Modeling microbial competition in food: Application to the behavior of Listeria monocytogenes and lactic acid flora in pork meat products

The Development of Machine Learning-Assisted Software for Predicting the Interaction Behaviours of Lactic Acid Bacteria and Listeria monocytogenes

Biopreservation technology has emerged as a promising approach to enhance food safety and extend shelf life by leveraging the antimicrobial properties of beneficial microorganisms. This study aims to develop precise predictive models to characterize the growth and interaction dynamics of lactic acid bacteria (LAB) and Listeria monocytogenes, which serve as bioprotective agents in food systems. Using both traditional and machine learning modelling approaches, we analyzed data from previously published growth curves in broth (BHI) and milk under isothermal conditions (4, 10, and 30 °C). The models evaluated mono-culture conditions for L. monocytogenes and LAB, as well as their competitive interactions in co-culture scenarios. The modified Gompertz model demonstrated the best performance for mono-culture simulations, while a combination of the modified Gompertz and Lotka-Volterra models effectively described co-culture interactions, achieving high adjusted R-squared values (adjusted R2 = 0.978 and 0.962) and low root mean square errors (RMSE = 0.324 and 0.507) for BHI and milk, respectively. Machine learning approaches further validated these findings, with improved statistical indices (adjusted R2 = 0.988 and 0.966, RMSE = 0.242 and 0.475 for BHI and milk, respectively), suggesting their potential as robust alternatives to traditional methods. The integration of machine learning-assisted software developed in this work into predictive microbiology demonstrates significant advancements by bypassing the conventional primary and secondary modelling steps, enabling a streamlined, precise characterization of microbial interactions in food products.

Application of Mechanistic Models and the Gaussian Process Model to Predict Bacterial Growth on Baby Spinach During Refrigerated Storage

Models that predict bacterial growth in food products can help industry with decision-making with regard to microbial food spoilage. Such models have recently been developed using machine learning (ML) rather than a mechanistic understanding of bacterial growth. Thus, our aim was to compare the performance of mechanistic (M) models and the Gaussian process (GP) model (i.e., an ML approach) for predicting bacterial growth on spinach from a US-based supply chain as well as a China-based supply chain; models were developed using previously published data, as well as new data collected in this study from the China-based supply chain. For the packaged spinach collected in this study from the China-based supply chain, the mean net growth of aerobic, mesophilic bacteria over 10 days of shelf life was 1.16 log10 (n = 11, local distribution) and 1.29 log10 (n = 8, eCommerce distribution); bacterial growth on spinach did not differ significantly by distribution channel. The data obtained in this study, as well as previously published data on the growth of (i) individual bacterial strains (i.e., strain-level growth) and (ii) the overall bacterial population on baby spinach (i.e., population-level growth), were used to fit models. Specifically, GP models were fit to population-level growth data only, while M models were fit to strain-level and population-level growth data. The RMSE values for the M models (i.e., 0.72, 0.77 and 1.09 log10 CFU/g, for three M models assessed here) and GP models (i.e., 0.68 and 0.81 log10 CFU/g, for the two GP models assessed here) are similar, which suggests that both M and GP models show comparable accuracy at predicting bacterial growth on spinach.

Quorum sensing: the "switch" in the competitive relationship between Gram-positive bacteria based on transcriptomic analysis

Competition phenomenon is widely presented in nature, however, few reports on the competition phenomenon between bacteria based on the perspective of quorum sensing (QS), especially between Gram-positive bacteria. Here, the Gram-positive bacteria Rhodococcus sp. HD1 and Microbacterium sp. HM-2 were co-cultured, and the epiphysiological indicators, transcriptomics combined with gene engineering technique were applied to clarify the role of QS in the competition between Gram-positive bacteria. The results showed that the morphology of strain HD1 was changed into ellipsoids from long rods, the surface-to-volume ratio increased, and the competition index increased within strains HM-2 and HD1. The biomass of strain HD1(8.06×107 CFU/mL) was decreased significantly (p＜0.05) under co-culture system, compared with mono-culture (5.75×108 CFU/mL), indicating that strain HM-2 had an inhibitory effect on HD1 at 12 h. Transcriptomic analysis revealed that QS-related genes were highly expressed in strain HM-2, and the expression level of the virulence gene TM_0352 was the highest (FPKM: 1774.19). Meanwhile, the ABC transporters-related genes in strain HD1 were significantly increased. Furthermore, QS pathway-related genes in strain HM-2 and ABC transporters-related genes in strain HD1 showed a significant correlation with the gene TM_0352 expression by the Mantel test analysis (p<0.05), surmising that the TM_0352 gene played a dominant role in the co-culture system. Knockout and complementation experiments confirmed that the function of gene TM_0352. The structural equation model showed that the QS up-regulation of strain HM-2 significantly promoted the expression of virulence genes, while strain HD1 promoted ABC transporters to cope with the up-regulation of TM_0352. The up-regulation of TM_0352 promoted the biomass of strain HM-2 and inhibited the biomass of HD1.The above results displayed that the competition phenomenon appeared by QS driving the up-regulation of TM_0352 gene in strain HM-2, which led to the up-regulation of ABC transporters in strain HD1. And these findings provided new insights into the perspective of factors related to competition inhibition between bacteria.

Mathematical modeling and comparative metabolomics analyses of interactions between Lactiplantibacillus plantarum and Morganella morganii

Morganella morganii is a spoilage microorganism in fish products that produces harmful biogenic amines (BAs). It has been discovered that Lactiplantibacillus plantarum His6 can inhibit the growth of this bacterium. The aim of this study was to quantitatively assess the inhibitory impact of the bioprotective culture Lpb. plantarum His6 on M. morganii YC16 in the matrix (fish and rice) using predictive microbiology models, and elucidate the interaction mechanism through untargeted metabolomics. The mathematical model results showed the inhibition effect of Lpb. plantarum His6 on M. morganii YC16 was dependent on temperature and inoculation concentration. In addition, the simultaneous growth of Lpb. plantarum His6 and M. morganii YC16 could be well simulated with the Lotka-Volterra model. Furthermore, significant decreased in histamine levels was observed in co-(1:3) at 25 °C. Finally, based on the metabolomics data, it was speculated that Lpb. plantarum His6 may enhance bacteriocin production while reducing the yield of glycerophospholipids and fatty acids associated with outer membrane formation, thereby inhibiting the growth of M. morganii YC16. These findings provide valuable insights into the interaction behavior and mechanism of Lpb. plantarum His6 and M. morganii YC16 in co-culture, facilitating the design of the biopreservation strategies for fish products.

Modeling the growth of Salmonella in raw ground pork under dynamic conditions of temperature abuse

Salmonella contamination of pork products is a significant public health concern. Temperature abuse scenarios, such as inadequate refrigeration or prolonged exposure to room temperature, can enhance Salmonella proliferation. This study aimed to develop and validate models for Salmonella growth considering competition with background microbiota in raw ground pork, under isothermal and dynamic conditions of temperature abuse between 10 and 40 °C. The maximum specific growth rate (μmax) and maximum population density (MPD) were estimated to quantitatively describe the growth behavior of Salmonella. To reflect more realistic microbial interactions in Salmonella-contaminated product, our model considered competition with the background microbiota, measured as mesophilic aerobic plate counts (APC). Notably, the μmax of Salmonella in low-fat samples (∼5 %) was significantly higher (p < 0.05) than that in high-fat samples (∼25 %) at 10, 20, and 30 °C. The average doubling time of Salmonella was 26, 4, 2, 1.5, 0.8, and 1.1 h at 10, 15, 20, 25, 30, and 40 °C, respectively. The initial concentration of Salmonella minimally impacted its growth in ground pork at any temperature. The MPD of APC consistently exceeded that of Salmonella, indicating the growth of APC without competition from Salmonella. The competition model exhibited excellent fit with the experimental data, as 95 % (627/660) of residual errors fell within the desired acceptable prediction zone (pAPZ >0.70). The theoretical minimum and optimum growth temperatures for Salmonella ranged from 5 to 6 °C and 35 to 36 °C, respectively. The dynamic model displayed strong predictive performance, with 90 % (57/63) of residual errors falling within the APZ. Dynamic models could be valuable tools for validating and refining simpler static or isothermal models, ultimately improving their predictive capabilities to enhance food safety.

Validation of competition and dynamic models for Shiga toxin-producing Escherichia coli (STEC) growth in raw ground pork during temperature abuse

Epidemiological evidence suggests that pork products may be a vehicle for STEC transmission to humans. This study was conducted to validate competition and dynamic models for the growth of STEC during simulated temperature abuse of raw ground pork. Maximum specific growth rates μmax were modeled as a function of temperature using the Cardinal parameter equation, and a dynamic model was validated using sinusoidal temperature profiles. The Acceptable Prediction Zone (APZ) method was used to evaluate the model's performance. The competition model was well fitted to the experimental data having 93% (1849/1981) residual errors within the desired APZ. Growth rates were not different between STEC O157 and non-O157; however, serogroup O91 showed two to three times lower μmax than other STEC at 10, 25, and 30 °C. The theoretical minimum and optimum growth temperature for all STEC groups ranged from 3.4 to 7.8 °C and 33-35 °C, respectively. The dynamic model showed good prediction performance (pAPZ = 0.98) with the experimental data. These results can be used to inform risk assessment models and to support the implementation of risk mitigation strategies to improve the microbiological safety of raw pork products.

Shelf life estimation of refrigerated vacuum packed beef accounting for uncertainty

This study estimates the shelf life of vacuum packed beef meat (three muscles: striploin (longissimus thoracis et lumborum, LTL), tenderloin (psoas major, PM) and outside chuck (trapezius thoracis, TT)) at refrigeration temperatures (0 °C-10 °C) based on modelling the growth of two relevant groups of spoilage microorganisms: lactic acid bacteria (LAB) and Enterobacteriaceae. The growth models were developed combining a two-step and a one-step approach. The primary modelling was used to identify the parameters affecting the growth kinetics, guiding the definition of secondary growth models. For LAB, the secondary model included the effect of temperature and initial pH on the specific growth rate. On the other hand, the model for Enterobacteriaceae incorporated the effect of temperature on the specific growth rate and the lag phase; as well as the effect of the initial pH on the specific growth rate, the lag phase and the initial microbial count. We did not observe any significant effect of the type of muscle on the growth kinetics. Once the equations were defined, the models were fitted to the complete dataset using a one-step approach. Model validation was carried out by cross-validation, mitigating the impact of an arbitrary division between training and validation sets. The models were used to estimate the shelf life of the product, based on the maximum admissible microbial concentration (7 log CFU/g for LAB, 5 log CFU/g for Enterobacteriaceae). Although LAB was the dominant microbiota, in several cases, both LAB and Enterobacteriaceae reached the critical concentration practically at the same time. Furthermore, in some scenarios, the end of shelf life would be determined by Enterobacteriaceae, pointing at the potential importance of non-dominant microorganisms for product spoilage. These results can aid in the implementation of effective control measures in the meat processing industry.

Growth behavior of Shiga toxin-producing Escherichia coli, Salmonella, and generic E. coli in raw pork considering background microbiota at 10, 25, and 40 °C

Recent epidemiological evidence suggests that pork products may be vehicles for the transmission of Shiga toxin-producing Escherichia coli (STEC) to humans. The severe morbidity associated with STEC infections highlights the need for research to understand the growth behavior of these bacteria in pork products. Classical predictive models can estimate pathogen growth in sterile meat. However, competition models considering background microbiota reflect a more realistic scenario for raw meat products. The objective of this study was to estimate the growth kinetics of clinically significant STEC (O157, non-O157, and O91), Salmonella, and generic E. coli in raw ground pork using competition primary growth models at temperature abuse (10 and 25 °C) and sublethal temperature (40 °C). A competition model incorporating the No lag Buchanan model was validated using the acceptable prediction zone (APZ) method where >92 % (1498/1620) of the residual errors fell within the APZ (pAPZ > 0.70). The background microbiota (mesophilic aerobic plate counts, APC) inhibited the growth of STEC and Salmonella indicating a simple one-directional competitive interaction between pathogens and the mesophilic microbiota of ground pork. The maximum specific growth rate (μ_max) of all the bacterial groups was not significantly different (p > 0.05) based on fat content (5 vs 25 %) except for generic E. coli at 10 °C. E. coli O157 and non-O157 behaved similarly in terms of μ_max and maximum population density (MPD). Salmonella showed a similar (p > 0.05) μ_max to E. coli O157 and non-O157 at 10 and 40 °C but a significantly higher rate (p < 0.05) at 25 °C. STEC were more prone to be inhibited by APC than Salmonella at 10 and 25 °C. The μ_max of O91 was lower (p < 0.05) than other STEC and Salmonella at 10 and 25 °C but similar (p > 0.05) at 40 °C. Generic E. coli showed a two- to five-times higher (p < 0.05) μ_max (0.028 ± 0.011 log₁₀ CFU/h) than other bacterial groups (0.006 ± 0.004 to 0.012 ± 0.003 log₁₀ CFU/h) at 10 °C making it a potential indicator bacteria for process control. Industry and regulators can use competitive models to develop appropriate risk assessment and mitigation strategies to improve the microbiological safety of raw pork products.

Protective Cultures in Food Products: From Science to Market

An ultimate goal in food production is to guarantee food safety and security. Fermented food products benefit from the intrinsic capabilities of the applied starter cultures as they produce organic acids and bactericidal compounds such as hydrogen peroxide that hamper most food pathogens. In addition, highly potent small peptides, bacteriocins, are being expelled to exert antibiotic effects. Based on ongoing scientific efforts, there is a growing market of food products to which protective cultures are added exclusively for food safety and for prolonged shelf life. In this regard, most genera from the order Lactobacillales play a prominent role. Here, we give an overview on protective cultures in food products. We summarize the mode of actions of antibacterial mechanisms. We display the strategies for the isolation and characterization of protective cultures in order to have them market-ready. A survey of the growing market reveals promising perspectives. Finally, a comprehensive chapter discusses the current legislation issues concerning protective cultures, leading to the conclusion that the application of protective cultures is superior to the usage of defined bacteriocins regarding simplicity, economic costs, and thus usage in less-developed countries. We believe that further discovery of bacteria to be implemented in food preservation will significantly contribute to customer's food safety and food security, badly needed to feed world's growing population but also for food waste reduction in order to save substantial amounts of greenhouse gas emissions.

Microbiological safety of aged meat

The impact of dry-ageing of beef and wet-ageing of beef, pork and lamb on microbiological hazards and spoilage bacteria was examined and current practices are described. As 'standard fresh' and wet-aged meat use similar processes these were differentiated based on duration. In addition to a description of the different stages, data were collated on key parameters (time, temperature, pH and aw) using a literature survey and questionnaires. The microbiological hazards that may be present in all aged meats included Shiga toxin-producing Escherichia coli (STEC), Salmonella spp., Staphylococcus aureus, Listeria monocytogenes, enterotoxigenic Yersinia spp., Campylobacter spp. and Clostridium spp. Moulds, such as Aspergillus spp. and Penicillium spp., may produce mycotoxins when conditions are favourable but may be prevented by ensuring a meat surface temperature of -0.5 to 3.0°C, with a relative humidity (RH) of 75-85% and an airflow of 0.2-0.5 m/s for up to 35 days. The main meat spoilage bacteria include Pseudomonas spp., Lactobacillus spp. Enterococcus spp., Weissella spp., Brochothrix spp., Leuconostoc spp., Lactobacillus spp., Shewanella spp. and Clostridium spp. Under current practices, the ageing of meat may have an impact on the load of microbiological hazards and spoilage bacteria as compared to standard fresh meat preparation. Ageing under defined and controlled conditions can achieve the same or lower loads of microbiological hazards and spoilage bacteria than the variable log10 increases predicted during standard fresh meat preparation. An approach was used to establish the conditions of time and temperature that would achieve similar or lower levels of L. monocytogenes and Yersinia enterocolitica (pork only) and lactic acid bacteria (representing spoilage bacteria) as compared to standard fresh meat. Finally, additional control activities were identified that would further assure the microbial safety of dry-aged beef, based on recommended best practice and the outputs of the equivalence assessment.

Initial and Final Cell Concentrations Significantly Influence the Maximum Growth Rate of Listeria monocytogenes in Published Literature Data for Whole Intact Fresh Produce

ABSTRACT

Listeria monocytogenes has shown the ability to grow on fresh uncut produce; however, the factors that control growth are not well understood. Peer-reviewed journal articles (n = 29) meeting the inclusion criteria and related to the growth of L. monocytogenes on fresh produce were found through university library databases and Google Scholar searches. Growth models were fit to each of the extracted 130 data sets to estimate log CFU per day rates of growth by using the DMFit tool. Multiple linear stepwise regression models for factors influencing growth rate were developed using R software. Factors included were temperature, nutrient level of inoculation buffer, initial cell concentration, final cell concentration, inoculation method, container permeability, and surface characteristics. The full model produced adjusted R2, Akaike information criterion, and root mean square error values of 0.41, 488, and 1.61, respectively. Stepwise regression resulted in a reduced model with parameters for incubation temperature, inoculation buffer type, initial and final cell concentrations, container characteristics, and produce surface characteristics. Model fit statistics improved slightly in the reduced model. A further reduced three-parameter model included storage temperature and initial and final cell concentrations, with interaction terms. This three-parameter model had adjusted R2, Akaike information criterion, and root mean square error values of 0.66, 417, and 1.24, respectively. Incubation temperature (P = 1.00E-09) initial cell concentration (P = 3.05E-12), and final cell concentration (P = 4.17E-09) all had highly significant effects on maximum growth rate. Our findings show the importance of inoculum concentration and produce microbial carrying capacity on the estimated growth rate and highlight the overall importance that temperature has on growth rate. Future experiments should consider initial inoculum concentration carefully when conducting growth studies for L. monocytogenes on whole produce.

HIGHLIGHTS

A Bayesian Approach to Describe and Simulate the pH Evolution of Fresh Meat Products Depending on the Preservation Conditions

Measuring the pH of meat products during storage represents an efficient way to monitor microbial spoilage, since pH is often linked to the growth of several spoilage-associated microorganisms under different conditions. The present work aimed to develop a modelling approach to describe and simulate the pH evolution of fresh meat products, depending on the preservation conditions. The measurement of pH on fresh poultry sausages, made with several lactate formulations and packed under three modified atmospheres (MAP), from several industrial production batches, was used as case-study. A hierarchical Bayesian approach was developed to better adjust kinetic models while handling a low number of measurement points. The pH changes were described as a two-phase evolution, with a first decreasing phase followed by a stabilisation phase. This stabilisation likely took place around the 13th day of storage, under all the considered lactate and MAP conditions. The effects of lactate and MAP on pH previously observed were confirmed herein: (i) lactate addition notably slowed down acidification, regardless of the packaging, whereas (ii) the 50%CO₂-50%N₂ MAP accelerated the acidification phase. The Bayesian modelling workflow—and the script—could be used for further model adaptation for the pH of other food products and/or other preservation strategies.

Lactiplantibacillus plantarum subsp. plantarum and Fructooligosaccharides Combination Inhibits the Growth, Adhesion, Invasion, and Virulence of Listeria monocytogenes

Listeria monocytogenes is a foodborne pathogen responsible for many food outbreaks worldwide. This study aimed to investigate the single and combined effect of fructooligosaccharides (FOS) and Lactiplantibacillus plantarum subsp. plantarum CICC 6257 (L. plantarum) on the growth, adhesion, invasion, and virulence of gene expressions of Listeria monocytogenes 19112 serotype 4b (L. monocytogenes). Results showed that L. plantarum combined with 2% and 4% (w/v) FOS significantly (p < 0.05) inhibited the growth of L. monocytogenes (3-3.5 log10 CFU/mL reduction) at the incubation temperature of 10 °C and 25 °C. Under the same combination condition, the invasion rates of L. monocytogenes to Caco-2 and BeWo cells were reduced more than 90% compared to the result of the untreated group. After L. plantarum was combined with the 2% and 4% (w/v) FOS treatment, the gene expression of actin-based motility, sigma factor, internalin A, internalin B, positive regulatory factor A, and listeriolysin O significantly (p < 0.05) were reduced over 91%, 77%, 92%, 89%, 79%, and 79% compared to the result of the untreated group, respectively. The inhibition level of the L. plantarum and FOS combination against L. monocytogenes was higher than that of FOS or L. plantarum alone. Overall, these results indicated that the L. plantarum and FOS combination might be an effective formula against L. monocytogenes.

A mathematical model to predict the antilisteria bioprotective effect of Latilactobacillus sakei CTC494 in vacuum packaged cooked ham

Biopreservation is a strategy that has been extensively covered by the scientific literature from a variety of perspectives. However, the development of quantitative modelling approaches has received little attention, despite the usefulness of these tools for the food industry to assess the performance and to set the optimal application conditions. The objective of this study was to evaluate and model the interaction between the antilisteria strain Latilactobacillus sakei CTC494 (sakacin K producer) and Listeria monocytogenes in vacuum-packaged sliced cooked ham. Cooked ham was sliced under aseptic conditions and inoculated with L. monocytogenes CTC1034 and/or L. sakei CTC494 in monoculture and coculture at 10:10, 10:10³ and 10:10⁵ cfu/g ratios of pathogen:bioprotective cultures. Samples were vacuum packaged and stored at isothermal temperature (2, 5, 10 and 15 °C). The growth of the two bacteria was monitored by plate counting. The Logistic growth model was applied to estimate the growth kinetic parameters (N₀, λ, μ_max, N_max). The effect of storage temperature was modelled using the hyperbola (λ) and Ratkowsky (μ_max) models. The simple Jameson-effect model, its modifications including the N_cri and the interaction γ factor, and the predator-prey Lotka Volterra model were used to characterize the interaction between both microorganisms. Two additional experiments at non-isothermal temperature conditions were also carried out to assess the predictive performance of the developed models through the Acceptable Simulation Zone (ASZ) approach. In monoculture conditions, L. monocytogenes and L. sakei CTC494 grew at all temperatures. In coculture conditions, L. sakei CTC494 had an inhibitory effect on L. monocytogenes by lowering the N_max, especially with increasing levels of L. sakei CTC494 and lowering the storage temperature. At the lowest temperature (2 °C) L. sakei CTC494 was able to completely inhibit the growth of L. monocytogenes when added at a concentration 3 and 5 Log higher than that of the pathogen. The inhibitory effect of the L. sakei CTC494 against L. monocytogenes was properly characterized and modelled using the modified Jameson-effect with interaction γ factor model. The developed interaction model was tested under non-isothermal conditions, resulting in ASZ values ≥83%. This study shows the potential of L. sakei CTC494 in the biopreservation of vacuum-packaged cooked ham against L. monocytogenes. The developed interaction model can be useful for the industry as a risk management tool to assess and set biopreservation strategies for the control of L. monocytogenes in cooked ham.

Behaviour of Listeria monocytogenes and Natural Microflora during the Manufacture of Riojano Chorizo (Spanish Dry Cured Sausage)

Riojano chorizo is a dry cured sausage manufactured with traditional technologies without adding starter cultures at low temperatures. Its characteristics differ from other types of chorizo since sugars and nitrites are no added and processing temperatures are low- This work evaluates the behaviour of Listeria monocytogenes during the processing of inoculated Riojano chorizo as well as the natural microflora that can play a technological role or be of interest as indicators. The sausage mixture was inoculated with a cocktail of three selected strains of L. monocytogenes (CECT 932, CECT 934 and CECT 4032) (4 log10 CFU/g) and after processed following the traditional production method. Samples were taken before inoculation, after inoculation, after stuffing (day 0) and on days 6, 13, 21 and 28 of processing. L. monocytogenes, mesophiles, Micrococcaceae, lactic acid bacteria, Enterobacteriaceae, S. aureus, sulfite-reducing clostridia and molds and yeast counts were evaluated. Furthermore, pH, water activity and humidity were determined. No growth of L mocytogenes was observed during the first 6 days, when the temperature of processing was 4 °C. The low temperature in the initial stages was a relevant hurdle to control L. monocytoegenes growth. A significant decrease (p ≤ 0.05) in L. monocytogenes counts was observed on day 13 compared to the initial counts. During drying (days 6 to 21) a reduction in this pathogen of 1.28 log CFU/g was observed. The low water activity below 0.92 on day 13 and 0.86 on day 21 seems to be critical for the reduction of L. monocytogenes.

Microrisk Lab: An Online Freeware for Predictive Microbiology

Microrisk Lab is an R-based online modeling freeware designed to realize parameter estimation and model simulation in predictive microbiology. A total of 36 peer-reviewed models were integrated for parameter estimation (including primary models of bacterial growth/inactivation under static and nonisothermal conditions, secondary models of specific growth rate, and competition models of two-flora growth) and model simulation (including integrated models of deterministic or stochastic bacterial growth/inactivation under static and nonisothermal conditions) in Microrisk Lab. Each modeling section was designed to provide numerical and graphical results with comprehensive statistical indicators depending on the appropriate data set and/or parameter setting. In this study, six case studies were reproduced in Microrisk Lab and compared in parallel with DMFit, GInaFiT, IPMP 2013/GraphPad Prism, Bioinactivation FE, and @Risk, respectively. The estimated and simulated results demonstrated that the performance of Microrisk Lab was statistically equivalent to that of other existing modeling systems. Microrisk Lab allows for a friendly user experience when modeling microbial behaviors owing to its interactive interfaces, high integration, and interconnectivity. Users can freely access this application at https://microrisklab.shinyapps.io/english/ or https://microrisklab.shinyapps.io/chinese/.

Behavior of Listeria monocytogenes and Other Microorganisms in Sliced Riojano Chorizo (Spanish Dry-Cured Sausage) during Storage under Modified Atmospheres

Sliced ready-to-eat meat products packaged under modified atmospheres are often marketed since they cover consumer demands. The slicing process could be a potential risk for consumers since contamination with Listeria monocytogenes could occur during this stage. The current study evaluated the behavior of L. monocytogenes and other microorganisms in commercial sliced Riojano chorizo. This meat product was sliced and inoculated with L. monocytogenes (3.5 log CFU/g) before packaging under different atmospheres (air, vacuum, 100% N2, 20% CO2/80% N2 and 40% CO2/60% N2) and stored at 4 °C for up to 60 days. Samples were taken on days 0, 7, 21, 28 and 60 of storage. L. monocytogenes, mesophiles, Enterobacteriaceae, lactic acid bacteria, Micrococcaceae, molds and yeast counts were evaluated. Additionally, water activity, humidity and pH were determined. L. monocytogenes counts decreased in inoculated sliced chorizo during storage. Packaging conditions and day of storage influenced microbial counts. After 60 days, a significant reduction (p ≤ 0.05) in the initial Listeria contamination levels (3.5. log CFU/g) between 1.1 and 1.46 logarithmic units was achieved in the sausages packaged in modified atmosphere. The highest reductions were observed in slices packaged in 40% CO2/60% N2 after 60 days of storage at 4 °C.

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.

Development and validation of a regression model for Listeria monocytogenes growth in roast beefs

Food business operators are responsible for food safety and assessment of shelf lives for their ready-to-eat products. For assisting them, a customized software based on predictive models, ListWare, is being developed. The aim of this study was to develop and validate a predictive model for the growth of Listeria monocytogenes in sliced roast beef. A challenge study was performed comprising 51 different combinations of variables. The growth curves followed the Baranyi and Roberts model with no clear lag phase and specific growth rates in the range <0.005-0.110 hr^-1. A linear regression model was developed based on 528 observations and had an adjusted R-square of 0.80. The significant predictors were storage temperature, sodium lactate, interactions between sodium acetate and temperature, and MAP packaging and temperature. The model was validated in four laboratories in three countries. For conditions where the model predicted up to + log 2 cfu/g Listeria concentration, the observed concentrations were true or below the predicted concentration in 90% of the cases. For the remaining 10%, the roast beef was coated with spices and therefore different from the others. The model will be implemented in ListWare web-application for calculation of "Listeria shelf life".

Critical Analysis of Pork QMRA Focusing on Slaughterhouses: Lessons from the Past and Future Trends

Foodborne microbial diseases have a significant impact on public health, leading to millions of human illnesses each year worldwide. Pork is one of the most consumed meat in Europe but may also be a major source of pathogens introduced all along the farm-to-fork chain. Several quantitative microbial risk assessment (QMRA) have been developed to assess human health risks associated with pork consumption and to evaluate the efficiency of different risk reduction strategies. The present critical analysis aims to review pork QMRA. An exhaustive search was conducted following the preferred reporting items for systematic reviews and meta-analyses (PRISMA) methodology. It resulted in identification of a collection of 2489 papers including 42 on QMRA, after screening. Among them, a total of 29 studies focused on Salmonella spp. with clear concern on impacts at the slaughterhouse, modeling the spreading of contaminations and growth at critical stages along with potential reductions. Along with strict compliance with good hygiene practices, several potential risk mitigation pathways were highlighted for each slaughterhouse step. The slaughterhouse has a key role to play to ensure food safety of pork-based products but consideration of the whole farm-to-fork chain is necessary to enable better control of bacteria. This review provides an analysis of pork meat QMRA, to facilitate their reuse, and identify gaps to guide future research activities.

Quantifying the bioprotective effect of Lactobacillus sakei CTC494 against Listeria monocytogenes on vacuum packaged hot-smoked sea bream

In this study, the bioprotective potential of Lactobacillus sakei CTC494 against Listeria monocytogenes CTC1034 was evaluated on vacuum packaged hot-smoked sea bream at 5 °C and dynamic temperatures ranging from 3 to 12 °C. The capacity of three microbial competition interaction models to describe the inhibitory effect of L. sakei CTC494 on L. monocytogenes was assessed based on the Jameson effect and Lotka-Volterra approaches. A sensory analysis was performed to evaluate the spoiling capacity of L. sakei CTC494 on the smoked fish product at 5 °C. Based on the sensory results, the bioprotection strategy against the pathogen was established by inoculating the product at a 1:2 ratio (pathogen:bioprotector, log CFU/g). The kinetic growth parameters of both microorganisms were estimated in mono-culture at constant storage (5 °C). In addition, the inhibition function parameters of the tested interaction models were estimated in co-culture at constant and dynamic temperature storage using as input the mono-culture kinetic parameters. The growth potential (δ log) of L. monocytogenes, in mono-culture, was 3.5 log on smoked sea bream during the experimental period (20 days). In co-culture, L. sakei CTC494 significantly reduced the capability of L. monocytogenes to grow, although its effectiveness was temperature dependent. The LAB strain limited the growth of the pathogen under storage at 5 °C (<1 log increase) and at dynamic profile 2 (<2 log increase). Besides, under storage at dynamic profile 1, the growth of L. monocytogenes was inhibited (<0.5 log increase). These results confirmed the efficacy of L. sakei CTC494 for controlling the pathogen growth on the studied fish product. The Lotka-Volterra competition model showed slightly better fit to the observed L. monocytogenes growth response than the Jameson-based models according to the statistical performance. The proposed modelling approach could support the assessment and establishment of bioprotective culture-based strategies aimed at reducing the risk of listeriosis linked to the consumption of RTE hot-smoked sea bream.

The potential of bacterial cultures to degrade the mutagen 2-methyl-1,4-dinitro-pyrrole in a processed meat model

Processed meats are classified by the International Agency for Research on Cancer as category 1 because their consumption increase the incidence of colorectal and stomach cancers. Meat processing widely employs nitrite and sorbate as preservatives. When these preservatives are concomitantly used in non-compliant processes, they may react and produce the mutagen 2-methyl-1,4-dinitro-pyrrole (DNMP). This study aimed to evaluate the ability of different bacteria isolated from food matrices to biodegrade DNMP in in vitro reactions and in a processed meat model. A possible mechanism of biodegradation was also tested. In vitro experiments were performed in two steps. In the first one, only one strain out of 13 different species did not interact with DNMP. In the following step, an empirical conversion factor was calculated to assess the conversion of DNMP to 4-amino-2-methyl-1-nitro-pyrrole by the strains. The most efficient strains were Staphylococcus xylosus LYOCARNI SXH-01, Lactobacillus fermentum LB-UFSC 0017, and Lactobacillus casei LB-UFSC 0019, which yielded conversion factors of 0.62, 0.60, and 0.43, respectively. Thus, such strains were individually added to the processed meat model and completely degraded the DNMP. Moreover, S. xylosus degraded DNMP in less than 30 min. The enzymatic mechanism was evaluated using its cell-free extract. It showed that, in the aerobic system, reduction rates were 30.321 and 22.411 nmol/mg of protein/min using NADH and NADPH, respectively. A DNMP reductase was assigned to the extract and a potential presence of an oxygen insensitive nitroreductase type I B was considered. Thus, biotechnological processes may be an efficient strategy to eliminate the DNMP from meat products and to increase food safety.

Influence of Meat Spoilage Microbiota Initial Load on the Growth and Survival of Three Pathogens on a Naturally Fermented Sausage

Meat products are potential vehicles for transmitting foodborne pathogens like Salmonella, S. aureus, and L. monocytogenes. We aimed to evaluate (1) the effect of the meat's initial natural microbiota on Salmonella, S. aureus, and L. monocytogenes growth and survival in a batter to prepare a naturally fermented sausage, made with and without curing salts and wine (2) the effect of a lactic acid bacteria (LAB) starter culture and wine on the survival of the three pathogens during the manufacturing of a naturally fermented sausage made with meat with a low initial microbial load. The results revealed that the reduced contamination that is currently expected in raw meat is favorable for the multiplication of pathogens due to reduced competition. The inhibitory effect of nitrite and nitrate on Salmonella, S. aureus, and L. monocytogenes was confirmed, particularly when competition in meat was low. In any attempt to reduce or eliminate nitrite from naturally fermented sausages, the use of LAB starters should be considered to ensure an unfavorable competition environment for pathogens. In the experiment with naturally fermented sausage, chouriço, the reduction in aw strongly inhibited the challenged pathogens, particularly when a LAB starter culture and wine were used.

Modeling the Growth and Interaction Between Brochothrix thermosphacta, Pseudomonas spp., and Leuconostoc gelidum in Minced Pork Samples

The aim of this study was to obtain the growth parameters of specific spoilage micro-organisms previously isolated in minced pork (MP) samples and to develop a three-spoilage species interaction model under different storage conditions. Naturally contaminated samples were used to validate this approach by considering the effect of the food microbiota. Three groups of bacteria were inoculated on irradiated samples, in mono- and in co-culture experiments (n = 1152): Brochothrix thermosphacta, Leuconostoc gelidum, and Pseudomonas spp. (Pseudomonas fluorescens and Pseudomonas fragi). Samples were stored in two food packaging [food wrap and modified atmosphere packaging (CO2 30%/O2 70%)] at three isothermal conditions (4, 8, and 12°C). Analysis was carried out by using both 16S rRNA gene amplicon sequencing and classical microbiology in order to estimate bacterial counts during the storage period. Growth parameters were obtained by fitting primary (Baranyi) and secondary (square root) models. The food packaging shows the highest impact on bacterial growth rates, which in turn have the strongest influence on the shelf life of food products. Based on these results, a three-spoilage species interaction model was developed by using the modified Jameson-effect model and the Lotka Volterra (prey-predator) model. The modified Jameson-effect model showed slightly better performances, with 40-86% out of the observed counts falling into the Acceptable Simulation Zone (ASZ). It only concerns 14-48% for the prey-predator approach. These results can be explained by the fact that the dynamics of experimental and validation datasets seems to follow a Jameson behavior. On the other hand, the Lotka Volterra model is based on complex interaction factors, which are included in highly variable intervals. More datasets are probably needed to obtained reliable factors, and so better model fittings, especially for three- or more-spoilage species interaction models. Further studies are also needed to better understand the interaction of spoilage bacteria between them and in the presence of natural microbiota.

Modelling Growth and Decline in a Two-Species Model System: Pathogenic Escherichia coli O157:H7 and Psychrotrophic Spoilage Bacteria in Milk

Shiga toxin-producing Escherichia coli O157:H7 is a food-borne pathogen and the major cause of hemorrhagic colitis. Pseudomonas is the genus most frequent psychrotrophic spoilage microorganisms present in milk. Two-species bacterial systems with E. coli O157:H7, non-pathogenic E. coli, and P. fluorescens in skimmed milk at 7, 13, 19, or 25 °C were studied. Bacterial interactions were modelled after applying a Bayesian approach. No direct correlation between P. fluorescens's growth rate and its effect on the maximum population densities of E. coli species was found. The results show the complexity of the interactions between two species in a food model. The use of natural microbiota members to control foodborne pathogens could be useful to improve food safety during the processing and storage of refrigerated foods.

Evaluation of the effect of Lactobacillus sakei strain L115 on Listeria monocytogenes at different conditions of temperature by using predictive interaction models

In this study, the inhibitory capacity of Lactobacillus sakei strain L115 against Listeria monocytogenes has been assayed at 4, 8, 11, 15 and 20 °C in broth culture. Besides, the use of predictive microbiology models for describing growth of both microorganisms in monoculture and coculture has been proposed. A preliminary inhibitory test confirmed the ability of Lb. sakei strain L115 to prevent the growth of a five-strain cocktail of L. monocytogenes. Next, the growth of microorganisms in isolation, i.e. in monoculture, was monitored and kinetic parameters maximum specific growth rate (μ_sp;max) and maximum population density (N_max) were estimated by fitting the Baranyi model to recorded data. Inhibition coefficients (α) were calculated for the two kinetic parameters tested (μ_sp:max and N_max) to quantify the percentage of reduction of growth when the microorganisms were in coculture in comparison with monoculture. The kinetic parameters were input into three interaction models, developed based on modifications of the Baranyi growth model, namely Jameson effect, new modified version of the Jameson effect and Lotka-Volterra models. Two approaches were utilized for simulation, one using the monoculture μ_sp;max, under the hypothesis that the growth potential is similar under monoculture and coculture conditions provided the environmental conditions are not modified, and the other one, based on adjusting the monoculture kinetic parameter by applying the corresponding α to reproduce the observed μ_sp;max under coculture conditions, assuming, in this approach, that the existence of a heterogeneous population can change the growth potential of each microbial population. It was observed that in coculture, μ_sp;max of L. monocytogenes decreased (e.g., α = 31% at 4 °C) and the N_max was much lower than that of monoculture (e.g., α = 36% at 4 °C). The best simulation performance was achieved applying α to adjust the estimated monoculture growth rate, with the modified Jameson and Lotka-Volterra models showing better fit to the observed microbial interaction data as demonstrated by the fact that 100% data points fell within the acceptable simulation zone (±0.5 log CFU/mL from the simulated data). More research is needed to clarify the mechanisms of interaction between the microorganisms as well as the role of temperature.

Staphylococcus aureus 2064 growth as affected by temperature and reduced water activity

Based on 247 growth data, the growth of S. aureus 2064 in dependence on temperatures (8-50°C) and a^w values (0.999-0.83) was described. Optimal values of a_wat all studied temperatures were determined by using Gibson model. Its compatibility was confirmed by several statistical indices, e.g. root mean square errors (RMSE 0.003-0.138), standard errors of prediction (%SEP 0.6-17.5). Cardinal values for S. aureus growth (T_min=7.7°C, T_opt=40.6°C, T_max=46.7°C, a_wmin=0.808, a_wopt=0.994, μ_opt=1.97 1/h) were determined by using CM model with indices RMSE=0.071, SEP=17.5%. Our findings can provide relevant growth information that can be used in S. aureus exposure assessment or in validation of other data regarding the growth of this opportunistic pathogen in foods.

Growth Potential of Listeria monocytogenes in Chef-Crafted Ready-to-Eat Fresh Cheese-Filled Pasta Meal Stored in Modified Atmosphere Packaging

This study evaluated the growth of lactic acid bacteria (LAB) in a fresh, filled-pasta meal, stored in modified atmosphere packaging and the influence of lactic acid (LA) and pH on the growth of Listeria monocytogenes (Lm). Samples were taken from three lots manufactured by a local catering company and stored at both 6 and 14°C. LAB numbers, LA concentration, pH, and the presence of Lm were evaluated at 1, 4, 6, 8, 10, 12, and 14 days of shelf life and the undissociated LA concentration ([LA]) was calculated. The LAB maximum cell density was greater in the products stored at 14°C than those stored at 6°C (10.1 ± 1.1 versus 5.6 ± 1.5 log CFU/g) and [LA] at 14 days was 9 to 21 ppm at 6°C and 509 to 1,887 ppm at 14°C. Challenge tests were made to evaluate the interference of LAB and [LA] on Lm growth. Aliquots of the samples (25 g) were inoculated at 1 to 10 days of shelf life and incubated at 9°C for 7 days, and the difference between Lm numbers at the end and at the beginning of the test (δ) was calculated. Logistic regression was used to model the probability of growth of Lm as a function of LAB and [LA]. The products inoculated at 1 day of shelf life had δ values between 4.2 and 5.6 log CFU/g, but the growth potential was progressively reduced during the shelf life. Lm growth was never observed in the products stored at 14°C. In those stored at 6°C, it grew only in the samples with LAB <5.7 log CFU/g. LAB interaction might thus inhibit the growth of Lm in temperature-abused products and limit its growth in refrigerated products. Logistic regression estimated that the probability of Lm growth was <10% if LAB was >6.6 log CFU/g or log[LA] was >2.2 ppm. The growth or inactivation kinetic of Lm was investigated with a homogenate of three samples with LAB numbers close to the maximum population density. After an initial growth, a subsequent reduction in the number of Lm was observed. This means that the maximum numbers of Lm might not be detected at the end of the product shelf life.

Antimicrobial activity of bioactive starch packaging films against Listeria monocytogenes and reconstituted meat microbiota on ham

Contamination with spoilage organisms and Listeria monocytogenes are major concerns for quality and safety of cooked ready-to-eat (RTE) meat products. Thus, the objective of this study was to investigate the use of antimicrobial starch packaging films to control competitive microbiota and L. monocytogenes growth on a RTE ham product. Starch packaging films were prepared with different bioactives, gallic acid, chitosan, and carvacrol, using subcritical water technology. The viability of the incorporated strains on ham in contact with different antimicrobial starch packaging films was examined during 28-day storage period at 4 °C. Starch films with gallic acid had the least effect on ham antimicrobial activity; starch films with chitosan and carvacrol fully inhibited L. monocytogenes growth throughout 4 weeks of storage. RTE meat microbiota was more resistant to the antimicrobials than L. monocytogenes. Starch films loaded with chitosan or chitosan and carvacrol did not fully inhibit growth of RTE meat microbiota but delayed growth of RTE meat microbiota by one to two weeks. Moreover, competitive meat microbiota fully inhibited growth of L. monocytogenes. Therefore, antimicrobial starch packaging films prepared by subcritical water technology used in this study showed a promising effect on inhibiting L. monocytogenes in RTE ham.

A quantitative model of Bacillus cereus ATCC 9634 growth inhibition by bifidobacteria for synbiotic effect evaluation

The present study is dedicated to the development of novel criteria for assessing the synbiotic effect of prebiotic and probiotic composition against a specific pathogen. These criteria were obtained from the quantitative model of Bifidobacterium adolescentis ATCC 15703 and Bacillus cereus ATCC 9634 (as a model food contaminant) competition in co-culture fermentation. The model is based on the hypothesis that probiotics can reduce the specific growth rate of non-probiotics by producing short-chain fatty acids. To define the relationship between the specific growth rate of non-probiotics and short-chain fatty acid yields, the inhibition constants were determined separately for each inhibitor produced by bifidobacteria (lactic, acetic and propionic acids) in a pure culture of bacilli. Two different equations based on the minimum inhibitor concentration (MIC) and inhibition constant (K_i) were used to connect the specific growth rate and concentrations of inhibitors. The yields of the inhibitors mentioned above were obtained from co-culture experiments. The experimental values and the values predicted by the model of Bacillus count did not differ significantly (R² not less than 0.83) in the competition experiments. Therefore, the general criterion of the synbiotic effect was derived from the model and presents the coefficient of non-probiotic specific growth rate reduction as a result of probiotic growth and inhibitor formation in the final co-culture fermentation. This criterion has been examined for different commercial prebiotics coupled with the Bifidobacterium adolescentis strain. The synergistic combination of inulin GR with bifidobacteria had the best effect against Bacillus cereus ATCC 9634.

Modelling the interaction of the sakacin-producing Lactobacillus sakei CTC494 and Listeria monocytogenes in filleted gilthead sea bream (Sparus aurata) under modified atmosphere packaging at isothermal and non-isothermal conditions

The objective of this work was to quantitatively evaluate the effect of Lactobacillus sakei CTC494 (sakacin-producing bioprotective strain) against Listeria monocytogenes in fish juice and to apply and validate three microbial interaction models (Jameson, modified Jameson and Lotka Volterra models) through challenge tests with gilthead sea bream (Sparus aurata) fillets under modified atmosphere packaging stored at isothermal and non-isothermal conditions. L. sakei CTC494 inhibited L. monocytogenes growth when simultaneously present in the matrix (fish juice and fish fillets) at different inoculation ratios pathogen:bioprotector (i.e. 1:1, 1:2 and 1:3). The higher the inoculation ratio, the stronger the inhibition of L. monocytogenes growth, with the ratio 1:3 yielding no growth of the pathogen. The maximum population density (N_max) was the most affected parameter for L. monocytogenes at all inoculation ratios. According to the microbiological and sensory analysis outcomes, an initial inoculation level of 4 log cfu/g for L. sakei CTC494 would be a suitable bioprotective strategy without compromising the sensory quality of the fish product. The performance of the tested interaction models was evaluated using the Acceptable Simulation Zone approach. The Lotka Volterra model showed slightly better fit than the Jameson-based models with 75-92% out of the observed counts falling into the Acceptable Simulation Zone, indicating a satisfactory model performance. The evaluated interaction models could be used as predictive modelling tool to simulate the simultaneous behaviour of bacteriocin-producing Lactobacillus strains and L. monocytogenes; thus, supporting the design and optimization of bioprotective culture-based strategies against L. monocytogenes in minimally processed fish products.

Inhibitory Effect of Lactic Acid Bacteria on Foodborne Pathogens: A Review

Foodborne pathogens are serious challenges to food safety and public health worldwide. Fermentation is one of many methods that may be used to inactivate and control foodborne pathogens. Many studies have reported that lactic acid bacteria (LAB) can have significant antimicrobial effects. The current review mainly focuses on the antimicrobial activity of LAB, the mechanisms of this activity, competitive growth models, and application of LAB for inhibition of foodborne pathogens.

Bioprotective Effect of Lactococcus piscium CNCM I-4031 Against Listeria monocytogenes Growth and Virulence

Listeria monocytogenes is a Gram-positive pathogen occurring in many refrigerated ready-to-eat foods. It is responsible for foodborne listeriosis, a rare but severe disease with a high mortality rate (20-30%). Lactococcus piscium CNCM I-4031 has the capacity to prevent the growth of L. monocytogenes in contaminated peeled and cooked shrimp and in a chemically defined medium using a cell-to-cell contact-dependent mechanism. To characterize this inhibition further, the effect of L. piscium was tested on a collection of 42 L. monocytogenes strains. All strains were inhibited but had different sensitivities. The effect of the initial concentration of the protective and the target bacteria revealed that the inhibition always occurred when L. piscium had reached its maximum population density, whatever the initial concentration of the protective bacteria. Viewed by scanning electron microscopy, L. monocytogenes cell shape and surface appeared modified in co-culture with L. piscium CNCM I-4031. Lastly, L. monocytogenes virulence, evaluated by a plaque-forming assay on the HT-29 cell line, was reduced after cell pre-treatment by the protective bacteria. In conclusion, the bioprotective effect of L. piscium toward L. monocytogenes growth and virulence was demonstrated, and a hypothesis for the inhibition mechanism is put forward.

Enhancing vitamin B12 content in co-fermented soy-milk via a Lotka Volterra model

Soybean products are popular because of its taste, digestibility, and health benefits. However, soybean lacks vitamin, mainly the low water-soluble vitamin B12. This study investigated the effects of fermentation conditions on the synthesis of vitamin B12, production of metabolites, and growth of Lactobacillus reuteri and Propionibacterium shermainii in fermented soy-milk. A Lotka Volterra model was successfully employed to describe the competition relationship between the two microorganisms under various fermentation conditions. A quadratic function between the ratio of interaction coefficients and vitamin B12 content was found. Higher vitamin B12 in soy-milk can be produced when the ratio of interaction coefficients approach to one. Compared with other fermented soybean products, fermented soy-milk contains more acetate, ethanol, and propionic acid. This study successfully demonstrated a mathematical model to enhance soy-milk vitamin B12 production.