Toward predictive food process models: A protocol for parameter estimation

An integrated multiphase dynamic genome-scale model explains batch fermentations led by species of the Saccharomyces genus

During batch fermentation, a variety of compounds are synthesized, as microorganisms undergo distinct growth phases: lag, exponential, growth-no-growth transition, stationary, and decay. A detailed understanding of the metabolic pathways involved in these phases is crucial for optimizing the production of target compounds. Dynamic flux balance analysis (dFBA) offers insight into the dynamics of metabolic pathways. However, explaining secondary metabolism remains a challenge. A multiphase and multi-objective dFBA scheme (MPMO model) has been proposed for this purpose. However, its formulation is discontinuous, changing from phase to phase; its accuracy in predicting intracellular fluxes is hampered by the lack of a mechanistic link between phases; and its simulation requires considerable computational effort. To address these limitations, we combine a novel model with a genome-scale model to predict the distribution of intracellular fluxes throughout batch fermentation. This integrated multiphase continuous model (IMC) has a unique formulation over time, and it incorporates empirical regulatory descriptions to automatically identify phase transitions and incorporates the hypotheses that yeasts might vary their cellular objective over time to adapt to the changing environment. We validated the predictive capacity of the IMC model by comparing its predictions with intracellular metabolomics data for Saccharomyces uvarum during batch fermentation. The model aligns well with the data, confirming its predictive capabilities. Notably, the IMC model accurately predicts trehalose accumulation, which was enforced in the MPMO model. We further demonstrate the generalizability of the IMC model, explaining the dynamics of primary and secondary metabolism of three Saccharomyces species. The model provides biological insights consistent with the literature and metabolomics data, establishing it as a valuable tool for exploring the dynamics of novel fermentation processes.IMPORTANCEThis work presents an integrated multiphase continuous dynamic genome-scale model (IMC model) for batch fermentation, a crucial process widely used in industry to produce biofuels, enzymes, pharmaceuticals, and food products or ingredients. The IMC model integrates a continuous kinetic model with a genome-scale model to address the critical limitations of existing dynamic flux balance analysis schemes, such as the difficulty of explaining secondary metabolism, the lack of mechanistic links between growth phases, or the high computational demands. The model also introduces the hypothesis that cells adapt the FBA objective over time. The IMC improves the accuracy of intracellular flux predictions and simplifies the implementation process with a unique dFBA formulation over time. Its ability to predict both primary and secondary metabolism dynamics in different Saccharomyces species underscores its versatility and robustness. Furthermore, its alignment with empirical metabolomics data validates its predictive power, offering valuable insights into metabolic processes during batch fermentation. These advances pave the way for optimizing fermentation processes, potentially leading to more efficient production of target compounds and novel biotechnological applications.

Traditional food processing and Acrylamide formation: A review

Tradition methods that are applied for the processing of food commonly use relatively high temperature and long cooking time for the preparation of foods. This relatively high temperature and long processing time of foods especially in the presence of carbohydrate is highly associated with the formation of acrylamide. Acrylamide is a process contaminant that is highly toxic to humans and remains as a global issue. The occurrence of acrylamide in traditional foods is a major public health problem. Studies that are conducted in different countries indicated that traditionally processed foods are highly linked to the formation of acrylamide. Therefore, understanding the factors influencing acrylamide formation during traditional food processing techniques is crucial for ensuring food safety and minimizing exposure to this harmful chemical compound. Several research reports indicate that proper food processing is the most effective solution to address food safety concerns by identifying foods susceptible to acrylamide formation. This review aims to provide an overview of traditional food processing techniques and their potential contribution to the formation acrylamide and highlight the importance of mitigating its formation in food products. The information obtained in this review may be of great value to future researchers, policymakers, society, and manufacturers.

Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review

Fish freshness can be considered as the combination of different nutritional and organoleptic attributes that rapidly deteriorate after fish capture, i.e., during processing (cutting, gutting, packaging), storage, transport, distribution, and retail. The rate at which this degradation occurs is affected by several stress variables such as temperature, water activity, or pH, among others. The food industry is aware that fish freshness is a key feature influencing consumers’ willingness to pay for the product. Therefore, tools that allow rapid and reliable assessment and prediction of the attributes related to freshness are gaining relevance. The main objective of this work is to provide a comprehensive review of the mathematical models used to describe and predict the changes in the key quality indicators in fresh fish and shellfish during storage. The work also briefly describes such indicators, discusses the most relevant stress factors affecting the quality of fresh fish, and presents a bibliometric analysis of the results obtained from a systematic literature search on the subject.

Monod model is insufficient to explain biomass growth in nitrogen-limited yeast fermentation

The yeast Saccharomyces cerevisiae is an essential microorganism in food biotechnology; particularly, in wine and beer making. During wine fermentation, yeasts transform sugars present in the grape juice into ethanol and carbon dioxide. The process occurs in batch conditions and is, for the most part, an anaerobic process. Previous studies linked limited-nitrogen conditions with problematic fermentations, with negative consequences for the performance of the process and the quality of the final product. It is, therefore, of the highest interest to anticipate such problems through mathematical models. Here we propose a model to explain fermentations under nitrogen-limited anaerobic conditions. We separated the biomass formation into two phases: growth and carbohydrate accumulation. Growth was modelled using the well-known Monod equation while carbohydrate accumulation was modelled by an empirical function, analogous to a proportional controller activated by the limitation of available nitrogen. We also proposed to formulate the fermentation rate as a function of the total protein content when relevant data are available. The final model was used to successfully explain experiments taken from the literature, performed under normal and nitrogen-limited conditions. Our results revealed that Monod model is insufficient to explain biomass formation kinetics in nitrogen-limited fermentations of S. cerevisiae. The goodness-of-fit of the herewith proposed model is superior to that of previously published models, offering the means to predict, and thus control fermentations. Importance: Problematic fermentations still occur in the winemaking industrial practise. Problems include sluggish rates of fermentation, which have been linked to insufficient levels of assimilable nitrogen. Data and relevant models can help anticipate poor fermentation performance. In this work, we proposed a model to predict biomass growth and fermentation rate under nitrogen-limited conditions and tested its performance with previously published experimental data. Our results show that the well-known Monod equation does not suffice to explain biomass formation.

Limonene nanoemulsified with soya lecithin reduces the intensity of non-isothermal treatments for inactivation of Listeria monocytogenes

Consumers' demands for ready-to-eat, fresh-like products are on the rise during the last years. This type of products have minimal processing conditions that can enable the survival and replication of pathogenic microorganisms. Among them, Listeria monocytogenes is of special concern, due to its relatively high mortality rate and its ability to replicate under refrigeration conditions. Previous research works have shown that nanoemulsified essential oils in combination with thermal treatments are effective for inactivating L. monocytogenes. However, previous research works were limited to isothermal conditions, whereas actual processing conditions in industry are dynamic. Under dynamic conditions, microorganism can respond unexpectedly to the thermal stress (e.g. adaptation, acclimation or increased sensitivity). In this work, we assess the combination of nanoemulsified D-limonene with thermal treatments under isothermal and dynamic conditions. The nanoemulsion was prepared following an innovative methodology using soya lecithin, a natural compound as well as the essential oil. Under isothermal heating conditions, the addition of the antimicrobial enables a reduction of the treatment time by a factor of 25. For time-varying treatments, dynamic effects were relevant. Treatments with a high heating rate (20 °C/min) are more effective than those with a slow heating rate (1 °C/min). This investigation demonstrates that the addition of nanoemulsified D-limonene can greatly reduce the intensity of the thermal treatments currently applied in the food industry. Hence, it can improve the product quality without impacting its safety.

Parameter Identification For Continuous Fluidized Bed Spray Agglomeration

Agglomeration represents an important particle formation process used in many industries. One particularly attractive process setup is continuous fluidized bed spray agglomeration, which features good mixing as well as high heat and mass transfer on the one hand and constant product throughput with constant quality as well as high flow rates compared to batch mode on the other hand. Particle properties such as agglomerate size or porosity significantly affect overall product properties such as re-hydration behavior and dissolubility. These can be influenced by different operating parameters. In this manuscript, a population balance model for a continuous fluidized bed spray agglomeration is presented and adapted to experimental data. Focus is on the description of the dynamic behavior in continuous operation mode in a certain neighborhood around steady-state. Different kernel candidates are evaluated and it is shown that none of the kernels are able to match the first six minutes with time independent parameters. Afterwards, a good fit can be obtained, where the Brownian and the volume independent kernel models match best with the experimental data. Model fit is improved for identification on a shifted time domain neglecting the initial start-up phase. Here, model identifiability is shown and parameter confidence intervals are computed via parametric bootstrap.

Relevance of the Induced Stress Resistance When Identifying the Critical Microorganism for Microbial Risk Assessment

Decisions regarding microbial risk assessment usually have to be carried out with incomplete information. This is due to the large number of possible scenarios and the lack of specific data for the problem considered. Consequently, risk assessment studies are based on the information obtained with a small number of bacterial cells which are considered the most heat resistant and/or more capable of multiplying during storage. The identification of the most resistant strains is usually based on D and z-values, normally estimated from isothermal experiments. This procedure omits the potential effect that the shape of the dynamic thermal profile applied in industry has on the microbial inactivation. One example of such effects is stress acclimation, which is related to a physiological response of the cells during sub-lethal treatments that increases their resistance. In this article, we use a recently published mathematical model to compare the development of thermal resistance for Escherichia coli K12 MG1655 and E. coli CECT 515 using inactivation data already published for these strains. Based only on the isothermal experiments, E. coli K12 MG1655 would be identified as more resistant to the thermal treatment than the CECT 515 strain in the 50-65°C temperature range. However, we conclude that stress acclimation is strain (and/or media)-dependent; the CECT 515 strain has a higher capacity for developing a stress acclimation than K12 MG1655 (300% increase of the D-value for CECT 515, 50% for K12 MG1655). It, thus, has the potential to be more resistant to the thermal treatment than the K12 MG1655 strain for some conditions allowing acclimation. A methodology is proposed to identify for which conditions this may be the case. After calibrating the model parameters representing acclimation using real experimental data, the applicability of the proposed approach is demonstrated using numerical simulations, showing how the CECT 515 strain can be more resistant for some heating profiles. Consequently, the most resistant bacterial strain to a dynamic heating profile should not be identified based only on isothermal experiments (D- and z-value). The relevance of stress acclimation for the treatment studied should also be evaluated.

Optimization of E. coli Inactivation by Benzalkonium Chloride Reveals the Importance of Quantifying the Inoculum Effect on Chemical Disinfection

Optimal disinfection protocols are fundamental to minimize bacterial resistance to the compound applied, or cross-resistance to other antimicrobials such as antibiotics. The objective is twofold: guarantee safe levels of pathogens and minimize the excess of disinfectant after a treatment. In this work, the disinfectant dose is optimized based on a mathematical model. The model explains and predicts the interplay between disinfectant and pathogen at different initial microbial densities (inocula) and dose concentrations. The study focuses on the disinfection of Escherichia coli with benzalkonium chloride, the most common quaternary ammonium compound. Interestingly, the specific benzalkonium chloride uptake (mean uptake per cell) decreases exponentially when the inoculum concentration increases. As a consequence, the optimal disinfectant dose increases exponentially with the initial bacterial concentration.

Saccharomyces cerevisiae and S. kudriavzevii Synthetic Wine Fermentation Performance Dissected by Predictive Modeling

Wineries face unprecedented challenges due to new market demands and climate change effects on wine quality. New yeast starters including non-conventional Saccharomyces species, such as S. kudriavzevii, may contribute to deal with some of these challenges. The design of new fermentations using non-conventional yeasts requires an improved understanding of the physiology and metabolism of these cells. Dynamic modeling brings the potential of exploring the most relevant mechanisms and designing optimal processes more systematically. In this work we explore mechanisms by means of a model selection, reduction and cross-validation pipeline which enables to dissect the most relevant fermentation features for the species under consideration, Saccharomyces cerevisiae T73 and Saccharomyces kudriavzevii CR85. The pipeline involved the comparison of a collection of models which incorporate several alternative mechanisms with emphasis on the inhibitory effects due to temperature and ethanol. We focused on defining a minimal model with the minimum number of parameters, to maximize the identifiability and the quality of cross-validation. The selected model was then used to highlight differences in behavior between species. The analysis of model parameters would indicate that the specific growth rate and the transport of hexoses at initial times are higher for S. cervisiae T73 while S. kudriavzevii CR85 diverts more flux for glycerol production and cellular maintenance. As a result, the fermentations with S. kudriavzevii CR85 are typically slower; produce less ethanol but higher glycerol. Finally, we also explored optimal initial inoculation and process temperature to find the best compromise between final product characteristics and fermentation duration. Results reveal that the production of glycerol is distinctive in S. kudriavzevii CR85, it was not possible to achieve the same production of glycerol with S. cervisiae T73 in any of the conditions tested. This result brings the idea that the optimal design of mixed cultures may have an enormous potential for the improvement of final wine quality.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

Mathematical quantification of the induced stress resistance of microbial populations during non-isothermal stresses

This contribution presents a mathematical model to describe non-isothermal microbial inactivation processes taking into account the acclimation of the microbial cell to thermal stress. The model extends the log-linear inactivation model including a variable and model parameters quantifying the induced thermal resistance. The model has been tested on cells of Escherichia coli against two families of non-isothermal profiles with different constant heating rates. One of the families was composed of monophasic profiles, consisting of a non-isothermal heating stage from 35 to 70°C; the other family was composed of biphasic profiles, consisting of a non-isothermal heating stage followed by a holding period at constant temperature of 57.5°C. Lower heating rates resulted in a higher thermal resistance of the bacterial population. This was reflected in a higher D-value. The parameter estimation was performed in two steps. Firstly, the D and z-values were estimated from the isothermal experiments. Next, the parameters describing the acclimation were estimated using one of the biphasic profiles. This set of parameters was able to describe the remaining experimental data. Finally, a methodology for the construction of diagrams illustrating the magnitude of the induced thermal resistance is presented. The methodology has been illustrated by building it for a biphasic temperature profile with a linear heating phase and a holding phase. This diagram provides a visualization of how the shape of the temperature profile (heating rate and holding temperature) affects the acclimation of the cell to the thermal stress. This diagram can be used for the design of inactivation treatments by industry taking into account the acclimation of the cell to the thermal stress.

Modeling Reveals the Role of Aging and Glucose Uptake Impairment in L1A1 Listeria monocytogenes Biofilm Life Cycle

Listeria monocytogenes is a food-borne pathogen that can persist in food processing plants by forming biofilms on abiotic surfaces. The benefits that bacteria can gain from living in a biofilm, i.e., protection from environmental factors and tolerance to biocides, have been linked to the biofilm structure. Different L. monocytogenes strains build biofilms with diverse structures, and the underlying mechanisms for that diversity are not yet fully known. This work combines quantitative image analysis, cell counts, nutrient uptake data and mathematical modeling to provide a mechanistic insight into the dynamics of the structure of biofilms formed by L. monocytogenes L1A1 (serotype 1/2a) strain. Confocal laser scanning microscopy (CLSM) and quantitative image analysis were used to characterize the structure of L1A1 biofilms throughout time. L1A1 forms flat, thick structures; damaged or dead cells start appearing early in deep layers of the biofilm and rapidly and massively loss biomass after 4 days. We proposed several reaction-diffusion models to explain the system dynamics. Model candidates describe biomass and nutrients evolution including mechanisms of growth and cell spreading, nutrients diffusion and uptake and biofilm decay. Data fitting was used to estimate unknown model parameters and to choose the most appropriate candidate model. Remarkably, standard reaction-diffusion models could not describe the biofilm dynamics. The selected model reveals that biofilm aging and glucose impaired uptake play a critical role in L1A1 L. monocytogenes biofilm life cycle.