On the use of the Weibull model to describe thermal inactivation of microbial vegetative cells

This paper evaluates the applicability of the Weibull model to describe thermal inactivation of microbial vegetative cells as an alternative for the classical Bigelow model of first-order kinetics; spores are excluded in this article because of the complications arising due to the activation of dormant spores. The Weibull model takes biological variation, with respect to thermal inactivation, into account and is basically a statistical model of distribution of inactivation times. The model used has two parameters, the scale parameter alpha (time) and the dimensionless shape parameter beta. The model conveniently accounts for the frequently observed nonlinearity of semilogarithmic survivor curves, and the classical first-order approach is a special case of the Weibull model. The shape parameter accounts for upward concavity of a survival curve (beta < 1), a linear survival curve (beta = 1), and downward concavity (beta > 1). Although the Weibull model is of an empirical nature, a link can be made with physiological effects. Beta < 1 indicates that the remaining cells have the ability to adapt to the applied stress, whereas beta > 1 indicates that the remaining cells become increasingly damaged. Fifty-five case studies taken from the literature were analyzed to study the temperature dependence of the two parameters. The logarithm of the scale parameter alpha depended linearly on temperature, analogous to the classical D value. However, the temperature dependence of the shape parameter beta was not so clear. In only seven cases, the shape parameter seemed to depend on temperature, in a linear way. In all other cases, no statistically significant (linear) relation with temperature could be found. In 39 cases, the shape parameter beta was larger than 1, and in 14 cases, smaller than 1. Only in two cases was the shape parameter beta = 1 over the temperature range studied, indicating that the classical first-order kinetics approach is the exception rather than the rule. The conclusion is that the Weibull model can be used to model nonlinear survival curves, and may be helpful to pinpoint relevant physiological effects caused by heating. Most importantly, process calculations show that large discrepancies can be found between the classical first-order approach and the Weibull model. This case study suggests that the Weibull model performs much better than the classical inactivation model and can be of much value in modelling thermal inactivation more realistically, and therefore, in improving food safety and quality.     

Combined effect of nisin and carvacrol at different pH and temperature levels on the viability of different strains of Bacillus cereus.

The influence of pH and temperature on the bactericidal action of nisin and carvacrol on vegetative cells of different Bacillus cereus strains was studied. The five strains tested showed significant differences in sensitivity towards nisin, at pH 7.0 and 30 degrees C. Carvacrol concentrations of 0.3 mmol l(-1) had no effect on viability of B. cereus cells. When the same carvacrol concentration was combined with nisin, however, it resulted in a greater loss of viability of cells than when nisin was applied alone. The concentration of carvacrol played an important role on the bactericidal effect of nisin and, therefore, on the synergistic action of both compounds combined. At lower pH values (6.30 and 5.75), nisin was more active against B. cereus cells than at pH 7.0 at 30 degrees C, with a different sensitivity of the strains tested. The combined effect of nisin and carvacrol was found to be significantly different at pH 7.0 and 5.75. When the temperature was 8 degrees C, nisin was significantly less active against B. cereus IFR-NL 94-25 than at 30 degrees C, both at pH 7.0 and 6.30. At 8 degrees C, there was a significant increased effect of nisin at lower pH values. Also at this low temperature, a synergistic effect between nisin and carvacrol on B. cereus cells was observed at the pHs tested. This study indicates the potential of nisin and carvacrol at lower pHs to be used for preservation of minimally processed foods.     

Inactivation of Bacillus cereus spores by high hydrostatic pressure at different temperatures

The effect of pH on the initiation of germination and on the inactivation of Bacillus cereus (KCTC 1012) spores during high hydrostatic pressure processing (HPP) with pressures of 0.1 to 600 MPa at different temperatures was investigated. Two different high-pressure treatments were adopted to evaluate the effect of pH on the inactivation of B. cereus on sporulation medium and in suspension medium. Inactivation of B. cereus spores with HPP treatment was affected more by sporulation medium pH than by suspension medium pH. B. cereus spores obtained through sporulation at pH 6.0 showed more resistance to inactivation by HPP at 20, 40, and 60 degrees C than did those obtained through sporulation at pHs of 7.0 and 8.0. Constituents of B. cereus spores obtained through sporulation at pH 6.0 may undergo electrochemical charge changes comparable to those for spores obtained through sporulation at pH 7.0. The initiation of B. cereus spore germination was more sensitive to pressure around 300 MPa at 20 degrees C. Increasing processing temperatures during HPP enhanced the effect of sporulation medium pH (i.e., environmental pH) on the inactivation of B. cereus spores.     

Temperature governs the inactivation rate of vegetative bacteria under growth-preventing conditions

Novel studies, in combination with a meta-analysis of available data, were undertaken to explore the kinetics of non-thermal inactivation of Escherichia coli with particular attention to inactivation in fermented meats and including analogous broth-based model systems. The analyses were based on rates of inactivation and specifically investigated the influence of temperature, pH and water activity at levels that alone, or in combination, prevented growth. When independently-derived inactivation data, obtained using different test conditions and diverse E. coli strains, were presented as Arrhenius plots, temperature was found to have a strong effect on the rate of inactivation, explaining 60% of the variance in the data. The slope of the Arrhenius plot changed, however, at temperatures above approximately 47 degrees C, corresponding to the maximum for growth of E. coli. A strong and consistent effect of pH or water activity on inactivation rate was not observed upon meta-analysis of collated data, but the relative effect of both factors was quantified in an analogous broth-based system. We also observed that inactivation rates of three strains of Listeria monocytogenes in the range 5 to 40 degrees C did not differ systematically from those of four strains of E. coli when growth was prevented by low pH and water activity. The observations of a consistent slope of Arrhenius plots for non-thermal inactivation rate of bacteria under diverse environmental conditions and for different strains and species, but which differ from slopes associated with thermal inactivation, raise the intriguing possibility of a mechanism of inactivation at sub-lethal temperatures, distinct from thermal inactivation, that is common to many vegetative bacteria.     

Quantifying the effects of heating temperature, and combined effects of heating medium pH and recovery medium pH on the heat resistance of Salmonella typhimurium

The influence of heating treatment temperature, pH of heating and recovery medium on the survival kinetics of Salmonella typhimurium ATCC 13311 is studied and quantified. From each non-log linear survival curve, Weibull model parameters were estimated. An average shape parameter value of 1.67 was found, which is characteristic of downward concavity curves and is in agreement with values estimated from other S. typhimurium strains. Bigelow type models quantifying the heating temperature, heating and recovery medium pH influences are fitted on scale parameter delta data (time of first decimal reduction), which reflects the bacterial heat resistance. The estimate of z(T) (4.64 degrees C) is in the range of values given in the literature for this species. The influence of pH of the heating medium on the scale parameter (z(pH): 8.25) is lower than that of the recovery pH medium influence (z(')(pH): 3.65).     

Impact of different pasteurization temperatures on the survival of microbial contaminants isolated from pasteurized milk

The thermal inactivation of selected microbes was studied using the low temperature long time (LTLT), high temperature short time (HTST) and 'pot' pasteurization methods. Survivors were enumerated after heating for up to 40 min for the LTLT and HTST pasteurization methods and after heating for up to 30 min for the 'pot' pasteurization method. With the exception of the Bacillus cereus strain, the selected microbes did not survive the LTLT and HTST pasteurization methods. The results from the 'pot' pasteurizer showed that B. cereus, Chryseobacterium meningosepticum, Pseudomonas putida, Acinetobacter baumannii and Escherichia coli strains survived the pasteurization conditions applied, showing that the 'pot' pasteurizer does not pasteurize effectively.     

Modelling thermal inactivation of Listeria monocytogenes in sucrose solutions of various water activities

The heat resistance of Listeria monocytogenes was determined in sucrose solutions with water activity (a(w)) ranging from 0.99 to 0.90. At all temperatures investigated shape of the survival curves depended on the a(w) of the treatment medium. The survival curves for a(w)=0.99 appeared to be linear, for a(w)=0.96 were slightly upwardly concaved and for a(w)=0.93 and 0.90 were markedly concave upward. A mathematical model based on the Weibull distribution provided a good fit for all the survival curves obtained in this investigation. The effect of the temperature and a(w) on the Weibull model parameters was also studied. The shape parameter (p) depended on the a(w) of the treatment medium but in each medium of different a(w) the temperature did not have a significant effect on this parameter. The p parameter followed a linear relationship with a(w). The scale parameter (delta) decreased with the temperature following an exponential relationship and increased by decreasing the a(w) in the range from 0.99 to 0.93. However the delta parameter of survival curves obtained at a(w)=0.90 were lower than those obtained at a(w)=0.93. A mathematical model based on the Weibull parameters was built to describe the joint effect of temperature and a(w) on thermal inactivation of L. monocytogenes. This model provides a more complete information on the influence of the a(w) on the L. monocytogenes than the data initially generated. The model developed indicated that the effect of the a(w) on the thermal resistance of L. monocytogenes varied depending upon the temperature of treatment.     

The effect of growth stage and growth temperature on high hydrostatic pressure inactivation of some psychrotrophic bacteria in milk

The effect of high hydrostatic pressure on the survival of the psychrotrophic organisms Listeria monocytogenes, Bacillus cereus, and Pseudomonas fluorescens was investigated in ultrahigh-temperature milk. Variation in pressure resistance between two strains of each organism were studied. The effect of growth stage (exponential and stationary phase), growth temperature (8 and 30 degrees C) on pressure resistance, and sublethal pressure injury were investigated. Exponential-phase cells were significantly less resistant to pressure than stationary-phase cells for all of the three species studied (P < 0.05). Growth temperature was found to have a significant effect at the two growth stages studied. Exponential cells grown at 8 degrees C were more resistant than those grown at 30 degrees C, but for stationary-phase cells the reverse was true. B. cereus stationary-phase cells grown at 30 degrees C were the most pressure resistant studied. L. monocytogenes showed the most sublethal damage compared to B. cereus and P. fluorescens. B. cereus spores were more resistant to pressure than vegetative cells. Pressure treatment at 400 MPa for 25 min at 30 degrees C gave a 0.45-log inactivation. Pressure treatment at 8 degrees C induced significantly less spore germination than at 30 degrees C. This study indicates the importance of the history of a bacterial culture prior to pressure treatment and that bacterial spores require more severe pressure treatments, probably in combination with other preservation techniques, to ensure inactivation.     

Survival curves of heated bacterial spores: effect of environmental factors on Weibull parameters

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.     

EFFECTS OF THE HEATING MEDIUM pH ON HEAT RESISTANCE OF BACILLUS CEREUS SPORES

The influence of the pH of the heating medium (which included several foods and buffers) on the thermal resistance (D and z-values) of spores of three Bacillus cereus strains was studied. Acidification from pH 7.0 to 4.0 produced a 5-fold decrease in D-values. Plots of log D vs pH gave straight lines, which made it possible to develop an equation to approximately predict the changes in heat sensitivity of B. cereus spores which occurred with changing pH. z-Values for two of the strains studied were not affected by acidification. On the other hand, with the strain ATCC 9818, a clear and statistically significant increase in z-value was observed as the pH decreased.     

Inactivation kinetics of pectin methylesterase in orange juice as a function of pH and temperature/time process conditions

Pasteurisation of orange juice (OJ) is necessary to prevent spoilage due to microorganisms and enzymes, mainly pectin methylesterase (PME). PME has a higher thermal resistance than the bacteria and yeasts existing in OJ and therefore its inactivation is used as a parameter to define the time/temperature combination of the thermal process. The enzyme has isoforms with different activities and thermal resistances. A three‐parameter model can be used to describe the kinetics of PME inactivation, where the more and less thermally resistant fractions are represented. In this study the thermal inactivation kinetics was evaluated at six pH values (3.6, 3.7, 3.8, 3.9, 4.0 and 4.1), three minimal temperatures (82.5, 85.0 and 87.5 °C) and at least six holding times for each condition. It was found that the thermolabile PME fraction (a) was influenced by pH and processing temperature. A slower reaction rate constant (k₁) was found for juices with pH values of 3.8 and 3.9 at the studied temperatures. The highest inactivation levels were obtained in juices with pH values of 3.6 and 3.7. Copyright © 2006 Society of Chemical Industry     

Effect of ohmic heating on electrochemical-thermal parameters and inactivation of Escherichia coli of well water drinkable

The effect of voltage gradient (15–30 V/cm) and holding time (45–150 s) were evaluated on electrode corrosion, energy consumption, thermal performance, pH change, electrical conductivity and inactivation of Escherichia coli in the well water during ohmic heating process. Results showed that the specific energy consumption increased with an increasing voltage gradient. The thermal performance and electrode corrosion were obtained between 67.16 and 75.12% and 0.06–8.32 mg/L, respectively. The pH of treatment samples was higher than the initial samples. The changes of electrical conductivity values were modeled as function of voltage gradient and sample temperature. No survived E. coli was observed at heating condition of 30 V/cm - 150 s.     

Effect of mayonnaise pH and storage temperature on the behavior of Listeria monocytogenes in ham salad and potato salad

This study examined and modeled the behavior of Listeria monocytogenes in ham salad and potato salad as affected by the pH of mayonnaise and storage temperature. An eight-strain cocktail of L. monocytogenes was inoculated on the surface of diced cooked ham or potato. The inoculated ham or potato was then mixed with regular mayonnaise (pH 3.8) or mayonnaise that was adjusted with NaOH to pH 4.2 or 4.6. The cell counts of L. monocytogenes in the salads during storage at 4, 8, or 12 degrees C were enumerated and used to model the behavior of L. monocytogenes in ham salad or potato salad. At each of the storage temperatures, L. monocytogenes was able to grow in ham salad, whereas L. monocytogenes was inactivated in potato salad. The growth rate (log CFU per hour) in ham salad or the inactivation rate (log CFU per hour) in potato salad increased as the storage temperature increased. The duration before growth in ham salad or inactivation in potato salad increased as storage temperature decreased. The mayonnaise pH showed no consistent effect on the growth rate or inactivation rate and duration before growth or inactivation occurred. Mathematical equations that described the growth rate or inactivation rate of L. monocytogenes in both salads as a function of mayonnaise pH and storage temperature were generated and shown to be satisfactory in describing the growth rate or inactivation rate of L. monocytogenes in the ham salad or potato salad.     

A predictive model that evaluates the effect of growth conditions on the thermal resistance of Listeria monocytogenes

A predictive model for Listeria monocytogenes was developed using cells grown in different pH and milkfat levels before subsequent thermal inactivation in identical pH and milkfat conditions. Inactivation of the cells used combinations of temperature (55, 60, 65 degrees C), pH (5.0, 6.0, 7.0), and milkfat (0%, 2.5%, 5.0%) in a complete 3 x 3 x 3 factorial design with each test done in triplicate. A modified Gompertz equation was used to model nonlinear survival curves with the following three parameter estimates: A for the shouldering region, B for the maximum death rate, and C for the tailing region. All treatment sets were analyzed together in a regression model using the modified Gompertz equation. There was good confidence in the overall model when it was used to predict values for the entire data set. The correlation of determination, R2, between the observed log surviving fraction (LSF) of cells from each of the conditions studied in the experiment, for the overall model was 0.811. For the A and B parameter estimates, temperature or milkfat alone, and the interaction of temperature and milkfat significantly (p < 0.05) affected the shouldering region and maximum death rate of a survival curve, respectively. These results were compared to a previously published predictive model, generated for cells grown under optimum conditions (pH 7.0, 0% milkfat), where pH was the only significant (p < 0.05) factor affecting the shoulder region. These results suggested that the conditions of the growth environment had an important impact on survival curve shape and the estimates of the predictive model. Specifically, there were more factor interactions involving temperature and milkfat level. These growth factors affected the shoulder region and maximum rate of death of the survival curve when cells were grown in identical medium conditions to which they were heated. Differences related to shouldering and inactivation rates for cells grown in different conditions may have important and practical importance for estimating inactivation of L. monocytogenes. This study provides some evidence on the importance of growing conditions when evaluating microbial heat resistance.     

Effect of dissolved carbon dioxide on thermal inactivation of microorganisms in milk

Postpasteurization addition of CO2 inhibits growth of certain microorganisms in dairy products, but few workers have investigated the effect of CO2 on the thermal inactivation of microorganisms during pasteurization. Concentrations of CO2 ranging from 44 to 58 mM added to raw whole milk significantly (P < 0.05) reduced the number of surviving standard plate count (SPC) organisms in milk heated over the range of 67 to 93 degrees C. A decrease in thermal survival rates (D-values) for Pseudomonas fluorescens R1-232 and Bacillus cereus ATCC 14579 spores in milk was positively correlated with CO2 concentrations (1 to 36 mM). D(50 degrees C)-values for P. fluorescens significantly decreased (P < 0.05) in a linear fashion from 14.4 to 7.2 min. D(89 degrees C)-values for B. cereus spores were significantly (P < 0.05) decreased from 5.56 min in control milk to 5.29 min in milk containing 33 mM CO2. The Weibull function was used as a model to describe the thermal inactivation of P. fluorescens, B. cereus spores, and SPC organisms in raw milk. Nonlinear parameters for the Weibull function were estimated, and survival data fitted to this model had higher R2 values than when fitted to the linear model, further providing support that the thermal inactivation of bacteria does not always follow first-order reaction rate kinetics. These results suggest that CO2 could be used as a processing aid to enhance microbial inactivation during pasteurization.     

The influence of non-lethal temperature on the rate of inactivation of vegetative bacteria in inimical environments may be independent of bacterial species

The influence of non-lethal temperature on the survival of two species of food-borne bacteria under growth-preventing pH and water activity conditions was investigated. Specifically, inactivation rates of four strains of Escherichia coli and three strains of Listeria monocytogenes were determined in culture broth adjusted to pH 3.5 and water activity 0.90, to prevent growth of both species, and for temperatures in the range 5–45 °C at 5 °C intervals. Sixty-three inactivation rates were obtained, plotted on Arrhenius co-ordinates, and lines of best-fit determined by simple linear regression. Differences in the mean inactivation rate of each species at a given temperature were not significant (p < 0.05) with the exception of the rates at 25 °C. The inactivation rate responses of both species were comparable to those reported by McQuestin et al. (Appl. Environ. Microbiol., 75:6963–6972, 2009) for a variety of E. coli strains under a wide range of growth-preventing pH and water activity conditions. The results support the hypothesis that non-lethal temperature is a key factor governing the rate of inactivation of vegetative bacteria in foods when other hurdles prevent their growth and indicate that the temperature effect may also be independent of bacterial species.     

Influence of pH and temperature on growth of Bacillus cereus in vegetable substrates

Bacillus cereus is a food-borne pathogen which most often contaminates foods of plant origin. Spores of psychrotrophic strains have the ability to germinate and grow at refrigeration temperatures in different vegetable substrates, such as carrot broth, zucchini broth, and cooked carrot purée. In some circumstances, factors such as pH, heat treatment, and storage temperature play a fundamental role in controlling the growth of these psychrotrophic strains and in extending the shelf life of refrigerated, minimally processed vegetable-based products in relation to pathogenic spore-forming bacteria. The combination of mild acidification (pH 5.0) and refrigeration (相似文献   

Influence of the sporulation temperature on the impact of the nutrients inosine and l-alanine on Bacillus cereus spore germination

The effect of sporulation temperature on Bacillus cereus spore germination triggered by the nutrient germinants inosine and l-alanine was investigated. The germination (expressed as % A(600nm) fall) of heat-activated spores of B. cereus strain ATCC14579 produced at 20 and 37 degrees C, and of psychrotrophic strains LM9 and D15 produced at 15 and 37 degrees C was followed in a germination buffer containing inosine at concentrations between 0.01 and 10mmoll(-1), or l-alanine between 1 and 100mmoll(-1). Spores wet-heat resistance at 90 degrees C was also determined. Spores of the three strains produced at the lowest temperatures generally showed a higher germination capacity in response to both inosine and in l-alanine than those produced at 37 degrees C, and were also more susceptible to heat. Low sporulation temperature is confirmed as a detrimental factor to B. cereus spore wet-heat resistance, and conversely gave spores with a sensitivity to the nutrient germinants inosine and l-alanine higher than that of spores formed close to the maximal sporulation temperature.     

牛肉中沙门氏菌热失活模型的建立

为了建立牛肉中沙门氏菌的热失活动力学模型,将4种不同血清型的沙门氏菌混合菌液接种到牛肉表面,将接种后的牛肉分别在55、57.5、60、62.5和65 ℃下进行加热处理。不同温度下的沙门氏菌热失活曲线用Weibull模型进行了拟合,判定系数(R2)分别为0.993(55 ℃)、0.984(57.5 ℃)、0.999(60 ℃)、0.999(62.5 ℃)和0.998(65 ℃)。进一步建立了温度对Weibull一级失活模型参数(b)影响的二级模型,即ln(b)=0.47T-28.07。用58.5和64 ℃下实际的沙门氏菌存活数对所建的模型进行验证,准确度(A_f)和偏差度(B_f)分别为1.071和1.056,0.998和1.002,均在可接受范围内。本研究所建立的模型能较好的模拟不同温度(55~65 ℃)对牛肉中沙门氏菌热失活的影响。     

Influence of controlled lactic fermentation on growth and sporulation of Bacillus cereus in milk

The growth and sporulation of Bacillus cereus NVH 45 in a fermentor with controlled pH or simulated pH conditions were investigated. The study was carried out in a fermentor to measure the influence of a rapid and a slow lactic acid production on the inhibition of B. cereus in a controlled environment during the initial part of fermentation and to observe if other factors than lactic acid influenced the inhibition. In the controlled pH experiments the pH was allowed to decrease to an end pH 5.0, 5.5 or 6.0 either by Lactobacillus casei 2756 (a fast acid producer) or Lactobacillus acidophilus NCFB 1748 (a slow acid producer). In co-cultures of Lb. casei 2756 and B. cereus NVH 45, low numbers (10-70 cfu/ml) of B. cereus NVH 45 were observed at end pH 5.5 (72 h) while at pH 5.0 no viable cells (<10 cfu/ml) were detected (48-72 h). B. cereus NVH 45 did not sporulate in co-culture with Lb. casei 2756. In co-culture with Lb. acidophilus NCFB 1748, B. cereus NVH 45 sporulated and survived as spores. In these co-cultures B. cereus NVH 45 grew to higher maximum counts (>10(7) cfu/ml) than with Lb. casei 2756 (<10(7) cfu/ml). Significantly different amounts of lactic acid were observed between the two co-cultures after 7 and 12 h. A rapid decrease of pH appears to prevent B. cereus from sporulating and it seems that it is enough to just reach pH 5.0 rapidly and keep that pH to achieve the desirable inhibition of B. cereus. In the simulated pH experiments B. cereus NVH 45 was inoculated in the fermentor and the different pH developments from different LAB strains were monitored by addition of lactic acid. These experiments showed the same tendency: a fast pH reduction during the initial hours of fermentation, simulating lactococci, resulted in complete inhibition of B. cereus NVH 45 (<10 cfu/ml). However, when simulating the pH development of the two different Lactobacillus strains, complete inhibition of B. cereus NVH 45 was not seen. In co-cultures competition for nutrients with consequences for cell density appears to be important. Based on these results it seems that B. cereus must reach a certain density to induce sporulation.