coarse-grained description of the functioning of cellular networks when experimental data are scarce and heterogeneous. We translate the primary literature data on the response of Escherichia coli to hyperosmotic stress caused by NaCl addition into a piecewise linear (PL) model. We provide a data file of the qualitative model, which can be used for simulation of changes of protein concentrations and of DNA coiling during the physiological response of the bacterium to the stress. The qualitative model predictions are directly comparable to the available experimental data. This data is related to the research article entitled “Piecewise linear approximations to model the dynamics of adaptation to osmotic stress by food-borne pathogens” (Metris et al., 2016) [1].