Mathematical modelling of the growth rate and lag time for Listeria monocytogenes

Intraspecific variability in cardinal growth temperatures and water activities within a large diversity of Penicillium roqueforti strains

Different strains of a given fungal species may display heterogeneous growth behavior in response to environmental factors. In predictive mycology, the consideration of such variability during data collection could improve the robustness of predictive models. Among food-borne fungi, Penicillium roqueforti is a major food spoiler species which is also used as a ripening culture for blue cheese manufacturing. In the present study, we investigated the intraspecific variability of cardinal temperatures and water activities (a_w), namely, minimal (T_min and a_wmin), optimal (T_opt and a_wopt) and maximal (T_max) temperatures and/or a_w estimated with the cardinal model for radial growth, of 29 Penicillium roqueforti strains belonging to 3 genetically distinct populations. The mean values of cardinal temperatures and a_w for radial growth varied significantly across the tested strains, except for T_max which was constant. In addition, the relationship between the intraspecific variability of the biological response to temperature and a_w and putative genetic populations (based on microsatellite markers) within the selected P. roqueforti strains was investigated. Even though no clear relationship was identified between growth parameters and ecological characteristics, PCA confirmed that certain strains had marginal growth response to temperature or a_w. Overall, the present data support the idea that a better knowledge of the response to abiotic factors such as temperature and a_w at an intraspecific level would be useful to model fungal growth in predictive mycology approaches.

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 (μ_max) 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 (T_min, T_opt, T_max) 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 μ_opt 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 (μ_opt, T_min, T_opt, T_max). In particular, the relationship highlighted between the b-slope of the Ratkowsky model and T_min (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 μ_opt is replaced by a function of T_min, T_opt and 2 strain-independent parameters. A correlation between the T_min 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 T_min and more realistic tails for the predicted distributions of μ_max. 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.

A Study on the Synbiotic Composition of Bifidobacterium bifidum and Fructans from Arctium lappa Roots and Helianthus tuberosus Tubers against Staphylococcus aureus

A number of mechanisms have been proposed explaining probiotics and prebiotics benefit human health, in particular, probiotics have a suppression effect on pathogen growth that can be enhanced with the introduction of prebiotics. In vitro models enhanced with computational biology can be useful for selecting a composition with prebiotics from new plant sources with the greatest synergism. Water extracts from burdock root and Jerusalem artichoke tubers were purified by ultrafiltration and activated charcoal and concentrated on a rotary evaporator. Fructans were precipitated with various concentrations of ethanol. Bifidobacterium bifidum 8 VKPM AC-2136 and Staphylococcus aureus ATCC 43300 strains were applied to estimate the synbiotic effect. The growth of bifidobacteria and staphylococci in monocultures and cocultures in broths with glucose, commercial prebiotics, as well as isolated fructans were studied. The minimum inhibitory concentrations (MICs) of lactic and acetic acids for the Staphylococcus strain were determined. A quantitative model joining the formation of organic acids by probiotics as antagonism factors and the MICs of pathogens (as the measure of their inhibition) was tested in cocultures and showed a high predictive value (R2 ≥ 0.86). The synbiotic factor obtained from the model was calculated based on the experimental data and obtained constants. Fructans precipitated with 20% ethanol and Bifidobacterium bifidum have the greater synergism against Staphylococcus.

On habit and habitat

Scientific theories based on mathematical models are frequently used in sciences to reveal natural behaviour of systems and eventually to be able in predicting such behaviour once the system's parameters and relevant conditions are known and can be specified. The integration of accumulated theoretical as well as experimental knowledge allows us to present such a unifying theory underlying the equivalence between habit and habitat in population growth. While the focus of the initial development was derived from microorganisms, the theory is extended to other population types too. The biological interpretation of ‘inertia’ or ‘habit’-based processes is provided as a consequence of this theory, and its relationship to the population ‘resource utilization’ available in the ‘habitat’ is derived. This paper focuses on the link between the ‘resource utilization’, which is related to the ‘habitat’, and ‘biological inertia’, which is related to population ‘habit’. This link extends the context of population growth and predictive modelling of microorganisms.

Development of a model for the alcoholic fermentation of cocoa beans by a Saccharomyces cerevisiae strain

The aromatic quality of chocolate requires the use of cocoa with high aromatic potential, this being acquired during the fermentation of cocoa beans. Traditional fermentation is still often carried out on a small scale with wild strains of yeasts and acetic bacteria and under poorly controlled conditions leading to cocoa quality ranging from best to worst. This study is the first part of a project aiming to control quality of cocoa to produce high aromatic quality chocolate by using a mixed starter of selected strains of yeast and acetic bacteria and by controlling the conditions of fermentation. To achieve this objective, a mathematical model of the alcoholic fermentation of cocoa beans has been developed. The growth, glucose consumption and ethanol production of Saccharomyces cerevisiae LM strain in synthetic broth were modeled for the most important intrinsic (pH, glucose, ethanol, free nitrogen and oxygen levels) and extrinsic (temperature, oxygen level) fermentation parameters. The model was developed by combining the effects of individual conditions in a multiplicative way using the gamma concept. The model was validated in liquid synthetic medium at two different inoculation levels 10⁴ and 10⁶ CFU/mL with an increase in temperature that recorded during spontaneous fermentations. The model clearly shows that the level of inoculation and the speed of the increase in temperature clearly drive yeast growth, while other factors including pH and ethanol, free nitrogen and oxygen levels have no significant impact on yeast growth.

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.

Mathematical modelling of the stress resistance induced in Listeria monocytogenes during dynamic, mild heat treatments

Modelling of stress acclimation induced by thermal inactivation of Listeria monocytogenes under dynamic conditions is analyzed in this work. A mathematical model that separates the effect of the instantaneous temperature from the one of stress acclimation, was used. The model was trained using isothermal inactivation experiments, and one biphasic dynamic treatment with a heating rate of 1 °C/min and a holding phase of 60 °C. These experiments were performed in laboratory media (Tryptic Soy Broth; TSB). The model parameters estimated through these experiments (D₅₅=12.87±0.82min, z=4.58±0.04°C, a=0.11±0.01min^-1, E=0.50±0.01°C and c=1.23±0.03) were successfully used to predict the microbial inactivation for another seven inactivation profiles, with and without a holding phase. Moreover, similar experiments were performed using milk as heating media, obtaining a good agreement between the model predictions and the empirical observations. The results of this study are compatible with the hypothesis that L. monocytogenes is able to develop a physiological response during dynamic treatments that increases its thermal resistance. Also, that the model used can be used to predict microbial inactivation of this microorganism taking into consideration stress acclimation.

Early detection of bacteria using SPR imaging and event counting: experiments with Listeria monocytogenes and Listeria innocua

Foodborne pathogens are of significant concern in the agrifood industry and the development of associated rapid detection and identification methods are of major importance. This paper describes the novel use of resolution-optimized prism-based surface plasmon resonance imaging (RO-SPRI) and data processing for the detection of the foodborne pathogens Listeria monocytogenes and Listeria innocua. With an imaging spatial resolution on the order of individual bacteria (2.7 ± 0.5 μm × 7.9 ± 0.6 μm) over a field of view 1.5 mm2, the RO-SPRI system enabled accurate counting of individual bacteria on the sensor surface. Using this system, we demonstrate the detection of two species of Listeria at an initial concentration of 2 × 102 CFU mL-1 in less than 7 hours. The surface density of bacteria at the point of positive detection was 15 ± 4 bacteria per mm2. Our approach offers great potential for the development of fast specific detection systems based on affinity monitoring.

An Agent-Based Model for Pathogen Persistence and Cross-Contamination Dynamics in a Food Facility

We used an agent-based modeling (ABM) framework and developed a mathematical model to explain the complex dynamics of microbial persistence and spread within a food facility and to aid risk managers in identifying effective mitigation options. The model explicitly considered personal hygiene practices by food handlers as well as their activities and simulated a spatially explicit dynamic system representing complex interaction patterns among food handlers, facility environment, and foods. To demonstrate the utility of the model in a decision-making context, we created a hypothetical case study and used it to compare different risk mitigation strategies for reducing contamination and spread of Listeria monocytogenes in a food facility. Model results indicated that areas with no direct contact with foods (e.g., loading dock and restroom) can serve as contamination niches and recontaminate areas that have direct contact with food products. Furthermore, food handlers' behaviors, including, for example, hygiene and sanitation practices, can impact the persistence of microbial contamination in the facility environment and the spread of contamination to prepared foods. Using this case study, we also demonstrated benefits of an ABM framework for addressing food safety in a complex system in which emergent system-level responses are predicted using a bottom-up approach that observes individual agents (e.g., food handlers) and their behaviors. Our model can be applied to a wide variety of pathogens, food commodities, and activity patterns to evaluate efficacy of food-safety management practices and quantify contamination reductions associated with proposed mitigation strategies in food facilities.

Characterization of damage on Listeria innocua surviving to pulsed light: Effect on growth, DNA and proteome

The effect of pulsed light treatment on the lag phase and the maximum specific growth rate of Listeria innocua was determined in culture media at 7 °C. Fluences of 0.175, 0.350 and 0.525 J/cm² were tested. The lag phase of the survivors increased as fluence did, showing significant differences for all the doses; an 8.7-fold increase was observed at 0.525 J/cm². Pulsed light decreased the maximum specific growth rate by 38% at the same fluence. Both parameters were also determined by time-lapse microscopy at 25 °C in survivors to 0.525 J/cm², with an increase of 13-fold of the lag phase and a 45% decrease of the maximum specific growth rate. The higher the fluence, the higher the variability of both parameters was. To characterize pulsed light damage on L. innocua, the formation of dimers on DNA was assessed, and a proteomic study was undertaken. In cells treated with 0.525 J/cm², cyclobutane pyrimidine dimers and pyrimidine (6-4) pyrimidone photoproducts were detected at 5:1 ratio. Pulsed light induced the expression of three proteins, among them the general stress protein Ctc. Furthermore, treated cells showed an up-regulation of proteins related to metabolism of nucleotides and fatty acids, as well as with translation processes, whereas flagellin and some glucose metabolism proteins were down-regulated. Differences in the proteome of the survivors could contribute to explain the mechanisms of adaptation of L. innocua after pulsed light treatment.

The impact of shelf life on exposure as revealed from quality control data associated with the quargel outbreak

A cluster of 34 human cases of listeriosis was traced to consumption of contaminated quargel cheese, a sour milk specialty sold in Austria, Germany and Czech Republic. Here, we try to assess how many portions were consumed by the Austrian population at a certain contamination level (CL). In total, 1623 cheese lots were produced during the outbreak period resulting in >3 million portions of cheese delivered to the market. From 650 sets of quality control data provided by the food business operator, we reconstructed the contamination scenario over time and identified 84 lots that were found to be positive. With regard to another sixteen lots, a CL was found ranging from one to 3,84 log₁₀ CFU L. monocytogenes/g, measured in product stored between one to 23 days after production. However the number of storage days at home before consumption is unknown. To resolve this issue, we modelled the theoretical CL of the product if consumed either 20, 30, 40 or 50 days post production. We found that 10 lots (approx. 27,350 portions) would have been contaminated at CLs higher than 3 log₁₀ CFU L. monocytogenes/g if all cheese had been consumed after 20 days of storage. This number shifts to 20 lots (approx. 54,700 portions) after 30 days of storage. If all cheese had been consumed at the end of shelf life (50 days of storage), theoretically 242,5 lots would have exceeded a CL of 6 log₁₀ CFU L. monocytogenes/g. We concluded that the extended shelf life given to the product was a driver of the outbreak scenario. It is stunning to note that so few cases were reported in spite of consumers' massive exposure to L. monocytogenes. We hypothesized that a low pathogenicity of both quargel outbreak clones (QOC1 and QOC2) could have contributed to this discrepancy. Our hypothesis was falsified since both strains QOC1 and QOC2 are fully virulent in an oral infection mouse model, showing even higher pathogenicity than the reference strain EGDe.

Listeria monocytogenes contamination of ready-to-eat foods and the risk for human health in the EU

Food safety criteria for Listeria monocytogenes in ready-to-eat (RTE) foods have been applied from 2006 onwards (Commission Regulation (EC) 2073/2005). Still, human invasive listeriosis was reported to increase over the period 2009-2013 in the European Union and European Economic Area (EU/EEA). Time series analysis for the 2008-2015 period in the EU/EEA indicated an increasing trend of the monthly notified incidence rate of confirmed human invasive listeriosis of the over 75 age groups and female age group between 25 and 44 years old (probably related to pregnancies). A conceptual model was used to identify factors in the food chain as potential drivers for L. monocytogenes contamination of RTE foods and listeriosis. Factors were related to the host (i. population size of the elderly and/or susceptible people; ii. underlying condition rate), the food (iii. L. monocytogenes prevalence in RTE food at retail; iv. L. monocytogenes concentration in RTE food at retail; v. storage conditions after retail; vi. consumption), the national surveillance systems (vii. improved surveillance), and/or the bacterium (viii. virulence). Factors considered likely to be responsible for the increasing trend in cases are the increased population size of the elderly and susceptible population except for the 25-44 female age group. For the increased incidence rates and cases, the likely factor is the increased proportion of susceptible persons in the age groups over 45 years old for both genders. Quantitative modelling suggests that more than 90% of invasive listeriosis is caused by ingestion of RTE food containing > 2,000 colony forming units (CFU)/g, and that one-third of cases are due to growth in the consumer phase. Awareness should be increased among stakeholders, especially in relation to susceptible risk groups. Innovative methodologies including whole genome sequencing (WGS) for strain identification and monitoring of trends are recommended.

Modeling Reveals the Role of Aging and Glucose Uptake Impairment in L1A1 Listeria monocytogenes Biofilm Life Cycle

Listeria monocytogenes is a food-borne pathogen that can persist in food processing plants by forming biofilms on abiotic surfaces. The benefits that bacteria can gain from living in a biofilm, i.e., protection from environmental factors and tolerance to biocides, have been linked to the biofilm structure. Different L. monocytogenes strains build biofilms with diverse structures, and the underlying mechanisms for that diversity are not yet fully known. This work combines quantitative image analysis, cell counts, nutrient uptake data and mathematical modeling to provide a mechanistic insight into the dynamics of the structure of biofilms formed by L. monocytogenes L1A1 (serotype 1/2a) strain. Confocal laser scanning microscopy (CLSM) and quantitative image analysis were used to characterize the structure of L1A1 biofilms throughout time. L1A1 forms flat, thick structures; damaged or dead cells start appearing early in deep layers of the biofilm and rapidly and massively loss biomass after 4 days. We proposed several reaction-diffusion models to explain the system dynamics. Model candidates describe biomass and nutrients evolution including mechanisms of growth and cell spreading, nutrients diffusion and uptake and biofilm decay. Data fitting was used to estimate unknown model parameters and to choose the most appropriate candidate model. Remarkably, standard reaction-diffusion models could not describe the biofilm dynamics. The selected model reveals that biofilm aging and glucose impaired uptake play a critical role in L1A1 L. monocytogenes biofilm life cycle.

Modelling the effect of combined antimicrobials: A base model for multiple-hurdles

Combining antimicrobials to reduce microbial growth and to combat the potential impact of antimicrobial resistance is an important subject both in foods and in pharmaceutics. Modelling of combined treatments designed to reduce or eliminate microbial contamination in foods (microbiological predictive modelling) has become commonplace. Two main reference models are used to analyse mixtures: the Bliss Independence and the Loewe reference models (LRM). By using optical density to analyse the growth of Aeromonas hydrophila, Cronobacter sakazakii and Escherichia coli in combined NaCl/NaCl (a mock combination experiment) and combined NaCl/KCl experiments, previous models for combined antimicrobials in foods, based on the Bliss approach, were shown to be inconsistent and that models based on the LRM more applicable. The LRM was shown, however, to be valid only in the specific cases where the concentration exponents of all components in a mixture were identical. This is assured for a mock combination experiment but not for a true mixture. This, essentially, invalidates the LRM as a general reference model. A new model, based on the LRM but allowing for mixed exponents, was used to analyse the combined inhibition data, and concluded that the NaCl/KCl system gave the additive effect expected from literature studies. This study suggests the need to revise current models used to analyse combined effects.

A Computational Study of Amensalistic Control of Listeria monocytogenes by Lactococcus lactis under Nutrient Rich Conditions in a Chemostat Setting

We study a previously introduced mathematical model of amensalistic control of the foodborne pathogen Listeria monocytogenes by the generally regarded as safe lactic acid bacteria Lactococcus lactis in a chemostat setting under nutrient rich growth conditions. The control agent produces lactic acids and thus affects pH in the environment such that it becomes detrimental to the pathogen while it is much more tolerant to these self-inflicted environmental changes itself. The mathematical model consists of five nonlinear ordinary differential equations for both bacterial species, the concentration of lactic acids, the pH and malate. The model is algebraically too involved to allow a comprehensive, rigorous qualitative analysis. Therefore, we conduct a computational study. Our results imply that depending on the growth characteristics of the medium in which the bacteria are cultured, the pathogen can survive in an intermediate flow regime but will be eradicated for slower flow rates and washed out for higher flow rates.

Predictive Model of Listeria Monocytogenes’ Growth Rate Under Different Temperatures and Acids

A response surface model of Listeria monocytogenes’ growth rate was built in this study under different temperatures (10 °C, 15 °C, 20 °C, 25 °C and 30 °C) and acid concentrations: citric acid (0–0.4%) and ascorbic acid (0–0.4%); two ingredients which are often used in the food industry as preservatives. Mathematical validation was performed with additional samples at different conditions within the range of the model, obtaining acceptable values of root mean square error (0.0466), standard error of prediction (18.84%), bias factor (1.05) and accuracy factor (1.16). The inhibitory effect on growth was more effective with citric acid than ascorbic acid, possibly due to the major dissociation of citric acid occurring inside microbial cells. The different conditions considered in the model will potentially allow L. monocytogenes’ response to be predicted in foods having a similar composition to the chemical and physical factors set out in this paper.

Effect of temperature, pH, and water activity on Mucor spp. growth on synthetic medium, cheese analog and cheese

The Mucor genus includes a large number of ubiquitous fungal species. In the dairy environment, some of them play a technological role providing typical organoleptic qualities to some cheeses while others can cause spoilage. In this study, we compared the effect of relevant abiotic factors for cheese production on the growth of six strains representative of dairy technological and contaminant species as well as of a non cheese related strain (plant endophyte). Growth kinetics were determined for each strain in function of temperature, water activity and pH on synthetic Potato Dextrose Agar (PDA), and secondary models were fitted to calculate the corresponding specific cardinal values. Using these values and growth kinetics acquired at 15 °C on cheese agar medium (CA) along with three different cheese types, optimal growth rates (μopt) were estimated and consequently used to establish a predictive model. Contrarily to contaminant strains, technological strains showed higher μopt on cheese matrices than on PDA. Interestingly, lag times of the endophyte strain were strongly extended on cheese related matrices. This study offers a relevant predictive model of growth that may be used for better cheese production control but also raises the question of adaptation of some Mucor strains to the cheese.

Development of Predictive Models for the Growth Kinetics of Listeria monocytogenes on Fresh Pork under Different Storage Temperatures

This study was conducted to develop a predictive model to estimate the growth of Listeria monocytogenes on fresh pork during storage at constant temperatures (5, 10, 15, 20, 25, 30, and 35°C). The Baranyi model was fitted to growth data (log CFU per gram) to calculate the specific growth rate (SGR) and lag time (LT) with a high coefficient of determination (R(2) > 0.98). As expected, SGR increased with a decline in LT with rising temperatures in all samples. Secondary models were then developed to describe the variation of SGR and LT as a function of temperature. Subsequently, the developed models were validated with additional independent growth data collected at 7, 17, 27, and 37°C and from published reports using proportion of relative errors and proportion of standard error of prediction. The proportion of relative errors of the SGR and LT models developed herein were 0.79 and 0.18, respectively. In addition, the standard error of prediction values of the SGR and LT of L. monocytogenes ranged from 25.7 to 33.1% and from 44.92 to 58.44%, respectively. These results suggest that the model developed in this study was capable of predicting the growth of L. monocytogenes under various isothermal conditions.

Comparative study of the effects of citral on the growth and injury of Listeria innocua and Listeria monocytogenes cells

This study investigates the effect of citral on growth and on the occurrence of sublethal damage in Listeria innocua Serovar 6a (CECT 910) and Listeria monocytogenes Serovar 4b (CECT 4032) cells that were exposed to citral as a natural antimicrobial agent. Two initial inoculum concentrations were considered in this investigation: 10² and 10⁶ cfu/mL. Citral exhibited antilisterial activity against L. innocua and L. monocytogenes, and the observed effects were dependent on the concentration of citral present in the culture medium (0, 0.150 and 0.250 μL/mL) (p ≤ 0.05). L. innocua had a shorter lag phase than L. monocytogenes, and the two species had nearly identical maximum specific growth rates. These results indicate that L. innocua could be used as surrogate for L. monocytogenes when testing the effects of this antimicrobial. Significant differences in the lag phase and growth rate were observed between the small and large inoculum concentration (p ≤ 0.05). Citral-treated L. innocua and L. monocytogenes that were recovered on selective medium (i.e., TSA-YE-SC) had a shorter lag phase and a higher maximum specific growth rate than cells that were recovered on non-selective medium (i.e., TSA-YE) (p ≤ 0.05). This result suggests that damage occurs at sublethal concentrations of citral.

Analysing and modelling the growth behaviour of Listeria monocytogenes on RTE cooked meat products after a high pressure treatment at 400 MPa

Various predictive models are available for high pressure inactivation of Listeria monocytogenes in food, but currently available models do not consider the growth kinetics of surviving cells during the subsequent storage of products. Therefore, we characterised the growth of L. monocytogenes in sliced cooked meat products after a pressurization treatment. Two inoculum levels (10(7) or 10(4) CFU/g) and two physiological states before pressurization (freeze-stressed or cold-adapted) were evaluated. Samples of cooked ham and mortadella were inoculated, high pressure processed (400 MPa, 5 min) and subsequently stored at 4, 8 and 12 °C. The Logistic model with delay was used to estimate lag phase (λ) and maximum specific growth rate (μmax) values from the obtained growth curves. The effect of storage temperature on μmax and λ was modelled using the Ratkowsky square root model and the relative lag time (RLT) concept. Compared with cold-adapted cells the freeze-stressed cells were more pressure-resistant and showed a much longer lag phase during growth after the pressure treatment. Interestingly, for high-pressure inactivation and subsequent growth, the time to achieve a concentration of L. monocytogenes 100-fold (2-log) higher than the cell concentration prior to the pressure treatment was similar for the two studied physiological states of the inoculum. Two secondary models were necessary to describe the different growth behaviour of L. monocytogenes on ready-to-eat cooked ham (lean product) and mortadella (fatty product). This supported the need of a product-oriented approach to assess growth after high pressure processing. The performance of the developed predictive models for the growth of L. monocytogenes in high-pressure processed cooked ham and mortadella was evaluated by comparison with available data from the literature and by using the Acceptable Simulation Zone approach. Overall, 91% of the relative errors fell into the Acceptable Simulation Zone.

Utilization of mathematical models to manage risk of holding cold food without temperature control

This document describes the development of a tool to manage the risk of the transportation of cold food without temperature control. The tool uses predictions from ComBase predictor and builds on the 2009 U.S. Food and Drug Administration Model Food Code and supporting scientific data in the Food Code annex. I selected Salmonella spp. and Listeria monocytogenes as the organisms for risk management. Salmonella spp. were selected because they are associated with a wide variety of foods and grow rapidly at temperatures >17°C. L. monocytogenes was selected because it is frequently present in the food processing environment, it was used in the original analysis contained in the Food Code Annex, and it grows relatively rapidly at temperatures <17°C. The suitability of a variety of growth models under changing temperature conditions is largely supported by the published literature. The ComBase predictions under static temperature conditions were validated using 148 ComBase database observations for Salmonella spp. and L. monocytogenes in real foods. The times and temperature changes encompassed by ComBase Predictor models for Salmonella spp. and L. monocytogenes are consistent with published data on consumer food transport to the home from the grocery store and on representative foods from a wholesale cash and carry food service supplier collected as part of this project. The resulting model-based tool will be a useful aid to risk managers and customers of wholesale cash and carry food service suppliers, as well as to anyone interested in assessing and managing the risks posed by holding cold foods out of temperature control in supermarkets, delis, restaurants, cafeterias, and homes.

Development of a time-to-detect growth model for heat-treated Bacillus cereus spores

The microbiological safety and quality of Refrigerated Processed Foods of Extended Durability (REPFEDs) relies on a combination of mild heat treatment and refrigeration, sometimes in combination with other inhibitory agents that are ineffective when used alone. In this context, a predictive model describing the time-to-detect growth (measured by turbidimetry) of psychrotrophic Bacillus cereus spores submitted to various combinations of pH, water activity (aw), heat treatment and storage temperature was developed. As the inoculum was high, the time-to-detect growth was the sum of two times: for a large part of the spore lag time (time before germination and outgrowth) and to a lesser extent of the time to have subsequent vegetative cells growing up to a detectable level. A dataset of 434 combinations (of pH, aw, heat treatment, storage temperature and B. cereus strain), originally collected at Ghent University to build a growth/no-growth model for two Bacillus cereus strains, was re-interpreted as time-to-detect growth values. In the growth area (223 combinations) the time-to-detect growth was set as the longest time where none, or only one, of the 8 replicated wells showed growth. In the no-growth area (211 combinations) the time-to-detect growth was set as longer than the time where the experiment was stopped (60days or more) and analysed as a censored response. The factors of variation were heat-treatment intensity (85°C, 87°C and 90°C in a time range of 1 to 38min), storage temperature (8-30°C), pH (5.2-6.4) and aw (0.973-0.995). Two different strains were analysed. The model had a Gamma multiplicative structure; it was solved by Bayesian inference with informative prior distributions. To be implemented in a decision tool, for instance to calculate the process and formulation conditions required to achieve a given detection time, each Gamma term had some constraints: they had to be monotonous, continuous and algebraically simple mathematical functions (i.e. having analytical solution). Overall, the cumulative effect of various stressful conditions (pasteurisation process, low temperature, and low pH) enables to extend the time-to-detect growth up to 60days or more, whereas the heat-treatment on its own did not have a similar effect. For example, with the most heat resistant strain (strain 1, FF140), for a product at aw0.99, stored at 10°C, heat-treated at 90°C for 10min, a time-to-detect growth of 2days was expected when the pH equalled 6.5. Under the same conditions, if the pH was reduced to 5.8, the time-to-detect growth was predicted to be 11days (and 33days at pH5.5). After a pasteurisation at 90°C for 10min, for a product kept at 10°C, combinations of pH and aw such as pH6.0-aw0.97, pH5.7-aw0.98 or pH5.5-aw0.99 were predicted to extend the time-to-detect growth up to 30days. The developed model is a useful tool for REPFED producers to guarantee the safety of their products towards psychrotrophic B. cereus.

Reduced growth of Listeria monocytogenes in two model cheese microcosms is not associated with individual microbial strains

Two model antilisterial microbial communities consisting of two yeasts, two Gram positive and two Gram negative bacteria, and originating from Livarot cheese smear were previously designed. They were used in the present study to analyse the impact of microbial population dynamics on growth of Listeria monocytogenes in cheese microcosm. Specific culture media and PCR primers were developed for simultaneous culture-dependent and real-time PCR quantification of strains belonging to Marinomonas sp., Paenibacillus sp., Staphylococcus equorum, Arthrobacter arilaitensis, Pseudomonas putida, Serratia liquefaciens, Candida natalensis, and Geotrichum candidum, in cheese microcosms. All strains were enumerated after 3, 5, 8 and 14 days at 15 °C. They established well at high counts in all cheese microcosms. Growth dynamics for all strains in presence of L. monocytogenes WSLC 1685 were compared to those of microbial communities obtained by omitting in turn one of the six members of the initial community. The growth of the microbial strains was neither markedly disturbed by Listeria presence nor by the removal of each strain in turn. Furthermore, these communities had a significant reducing effect on growth of L. monocytogenes independently of pH, as confirmed by mathematical modelling. A barrier effect was observed, that could be explained by specific competition for nutrients.

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.

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.

Biosynthesis of PHB, a New Packaging Material by Methane-Utilizing Mixed Culture HD6T

Poly-3-hydroxybutyrate (PHB) has already become the hot spot research in food packaging area because of its excellent biocompatibility and biodegradability as a kind of new plastic substitute. The Methane-Utilizing mixed Culture HD6T is able to synthesize PHB with methane in an open system. In order to obtain microbial species of high production PHB low carbon cost in an open system, the ability of accumulating PHB was studied. Through inspecting the culture medium component, the results indicated that: Cultivation was performed in two stages: a continuous growth phase and a PHB accumulation phase under different concentration of essential nutrient (ammonium, nitrate, magnesium or copper) in batch culture. The highest density of cultivated cells was 0.72g dry wtL-1, and PHB content of biomass was as high as 31%.A bacterial mixed culture being used for the biotechnological production of PHB is an important step towards the development of a viable large-scale process for the production of PHB using cheap substrates like methane.content of biomass was as high as 31%.A bacterial mixed culture being used for the biotechnological production of PHB is an important step towards the development of a viable large-scale process for the production of PHB using cheap substrates like methane.