Integrated kinetic and probabilistic modeling of the growth potential of bacterial populations

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.

Establishing equivalence for microbial-growth-inhibitory effects ("iso-hurdle rules") by analyzing disparate listeria monocytogenes data with a gamma-type predictive model

Preservative factors act as hurdles against microorganisms by inhibiting their growth; these are essential control measures for particular food-borne pathogens. Different combinations of hurdles can be quantified and compared to each other in terms of their inhibitory effect ("iso-hurdle"). We present here a methodology for establishing microbial iso-hurdle rules in three steps: (i) developing a predictive model based on existing but disparate data sets, (ii) building an experimental design focused on the iso-hurdles using the model output, and (iii) validating the model and the iso-hurdle rules with new data. The methodology is illustrated with Listeria monocytogenes. Existing data from industry, a public database, and the literature were collected and analyzed, after which a total of 650 growth rates were retained. A gamma-type model was developed for the factors temperature, pH, a(w), and acetic, lactic, and sorbic acids. Three iso-hurdle rules were assessed (40 logcount curves generated): salt replacement by addition of organic acids, sorbic acid replacement by addition of acetic and lactic acid, and sorbic acid replacement by addition of lactic/acetic acid and salt. For the three rules, the growth rates were equivalent in the whole experimental domain (γ from 0.1 to 0.5). The lag times were also equivalent in the case of mild inhibitory conditions (γ ≥ 0.2), while they were longer in the presence of salt than acids under stress conditions (γ < 0.2). This methodology allows an assessment of the equivalence of inhibitory effects without intensive data generation; it could be applied to develop milder formulations which guarantee microbial safety and stability.

Modeling the effect of storage atmosphere on growth-no growth interface of Listeria monocytogenes as a function of temperature, sodium lactate, sodium diacetate, and NaCl

The effect of aerobic and anaerobic conditions on growth initiation by a 10-strain composite of Listeria monocytogenes (10(4) CFU/ml) was evaluated in tryptic soy broth with 0.6% yeast extract (TSBYE) as a function of 220 combinations of pH (3.82 to 7.42), sodium lactate (SL) (0 to 10%, vol/vol), and sodium diacetate (SD) (0 to 0.5%, wt/vol) at 10 or 30 degrees C (a slightly abusive and the optimal growth temperature, both above the growth limiting range of 0 to 3 degrees C for L. monocytogenes) in 96-well microplates. In addition, four probability-of-growth models were developed to quantify the effect of 346 aerobic and 346 anaerobic combinations of temperature (4 to 30 degrees C), SL (0 to 6%, vol/vol), and SD (0 to 0.5%, wt/vol) in the presence of NaCl (0.5 or 2.5%, wt/vol) on the growth-no growth responses of the same L. monocytogenes strain composite, with a microplate reader. Growth responses were evaluated turbidimetrically (620 nm) every 5 days for a total of 40 days. Data were modeled with logistic regression to determine the growth-no growth interfaces. The minimum pH values at which growth of L. monocytogenes occurred were higher under anaerobic than under aerobic conditions, and this difference was more evident at 10 degrees C or at higher SL and SD concentrations. The MIC of SD decreased with increasing SL levels. Anaerobic storage reduced the levels of SL-SD, allowing the growth of L. monocytogenes compared with aerobic storage, especially at low temperatures. In the presence of 2.5% NaCl, the MICs for SD were lower than those obtained with 0.5% NaCl, especially at 4 and 10 degrees C, or in the presence of 5 to 6% SL. The developed models for anaerobic incubation showed good performance (80% successful predictions; i.e., in 40 of 50 comparisons) with independent data from studies on survival-growth of L. monocytogenes on meat products. The study provides quantitative data on the antimicrobial activity of SL (0 to 10%) and SD (0 to 0.5%), temperature (4 to 30 degrees C), and pH (3.82 to 7.42) and on the probability of growth of L. monocytogenes under anaerobic or aerobic conditions in the presence of 0.5 or 2.5% NaCl, and hence, addresses important needs for risk assessment activities.

Modelling of the growth–no growth interface of Issatchenkia occidentalis, an olive spoiling yeast, as a function of the culture media, NaCl, citric and sorbic acid concentrations: Study of its inactivation in the no growth region

A global logistic model incorporating a dummy variable for the growth medium (laboratory media or table olives brine) was used for the estimation of the growth-no growth interface of Issatchenkia occidentalis as a function of NaCl, citric and sorbic acid concentrations. The model permitted the deduction of the region where the combination of citric and sorbic acids in laboratory media (above 0.3% and 0.03% wt/vol, respectively) and brine (above 0.1% and 0.03% wt/vol), at 5% NaCl, inhibited the growth of the yeast. Subsequently, the model was validated in laboratory media within the no growth region by a response surface D-optimal design. Inactivation concentrations of sorbic acid produced a progressive loss of viability in I. occidentalis that followed a first order kinetic or downward concave inactivation curves, depending on environmental variables. These curves were properly described by a (primary) model deduced from the Weibull distribution, whose parameters, first decimal reduction time (D(beta)) and shape (beta), were expressed as a function of sorbic acid concentrations (secondary model). At 5% NaCl and within the experimental region checked, an increase of 0.010% and 0.008% sorbic acid reduced D(beta) in 10 h and decrease beta by 10%. Finally, the model was also validated in real "seasoned" table olives packing reporting a complete inactivation of the yeasts' population.

The use of a D-optimal design to model the effects of temperature, NaCl, type and acid concentration on Lactobacillus pentosus IGLAC01

AIMS

To study the effects of temperature, NaCl and acid (HCl, citric, acetic and lactic) concentrations on the specific growth rate (mu), lag phase (lambda), and h0 of Lactobacillus pentosus IGLAC01.

METHODS AND RESULTS

Response surface (RS) methodology (D-optimal design) was used with a dummy variable, to account for the different types of acids. The variable ranges were: 16-30 degrees C, 0-70 g l-1 NaCl, and 0-5 g l-1 acid (or 0-2.5 g l-1 HCl). Time to detection from optical density data was used to deduce mu and lambda. The RS models for log2mu and log2lambda, according to acid types, were estimated and the effects of variables were quantified by their z-generalized values. A relationship between ln h0 with temperature was also found.

CONCLUSIONS

The mu of L. pentosus IGLAC01 can be doubled by increasing temperature by 10.3 degrees C or by decreasing NaCl by 48 g l-1 (harmonic, averaged, z values, Z); citric was the least inhibitory acid (zmu=-96.2) and lactic the strongest (zmu=-5.7), according to their generalized z values, z. A twofold lambda increase was achieved from a decrease of 3.1 degrees C (HCl), or 4.27 degrees C (citric) or 36 g l-1 NaCl increase (both acids) (expressed as zlambda ); the same effect was obtained from a decrease of 4.37 degrees C, 54 g l-1 NaCl increase, or 10 g l-1 acetic or lactic acid additions (expressed as Zlambda values).

SIGNIFICANCE AND IMPACT OF THE STUDY

Valuable information on the effects of environmental variables on the biological parameters of L. pentosus IGLAC01, which could be used for the optimization of olive, cucumber or other vegetable fermentations, is obtained.

Relationship between time-to-detection (TTD) and the biological parameters of Pichia anomala IG02; modelling of TTD as a function of temperature, NaCl concentration, and pH and quantification of their effects

The time to detection (TTD) for Pichia anomala IG02 was defined, for inoculum sizes lower than 6 log(10)cfu/ml, as the time elapsed from inoculation to the moment at which an OD of 0.12 was reached. In other cases, TTD can be estimated by interpolation within the time elapsed from the previous readings below OD=0.12 and the next above it. A linear relationship, which depended on the inoculum size, between lnTTD with ln lambda and ln mu(m) was found. These relationships can be used to estimate the biological parameters of cultures with low inoculum levels. In addition, TTD for P. anomala IG02 could be modelled as a function of environmental conditions. The model can also be applied to lambda and mu(m) through their relationships with TTD. The effects of temperature, NaCl content and pH were quantified by the generalized z-values. An increase of 5.97 in NaCl concentration, a decrease of 1.97 units of pH, or a decrease of 6.08 degrees C doubled the TTD or caused a 2.53-fold increase in lambda and a 2.56-fold decrease in the mu(m).

Growth rate and growth probability of Listeria monocytogenes in dairy, meat and seafood products in suboptimal conditions

AIMS

To evaluate the performances of models predicting the growth rate or the growth probability of Listeria monocytogenes in food.

METHODS AND RESULTS

Cardinal and square root type models including or not interactions between environmental factors and probability models were evaluated for their ability to describe the behaviour of L. monocytogenes in liquid dairy products, cheese, meat and seafood products. Models excluding interactions seemed sufficient to predict the growth rate of L. monocytogenes. However, the accurate prediction of growth/no-growth limits needed to take interactions into account. A complete and a simplified form (preservatives deducted) of a new cardinal model including interactions and parameter values were suggested to predict confidence limits for the growth rate of L. monocytogenes in food. This model could also be used for the growth probability prediction.

CONCLUSIONS

The new cardinal model including interactions was efficient to predict confidence limits for the growth rate of L. monocytogenes and its growth probability in liquid dairy products, meat and seafood products. In cheese, the model was efficient to predict the absence of growth of the pathogen.

SIGNIFICANCE AND IMPACT OF THE STUDY

The suggested model can be used for risk assessment and risk management concerning L. monocytogenes in dairy, meat and seafood products.

Use of the generalized z-value concept to study the effects of temperature, NaCl concentration and pH on Pichia anomala, a yeast related to table olive fermentation

The effects of temperature, NaCl concentration and pH on the growth and lag phase time of Pichia anomala was studied by means of a central composite design. From the response surface obtained, using log2 transformations of maximum specific growth rates (mu) and lag times (lambda) as responses, it was deduced that mu depended on the temperature (linear and quadratic effects); while lambda was affected (linear effects) by the three variables. The relative effects of variables were studied by means of the generalized z-value. The results for mu were: Ztemp, mu (harmonic average of ztemp, mu)=6.90, zNaCl, mu=-5.61. The values for lambda were: ztemp, lambda=-4.87, zNaCl, lambda=3.36, and zpH, lambda=-1.08. The product of the specific growth rate and the lag, h0 (the "work to be done" during the lag phase) depended (p<0.05) on pH. The effects of NaCl and temperature on h0 were not significant though they produced a 1.32- and 1.23-fold increase on it.

Effect of chemicals on the microbial evolution in foods

In contrast with most chemical hazardous compounds, the concentration of food pathogens changes during processing, storage, and meal preparation, making it difficult to estimate the number of microorganisms or the concentration of their toxins at the moment of ingestion by the consumer. These changes are attributed to microbial proliferation, survival, and/or inactivation and must be considered when exposure to a microbial hazard is assessed. The number of microorganisms can also change as a result of physical removal, mixing of food ingredients, partitioning of a food product, or cross-contamination (M. J. Nauta. 2002. Int. J. Food Microbiol. 73:297-304). Predictive microbiology, i.e., relating these microbial evolutionary patterns to environmental conditions, can therefore be considered a useful tool for microbial risk assessment, especially in the exposure assessment step. During the early development of the field (late 1980s and early 1990s), almost all research was focused on the modeling of microbial growth over time and the influence of temperature on this growth. Later, modeling of the influence of other intrinsic and extrinsic parameters garnered attention. Recently, more attention has been given to modeling of the effects of chemicals on microbial inactivation and survival. This article is an overview of different applied strategies for modeling the effect of chemical compounds on microbial populations. Various approaches for modeling chemical growth inhibition, the growth-no growth interface, and microbial inactivation by chemicals are reviewed.

Analysis and validation of a predictive model for growth and death of Aeromonas hydrophila under modified atmospheres at refrigeration temperatures

Specific growth and death rates of Aeromonas hydrophila were measured in laboratory media under various combinations of temperature, pH, and percent CO(2) and O(2) in the atmosphere. Predictive models were developed from the data and validated by means of observations obtained from (i) seafood experiments set up for this purpose and (ii) the ComBase database (http://www.combase.cc; http://wyndmoor.arserrc.gov/combase/). Two main reasons were identified for the differences between the predicted and observed growth in food: they were the variability of the growth rates in food and the bias of the model predictions when applied to food environments. A statistical method is presented to quantitatively analyze these differences. The method was also used to extend the interpolation region of the model. In this extension, the concept of generalized Z values (C. Pin, G. García de Fernando, J. A. Ordóñez, and J. Baranyi, Food Microbiol. 18:539-545, 2001) played an important role. The extension depended partly on the density of the model-generating observations and partly on the accuracy of extrapolated predictions close to the boundary of the interpolation region. The boundary of the growth region of the organism was also estimated by means of experimental results for growth and death rates.