Inactivation Kinetics of Listeria monocytogenes by High-Pressure Processing: Pressure and Temperature Variation

The enhanced quasi-chemical kinetics (EQCK) model is presented as a methodology to evaluate the nonlinear inactivation kinetics of baro-resistant Listeria monocytogenes in a surrogate protein food system by high-pressure processing (HPP) for various combinations of pressure (P= 207 to 414 MPa) and temperature (T= 20 to 50 °C). The EQCK model is based on ordinary differential equations derived from 6 "quasi-chemical reaction" steps. The EQCK model continuously fits the conventional stages of the microbial lifecycle: lag, growth, stationary phase, and death; and tailing. Depending on the conditions, the inactivation kinetics of L. monocytogenes by HPP show a lag, inactivation, and tailing. Accordingly, we developed a customized, 4-step subset version of the EQCK model sufficient to evaluate the HPP inactivation kinetics of L. monocytogenes and obtain values for the model parameters of lag (λ), inactivation rate (μ), rate constants (k), and "processing time" (tp). This latter parameter was developed uniquely to evaluate kinetics data showing tailing. Secondary models are developed by interrelating the fitting parameters with experimental parameters, and Monte Carlo simulations are used to evaluate parameter reproducibility. This 4-step model is also compared with the empirical Weibull and Polylog models. The success of the EQCK model (as its 4-step subset) for the HPP inactivation kinetics of baro-resistant L. monocytogenes showing tailing establishes several advantages of the EQCK modeling approach for investigating nonlinear microbial inactivation kinetics, and it has implications for determining mechanisms of bacterial spore inactivation by HPP. Practical Application: Results of this study will be useful to the many segments of the food processing industry (ready-to-eat meats, fresh produce, seafood, dairy) concerned with ensuring the safety of consumers from the health hazards of Listeria monocytogenes, particularly through the use of emerging food preservation technologies such as high-pressure processing.     

A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing

Predictive microbial models generally rely on the growth of bacteria in laboratory broth to approximate the microbial growth kinetics expected to take place in actual foods under identical environmental conditions. Sigmoidal functions such as the Gompertz or logistics equation accurately model the typical microbial growth curve from the lag to the stationary phase and provide the mathematical basis for estimating parameters such as the maximum growth rate (MGR). Stationary phase data can begin to show a decline and make it difficult to discern which data to include in the analysis of the growth curve, a factor that influences the calculated values of the growth parameters. In contradistinction, the quasi-chemical kinetics model provides additional capabilities in microbial modelling and fits growth-death kinetics (all four phases of the microbial lifecycle continuously) for a general set of microorganisms in a variety of actual food substrates. The quasi-chemical model is differential equations (ODEs) that derives from a hypothetical four-step chemical mechanism involving an antagonistic metabolite (quorum sensing) and successfully fits the kinetics of pathogens (Staphylococcus aureus, Escherichia coli and Listeria monocytogenes) in various foods (bread, turkey meat, ham and cheese) as functions of different hurdles (a_w, pH, temperature and anti-microbial lactate). The calculated value of the MGR depends on whether growth-death data or only growth data are used in the fitting procedure. The quasi-chemical kinetics model is also exploited for use with the novel food processing technology of high-pressure processing. The high-pressure inactivation kinetics of E. coli are explored in a model food system over the pressure (P) range of 207–345 MPa (30,000–50,000 psi) and the temperature (T) range of 30–50 °C. In relatively low combinations of P and T, the inactivation curves are non-linear and exhibit a shoulder prior to a more rapid rate of microbial destruction. In the higher P, T regime, the inactivation plots tend to be linear. In all cases, the quasi-chemical model successfully fit the linear and curvi-linear inactivation plots for E. coli in model food systems. The experimental data and the quasi-chemical mathematical model described herein are candidates for inclusion in ComBase, the developing database that combines data and models from the USDA Pathogen Modeling Program and the UK Food MicroModel.     

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.     

淡腌黄鱼微生物生长动力学参数的初步研究

对淡腌黄鱼产品在不同温度条件下进行贮藏性实验，研究贮藏期间产品的微生物生长情况及产品的品质变化，根据实验数据用运Gompertz动力学方程，得出产品中微生物生长动力学参数。从产品感官、TVBN评价和微生物生长动态分析中，得出产品在不同贮藏条件下的货架期。通过温度对微生物生长速率的影响，分析栅栏效应。食品在联合栅栏作用下，存在着微生物生长／非生长界面，探讨通过从微生物生长动力学模型的参数来限定微生物生长/非生长界面的可能性，即量化栅栏技术。为开发一种最低限度影响产品质量和保障产品安全的新一代食品保藏技术提供一些有用的实验参数。     

基于Baranyi模型的波动温度下鲐鱼微生物生长动力学模型

以鲐鱼为研究对象,进行恒温下细菌总数的计数并建立基于Baranyi模型的微生物生长动力学模型。对Baranyi模型进行改进,构建波动温度下的微生物生长动力学模型,并运用模拟实验对模型进行验证,验证结果是偏差因子为1.23,准确因子为1.12,表明所构建的微生物生长动力学模型能够很好的拟合波动温度下鲐鱼中微生物的变化情况。     

Modeling UV-induced inactivation of microorganisms on surfaces

A model is presented to account for inactivation by UV light of microorganisms on the surfaces of solid materials. In the model, the surface is divided into a discrete number of zones, each having a characteristic exposure factor (alpha). This is the ratio of UV intensity actually "seen" by the microorganism to that incident on the surface. Application of the model requires inactivation data obtained under conditions where the surface microorganisms are fully exposed to incident UV (alpha = 1) as well as kinetic inactivation data for the same microorganisms actually present on the surface of interest during UV irradiation. The kinetics in question may apply either to a single species or to the characteristic microflora associated with a particular material. Standard nonlinear programming techniques were used to determine the number of zones among which the microorganisms are distributed, the alpha for each zone, and the fraction of the microbial population present in each zone. The model was applied to data previously published by Gardner and Shama for UV inactivation of Bacillus subtilis spores on the surfaces of filter papers and also to the data of Stermer et al. for UV irradiation of beef. Good representation of the kinetics was obtained, and a maximum of three zones was required to adequately represent the experimental data. One direct application of the model is that it yields quantitative information about the UV fluences necessary to achieve specified reductions in microbial viability.     

Predictive modeling of microbial single cells: A review

In practice, food products tend to be contaminated with food-borne pathogens at a low inoculum level. However, the huge potential risk cannot be ignored because microbes may initiate high-speed growth suitable conditions during the food chain, such as transportation or storage. Thus, it is important to perform predictive modeling of microbial single cells. Several key aspects of microbial single-cell modeling are covered in this review. First, based on previous studies, the techniques of microbial single-cell data acquisition and growth data collection are presented in detail. In addition, the sources of microbial single-cell variability are also summarized. Due to model microbial growth, traditional deterministic mathematical models have been developed. However, most models fail to make accurate predictions at low cell numbers or at the single-cell level due to high cell-to-cell heterogeneity. Stochastic models have been a subject of great interest; and these models take into consideration the variability in microbial single-cell behavior.     

Comparing uncertainty resulting from two-step and global regression procedures applied to microbial growth models

Two different microbial modeling procedures were compared and validated against independent data for Listeria monocytogenes growth. The most generally used method is two consecutive regressions: growth parameters are estimated from a primary regression of microbial counts, and a secondary regression relates the growth parameters to experimental conditions. A global regression is an alternative method in which the primary and secondary models are combined, giving a direct relationship between experimental factors and microbial counts. The Gompertz equation was the primary model, and a response surface model was the secondary model. Independent data from meat and poultry products were used to validate the modeling procedures. The global regression yielded the lower standard errors of calibration, 0.95 log CFU/ml for aerobic and 1.21 log CFU/ml for anaerobic conditions. The two-step procedure yielded errors of 1.35 log CFU/ml for aerobic and 1.62 log CFU/ ml for anaerobic conditions. For food products, the global regression was more robust than the two-step procedure for 65% of the cases studied. The robustness index for the global regression ranged from 0.27 (performed better than expected) to 2.60. For the two-step method, the robustness index ranged from 0.42 to 3.88. The predictions were overestimated (fail safe) in more than 50% of the cases using the global regression and in more than 70% of the cases using the two-step regression. Overall, the global regression performed better than the two-step procedure for this specific application.     

Modeling microbial survival during exposure to a lethal agent with varying intensity

Traditionally, the efficacy of preservation and disinfection processes has been assessed on the basis of the assumption that microbial mortality follows a first-order kinetic. However, as departures from this assumed kinetics are quite common, various other models, based on higher-order kinetics or population balance, have also been proposed. The database for either type of models is a set of survival curves of the targeted organism or spores determined under constant conditions, that is, constant temperature, chemical agent concentration, etc. Hence, to calculate the outcome of an actual industrial process, where conditions are changing, as in heating and cooling during a thermal treatment or when the agent dissipates as in chlorination or hydrogen peroxide application, one has to integrate the momentary effects of the lethal agent. This involves mathematical models based on assumed mortality kinetics, and simulated or measured history, for example, temperature-time or concentration-time relationships at the "coldest" point. It is shown that the survival curve under conditions where the agent intensity increases, decreases, or oscillates can be constructed without assuming any mortality kinetics and without the use of the traditional D and Z values, which require linear approximation, and without thermal death times, which require extrapolation. The actual survival curves can be compiled from the isothermal survival curves provided that growth and damage repair do not occur over the pertinent time scale and that the mortality rate is a function of only the momentary agent intensity and of the organism's or spore's survival fraction (but not of the rate at which this fraction has been reached). The calculation is greatly facilitated if both the "isothermal" survival curves and the time-dependent agent intensity can be expressed algebraically. The differential equation derived from these considerations can be solved numerically to produce the required survival curve under the changing conditions. The concept is demonstrated with simulated survival curves during heating at different rates, heating and cooling cycles, oscillating temperature, and exposure to a dissipating chemical agent. The simulated thermal processes are based on published data of Clostridium botulinum spores, whose semilogarithmic survival curves have upward concavity and on a hypothetical "Listeria-like" organism whose semilogarithmic curves have downward concavity.     

SHELF-LIFE AND MICROBIAL GROWTH KINETICS OF FRESH CITRUS JUICES: SHAMOUTI ORANGE

The paper deals with the shelf-life and endogenous microbial growth kinetics of freshly squeezed unpasteurized Shamouti orange juice. Microbial and organoleptic data was evaluated for seven temperatures (range of 2.0 to 14°C). Microbial lag-time was more sensitive to temperature change in the lower range (E _a = 42.4 Kcal/mol). The effect of temperature on growth rate was quite moderate in the lower range but in the order of 12.1 Kcal/mol at the upper end. Organoleptic data kinetics indicated that unpasteurized Shamouti juice can maintain its initial quality for 4 days if kept a 2°C and about 2 days if kept at 7°C. The kinetics data (both microbial and taste) was used successfully for the prediction of microbial growth and for taste deterioration under variable time-temperature conditions (i.e., simulation of cold chain path).     

A novel approach to predicting microbial inactivation kinetics during high pressure processing

The inactivation kinetics of Escherichia coli (ATCC 25922) during high pressure processing (HPP) was examined from 200 to 400 MPa in 50 MPa increments at 15 degrees C. Although the time course of HPP-induced E. coli inactivation in 0.1% peptone water successfully fitted the Weibull function, this procedure involved curve fitting, and not prediction. The objective of this study was to develop a novel HPP-induced microbial inactivation model to simulate the inactivation kinetics under various pressure conditions. The maximum inactivation rate during HPP was calculated from the inactivation curves at different pressure conditions on a semi-log plot. The relationship between the square root of the absolute value of the inactivation rate (k(max)) and treatment pressure was linear (R(2)=0.99). The linear relationship between k(max) and treatment pressure also successfully described independent data from other studies in the literature. Overall, the newly developed differential equation model, into which was substituted the square root function of the inactivation rate, was capable of simulating the inactivation kinetics during HPP at constant pressure. Additionally, the model could successfully describe the inactivation kinetics during HPP using other researchers' data. The accuracy of prediction of the new model was comparable to that derived from Weibull or modified Gompertz fitting to the observed data. Furthermore, the new model could successfully simulate the inactivation kinetics during dynamic pressure conditions, which included come-up time, changes in holding pressure during treatment, and pressure-release time. Moreover, the effect of pulsed pressure treatment was also simulated successfully using this model. Therefore, the modeling procedure presented in this study will contribute to the advancement of predictive modeling for HPP-induced microbial inactivation.     

Effect of chemicals on the microbial evolution in foods

In contrast with most chemical hazardous compounds, the concentration of food pathogens changes during processing, storage, and meal preparation, making it difficult to estimate the number of microorganisms or the concentration of their toxins at the moment of ingestion by the consumer. These changes are attributed to microbial proliferation, survival, and/or inactivation and must be considered when exposure to a microbial hazard is assessed. The number of microorganisms can also change as a result of physical removal, mixing of food ingredients, partitioning of a food product, or cross-contamination (M. J. Nauta. 2002. Int. J. Food Microbiol. 73:297-304). Predictive microbiology, i.e., relating these microbial evolutionary patterns to environmental conditions, can therefore be considered a useful tool for microbial risk assessment, especially in the exposure assessment step. During the early development of the field (late 1980s and early 1990s), almost all research was focused on the modeling of microbial growth over time and the influence of temperature on this growth. Later, modeling of the influence of other intrinsic and extrinsic parameters garnered attention. Recently, more attention has been given to modeling of the effects of chemicals on microbial inactivation and survival. This article is an overview of different applied strategies for modeling the effect of chemical compounds on microbial populations. Various approaches for modeling chemical growth inhibition, the growth-no growth interface, and microbial inactivation by chemicals are reviewed.     

Cell division theory and individual-based modeling of microbial lag: part I. The theory of cell division

This series of two papers deals with the theory of cell division and its implementation in an individual-based modeling framework. In this first part, the theory of cell division is studied on an individual-based level in order to learn more about the mechanistic principles behind microbial lag phenomena. While some important literature on cell division theory dates from 30 to 40 years ago, until now it has hardly been introduced in the field of predictive microbiology. Yet, it provides a large amount of information on how cells likely respond to changing environmental conditions. On the basis of this theory, a general theory on microbial lag behavior caused by a combination of medium and/or temperature changes has been developed in this paper. The proposed theory then forms the basis for a critical evaluation of existing modeling concepts for microbial lag in predictive microbiology. First of all, a more thorough definition can be formulated to define the lag time lambda and the previously only vaguely defined physiological state of the cells in terms of mechanistically defined parameters like cell mass, RNA or protein content, specific growth rate and time to perform DNA replication and cell division. On the other hand, existing predictive models are evaluated with respect to the newly developed theory. For the model of , a certain fitting parameter can also be related to physically meaningful parameters while for the model of [Augustin, J.-C., Rosso, L., Carlier, V.A. 2000. A model describing the effect of temperature history on lag time for Listeria monocytogenes. Int. J. Food Microbiol. 57, 169-181] a new, mechanistically based, model structure is proposed. A restriction of the proposed theory is that it is only valid for situations where biomass growth responds instantly to an environment change. The authors are aware of the fact that this assumption is not generally acceptable. Lag in biomass can be caused, for example, by a delayed synthesis of some essential growth factor (e.g., enzymes). In the second part of this series of papers [Dens, E.J., Bernaerts, K., Standaert, A.R., Kreft, J.-U., Van Impe, J.F., this issue. Cell division theory and individual-based modeling of microbial lag: part II. Modeling lag phenomena induced by temperature shifts. Int. J. Food Microbiol], the theory of cell division is implemented in an individual-based simulation program and extended to account for lags in biomass growth. In conclusion, the cell division theory applied to microbial populations in dynamic medium and/or temperature conditions provides a useful framework to analyze microbial lag behavior.     

Fitting semi‐empirical drying models using a tool based on wavelet neural networks: Modeling a maize drying process

Maize drying is an important process, especially for storage and conservation. For this study, the experimental stage was carried out using a forced convection dryer with air heated at different temperature conditions (306.05–441.85 K) and flow (0.13–0.256 m³/hr), totalizing 15 drying curves. Then the performances of the classic drying kinetics methodology and the approach proposed in this paper, in which the increase in moisture content of the product with time was represented combining exponential models and neural networks based on wavelets, were compared. Good performance was obtained in predictions using the proposed approach. One of the main differentials of the methodology adopted was the obtainment of a model that has a global predictive capacity, within the range of tested operating conditions, which can be used in predicting drying curves for different operating conditions.

Practical applications

The drying process is also one of the most widely used methods for preserving food, and has the advantage of reducing the costs of storage and transport because of the low volume and weight of the end product. During the last years, this topic has attracted a broad industrial interest, resulting in many research studies investigating the drying process. Usually, with regard to the classic approach for modeling of the drying process, the kinetics of drying curves obtained in different operating conditions is affected separately, that is, the parameters are estimated independently, resulting in different regression problems. With the classical approach, in general, it is not possible to obtain a comprehensive prediction model with regards to operating conditions. We have proposed an alternative modeling method. Aiming to obtain a modeling tool with an overall predictive ability, an approach for drying kinetics prediction that combines exponential models and neural networks was proposed. The proposed modeling method was able to predict drying curves for different operating conditions.     

Prediction of microbial growth in fresh-cut vegetables treated with acidic electrolyzed water during storage under various temperature conditions.

Effects of storage temperature (1, 5, and 10 degrees C) on growth of microbial populations (total aerobic bacteria, coliform bacteria, Bacillus cereus, and psychrotrophic bacteria) on acidic electrolyzed water (AcEW)-treated fresh-cut lettuce and cabbage were determined. A modified Gompertz function was used to describe the kinetics of microbial growth. Growth data were analyzed using regression analysis to generate "best-fit" modified Gompertz equations, which were subsequently used to calculate lag time, exponential growth rate, and generation time. The data indicated that the growth kinetics of each bacterium were dependent on storage temperature, except at 1 degrees C storage. At 1 degrees C storage, no increases were observed in bacterial populations. Treatment of vegetables with AcEW produced a decrease in initial microbial populations. However, subsequent growth rates were higher than on nontreated vegetables. The recovery time required by the reduced microbial population to reach the initial (treated with tap water [TW]) population was also determined in this study, with the recovery time of the microbial population at 10 degrees C being <3 days. The benefits of reducing the initial microbial populations on fresh-cut vegetables were greatly affected by storage temperature. Results from this study could be used to predict microbial quality of fresh-cut lettuce and cabbage throughout their distribution.     

Engineering modeling frameworks for microbial food safety at various scales

The landscape of mathematical model-based understanding of microbial food safety is wide and deep, covering interdisciplinary fields of food science, microbiology, physics, and engineering. With rapidly growing interest in such model-based approaches that increasingly include more fundamental mechanisms of microbial processes, there is a need to build a general framework that steers this evolutionary process by synthesizing literature spread over many disciplines. The framework proposed here shows four interconnected, complementary levels of microbial food processes covering sub-cellular scale, microbial population scale, food scale, and human population scale (risk). A continuum of completely mechanistic to completely empirical models, widely-used and emerging, are integrated into the framework; well-known predictive microbiology modeling being a part of this spectrum. The framework emphasizes fundamentals-based approaches that should get enriched over time, such as the basic building blocks of microbial population scale processes (attachment, migration, growth, death/inactivation and communication) and of food processes (e.g., heat and moisture transfer). A spectrum of models are included, for example, microbial population modeling covers traditional predictive microbiology models to individual-based models and cellular automata. The models are shown in sufficient quantitative detail to make obvious their coupling, or their integration over various levels. Guidelines to combine sub-processes over various spatial and time scales into a complete interdisciplinary and multiphysics model (i.e., a system) are provided, covering microbial growth/inactivation/transport and physical processes such as fluid flow and heat transfer. As food safety becomes increasingly predictive at various scales, this synthesis should provide its roadmap. This big picture and framework should be futuristic in driving novel research and educational approaches.     

肉品微生物生长预测模型研究进展

预测微生物学是一门利用现有的数据去预测未来发展趋势的新兴学科,这种方式可以对实际生产和流通过程进行监控.本文介绍了肉品微生物生长预测模型构建的基本过程、模型选择原则和评价方法.肉品介质是一个复杂的环境体系,在微生物生长预测模型预测过程中影响因素较多,应该根据具体的情况建立或推导出合适的模型来预测肉品中微生物的生长.