Cardinal models to describe the effect of temperature and pH on the growth of Anoxybacillus flavithermus & Bacillus licheniformis.

Anoxybacillus flavithermus and Bacillus licheniformis are among the predominant spore-formers of heat-processed foods. To our knowledge, no systematic analysis of growth kinetic data of A. flavithermus or B. licheniformis is currently available. In the present study, the growth kinetics of A. flavithermus and B. licheniformis in broth at various temperature and pH conditions were studied. Cardinal models were used to model the effect of the above-mentioned factors on the growth rates. The estimated values for the cardinal parameters Tmin,Topt,Tmax,pHmin and pH1/2 for A. flavithermus were 28.70 ± 0.26, 61.23 ± 0.16 and 71.52 ± 0.32 °C, 5.52 ± 0.01 and 5.73 ± 0.01, respectively, while for B. licheniformis they were 11.68 ± 0.03, 48.05 ± 0.15, 57.14 ± 0.01 °C, 4.71 ± 0.01 and 5.670 ± 0.08, respectively. The growth behaviour of these spoilers was also investigated in a pea beverage at 62 and 49 °C, respectively, to adjust the models to this product. The adjusted models were further validated at static and dynamic conditions and demonstrated good performance with 85.7 and 97.4% of predicted populations for A. flavithermus and B. licheniformis, respectively, being within the -10%-10% relative error (RE) zone. The developed models can be useful tools in assessing the potential of spoilage of heat-processed foods including plant-based milk alternatives.

Modelling the thermal inactivation of spores from different phylogenetic groups of Bacillus cereus.

The objective of this work is to match available phylogenetic information for Bacillus cereus strains with published thermal resistance parameters (D90°C, z) and to use this information to develop refined inactivation models for B. cereus sensu lato. To do so, the thermal resistance parameters were retrieved for 57 strains of B. cereus that could be assigned to a phylogenetic group. This information was used to build specific distributions for D90°C and z for the different phylogenetic groups of B. cereus to build refined thermal inactivation models for B. cereus. For validation purposes, thermal parameters were also retrieved for additional strains of unknown groups, but which had been classified as psychrotrophic or mesophilic. Monte Carlo simulations were first performed assuming that the model parameters D90°C and z are independent. However, based on the observation that combinations of very high D90°C and high z-values were not reported, an alternative Monte Carlo simulation set was explored for the phylogenetic Groups with very high z-values (i.e.i.e. Groups IV and VI). With both simulation sets, the predicted lower and upper limits of the D-values are close to the lowest and highest D-values reported in two previous meta-analysis studies. However, a better correspondence between the predicted and observed limits is obtained when using the alternative simulation set.

Predicting B. cereus growth and cereulide production in dairy mix.

This study aims to quantify growth and cereulide production by Bacillus cereus and their potential correlation in an intermediate dairy wet-mix. Systematic experiments were carried out using the emetic reference strain F4810/72 in the suboptimal range of temperature of 12 °C to 20 °C. Growth and cereulide kinetic parameters were estimated and the three parameters (i) time to first cereulide quantification (tcer), (ii) maximum specific growth rates (µmax) and (iii) cereulide production rates (k) were modelled as a function of temperature. As temperature increased, growth lag time and tcer were shorter while microbial increase and cereulide production happened earlier, and at higher rates. Maximum concentration of cells and maximum cereulide concentration proved to be temperature-independent, reaching the average values of 7.9 ± 0.3 log10(CFU/mL) and 2.6 ± 0.2 log10(ng.g-1) respectively. Moreover, the time to reach the widely used threshold of 5 log10CFU/mL (t5log) was tested against tcer, and this suggested that this threshold can be used with increased confidence at lower temperatures to assure toxin is not quantified in this matrix. The average tcer were equal to 314 h, 118 h, 73 h and 45 h for 12 °C, 15 °C, 18 °C and 20 °C respectively. A validation study was performed using independent data sets obtained with the same strain in other dairy matrices. The microbial growth models presented good predictive power even when extrapolated beyond the temperature range of construction. Nevertheless, the models proposed for prediction of toxin production over time presented limitations, especially for food matrices that deviate significantly from the original matrix for which the model was developed, making cereulide predictions less accurate. Our findings suggest that similar modelling approaches can be used to predict growth, time to first cereulide quantification as well as cereulide formation over time for a specific matrix, but that matrix-extrapolations are more suitable for growth than for cereulide.

Corrigendum: Modeling Bacillus cereus Growth and Cereulide Formation in Cereal-, Dairy-, Meat-, Vegetable-Based Food and Culture Medium.

[This corrects the article DOI: 10.3389/fmicb.2021.639546.].

The effect of pH on the growth rate of Bacillus cereus sensu lato: Quantifying strain variability and modelling the combined effects of temperature and pH.

In this study, the effect of pH, alone or in combination with temperature, on the maximum growth rate (µmax) of B. cereus sensu lato was investigated. In phase 1, the effect of pH at 30 °C was studied for 16 mesophilic strains and 2 psychrotrophic strains of Bacillus cereus sensu lato. The µmax vs. pH relationship was found to show a similar pattern for all the strains. Several pH models from literature were evaluated and the best performing 'growth rate vs. pH' model selected. A stochastic model was then developed to predict the maximum specific growth rate of mesophilic B. cereus at 30 °C as a function of pH, the intra-species variability being incorporated via considering the model parameters (e.g. pHmin) randomly distributed. The predicted maximum specific growth rates were acceptably close to independent published data. In phase 2, the combined effects of temperature and pH were studied. Growth rates were also generated at 15, 20 and 40 °C for a selection of strains and the pH model was fitted at each temperature. Interestingly, the results showed that the estimates for the pHmin parameter for mesophilic strains were lower at 20-30 °C than near the optimum temperature (40 °C), suggesting that experiments for the determination of this parameter should be conducted at lower-than-optimum temperatures. New equations were proposed for the relationship between temperature and the minimum pH-values, which were also consistent with the experimental growth boundaries. The parameters defining this equation quantify the minimum temperature for growth observed experimentally, the temperature of maximum enzyme stability and the maximum temperature for growth. Deviations from the Gamma hypothesis (multiplicative effects of environmental factors on the maximum specific growth rate) were observed near the growth limits, especially at 40 °C. To improve model performance, two approaches, one based on a minimum pH-term (doi: https://doi.org/10.3389/fmicb.2019.01510) and one based on an interaction term (doi: http://dx.doi.org/10.1016/S0168-1605(01)00640-7) were evaluated.

A stochastic approach for modelling the effects of temperature on the growth rate of Bacillus cereus sensu lato.

A stochastic model that predicts the maximum specific growth rate (µmax) of Bacillus cereus sensu lato as a function of temperature was developed. The model integrates the intra-species variability by incorporating distributions of cardinal parameters (Tmin, Topt, Tmax) in the model. Growth rate data were generated for 22 strains, covering 5 major phylogenetic groups of B. cereus, and their cardinal temperatures identified. Published growth rate data were also incorporated in the model fitting, resulting in a set of 33 strains. Based on their cardinal temperatures, we identified clusters of Bacillus cereus strains that show similar response to temperature and these clusters were considered separately in the stochastic model. Interestingly, the µopt values for psychrotrophic strains were found to be significantly lower than those obtained for mesophilic strains. The model developed within this work takes into account some correlations existing between parameters (µopt, Tmin, Topt, Tmax). In particular, the relationship highlighted between the b-slope of the Ratkowsky model and Tmin (doi: https://doi.org/10.3389/fmicb.2017.01890) was adapted to the case of the popular Cardinal Temperature Model. This resulted in a reduced model in which µopt is replaced by a function of Tmin, Topt and 2 strain-independent parameters. A correlation between the Tmin parameter and the experimental minimal growth temperature was also highlighted and integrated in the model for improved predictions near the temperature growth limits. Compared to the classical approach, the model developed in this study leads to improved predictions for temperatures around Tmin and more realistic tails for the predicted distributions of µmax. It can be useful for describing the variability of the Bacillus cereus Group in Quantitative Microbial Risk Assessment (QMRA). An example of application of the stochastic model to Reconstituted Infant Formulae (RIF) was proposed.

Modeling Bacillus cereus Growth and Cereulide Formation in Cereal-, Dairy-, Meat-, Vegetable-Based Food and Culture Medium.

This study describes the simultaneous Bacillus cereus growth and cereulide formation, in culture medium and cereal-, dairy-, meat-, and vegetable-based food matrices. First, bacterial growth experiments were carried out under a wide range of temperatures (from 9 to 45°C), using the emetic reference strain F4810/72, in the above-mentioned matrices. Then, the generated data were put in a modeling framework where the response variable was a vector of two components: the concentration of B. cereus and that of its toxin, cereulide. Both were considered time-, temperature- and matrix-dependent. The modeling was carried out in a series of steps: the parameters fitted in one step became the response variable of the following step. Using the square root link function, the maximum specific growth rate of the organism and the time to the appearance of quantifiable cereulide were modeled against temperature by cardinal parameters models (CPM), for each matrix. Finally, a validation study was carried out on an independent data set obtained in the same matrices and using various Bacillus cereus strains. Results showed that both growth and toxin-formation depended on the food matrix and on the environment but not in the same way. Thus, the matrix (culture medium), where the highest growth rate of B. cereus was observed, was not the medium where the shortest time to quantifiable cereulide occurred. While the cereal-based matrix generated the smallest growth rates (0.41-times smaller than culture medium did), quantifiable cereulide appeared in it at earlier times compared to the other tested matrices. In fact, three groups of matrices could be distinguished based on their ability to support cereulide formation (1) the cereal-based matrix (highest), (2) the culture medium and the dairy-based matrix (intermediate), and (3) the meat- and vegetable-based matrices (lowest). This ranking between the matrices is quite different from that based on their suitability to the growth of the organism. Our models can be used in HACCP studies, to improve shelf-life predictions and, generally, microbiological food safety assessments of products for which B. cereus is the main concern.

Cardinal parameter meta-regression models describing Listeria monocytogenes growth in broth.

Since Listeria monocytogenes has a high case-fatality rate, substantial research has been devoted to estimate its growth rate under different conditions of temperature, pH and water activity (aw). In this study, published findings on L. monocytogenes growth in broth were extracted and unified by constructing meta-regression models based on cardinal models for (i) temperature (CM[T]), (ii) temperature and pH (CM[T][pH]), and (iii) temperature, pH and aw (CM[T][pH][aw]). After assessing all the sources retrieved between 1988 until 2017, forty-nine primary studies were considered appropriate for inclusion. Apart from the modelling variables, study characteristics such as: type of broth (BHI, TSB, TPB), reading method (colony-forming-units, CFU; or binary-dilution optical density methods, OD), inoculum concentration and strain serotype, were also extracted. Meta-regressions based on CM[T] and CM[T][pH] were fitted on subsets of the 2009 growth rate measures and revealed that type of broth and reading method significantly modulated the cardinal parameter estimates. In the most parsimonious CM[T][pH][aw] meta-regression model, whereby the variability due to type of broth was extracted in a nested random-effects structure, the optimum growth rate µopt of L. monocytogenes was found to be lower when measured as CFU (0.947 log CFU/h; SE = 0.094 log CFU/h) than when measured as OD (1.289 log CFU/h; SE = 0.092 log CFU/h). Such a model produced the following cardinal estimates: Tmin = -1.273 °C (SE = 0.179 °C), Topt = 37.26 °C (SE = 0.688 °C), Tmax = 45.12 °C (SE = 0.013 °C), pHmin = 4.303 (SE = 0.014), pHopt = 7.085 (SE = 0.080), pHmax = 9.483 (SE = 0.080), awmin = 0.894 (SE = 0.002) and awopt = 0.995 (SE = 0.001). Integrating the outcomes from numerous L. monocytogenes growth experiments, this meta-analysis has estimated pooled cardinal parameters that can be used as reference values in quantitative risk assessment studies.

Detoxification Assays of Tunisian Tannery Wastewater under Nonsterile Conditions Using the Filamentous Fungus Aspergillus niger.

The ability of Aspergillus niger strain to reduce organic and mineral pollution as well as the toxicity of two tannery wastewaters, the unhairing effluent (UE) and the final effluent (FE), taken from a local Tunisian tannery and under nonsterile conditions, was studied. Raw effluents show alkaline pH ≥11; thus experiments were carried out at initial pH values and at pH adjusted to 6. Characterization of effluents also revealed high salt levels (EC > 17 mS/cm) and high organic matter content (25 g/L for the UE and 7.2 g/L for the FE) but a low biodegradability since BOD5 did not exceed 2.5 and 1.25 g/L for the UE and the FE, respectively. The results of the biological treatment showed that A. niger was able not only to grow at high pH and salinity values, but also to reduce organic and mineral pollutant load. After treatment, the COD reduction for the UE reached 90% and 70% at pH=6 and at initial pH (12.13), respectively. For the FE, the decrease of COD values reached 75% at pH=6 and 64% at initial pH (11.64). Monitoring of mineral pollution levels showed a reduction in chromium (Cr) concentrations reaching 70% for the FE. This was reflected by an increase of the biomass of A. niger from 9.25 g/L (control) to 9.84 g/L for the FE. To confirm the efficiency of the biological treatment using A. niger, phytotoxicity (tomato seeds) and microtoxicity (Escherichia coli and Bacillus subtilis) tests were carried out. Results of this monitoring showed an important decrease in the toxicity levels for both effluents.

Optimization of turbidity experiments to estimate the probability of growth for individual bacterial cells.

Using turbidity measurements to quantify bacterial growth is a common and well-established practice in microbiology. Automated devices offering high throughput analyses have largely contributed to the increase of its use. A main difficulty of this method is that it detects growth only at late exponential phase, making turbidity measurements limited for studies focussing on low cell numbers. This work proposes an improved estimator for the probability of growth of individual cells using turbidity-based measurements, when the initial number of cells is low and random. We modify the currently used estimator for the expected cell number per well, a Poisson-parameter, and show that an optimal scenario is when ca 20% of the wells do not become turbid, resulting in improved accuracy and precision.

Next generation of microbiological risk assessment: Potential of omics data for exposure assessment.

In food safety and public health risk evaluations, microbiological exposure assessment plays a central role as it provides an estimation of both the likelihood and the level of the microbial hazard in a specified consumer portion of food and takes microbial behaviour into account. While until now mostly phenotypic data have been used in exposure assessment, mechanistic cellular information, obtained using omics techniques, will enable the fine tuning of exposure assessments to move towards the next generation of microbiological risk assessment. In particular, metagenomics can help in characterizing the food and factory environment microbiota (endogenous microbiota and potentially pathogens) and the changes over time under the environmental conditions associated with processing, preservation and storage. The difficulty lies in moving up to a quantitative exposure assessment, because the development of models that enable the prediction of dynamics of pathogens in a complex food ecosystem is still in its infancy in the food safety domain. In addition, collecting and storing the environmental data (metadata) required to inform the models has not yet been organised at a large scale. In contrast, progress in biomarker identification and characterization has already opened the possibility of making qualitative or even quantitative connection between process and formulation conditions and microbial responses at the strain level. In term of modelling approaches, without changing radically the usual model structure, changes in model inputs are expected: instead of (or as well as) building models upon phenotypic characteristics such as for example minimal temperature where growth is expected, exposure assessment models could use biomarker response intensity as inputs. These new generations of strain-level models will bring an added value in predicting the variability in pathogen behaviour. Altogether, these insights based upon omics techniques will increase our (quantitative) knowledge on pathogenic strains and consequently will reduce our uncertainty; the exposure assessment of a specific combination of pathogen and food will be then more accurate. This progress will benefit the whole community of safety assessors and research scientists from academia, regulatory agencies and industry.

Rethinking Tertiary Models: Relationships between Growth Parameters of Bacillus cereus Strains.

The maximum specific growth rates of 12 strains, pair-wise belonging to six groups of Bacillus cereus sensu lato, were fitted against temperature by a reparametrized version of the model of Ratkowsky et al. (1983). This way, the interpretation of the new parameter set was similar to that of the cardinal-values-model of Rosso and Robinson (2001), both models including the minimum, optimum and maximum temperatures for growth as well as a fourth parameter scaling along the dependent variable. The modularity of the reparametrized version of the Ratkowsky model was utilized to show a so-far undetected relationship between this scaling parameter and the cardinal temperatures, which linked even distant (e.g., mesophilic and psychotropic) strains of B. cereus. We propose that the name "tertiary modeling" should be used for investigations like ours, as logically derived from the concepts of "primary" and "secondary" modeling. Such tertiary models may reveal biological relationships between kinetic parameters within a group of strains. It can also be used to create an overarching predictive model for mixed cultures, when different strains grow together but independently of each other.

From Culture-Medium-Based Models to Applications to Food: Predicting the Growth of B. cereus in Reconstituted Infant Formulae.

Predictive models of the growth of foodborne organisms are commonly based on data generated in laboratory medium. It is a crucial question how to apply the predictions to realistic food scenarios. A simple approach is to assume that the bias factor, i.e., the ratio between the maximum specific growth rate in culture medium and the food in question is constant in the region of interest of the studied environmental variables. In this study, we investigate the validity of this assumption using two well-known link functions, the square-root and the natural logarithm, both having advantageous properties when modeling the variation of the maximum specific growth rate with temperature. The main difference between the two approaches appears in terms of the respective residuals as the temperature decreases to its minimum. The model organism was Bacillus cereus. Three strains (B594, B596, and F4810/72) were grown in Reconstituted Infant Formulae, while one of them (F4810/72) was grown also in culture medium to calculate the bias factor. Their growth parameters were estimated using viable count measurements at temperatures ranging from 12 to 25°C. We utilized the fact that, if the bias factor is independent of the temperature, then the minimum growth temperature parameter of the square-root model of Ratkowsky et al. (1982) is the same for culture medium and food. We concluded, supported also by mathematical analysis, that the Ratkowsky model works well but its rearrangement for the natural logarithm of the specific growth rate is more appropriate for practical regression. On the other hand, when analyzing mixed culture data, available in the ComBase database, we observed a trend different from the one generated by pure cultures. This suggests that the identity of the strains dominating the growth of mixed cultures depends on the temperature. Such analysis can increase the accuracy of predictive models, based on culture medium, to food scenarios, bringing significant saving for the food industry.

Extending the gamma concept to non-thermal inactivation: a dynamic model to predict the fate of Salmonella during the dried sausages process.

The process of dried fermented sausages is recognized to be favourable to the reduction of the Salmonella population. The objective of this study was to develop a model describing the evolution of Salmonella during the fabrication process of dried sausages and to optimize the food formulation to prevent pathogen presence at the end of the process. An experimental design was set to investigate the effects of the fermentation and drying process for several formulations, taking into account the type of starter culture, the sodium chloride concentration, the dextrose and lactose concentration on the Salmonella Typhimurium strain behaviour. A growth-inactivation model based on the gamma concept was then developed to quantify Salmonella behaviour in dynamic process conditions of temperature, pH, lactic acid and water activity. This behaviour was characterized by a first growth step, followed by an inactivation step. The Salmonella fate was well described by the model in terms of population size variation and transition from growth to inactivation. The Salmonella behaviour was influenced by the initial sugar concentration and the starter type but not by sodium chloride content. This model can be a valuable tool to design the food process and formulation to control Salmonella.

Software for predictive microbiology and risk assessment: a description and comparison of tools presented at the ICPMF8 Software Fair.

The 8th International Conference on Predictive Modelling in Food was held in Paris, France in September 2013. One of the major topics of this conference was the transfer of knowledge and tools between academics and stakeholders of the food sector. During the conference, a "Software Fair" was held to provide information and demonstrations of predictive microbiology and risk assessment software. This article presents an overall description of the 16 software tools demonstrated at the session and provides a comparison based on several criteria such as the modeling approach, the different modules available (e.g. databases, predictors, fitting tools, risk assessment tools), the studied environmental factors (temperature, pH, aw, etc.), the type of media (broth or food) and the number and type of the provided micro-organisms (pathogens and spoilers). The present study is a guide to help users select the software tools which are most suitable to their specific needs, before they test and explore the tool(s) in more depth.

Global sensitivity analysis applied to a contamination assessment model of listeria monocytogenes in cold smoked salmon at consumption.

In this study, a variance-based global sensitivity analysis method was first applied to a contamination assessment model of Listeria monocytogenes in cold smoked vacuum packed salmon at consumption. The impact of the choice of the modeling approach (populational or cellular) of the primary and secondary models as well as the effect of their associated input factors on the final contamination level was investigated. Results provided a subset of important factors, including the food water activity, its storage temperature, and duration in the domestic refrigerator. A refined sensitivity analysis was then performed to rank the important factors, tested over narrower ranges of variation corresponding to their current distributions, using three techniques: ANOVA, Spearman correlation coefficient, and partial least squares regression. Finally, the refined sensitivity analysis was used to rank the important factors.

Assessment of the impact of excessive chemical additions to municipal wastewaters and comparison of three technologies in the removal performance of pathogens and toxicity.

The removal efficiencies of pathogens such as Salmonella (S), helminths ova (H), protozoan cysts (P), total coliforms (TC), faecal coliforms (FC) and faecal streptococci (FS) by three treatment processes: aerated lagoon (AL), activated sludge (AS) and anaerobic membrane bioreactor (MBR) were evaluated by means of standard microbiological numeration methods. The micro-toxicity and phyto-toxicity of wastewaters were monitored by LUMIStox and germination index (GI) of Lepidium sativum tests. The results of municipal wastewaters receiving industrial effluents such as Sfax and Mahres were compared with other municipal wastewaters receiving mainly domestic effluents such as Ksour-Essaf. The anaerobic MBR allowed an effective removal of 100% for all the microorganisms tested. The average removal of TC, FC, FS, S, H and P was 1.65log(10), 1.42log(10), 1.23log(10), 0.91log(10), 52.23% and 76.15% in AL system and 0.62-0.84log(10), 0.87-0.93log(10), 0.71-0.78log(10), 0.81-2.71log(10), 59-74.1% and 59.84-72.2% in AS processes, respectively. LUMIStox and GI of L. sativum tests demonstrated that Ksour-Essaf wastewater (KW) was fairly toxic, while Sfax wastewater (SW) exhibited a high toxicity. This toxicity caused the inhibition of the anaerobic consortia when the MBR was fed with the SW. Moreover, the COD and the micro-toxicity increased during the day, parallel to the industrial and domestic activities resulting in the toxic character of SW during the day. SW treated in the AL remained toxic whereas the toxicity of KW treated in the AS or in anaerobic MBR decreased considerably. However, the anaerobic MBR showed a high efficiency in removing toxicity for both SW and KW. The quality of the anaerobic MBR permeate largely conforms with the microbiological WHO guidelines for unrestricted irrigation.

Detoxification of Tunisian landfill leachates by selected fungi.

Young landfill leachates (LFL) collected from Djebel Chekir (Tunisia) discharge area were found to be highly loaded with organic matter, ammonia, salts, heavy metals, phenols and hydrocarbons. Despite the possibility of their biodegradability, they represent a threat to the environment and show some resistance to conventional wastewater treatment processes. For these reasons, this study attempted to develop a biological process for the treatment of LFL using selected strains of Trametes trogii, Phanerochaete chrysosporium, Lentinus tigrinus and Aspergillus niger. Experiments were undertaken at different concentrations of the effluent up to 100%. COD removal efficiencies for P. chrysosporium, T. trogii and L. tigrinus were of 68, 79 and 90%, respectively, when LFL underwent a two-fold dilution. COD abatements were accompanied with an important enzyme secretion and a high reduction in the toxicity, expressed as percent bioluminescence inhibition (%BI<20%). Above 50% of LFL, the effluent was toxic to these strains and caused growth inhibition indicating the sensitivity of these strains to concentrated LFL. Comparatively to the other tested strains, A. niger showed to tolerate raw LFL since it grew at 100% of LFL. However, this strain is inefficient in removing phenols and hydrocarbons. Consequently, toxicity abatement was very low (%BI>70%).