Modeling the effect of inoculum size and acid adaptation on growth/no growth interface of Escherichia coli O157:H7

The objective of this study was to model with logistic regression the growth/no growth interface of different initial inoculation levels (10¹, 10³ and 10⁵ CFU/ml; study 1), or nonadapted vs acid-adapted (study 2) Escherichia coli O157:H7 as influenced by pH, NaCl concentration and incubation temperature. Study 1 was conducted with a mixture of four E. coli O157:H7 strains grown (35 °C, 24 h) in tryptic soy broth (TSB). Study 2 was conducted with the same mixture of four E. coli O157:H7 strains grown (35 °C, 24 h) in glucose-free TSB with 1% added glucose (final pH 4.83), or in diluted lactic acid meat decontamination runoff fluids (washings; final pH 4.92), or nonadapted cultures prepared in glucose-free TSB (final pH 6.45), or in water washings (final pH 6.87). Parameters included incubation temperature (10–35 °C), pH (3.52–7.32), and NaCl concentration (0–10% w/v). Growth responses were evaluated for 60 days turbidimetrically (610 nm) every 5 days in 160 (study 1) and 360 (study 2) combinations in quadruplicate samples, with a microplate reader. The lower the initial inoculum the higher were the minimum pH and a_w values permitting growth. Differences in the pH and a_w growth limits among inoculum concentrations increased at 15 and 10 °C. Acid-adapted cultures were able to grow at lower pH than nonadapted cultures, while at temperatures below 25 °C, growth initiation of nonadapted cultures stopped at higher a_w compared to acid-adapted cultures for the whole pH range of 3.52 to 7.32. A comparison with available data indicated that our model for acid-adapted E. coli O157:H7 in different environments may provide representative growth probabilities covering both nonadapted and stress-adapted contaminants.     

环境因子及接种量对单增李斯特菌生长/非生长界面的影响

单增李斯特菌在实验设定的环境条件下,通过10倍梯度稀释将菌悬液分别稀释到101、103、105、107CFU/m L四个接种水平,然后接种到TSB-YE肉汤中,培养基置于恒温培养箱中进行培养,然后通过肉眼观察培养基浊度并结合涂布TSA-YE平板对其生长/非生长情况进行判定,通过Logistics多项式回归模型对处理的数据建立了单增李斯特菌生长/非生长的界面模型。实验结果表明不同生长温度,p H和盐度的交互作用对单增李斯特菌的生长/非生长界面的影响较大,接种量的大小也会影响单增李斯特菌生长/非生长过渡区域的具体位置,但具体原因和作用机制还有待进一步研究。该研究为抑制单增李斯特菌生长的环境因子条件范围和实际产品中的污染严重程度提供一定的参考依据,对于有潜在单增李斯特菌污染的产品来说,这为加强产品的栅栏因子,优化工艺条件以提高其安全度也提供了重要的参考。     

环境因子及接种量对单增李斯特菌生长/非生长界面的影响

单增李斯特菌在实验设定的环境条件下,通过10倍梯度稀释将菌悬液分别稀释到101、103、105、107CFU/m L四个接种水平,然后接种到TSB-YE肉汤中,培养基置于恒温培养箱中进行培养,然后通过肉眼观察培养基浊度并结合涂布TSA-YE平板对其生长/非生长情况进行判定,通过Logistics多项式回归模型对处理的数据建立了单增李斯特菌生长/非生长的界面模型。实验结果表明不同生长温度,p H和盐度的交互作用对单增李斯特菌的生长/非生长界面的影响较大,接种量的大小也会影响单增李斯特菌生长/非生长过渡区域的具体位置,但具体原因和作用机制还有待进一步研究。该研究为抑制单增李斯特菌生长的环境因子条件范围和实际产品中的污染严重程度提供一定的参考依据,对于有潜在单增李斯特菌污染的产品来说,这为加强产品的栅栏因子,优化工艺条件以提高其安全度也提供了重要的参考。      

接种量对单增李斯特菌生长期及生长界面的影响

为了初步了解接种量对单增李斯特菌生长状况及生长/非生长界面的影响,本实验对单增李斯特菌在0、4、10、25℃下通过培养菌液在600nm下的吸光光度值对其生长周期曲线分别进行了测定,并分析了不同接种量的单增李斯特菌菌液在25℃下的生长周期状况,探讨了纯培养条件下不同盐度和pH下,接种量对单增李斯特菌生长/非生长状况的影响。结果表明:不同的温度下,单增李斯特菌的生长周期有很大的差别;而在相同温度下,接种量对单增李斯特菌的生长周期有较大的影响,随着接种水平的降低,菌种生长所需的延滞时间越长,接种量为107CFU/mL时,其生长延滞期为0~4h,而当接种量减少为10CFU/mL时,其生长延滞期为0~16h;而对于单增李斯特菌的生长/非生长界面而言,接种量对其也有一定的影响,但其作用机制还有待进一步深入的研究。      

The effect of inoculum size on the growth of Penicillium expansum in apples

Penicillium expansum is the most important cause of blue mould rot, a major post-harvest disease of apples worldwide. The objective of this study was to evaluate the effect of the inoculum size on the germination and growth parameters of P. expansum under different storage conditions in apples. Growth of P. expansum was observed in more than 90% of the inoculations, when the inoculum was equal or higher than 2x10(4) spores. The use of a low inoculum level resulted in longer lag phases and a larger variability of the estimated lag phase. This indicates that more replications are necessary to estimate the lag phase of the mould in the specified circumstances. At lower temperature, more inoculum was necessary to reduce the variability of the estimated lag phase, showing that this effect is temperature dependent. Moreover, the effect of the inoculum level on the lag phase is even more pronounced for a slower growing strain. These results imply that the inoculum size influences the estimated growth parameters and should be considered in quantitative risk assessments and for the design of challenge tests and experiments to gather data for predictive growth models.     

The effect of incubation temperature and inoculum size on growth of salmonellae in minced beef

Growth rates and lag times of Salmonella organisms were determined in minced beef at temperatures between 10 and 35 degrees C. A mixture of serotypes containing antibiotic-resistance markers was used to allow small numbers of salmonellae to be counted in the presence of an excess of competing organisms. Maximum growth rates and lag times of salmonellae were unaffected by inoculum size. The effect of temperature on growth rate could be described by the simple square root relationship of Ratkowsky et al. (J. Bacteriol. 149, 1-5, 1982).     

Modelling the effect of temperature and water activity on the growth rate and growth/no growth interface of Byssochlamys fulva and Byssochlamys nivea

The purpose of the present study was to apply a modelling approach to define the growth rate and growth/no growth interface of Byssochlamys fulva and Byssochlamys nivea on a synthetic medium as a function of temperature and water activity. Both fungal species were grown on malt extract agar at different temperatures (10, 15, 20, 25, 30, 35, 40 and 45 °C) and a_w levels (0.88, 0.90, 0.92, 0.94, 0.96 and 0.99) for a period of 30 days. Growth responses were evaluated over time in terms of colony diameter changes. Growth data were fitted to the primary model of Baranyi and the resulting growth rates were further modeled as a function of temperature and water activity using the cardinal model with inflection (CMI) ( Rosso et al., 1993). A logistic regression quadratic polynomial model was also employed to predict the probability of growth over storage time. Estimated parameters for minimum, maximum and optimum temperatures for growth were 9.1 °C, 46.4 °C and 32.1 °C for B. fulva and 10.5 °C, 43.2 °C and 32.1 °C for B. nivea. The respective values for a_w were 0.893, 0.993 and 0.985 for B. fulva and 0.892, 0.992 and 0.984 for B. nivea. No growth was observed at 0.88 a_w regardless of temperature for both species, whereas B. nivea ascospores could not grow at 10 and 45 °C irrespective of a_w. Regarding growth boundaries, the degree of agreement between predictions and observations was >98% concordant for both species. The erroneously predicted growth cases were 1.4–4.2% false positive and 2.1–3.5% false negative for B. nivea and B. fulva, respectively. The developed logistic model was validated with two literature data sets as well as with data from independent experiments carried out on fruit juices. Validation results showed that agreement with literature data for growth was 25 out of 36 (69.4%) cases, whereas validation on fruit juice data failed in only 6 cases (5 false positives and 1 false negative) out of 128 cases.     

Quantifying the hurdle concept by modelling the bacterial growth/no growth interface

The hurdle concept described eloquently over many years by Professor Leistner and his colleagues draws attention to the interaction of factors that affect microbial behaviour in foods. Under some circumstances these effects are additive. Under others the implication is that synergistic interactions lead to a combined effect of greater magnitude than the sum of constraints applied individually. Predictive modelling studies on the combined effects of temperature and water activity and temperature and pH suggest that the effect of these combinations on growth rate is independent. Where the effect of the two factors is interactive rather than independent is at the point where growth ceases--the growth/no growth interface. An interesting and consistent observation is that a very sharp cut off occurs between conditions permitting growth and those preventing growth, allowing those combinations of factors to be defined precisely and modelled. Growth/no growth interface models quantify the effects of various hurdles on the probability of growth and define combinations at which the growth rate is zero or the lag time infinite. Increasing the stringency of one or more hurdles at the interface by only a small amount will significantly decrease the probability of an organism growing. Understanding physiological processes occurring near the growth/no growth interface and changes induced by moving from one side of the interface to the other may well provide insights that can be exploited in a new generation of food preservation techniques with minimal impact on product quality.     

Effect of the inoculum size on Listeria monocytogenes growth in structured media

Obtaining quantitative data concerning the relative impact of various factors that may influence bacterial growth is of great importance for microbial risk assessment and predictive microbiology. The objective of this work was to investigate the effect of the initial Listeria monocytogenes density on all the growth parameters of this pathogen (lag phase duration, growth rate and maximum population density attained) on a sterile solid model system mimicking smoked fishery products, and in real cold-smoked salmon, a product likely to be contaminated with L. monocytogenes. Growth of the pathogen was monitored using a sensitive enumeration method, recently developed, based on membrane filtration followed by the transfer of the filter on a selective media [Gnanou Besse, N., Audinet, N., Beaufort, A., Colin, P., Cornu, M. and Lombard, B., 2004. A contribution to the improvement of Listeria monocytogenes enumeration in smoked salmon. International Journal of Food Microbiology, 91, 119-127.]. Depending on the experimental conditions, we found a significant effect of the inoculum size, both on lag phase duration, and on the maximal population attained. Moreover, the effect of the inoculum size on the growth of L. monocytogenes was dependent on a complex set of interactions. Factors which have appeared to impact on this effect include the cells physiological state, the background microflora, the texture of the media and the packaging system. It is important to understand how these interactions affect the growth of Listeria in order to predict and control its development in food.     

Modelling mould growth under suboptimal environmental conditions and inoculum size

Predictive models can be a tool to develop strategies to prevent mould development and consequently mycotoxin production. The aims of this work were to assess the impact of a) high/low levels of inoculum and b) optimal/suboptimal environmental conditions on fungal responses based on both kinetic and probabilistic models. Different levels of spore suspensions of Aspergillus carbonarius and Penicillium expansum were prepared and inoculated centrally with a needlepoint load on malt extract agar (MEA) with 50 replicates. While optimum conditions led to a colony diameter increase which followed Baranyi’s function, suboptimal conditions led to different grow functions. In general, growth rate (μ) and lag phase (λ) were normally distributed. Specifically, the growth rate (μ) showed similar distributions under optimal growth conditions, regardless of the inoculum level, while suboptimal a_w and temperature conditions led to higher kurtosis distributions, mainly when the inoculum levels were low. Regarding λ, more skewed distributions were observed, mainly when the inoculum levels were low. Probability models were not much affected by the inoculum size. Lower probabilities of growth were in general predicted under marginal conditions at a given time for both strains. The slopes of the probability curves were smaller under suboptimal growth conditions due to wider distributions. Results showed that a low inoculum level and suboptimal conditions lead to high variability of the estimated growth parameters and growth probability.     

The effect of inoculum size on the lag phase of Listeria monocytogenes.

The effect of inoculum size on population lag times of Listeria monocytogenes was investigated using the Bioscreen automated microtitre plate incubator and reader. Under optimum conditions, lag times were little affected by inoculum size and there was little variation between replicate inocula even at very low cell numbers. However, in media containing inhibitory concentrations of NaCl, both the mean lag time and variation between replicate inocula increased as the inoculum size became smaller. The variation in lag time of cells within a population was investigated in more detail by measuring the distribution of detection times from 64 replicate inocula containing only one or two cells capable of initiating growth. The variance of the lag time distribution increased with increasing salt concentration and was greater in exponential than in stationary phase inocula. The number of cells required to initiate growth increased from one cell under optimum conditions to 10(5) cells in medium with 1.8 M NaCl. The addition of spent medium from a stationary phase culture reduced the variance and decreased lag times. The ability to initiate growth under severe salt stress appears to depend on the presence of a resistant sub-fraction of the population, although high cell densities assist adaptation of those resistant cells to the unfavourable growth conditions by some unspecified medium conditioning effect. These results are relevant to the prediction of lag times and probability of growth from low numbers of stressed cells in food.     

蜡样芽胞杆菌生长/非生长界面模型的建立和评价

蜡样芽胞杆菌是软烤虾仁产品的主要变质菌,它是一种条件致病菌,通过产生腹泻毒素和呕吐毒素导致食物中毒。该研究旨在建立一种概率模型来预测出蜡样芽胞杆菌的生长/非生长情况或者生长概率。用lo-gistic回归模型建立不同温度、水分活度和pH环境因子作用下蜡样芽胞杆菌的生长/非生长界面模型。实验结果表明蜡样芽胞杆菌在脑心浸液肉汤培养基中生长的最低温度为9.99℃,最低水分活度为0.931,最小pH值为4.5。在此基础上建立的蜡样芽胞杆菌生长/非生长界面模型的χ2=49.73,P<0.000 1。用logistic回归模型建立的生长/非生长模型拟合效果达到极显著水平。模型的预测值同时很好地量化了环境因子对蜡样芽胞杆菌的协同作用,为软烤虾仁产品中蜡样芽胞杆菌的生长/非生长界面模型的建立提供了参考。     

Effect of inoculum size on the combined temperature, pH and aw limits for growth of Listeria monocytogenes

The growth/no growth responses of Listeria monocytogenes inoculated at four levels (0.90, 2.58, 4.20 and 6.81 log cfu/well; 300 microl medium/well) into tryptic soy broth (TSB) were monitored at different combinations of temperature (4 to 30 degrees C), pH (3.76 to 6.44) and aw (0.888 to 0.997) for 60 days. The study was conducted in 96-well microtiter plates and growth was monitored visually and by recording the turbidity of the medium with an automated microplate reader. The growth limits of the pathogen and hence the position of the growth boundary were found to be affected by the size of the inoculum. For example, at 25 degrees C and aw 0.997 the minimum pH values that allowed growth were 4.45 and 3.94 for inoculum levels of 0.90 and 6.81 log cfu/well, respectively. Similarly, at 25 degrees C and pH 6.44 the minimum aw values where growth was observed ranged from 0.900 to 0.928 depending on the inoculum level. The results showed that at temperatures from 10 to 30 degrees C the difference in the growth limits between the tested inoculum levels was higher in environments where a single factor (pH or aw) was inhibitory than in environments where pH and aw together were inhibitory. The data were used to develop a growth/no growth interface model for each inoculum level tested, using logistic polynomial regression. The concordance indices of the models ranged from 99.8% to 99.9% and showed a good fit to the observed data in all models. This study indicates the importance of inoculum size for microbial growth initiation and provides quantitative data that show how the combinations of hurdles which prevent growth vary with inoculum size.     

Development of a multi-classification neural network model to determine the microbial growth/no growth interface

Boundary models have been recognized as useful tools to predict the ability of microorganisms to grow at limiting conditions. However, at these conditions, microbial behaviour can vary, being difficult to distinguish between growth or no growth. In this paper, the data from the study of Valero et al. [Valero, A., Pérez-Rodríguez, F., Carrasco, E., Fuentes-Alventosa, J.M., García-Gimeno, R.M., Zurera, G., 2009. Modelling the growth boundaries of Staphylococcus aureus: Effect of temperature, pH and water activity. International Journal of Food Microbiology 133 (1-2), 186-194] belonging to growth/no growth conditions of Staphylococcus aureus against temperature, pH and a_w were divided into three categorical classes: growth (G), growth transition (GT) and no growth (NG). Subsequently, they were modelled by using a Radial Basis Function Neural Network (RBFNN) in order to create a multi-classification model that was able to predict the probability of belonging at one of the three mentioned classes. The model was developed through an over sampling procedure using a memetic algorithm (MA) in order to balance in part the size of the classes and to improve the accuracy of the classifier. The multi-classification model, named Smote Memetic Radial Basis Function (SMRBF) provided a quite good adjustment to data observed, being able to correctly classify the 86.30% of training data and the 82.26% of generalization data for the three observed classes in the best model. Besides, the high number of replicates per condition tested (n = 30) produced a smooth transition between growth and no growth. At the most stringent conditions, the probability of belonging to class GT was higher, thus justifying the inclusion of the class in the new model. The SMRBF model presented in this study can be used to better define microbial growth/no growth interface and the variability associated to these conditions so as to apply this knowledge to a food safety in a decision-making process.     

Fumonisin production on irradiated corn kernels: effect of inoculum size.

Production of fumonisins B1, B2, and B3 by Fusarium moniliforme was evaluated on irradiated corn kernels inoculated with different spore concentrations (10, 10(2), 10(3), 10(5), and 10(6)), a water activity of 0.97, and a temperature of 25 degrees C. There was a direct relationship between the level of toxin produced and inoculum size. The highest levels of total fumonisin produced after 35 days of incubation were 5,028 and 9,063 ng/g at 10(5) and 10(6) spores per ml, respectively. The pattern of fumonisin production (FB1 > FB2 > FB3) in cultures growing from different inocula was not affected during the 35 days of incubation. The ratio between FB2 and FB1 varied from 0.15 to 0.42, whereas the ratio between FB3 and FB1 varied from 0.34 to 0.87.     

Extrapolation of a predictive model for growth of a low inoculum size of Salmonella Typhimurium DT104 on chicken skin to higher inoculum sizes

Validation of model predictions for independent variables not included during model development can save time and money by identifying conditions for which new models are not needed. A single strain of Salmonella Typhimurium DT104 was used to develop a general regression neural network (GRNN) model for growth of a low inoculum size (0.9 log) on chicken skin with native microflora as a function of time (0 to 8 h) and temperature (20 to 45°C). The ability of the GRNN model to predict growth of higher inoculum sizes (2, 3, or 4.1 log) was evaluated. When the proportion of residuals in an acceptable prediction zone (pAPZ) from -1 log (fail-safe) to 0.5 log (fail-dangerous) was ≥0.7, the GRNN model was classified as providing acceptable predictions of the test data. The pAPZ for dependent data was 0.93 and for independent data for interpolation was 0.88. The pAPZs for extrapolation to higher inoculum sizes of 2, 3, or 4.1 log were 0.92, 0.73, and 0.77, respectively. However, residual plots indicated local prediction problems with pAPZs of < 0.7 for an inoculum size of 3 log at 30, 35, and 40°C and for an inoculum size of 4.1 log at 35 and 40°C where predictions were fail-dangerous, indicating faster growth at higher inoculum sizes. The model provided valid predictions of Salmonella Typhimurium DT104 growth on chicken skin from inoculum sizes of 0.9 and 2 log at all temperatures investigated and from inoculum sizes of 3 and 4.1 log at some but not all temperatures investigated. Thus, the model can be improved by including inoculum size as an independent variable.     

Simulation and modelling of the effect of small inoculum size on time to spoilage by Bacillus stearothermophilus

Mathematical models developed in predictive food microbiology typically use large (approx. 10⁵cfu ml⁻¹) inoculum sizes. Real food systems may contain low microbial loads (1–10 cfu ml⁻¹) introducing an additional uncertainty unaccounted for by model predictions. This research investigated the effects of very low inoculum sizes on the time to spoilage of Bacillus stearothermophilus ATCC 12980 spores. Microtiter plates (96-well) were filled with tryptic soy broth and inoculated with various concentrations of B. stearothermophilus spores. Time to spoilage was defined as colour change of the medium containing bromcresol purple (corresponding to c. 10⁸cfu ml⁻¹) from purple to yellow. A Poisson distribution best described the number of spores in a well. Spoilage times showed maximum variability (7·25–17 h) at 1 spore well⁻¹, and negligible variability (c. 6·5 h) at 500 spores well⁻¹. A simplified Gompertz function described spoilage kinetics. Mathematical modelling and simulation approaches were used to study spoilage times. The modelling approach had a fail-safe bias in its predictions and provided greater accuracy than the simulation, which was fail-dangerous. The simulation approach provided potentially greater mechanistic insight into the causes of spoilage time variability, and supported the notion that the effects of biovariability and interactions among individual spores manifest at very low inoculum sizes.     

软烤贻贝中蜡样芽孢杆菌生长/非生长界面模型建立与评价

建立软烤贻贝中蜡样芽孢杆菌标准菌株(ATCC49064与DSMZ 4312)在不同贮藏温度(T)、pH、水分活度(Aw)下生长/非生长界面模型,对其拟合情况和来自软烤贻贝蜡样芽孢杆菌(YB001)的验证情况进行分析和评价,并与已建立的脑心浸出液肉汤(BHI)中蜡样芽孢杆菌生长/非生长界面模型进行比较。所建模型总方程为Lopit(P)=-208.457-2.167·T+35.304·pH+705.573·Bw+1.117·T·pH-7.072·T·Bw-174.946·pH·Bw,其中R2-Nagelkerke=0.979和χ~2=0.019(df=8,P=1)显示拟合度较高,而且其预测一致率明显高于BHI培养基中建立的模型,表明该模型在预测软烤贻贝中蜡样芽孢杆菌的生长/非生长情况有很高的精确度和很好的适用性。此外,贮藏温度、水分活度、pH及其交互作用显著影响蜡样芽孢杆菌的生长/非生长(P0.05)。因此可以通过所建生长/非生长界面模型量化温度、水分活度、pH值等栅栏因子并结合其交互效应来确保软烤贻贝的高品质与安全性。     

Growth/no growth interface of Brochothrix thermosphacta as a function of pH and water activity

A growth/no growth boundary model based on interpolated probabilities is presented in this paper. The boundary is defined as the loci where the probability of growth for a sample is equal to its chance of no growth, P (growth)=P (no growth). Brochothrix thermosphacta was used as a test micro-organism to collect data near the boundary of growth/no growth, in a pH/NaCl grid. Results showed a dramatic change in the probability of growth at the boundary with minor changes of pH or NaCl, and that the location of the boundary was affected by the inoculum level. A quadratic polynomial was used to describe the boundary of the growth region (interpolated P=0·5). The importance of growth/no growth boundary models as limits for the application of kinetic models is discussed.     

The importance of expressing antimicrobial agents on water basis in growth/no growth interface models: a case study for Zygosaccharomyces bailii

In a previous study on Zygosaccharomyces bailii, three growth/no growth models have been developed, predicting growth probability of the yeast at different conditions typical for acidified foods (Dang, T.D.T., Mertens, L., Vermeulen, A., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2010. Modeling the growth/no growth boundary of Z. bailii in acidic conditions: A contribution to the alternative method to preserve foods without using chemical preservatives. International Journal of Food Microbiology 137, 1-12). In these broth-based models, the variables were pH, water activity and acetic acid, with acetic acid concentration expressed in volume % on the total culture medium (i.e., broth). To continue the previous study, validation experiments were performed for 15 selected combinations of intrinsic factors to assess the performance of the model at 22 °C (60 days) in a real food product (ketchup). Although the majority of experimental results were consistent, some remarkable deviations between prediction and validation were observed, e.g., Z. bailii growth occurred in conditions where almost no growth had been predicted. A thorough investigation revealed that the difference between two ways of expressing acetic acid concentration (i.e., on broth basis and on water basis) is rather significant, particularly for media containing high amounts of dry matter. Consequently, the use of broth-based concentrations in the models was not appropriate. Three models with acetic acid concentration expressed on water basis were established and it was observed that predictions by these models well matched the validation results; therefore a “systematic error” in broth-based models was recognized. In practice, quantities of antimicrobial agents are often calculated based on the water content of food products. Hence, to assure reliable predictions and facilitate the application of models (developed from lab media with high dry matter contents), it is important to express antimicrobial agents' concentrations on a common basis—the water content. Reviews over other published growth/no growth models in literature are carried out and expressions of the stress factors' concentrations (on broth basis) found in these models confirm this finding.