Simen Akkermans

Introducing a novel interaction model structure for the combined effect of temperature and pH on the microbial growth rate.

Efficient modelling of the microbial growth rate can be performed by combining the effects of individual conditions in a multiplicative way, known as the gamma concept. However, several studies have illustrated that interactions between different effects should be taken into account at stressing environmental conditions to achieve a more accurate description of the growth rate. In this research, a novel approach for modeling the interactions between the effects of environmental conditions on the microbial growth rate is introduced. As a case study, the effect of temperature and pH on the growth rate of Escherichia coli K12 is modeled, based on a set of computer controlled bioreactor experiments performed under static environmental conditions. The models compared in this case study are the gamma model, the model of Augustin and Carlier (2000), the model of Le Marc et al. (2002) and the novel multiplicative interaction model, developed in this paper. This novel model enables the separate identification of interactions between the effects of two (or more) environmental conditions. The comparison of these models focuses on the accuracy, interpretability and compatibility with efficient modeling approaches. Moreover, for the separate effects of temperature and pH, new cardinal parameter model structures are proposed. The novel interaction model contributes to a generic modeling approach, resulting in predictive models that are (i) accurate, (ii) easily identifiable with a limited work load, (iii) modular, and (iv) biologically interpretable.

Improving microbiological safety and quality characteristics of wheat and barley by high voltage atmospheric cold plasma closed processing

Contamination of cereal grains as a key global food resource with insects or microorganisms is a persistent concern for the grain industry due to irreversible damage to quality and safety characteristics and economic losses. Atmospheric cold plasma presents an alternative to conventional grain decontamination methods owing to the high antimicrobial potential of reactive species generated during the treatment, but effects against product specific microflora are required to understand how to optimally develop this approach for grains. This work investigated the influence of ACP processing parameters for both cereal grain decontamination and grain quality as important criteria for grain or seed use. A high voltage (HV) (80 kV) dielectric barrier discharge (DBD) closed system was used to assess the potential for control of native microflora and pathogenic bacterial and fungal challenge microorganisms, in tandem with effects on grain functional properties. Response surface modelling of experimental data probed the key factors in relation to microbial control and seed germination promotion. The maximal reductions of barley background microbiota were 2.4 and 2.1 log10 CFU/g and of wheat - 1.5 and 2.5 log10 CFU/g for bacteria and fungi, respectively, which required direct treatment for 20 min followed by a 24 h sealed post-treatment retention time. In the case of challenge organisms inoculated on barley grains, the highest resistance was observed for Bacillus atrophaeus endospores, which, regardless of retention time, were maximally reduced by 2.4 log10 CFU/g after 20 min of direct treatment. The efficacy of the plasma treatment against selected microorganisms decreased in the following order: E. coli > P. verrucosum (spores) > B. atrophaeus (vegetative cells) > B. atrophaeus (endospores). The challenge microorganisms were more susceptible to ACP treatment than naturally present background microbiota. No major effect of short term plasma treatment on the retention of quality parameters was observed. Germination percentage measured after 7 days cultivation was similar for samples treated for up to 5 min, but this was decreased after 20 min of direct treatment. Overall, ACP proved effective for cereal grain decontamination, but it is noted that the diverse native micro-flora may pose greater resistance to the closed, surface decontamination approach than the individual fungal or bacterial challenges, which warrants investigation of grain microbiome responses to ACP.

Optimal experimental design for discriminating between microbial growth models as function of suboptimal temperature: From in silico to in vivo

Temperature is an important food preservation factor, affecting microbial growth. Secondary predictive models can be used for describing the impact of this factor on microbial growth. In other words, the microbial behavior can be described in a dynamic environment with the use of a primary and secondary model. Two models for describing the effect of temperature on the microbial growth rate are the cardinal temperature model with inflection (CTMI) (Rosso et al., 1993) and its adapted version (aCTMI) (Le Marc et al., 2002). Although Escherichia coli is commonly modeled using CTMI, there are indications that aCTMI may be more appropriate (Van Derlinden and Van Impe, 2012a). For clarifying this, the method of Optimal experiment design for model discrimination (OED/MD) will be used in this work (Donckels et al., 2009; Schwaab et al., 2008). Results from an in silico study point out the required direction. Whereas the results of the in vivo study give a more realistic answer to the research question. Finally, discrimination unravelled the appropriate model for the needed use.

On the effect of sampling rate and experimental noise in the discrimination between microbial growth models in the suboptimal temperature range

Abstract Biochemical and microbial processes benefit from mathematical models. Often microbial kinetics are described as a function of environmental conditions in models exploited in predictive microbiology. Based on the organism different model structures are available. However, the aim is to determine the model that describes the system best. This work deals with secondary models describing microbial kinetics in the suboptimal temperature range and their possibility to be discriminated. The used models are the cardinal temperature model with inflection and its adapted version. The method of Optimal Experiment Design for Model Discrimination is used to investigate the practical (in)feasibility of model discrimination given different noise and sampling frequency values. Results point out the required steps and the possibilities of the method for model discrimination. It has been observed that discrimination is possible at various noise and sampling frequency levels. Moreover, also the corresponding increase in required experimental effort has been obtained.

Parameter estimations in predictive microbiology: Statistically sound modelling of the microbial growth rate

When building models to describe the effect of environmental conditions on the microbial growth rate, parameter estimations can be performed either with a one-step method, i.e., directly on the cell density measurements, or in a two-step method, i.e., via the estimated growth rates. The two-step method is often preferred due to its simplicity. The current research demonstrates that the two-step method is, however, only valid if the correct data transformation is applied and a strict experimental protocol is followed for all experiments. Based on a simulation study and a mathematical derivation, it was demonstrated that the logarithm of the growth rate should be used as a variance stabilizing transformation. Moreover, the one-step method leads to a more accurate estimation of the model parameters and a better approximation of the confidence intervals on the estimated parameters. Therefore, the one-step method is preferred and the two-step method should be avoided.

Occurrence, distribution and contamination levels of heat-resistant moulds throughout the processing of pasteurized high-acid fruit products

Heat-resistant moulds (HRMs) are well known for their ability to survive pasteurization and spoil high-acid food products, which is of great concern for processors of fruit-based products worldwide. Whilst the majority of the studies on HRMs over the last decades have addressed their inactivation, few data are currently available regarding their contamination levels in fruit and fruit-based products. Thus, this study aimed to quantify and identify heat-resistant fungal ascospores from samples collected throughout the processing of pasteurized high-acid fruit products. In addition, an assessment on the effect of processing on the contamination levels of HRMs in these products was carried out. A total of 332 samples from 111 batches were analyzed from three processing plants (=three processing lines): strawberry puree (n = 88, Belgium), concentrated orange juice (n = 90, Brazil) and apple puree (n = 154, the Netherlands). HRMs were detected in 96.4% (107/111) of the batches and 59.3% (197/332) of the analyzed samples. HRMs were present in 90.9% of the samples from the strawberry puree processing line (1-215 ascospores/100 g), 46.7% of the samples from the orange juice processing line (1-200 ascospores/100 g) and 48.7% of samples from the apple puree processing line (1-84 ascospores/100 g). Despite the high occurrence, the majority (76.8%, 255/332) of the samples were either not contaminated or presented low levels of HRMs (<10 ascospores/100 g). For both strawberry puree and concentrated orange juice, processing had no statistically significant effect on the levels of HRMs (p > 0.05). On the contrary, a significant reduction (p < 0.05) in HRMs levels was observed during the processing of apple puree. Twelve species were identified belonging to four genera - Byssochlamys, Aspergillus with Neosartorya-type ascospores, Talaromyces and Rasamsonia. N. fumigata (23.6%), N. fischeri (19.1%) and B. nivea (5.5%) were the predominant species in pasteurized products. The quantitative data (contamination levels of HRMs) were fitted to exponential distributions and will ultimately be included as input to spoilage risk assessment models which would allow better control of the spoilage of heat treated fruit products caused by heat-resistant moulds.

Simulation of Escherichia coli Dynamics in Biofilms and Submerged Colonies with an Individual-Based Model Including Metabolic Network Information

Clustered microbial communities are omnipresent in the food industry, e.g., as colonies of microbial pathogens in/on food media or as biofilms on food processing surfaces. These clustered communities are often characterized by metabolic differentiation among their constituting cells as a result of heterogeneous environmental conditions in the cellular surroundings. This paper focuses on the role of metabolic differentiation due to oxygen gradients in the development of Escherichia coli cell communities, whereby low local oxygen concentrations lead to cellular secretion of weak acid products. For this reason, a metabolic model has been developed for the facultative anaerobe E. coli covering the range of aerobic, microaerobic, and anaerobic environmental conditions. This metabolic model is expressed as a multiparametric programming problem, in which the influence of low extracellular pH values and the presence of undissociated acid cell products in the environment has been taken into account. Furthermore, the developed metabolic model is incorporated in MICRODIMS, an in-house developed individual-based modeling framework to simulate microbial colony and biofilm dynamics. Two case studies have been elaborated using the MICRODIMS simulator: (i) biofilm growth on a substratum surface and (ii) submerged colony growth in a semi-solid mixed food product. In the first case study, the acidification of the biofilm environment and the emergence of typical biofilm morphologies have been observed, such as the mushroom-shaped structure of mature biofilms and the formation of cellular chains at the exterior surface of the biofilm. The simulations show that these morphological phenomena are respectively dependent on the initial affinity of pioneer cells for the substratum surface and the cell detachment process at the outer surface of the biofilm. In the second case study, a no-growth zone emerges in the colony center due to a local decline of the environmental pH. As a result, cellular growth in the submerged colony is limited to the colony periphery, implying a linear increase of the colony radius over time. MICRODIMS has been successfully used to reproduce complex dynamics of clustered microbial communities.

An interaction model for the combined effect of temperature, pH and water activity on the growth rate of E. coli K12

Previous research has indicated that more complex model structures than the commonly used gamma model are needed to obtain an accurate prediction of the effect of multiple environmental conditions on the microbial growth rate. Due to the complexity associated with the development of such model structures, it is recommended that the model structure is compatible with a modular model building method. In this research, a gamma-interaction model was built to describe the combined effect of temperature, pH and water activity on the microbial growth rate of E. coli K12 based on a dataset of 68 bioreactor experiments. This novel interaction model was compared with the standard gamma model. The model structures were tested separately for the combined effects of (i) temperature and pH, (ii) pH and water activity, (iii) temperature and water activity and (iv) temperature, pH and water activity. Based on the results of this research, it was concluded that models for the combined effect of environmental conditions need to allow for sufficient flexibility for the description of combined effects of environmental conditions to obtain accurate model predictions. In the current study, this flexibility was successfully introduced by using the gamma-interaction model. A cross-validation study also demonstrated that the predictions of the interaction model are more robust with respect to the specific data used than the gamma model. As such, the gamma-interaction model provides food producers and food safety authorities with a more accurate and reliable tool for the prediction of the microbial growth rate as a function of multiple environmental conditions.

A low-complexity metabolic network model for the respiratory and fermentative metabolism of Escherichia coli

Over the last decades, predictive microbiology has made significant advances in the mathematical description of microbial spoiler and pathogen dynamics in or on food products. Recently, the focus of predictive microbiology has shifted from a (semi-)empirical population-level approach towards mechanistic models including information about the intracellular metabolism in order to increase model accuracy and genericness. However, incorporation of this subpopulation-level information increases model complexity and, consequently, the required run time to simulate microbial cell and population dynamics. In this paper, results of metabolic flux balance analyses (FBA) with a genome-scale model are used to calibrate a low-complexity linear model describing the microbial growth and metabolite secretion rates of Escherichia coli as a function of the nutrient and oxygen uptake rate. Hence, the required information about the cellular metabolism (i.e., biomass growth and secretion of cell products) is selected and included in the linear model without incorporating the complete intracellular reaction network. However, the applied FBAs are only representative for microbial dynamics under specific extracellular conditions, viz., a neutral medium without weak acids at a temperature of 37℃. Deviations from these reference conditions lead to metabolic shifts and adjustments of the cellular nutrient uptake or maintenance requirements. This metabolic dependency on extracellular conditions has been taken into account in our low-complex metabolic model. In this way, a novel approach is developed to take the synergistic effects of temperature, pH, and undissociated acids on the cell metabolism into account. Consequently, the developed model is deployable as a tool to describe, predict and control E. coli dynamics in and on food products under various combinations of environmental conditions. To emphasize this point,three specific scenarios are elaborated: (i) aerobic respiration without production of weak acid extracellular metabolites, (ii) anaerobic fermentation with secretion of mixed acid fermentation products into the food environment, and (iii) respiro-fermentative metabolic regimes in between the behaviors at aerobic and anaerobic conditions.

Including experimental uncertainty on the independent variables when modelling microbial dynamics: The combined effect of pH and acetic acid on the growth rate of E. coli K12

Modelling methods applied in predictive microbiology generally neglect the importance of uncertainty on the measurement of the independent variables. The Ordinary Least Squares (OLS) method that is commonly applied in predictive microbiology is only applicable if the experimental error on the inputs of the model are insignificant. However, this does not apply for many types of experimental measurements of the independent variables. Therefore, a parameter estimation method was adapted in this research for the estimation of the parameters of secondary models, taking into account uncertainty on the measurement of the influencing food characteristics. This parameter estimation method was based on the work of Stortelder (1996) and is referred to as the Weighted Total Least Squares method (WTLS). The method is formulised as an extension of the commonly used OLS method. Consequently the current WTLS method (i) is easily implemented using similar numerical methods, (ii) reduces to an OLS method when the measurement error on the model inputs is negligible and (iii) enables the evaluation of the accuracy of the model parameter estimates based on the same approximations.