Mathematical Models for Prediction of Temperature Effects on Kinetic Parameters of Microorganisms’ Inactivation: Tools for Model Comparison and Adequacy in Data Fitting

Thermal Inactivation Kinetics and Radio Frequency Control of Aspergillus in Almond Kernels

Mold infections in almonds are a safety issue during post-harvest, storage and consumption, leading to health problems for consumers and causing economic losses. The aim of this study was to isolate mold from infected almond kernels and identify it by whole genome sequence (WGS). Then, the more heat resistant mold was selected and the thermal inactivation kinetics of this mold influenced by temperature and water activity (a_w) was developed. Hot air-assisted radio frequency (RF) heating was used to validate pasteurization efficacy based on the thermal inactivation kinetics of this target mold. The results showed that the two types of molds were Penicillium and Aspergillus identified by WGS. The selected Aspergillus had higher heat resistance than the Penicillium in the almond kernels. Inactivation data for the target Aspergillus fitted the Weibull model better than the first-order kinetic model. The population changes of the target Aspergillus under the given conditions could be predicted from Mafart’s modified Bigelow model. The RF treatment was effectively used for inactivating Aspergillus in almond kernels based on Mafart’s modified Bigelow model and the cumulative lethal time model.

Modelling the Efficacy of Febrile Heating in Infected Endotherms

Fever is a response to infection characterised by an increase in body temperature. The adaptive value of this body temperature increase for endotherms is unclear, given the relatively small absolute temperature increases associated with endotherm fever, its substantial metabolic costs, and the plausibility for pathogens to adapt to higher temperatures. We consider three thermal mechanisms for fever's antimicrobial effect: (1) direct growth inhibition by elevating temperature above the pathogens optimal growth temperature; (2) further differentiating the host body from the wider environment; and (3) through increasing thermal instability of the pathogen environment. We assess these by modelling their effects pathogen on temperature dependent growth, finding thermal effects can vary from highly to minimally effective depending on pathogen species. We also find, depending on the specification of a simple physical model, intermittent heating can inhibit pathogen growth more effectively than continuous heating with an energy constraint.

A phenomenological model to infer the microbial growth: A case study for psychrotrophic pathogenic bacteria

AIMS

The two-parameter (α and β) Schiraldi's model reliably fits growth curves of psychrotrophic pathogens and suggests a different description of the latency phase.

METHODS AND RESULTS

Data obtained at various temperatures and different starting cell densities for Aeromonas hydrophila, Listeria monocytogenes and Yersinia enterocolitica have been fitted with the Baranyi and Roberts' model and the new one. On average, the former showed higher standard error and R² values (0.140 and 0.991) than the Schiraldi's one (0.079 and 0.983). Around 15℃, the increase of temperature showed a milder effect on the growth rate than that expected. Y. enterocolitica showed a practically null duration of the lag phase, no matter the value of the starting density, whereas A. hydrophila and L. monocytogenes revealed slower onset trends.

CONCLUSIONS

Parameter β defines the number of cell duplications and appears independent on temperature, while (β/α)^1/2 is proportional to the maximum specific growth rate. The α^-1/2 versus temperature trend directly reflects the corresponding behaviour of the growth rate and does not require the use of Arrhenius plots.

SIGNIFICANCE AND IMPACT OF THE STUDY

Values of the parameters α and β, as well as the duration of the latency phase, allowed some considerations about the effect of storage temperature in terms of food safety, especially for psychrotrophic bacteria of concern.

Bayesian Generalized Linear Model for Simulating Bacterial Inactivation/Growth Considering Variability and Uncertainty

Conventional regression analysis using the least-squares method has been applied to describe bacterial behavior logarithmically. However, only the normal distribution is used as the error distribution in the least-squares method, and the variability and uncertainty related to bacterial behavior are not considered. In this paper, we propose Bayesian statistical modeling based on a generalized linear model (GLM) that considers variability and uncertainty while fitting the model to colony count data. We investigated the inactivation kinetic data of Bacillus simplex with an initial cell count of 10⁵ and the growth kinetic data of Listeria monocytogenes with an initial cell count of 10⁴. The residual of the GLM was described using a Poisson distribution for the initial cell number and inactivation process and using a negative binomial distribution for the cell number variation during growth. The model parameters could be obtained considering the uncertainty by Bayesian inference. The Bayesian GLM successfully described the results of over 50 replications of bacterial inactivation with average of initial cell numbers of 10¹, 10², and 10³ and growth with average of initial cell numbers of 10^–1, 10⁰, and 10¹. The accuracy of the developed model revealed that more than 90% of the observed cell numbers except for growth with initial cell numbers of 10¹ were within the 95% prediction interval. In addition, parameter uncertainty could be expressed as an arbitrary probability distribution. The analysis procedures can be consistently applied to the simulation process through fitting. The Bayesian inference method based on the GLM clearly explains the variability and uncertainty in bacterial population behavior, which can serve as useful information for risk assessment related to food borne pathogens.

A new expanded modelling approach for investigating the bioprotective capacity of Latilactobacillus sakei CTC494 against Listeria monocytogenes in ready-to-eat fish products

Understanding the role of food-related factors on the efficacy of protective cultures is essential to attain optimal results for developing biopreservation-based strategies. The aim of this work was to assess and model growth of Latilactobacillus sakei CTC494 and Listeria monocytogenes CTC1034, and their interaction, in two different ready-to-eat fish products (i.e., surimi-based product and tuna pâté) at 2 and 12 °C. The existing expanded Jameson-effect and a new expanded Jameson-effect model proposed in this study were evaluated to quantitatively describe the effect of microbial interaction. The inhibiting effect of the selected lactic acid bacteria strain on the pathogen growth was product dependent. In surimi product, a reduction of lag time of both strains was observed when growing in coculture at 2 °C, followed by the inhibition of the pathogen when the bioprotective L. sakei CTC494 reached the maximum population density, suggesting a mutualism-antagonism continuum phenomenon between populations. In tuna pâté, L. sakei CTC494 exerted a strong inhibition of L. monocytogenes at 2 °C (<0.5 log increase) and limited the growth at 12 °C (<2 log increase). The goodness-of-fit indexes indicated that the new expanded Jameson-effect model performed better and appropriately described the different competition patterns observed in the tested fish products. The proposed expanded competition model allowed for description of not only antagonistic but also mutualism-based interactions based on their influence on lag time.

To pool or not to pool: That is the question in microbial kinetics

Variation observed in heat inactivation of Salmonella strains (data from Combase) was characterized using multilevel modeling with two case studies. One study concerned repetitions at one temperature, the other concerned isothermal experiments at various temperatures. Multilevel models characterize variation at various levels and handle dependencies in the data. The Weibull model was applied using Bayesian regression. The research question was how parameters varied with experimental conditions and how data can best be analyzed: no pooling (each experiment analyzed separately), complete pooling (all data analyzed together) or partial pooling (connecting the experiments while allowing for variation between experiments). In the first case study, level 1 consisted of the measurements, level 2 of the group of repetitions. While variation in the initial number parameter was low (set by the researchers), the Weibull shape factor varied for each repetition from 0.58-1.44, and the rate parameter from 0.006-0.074 h. With partial pooling variation was much less, with complete pooling variation was strongly underestimated. In the second case study, level 1 consisted of the measurements, level 2 of the group of repetitions per temperature experiment, level 3 of the cluster of various temperature experiments. The research question was how temperature affected the Weibull parameters. Variation in initial numbers was low (set by the researchers), the rate parameter was obviously affected by temperature, the estimate of the shape parameter depended on how the data were analyzed. With partial pooling, and one-step global modeling with a Bigelow-type model for the rate parameter, shape parameter variation was minimal. Model comparison based on prediction capacity of the various models was explored. The probability distribution of calculated decimal reduction times was much narrower using multilevel global modeling compared to the usual single level two-step approach. Multilevel modeling of microbial heat inactivation appears to be a suitable and powerful method to characterize and quantify variation at various levels. It handles possible dependencies in the data, and yields unbiased parameter estimates. The answer on the question "to pool or not to pool" depends on the goal of modeling, but if the goal is prediction, then partial pooling using multilevel modeling is the answer, provided that the experimental data allow that.

Model of Fungal Development in Stored Barley Ecosystems as a Prognostic Auxiliary Tool for Postharvest Preservation Systems

Postharvest preservation and storage have a crucial impact on the technological quality and safety of grain. The important threat to stored grain quality and nutritional safety of cereal products is mould development and their toxic metabolites, mycotoxins. Models based on predictive microbiology, which are able to estimate the kinetics of fungal growth, and thus, the risks of mycotoxin accumulation in a mass of grain are promising prognostic tools that can be applied in postharvest management systems. The study developed a modelling approach to describe total fungal growth in barley ecosystems stored at different temperatures (T = 12–30 °C) and water activity in grain (aw = 0.78–0.96). As the pattern of fungal growth curves was sigmoidal, the experimental data were modelled using the modified Gompertz equation, in which constant coefficients reflecting biological parameters of mould development (i.e. lag phase duration (τlag), maximum growth rate (μmax) and the maximum increase in fungal population level (Δmaxlog(CFU)) were expressed as functions of storage conditions, i.e. aw and T. The criteria used to evaluate the overall model performance indicated its good precision (R2 = 0.95; RMSE = 0.23) and high prediction accuracy (bias factor and accuracy factor Bf = 1.004, Af = 1.035). The formulated model is able to estimate the extension of fungal contamination in a bulk of grain versus time by monitoring temperature and intergranular relative humidity that are readily measurable in practice parameters; therefore, it may be used as a prognostic support tool in modern postharvest management systems.

Microbial Dose-Response Curves and Disinfection Efficacy Models Revisited

The same term “dose-response curve” describes the relationship between the number of ingested microbes or their logarithm, and the probability of acute illness or death (type I), and between a disinfectant’s dose and the targeted microbe’s survival ratio (type II), akin to survival curves in thermal and non-thermal inactivation kinetics. The most common model of type I curves is the cumulative form of the beta-Poisson distribution which is sometimes indistinguishable from the lognormal or Weibull distribution. The most notable survival kinetics models in static disinfection are of the Chick-Watson-Hom’s kind. Their published dynamic versions, however, should be viewed with caution. A microbe population’s type II dose-response curve, static and dynamic, can be viewed as expressing an underlying spectrum of individual vulnerabilities (or resistances) to the particular disinfectant. Therefore, such a curve can be described mathematically by the flexible Weibull distribution, whose scale parameter is a function of the disinfectant’s intensity, temperature, and other factors. But where the survival ratio’s drop is so steep that the static dose-response curve resembles a step function, the Fermi distribution function becomes a suitable substitute. The utility of the CT (or Ct) concept primarily used in water disinfection is challenged on theoretical grounds and its limitations highlighted. It is suggested that stochastic models of microbial inactivation could be used to link the fates of individual viruses or bacteria to their manifestation in the survival curve’s shape. Although the emphasis is on viruses and bacteria, most of the discussion is relevant to fungi, protozoa, and perhaps worms too.