A modified Weibull model for bacterial inactivation

Microbiological safety has been a critical issue for acid and acidified foods since it became clear that acid-tolerant pathogens such as Escherichia coli O157:H7 can survive (even though they are unable to grow) in a pH range of 3 to 4, which is typical for these classes of food products. The primary antimicrobial compounds in these products are acetic acid and NaCl, which can alter the intracellular physiology of E. coli O157:H7, leading to cell death. For combinations of acetic acid and NaCl at pH 3.2 (a pH value typical for non-heatprocessed acidified vegetables), survival curves were described by using a Weibull model. The data revealed a protective effect of NaCl concentration on cell survival for selected acetic acid concentrations. The intracellular pH of an E. coli O157:H7 strain exposed to acetic acid concentrations of up to 40 mM and NaCl concentrations between 2 and 4% was determined. A reduction in the intracellular pH was observed for increasing acetic acid concentrations with an external pH of 3.2. Comparing intracellular pH with Weibull model predictions showed that decreases in intracellular pH were significantly correlated with the corresponding times required to achieve a 5-log reduction in the number of bacteria.

mentioning

confidence: 99%

Modeling the Effects of Sodium Chloride, Acetic Acid, and Intracellular pH on Survival of Escherichia coli O157:H7

Hosein

Breidt

Smith

2011

“…This type of model can describe linear, concave, or convex curves. It was modified and extended to sigmoidal curves in heat treatment studies (2). The model of Baranyi and Roberts (3) and the model of Geeraerd et al (17) can describe a linear shape with or without shoulder or tail and sigmoidal shapes (21,22).…”

mentioning

confidence: 99%

General Model, Based on Two Mixed Weibull Distributions of Bacterial Resistance, for Describing Various Shapes of Inactivation Curves

Coroller¹,

Leguérinel²,

Mettler³

et al. 2006

181

110

Cells of Listeria monocytogenes or Salmonella enterica serovar Typhimurium taken from six characteristic stages of growth were subjected to an acidic stress (pH 3.3). As expected, the bacterial resistance increased from the end of the exponential phase to the late stationary phase. Moreover, the shapes of the survival curves gradually evolved as the physiological states of the cells changed. A new primary model, based on two mixed Weibull distributions of cell resistance, is proposed to describe the survival curves and the change in the pattern with the modifications of resistance of two assumed subpopulations. This model resulted from simplification of the first model proposed. These models were compared to the Whiting's model. The parameters of the proposed model were stable and showed consistent evolution according to the initial physiological state of the bacterial population. Compared to the Whiting's model, the proposed model allowed a better fit and more accurate estimation of the parameters. Finally, the parameters of the simplified model had biological significance, which facilitated their interpretation.When thermal or nonthermal inactivation of spores or vegetative microorganisms is considered, the log-linear shape of bacterial survival curves is a particular case among types of curves (12,17,43,49). In the case of nonthermal inactivation caused by unfavorable environmental conditions, the shape of curves indicates more pronounced heterogeneity according to the intensity of the stress. A bacterial strain can produce different shapes of survival curves. Frequently, concave curves may become convex or sigmoidal when the intensity of the stress varies (6,7,10,19,24,38,45,47,48). The patterns of survival curves may also vary with the physiological state of the cells and are dependent on the phase of growth (exponential or stationary phase) and also on the conditions of adaptation before the stress (18,25,36).In order to model nonthermal inactivation curves, a number of primary models have been proposed. Among these models are the vitalistic models proposed by Cole et al. (13,28,39), models describing both growth and inactivation (26,27,32,37,40,41), the modified Gompertz model (24, 32), the exponential model (31), and the log-linear model with latency time (6) and/or with a tail (5). These models cannot deal with all shapes of curves, and most of them are based on log-linear inactivation.Some models can describe non-log-linear decrease or sigmoidal inactivation curves. The Weibull model has largely been used in thermal and nonthermal treatment studies. It is based on the hypothesis that the resistance to stress of a population follows a Weibull distribution (14,19,34,44,45). This type of model can describe linear, concave, or convex curves. It was modified and extended to sigmoidal curves in heat treatment studies (2). The model of Baranyi and Roberts (3) and the model of Geeraerd et al. (17) can describe a linear shape with or without shoulder or tail and sigmoidal shapes (21,22). These models, which can...

“…For the modeling of the experimental data, GInaFiT (version 1.4), a freeware add-in for Microsoft Excel, was used (14). This software tool can calibrate the following models to the experimental data: (i) the traditional log-linear model (e.g., see reference 3), (ii) the log-linear model with shoulder and/or tail (13), (iii) Weibull-type models (2,24), and (iv) a biphasic model (10) and a newly proposed biphasic model with a preceding shoulder period (14). Next to the parameter values, the tool also computes statistical measures such as the sum of squared errors (SSE), the mean sum of squared errors (MSE), and the root mean sum of squared errors (RMSE).…”

Section: ϫ3mentioning

confidence: 99%

Individual and Combined Effects of pH and Lactic Acid Concentration on Listeria innocua Inactivation: Development of a Predictive Model and Assessment of Experimental Variability

Janssen

Geeraerd

Cappuyns

et al. 2007

In food technology, organic acids (e.g., lactic acid, acetic acid, and citric acid) are popular preservatives. The purpose of this study was to separate the individual effects of the influencing factors pH and undissociated lactic acid on Listeria innocua inactivation. Therefore, the inactivation process was investigated under controlled, initial conditions of pH (pH 0 ) and undissociated lactic acid ([LaH] 0 ). The resulting inactivation curves consisted of a (sometimes negligible) shoulder period followed by a descent phase. In a few cases, a tailing phase was observed. Depending on the conditions, the descent phase contained one or two log-linear parts or had a convex or concave shape. In addition, the inactivation process was characterized by a certain variability, dependent on the severity of the conditions. Furthermore, in the neighborhood of the growth/no growth interface sometimes contradictory observations occurred. Overall, the individual effects of the influencing factors pH and undissociated lactic acid could clearly be distinguished and were also apparent based on fluorescence microscopy. Appropriate model types were developed and enabled prediction of which conditions of pH 0 and [LaH] 0 are necessary to obtain a predetermined inactivation (number of decimal reductions) within a predetermined time range.Favored by their activity against a broad spectrum of pathogenic and spoilage microorganisms, even at low concentrations, organic acids (e.g., lactic acid, acetic acid, and citric acid) are popular preservatives in the food industry, where a tendency towards minimal processing is observed. In addition, lactic acid bacteria are used in food production processes to produce fermented foods. Secondary to the fermentative effect, the lactic acid metabolism has a preservative effect due to the production of other antimicrobial substances such as hydrogen peroxide and organic acids (34).The organic acid antimicrobial activity is twofold: (i) release of protons at dissociation lowers the extracellular pH, and (ii) the undissociated form of the acid is able to diffuse into the cell, affecting the cell metabolism. The latter effect is reported to result in a global inhibition due to acidification of the cytoplasm and a more specific inhibition of several metabolic and anabolic functions (1,23,35). The said antimicrobial activity can reveal itself in (i) inhibition, i.e., an early induction of the stationary phase, and (afterwards) (ii) inactivation, i.e., a decrease in cell concentration to values below the detection limit of the so-called target (pathogenic or spoilage) organism.In predictive microbiology, the knowledge of microbial growth or death responses to environmental factors is translated into mathematical equations that enable prediction of microbial proliferation or inactivation in foods. Final application lies in the quantitative assessment of the microbial safety and quality of food products, e.g., in defining the critical control points within a hazard analysis and critical control point framewo...