Predictive microbiology theory and application: Is it all about rates?

Optimal experimental design (OED) for the growth rate of microbial populations. Are they really more "optimal" than uniform designs?

Secondary growth models from predictive microbiology can describe how the growth rate of microbial populations varies with environmental conditions. Because these models are built based on time and resource consuming experiments, model-based Optimal Experimental Design (OED) can be of interest to reduce the experimental load. In this study, we identify optimal experimental designs for two common models (full Ratkowsky and Cardinal Parameters Model (CPM)) for a different number of experiments (10-30). Calculations are also done fixing one or more model parameters, observing that this decision strongly affects the layout of the OED. Using in silico experiments, we conclude that OEDs are more informative than conventional (equidistant) designs with the same number of experiments. However, OEDs cluster the experiments near the growth limits (Xmin and Xmax) resulting in impractical designs with aggregated experimental runs ~10 times longer than conventional designs. To mitigate this, we propose a novel optimality criterion (i.e., the objective function) that accounts for the aggregated time. The novel criterion provides a reduction in parameter uncertainty with respect to the conventional design, without an increase in the experimental load. These results underline that an OED is only based on information theory (Fisher information), so the results can be impractical when actual experimental limitations are considered. The study also emphasizes that most OED schemes identify where to measure, but do not give an indication on how many experiments should be made. In this sense, numerical simulations can estimate the parameter uncertainty that would be obtained for a particular experimental design (OED or not). These results and methodologies (available in Open Code) can guide the design of future experiments for the development of secondary growth models.

The effect of pH on the growth rate of Bacillus cereus sensu lato: Quantifying strain variability and modelling the combined effects of temperature and pH

In this study, the effect of pH, alone or in combination with temperature, on the maximum growth rate (μ_max) of B. cereus sensu lato was investigated. In phase 1, the effect of pH at 30 °C was studied for 16 mesophilic strains and 2 psychrotrophic strains of Bacillus cereus sensu lato. The μ_max vs. pH relationship was found to show a similar pattern for all the strains. Several pH models from literature were evaluated and the best performing 'growth rate vs. pH' model selected. A stochastic model was then developed to predict the maximum specific growth rate of mesophilic B. cereus at 30 °C as a function of pH, the intra-species variability being incorporated via considering the model parameters (e.g. pH_min) randomly distributed. The predicted maximum specific growth rates were acceptably close to independent published data. In phase 2, the combined effects of temperature and pH were studied. Growth rates were also generated at 15, 20 and 40 °C for a selection of strains and the pH model was fitted at each temperature. Interestingly, the results showed that the estimates for the pH_min parameter for mesophilic strains were lower at 20-30 °C than near the optimum temperature (40 °C), suggesting that experiments for the determination of this parameter should be conducted at lower-than-optimum temperatures. New equations were proposed for the relationship between temperature and the minimum pH-values, which were also consistent with the experimental growth boundaries. The parameters defining this equation quantify the minimum temperature for growth observed experimentally, the temperature of maximum enzyme stability and the maximum temperature for growth. Deviations from the Gamma hypothesis (multiplicative effects of environmental factors on the maximum specific growth rate) were observed near the growth limits, especially at 40 °C. To improve model performance, two approaches, one based on a minimum pH-term (doi: https://doi.org/10.3389/fmicb.2019.01510) and one based on an interaction term (doi: http://dx.doi.org/10.1016/S0168-1605(01)00640-7) were evaluated.

Effect of pepper extracts on the viability kinetics, topography and Quantitative NanoMechanics (QNM) of Campylobacter jejuni evaluated with AFM

Campylobacter jejuni is a pathogen bacterium that causes foodborne gastroenteritis in humans. However, phenolic compounds extracted from natural sources such as capsicum pepper plant (Capsicum annuum L. var. aviculare) could inhibit the growth of C. jejuni. Therefore, different extracts were prepared using ultrasonic extraction (USE), conventional extraction (CE) and thermosonic extraction (TSE). C. jejuni was then exposed to chili extracts to examine the antimicrobial effect and their growth/death bacterial kinetics were studied using different mathematical models. Atomic force microscopy was applied to investigate the microstructural and nanomechanical changes in the bacteria. Extracts obtained by TSE had the highest phenolic content (4.59 ± 0.03 mg/g of chili fresh weight [FW]) in comparison to USE (4.12 ± 0.05 mg/g of chili FW) and CE (4.28 ± 0.07 mg/g of chili FW). The inactivation of C. jejuni was more efficient when thermosonic extract was used. The Gompertz model was the most suitable mathematical model to describe the inactivation kinetics of C. jejuni. Roughness and nanomechanical analysis performed by atomic force microscopy (AFM) provided evidence that the chili extracts had significant effects on morphology, surface, and the reduced Young's modulus of C. jejuni. The novelty of this work was integrating growth/death bacterial kinetics of C. jejuni using different mathematical models and chili extracts, and its relationship with the morphological, topographic and nanomechanical changes estimated by AFM.

Forecast of the outbreak of COVID-19 using artificial neural network: Case study Qatar, Spain, and Italy

The present study illustrates the outbreak prediction and analysis on the growth and expansion of the COVID-19 pandemic using artificial neural network (ANN). The first wave of the pandemic outbreak of the novel Coronavirus (SARS-CoV-2) began in September 2019 and continued to March 2020. As declared by the World Health Organization (WHO), this virus affected populations all over the globe, and its accelerated spread is a universal concern. An ANN architecture was developed to predict the serious pandemic outbreak impact in Qatar, Spain, and Italy. Official statistical data gathered from each country until July 6th was used to validate and test the prediction model. The model sensitivity was analyzed using the root mean square error (RMSE), the mean absolute percentage error and the regression coefficient index R2, which yielded highly accurate values of the predicted correlation for the infected and dead cases of 0.99 for the dates considered. The verified and validated growth model of COVID-19 for these countries showed the effects of the measures taken by the government and medical sectors to alleviate the pandemic effect and the effort to decrease the spread of the virus in order to reduce the death rate. The differences in the spread rate were related to different exogenous factors (such as social, political, and health factors, among others) that are difficult to measure. The simple and well-structured ANN model can be adapted to different propagation dynamics and could be useful for health managers and decision-makers to better control and prevent the occurrence of a pandemic.

A stochastic approach for modelling the effects of temperature on the growth rate of Bacillus cereus sensu lato

A stochastic model that predicts the maximum specific growth rate (μ_max) of Bacillus cereus sensu lato as a function of temperature was developed. The model integrates the intra-species variability by incorporating distributions of cardinal parameters (T_min, T_opt, T_max) in the model. Growth rate data were generated for 22 strains, covering 5 major phylogenetic groups of B. cereus, and their cardinal temperatures identified. Published growth rate data were also incorporated in the model fitting, resulting in a set of 33 strains. Based on their cardinal temperatures, we identified clusters of Bacillus cereus strains that show similar response to temperature and these clusters were considered separately in the stochastic model. Interestingly, the μ_opt values for psychrotrophic strains were found to be significantly lower than those obtained for mesophilic strains. The model developed within this work takes into account some correlations existing between parameters (μ_opt, T_min, T_opt, T_max). In particular, the relationship highlighted between the b-slope of the Ratkowsky model and T_min (doi: https://doi.org/10.3389/fmicb.2017.01890) was adapted to the case of the popular Cardinal Temperature Model. This resulted in a reduced model in which μ_opt is replaced by a function of T_min, T_opt and 2 strain-independent parameters. A correlation between the T_min parameter and the experimental minimal growth temperature was also highlighted and integrated in the model for improved predictions near the temperature growth limits. Compared to the classical approach, the model developed in this study leads to improved predictions for temperatures around T_min and more realistic tails for the predicted distributions of μ_max. It can be useful for describing the variability of the Bacillus cereus Group in Quantitative Microbial Risk Assessment (QMRA). An example of application of the stochastic model to Reconstituted Infant Formulae (RIF) was proposed.

Development of Dynamic Model for Real-Time Monitoring of Ripening Changes of Kimchi during Distribution

This study describes the development of a method for predicting the ripening of Kimchi according to temperature to provide information on how the ripening of Kimchi changes during distribution. Various Kimchi quality factors were assessed according to temperature and time. The acidity (lactic acid %) was selected as a good freshness index, as it is dependent on temperature and correlates strongly with the sensory quality evaluation. Moreover, it is easy to measure and reproducible in the field. The maximum value of acidity in the stationary phase was observed to increase with the storage temperature. A predictive model was developed using the Baranyi and Roberts and Polynomial models to mathematically predict the acidity. A method using the mean kinetic temperature (MKT) was proposed. The accuracy of the model using the MKT was high. It was confirmed that there is no great variation in the maximum acidity, as MKT does not change much if the temperature changes in the stationary phase where the maximum acidity is constant. This study provides important information about the development of models to predict changes in food quality index under fluctuating temperature environments. The developed kinetic model uniquely treated the quality index at the stationary phase as a function of MKT. The predictions using the food temperature histories could help suppliers and consumers make a reasonable decision on the sales, storage, and consumption of foods. The developed model could be applied to other products such as beef for which the quality index at the stationary phase also changes with temperature histories.

The Effects of Constant and Fluctuating Temperatures on Development of Diaphorina citri (Hemiptera: Liviidae), the Asian Citrus Psyllid

The effects of six average daily temperatures, 15, 20, 25, 30, 32, and 35°C, that were either constant or fluctuating over 24 h on development times of California-sourced Diaphorina citri Kuwayama nymphs were examined. Thermal performance curves for immature stages of D. citri were characterized using one linear and six nonlinear models (i.e., Ratkowsky, Lobry-Rosso-Flandrois, Lactin-2, Brière-2, Beta, and Performance-2). Daily thermal fluctuations had significant effects on development times of D. citri nymphs, which differed across experimental temperatures. Diaphorina citri nymphs reared at constant temperatures completed development faster than those reared under fluctuating profiles with equivalent temperature means. Linear model estimates of degree-days required for completion of cumulative development of D. citri were 25% lower for constant temperatures when compared with fluctuating temperature regimens. Nonlinear model estimations of optimum developmental temperature and upper theoretical temperature bounds for development were similar for individuals reared under constant and fluctuating temperatures. Nevertheless, the estimated values of lower theoretical temperature limits above which development occurred were lower under fluctuating than constant temperatures. A meta-analysis of published D. citri temperature-dependent development literature, synthesizing datasets of five globally distributed populations (Brazil, California, China, Florida, and Japan) reared under different constant temperatures on six different host plants (i.e., Citrus limonia, C. sinensis cv Natal, C. sinensis cv. Pêra, C. reticulata, Fortunella margarita, and Murraya paniculata), together with the results of this study (C. volkameriana), revealed convergence in estimates of developmental parameters. These results have implications for predicting D. citri invasion and establishment risk and subsequent population performance across various climactic gradients and geographic regions.

Comparing temperature sensitivity of bacterial growth in Antarctic marine water and soil

The western Antarctic Peninsula is an extreme low temperature environment that is warming rapidly due to global change. Little is known, however, on the temperature sensitivity of growth of microbial communities in Antarctic soils and in the surrounding oceanic waters. This is the first study that directly compares temperature adaptation of adjacent marine and terrestrial bacteria in a polar environment. The bacterial communities in the ocean were adapted to lower temperatures than those from nearby soil, with cardinal temperatures for growth in the ocean being the lowest so far reported for microbial communities. This was reflected in lower minimum (Tmin ) and optimum temperatures (Topt ) for growth in water (-17 and +20°C, respectively) than in soil (-11 and +27°C), with lower sensitivity to changes in temperature (Q10 ; 0-10°C interval) in Antarctic water (2.7) than in soil (3.9). This is likely due to the more stable low temperature conditions of Antarctic waters than soils, and the fact that maximum in situ temperatures in water are lower than in soils, at least in summer. Importantly, the thermally stable environment of Antarctic marine water makes it feasible to create a single temperature response curve for bacterial communities. This would thus allow for calculations of temperature-corrected growth rates, and thereby quantifying the influence of factors other than temperature on observed growth rates, as well as predicting the effects of future temperature increases on Antarctic marine bacteria.

The Combined Effect of pH and Temperature on the Survival of Salmonella enterica Serovar Typhimurium and Implications for the Preparation of Raw Egg Mayonnaise

Raw egg products are often associated with salmonellosis. The Australian guidelines recommend raw egg mayonnaise to be prepared and stored under 5 °C and adjusted to a pH less than 4.6 or 4.2. Despite these guidelines, a significant amount of salmonellosis outbreaks are recorded annually in Australia. The aim of this study was to investigate the effect of pH and temperature on the survival of Salmonella Typhimurium (ST) in peptone water (PW) and mayonnaise. The pH of PW and mayonnaise was adjusted to 4.2, 4.4 and 4.6 using acetic acid and vinegar, respectively. The PW and mayonnaise were inoculated with ST and incubated at 37 °C, 23 °C, and 4 °C. The survival of Salmonella was determined using the drop plate method. Survival was significantly (p < 0.05) improved at 4 °C. In both mayonnaise and PW, following 24 h, there was no ST growth at pH 4.2. Resuscitation of ST was rapidly observed at 4 °C while complete inactivation was observed at 37 °C at pH 4.2, 4.4, and 4.6 in both PW and mayonnaise. Lower temperatures protected ST from the bactericidal effect of low pH. “The preparation of mayonnaise at pH 4.2 or less and incubating it at room temperature for at least 24 h could reduce the incidence of salmonellosis”.

The impact of environmental parameters on the conversion of toluene to CO2 and extracellular polymeric substances in a differential soil biofilter

The fraction of pollutant converted to CO₂ versus biomass in biofiltration influences the process efficacy and the lifetime of the bed due to pressure drop increases. This work determined the relative quantitative importance and potential interactions between three critical environmental parameters: toluene concentration (Tol), matric potential (ψ) and temperature (T) on % CO₂, elimination capacity (EC) and the production rate of non-CO₂ products. These parameters are the most variable in typical biofilter operation. The data was fit to a non-linear model of the form y=a(Tol)^bT^cψ^d. A rigorous carbon balance (100.5 ± 7.0%) tracked the fate of degraded toluene as CO₂ and non-CO₂ carbon endpoints. The % CO₂ mineralization varied from (34-91%) with environmental parameters: temperature (20-40 °C), matric potential, (-10 to -100 cm_H2O) and residual toluene, (20-180 ppm). The highest conversion to CO₂ was at the wettest conditions (-10 cm_H2O) and lowest residual toluene concentration (18 ppm). Matric potential had twice the impact of toluene concentration on % CO₂, while temperature had less impact. The elimination capacity varied from 11 to 50 g_C⋅m^-3h^-1 and was highest at 40 °C, the wettest conditions with limited impact by toluene concentrations. Temperature increased the EC and non-CO₂ production rates strongly while matric potential and toluene concentration had less influence (4x - 10x less). This study illustrated the quantitative significance and simultaneous interaction between critical environmental parameters on carbon endpoints and biofilter performance. This kind of multivariable parameter study provides valuable insights which can address performance and clogging issues in biofilters.

The Influence of Temperature Variation on Life History Parameters and Thermal Performance Curves of Tamarixia radiata (Hymenoptera: Eulophidae), a Parasitoid of the Asian Citrus Psyllid (Hemiptera: Liviidae)

This study examined the effects of seven constant and fluctuating temperature profiles with corresponding averages of 12 to 38°C on the life history of the Punjab, Pakistan-sourced Tamarixia radiata (Waterston) released in California for biological control of Diaphorina citri Kuwayama. One linear and seven nonlinear regression functions were fit to egg-to-adult development rate data to characterize thermal performance curves. Temperature fluctuations significantly affected both development and longevity of T. radiata. Estimates of degree-days predicted by the linear model were 30% higher for the fluctuating regime than the constant regime. Nonlinear model estimations of theoretical minimum and maximum developmental thresholds were lower for the fluctuating regime when compared to the constant regime. These predictions align with experimental observations. Parasitoids reared under fluctuating profiles at low average temperatures developed faster (15°C) and survived longer (15-20°C) when compared to those reared under constant regimes with corresponding means. In contrast, high average fluctuating temperatures produced parasitoids with an extended developmental period (35°C) and reduced longevity (30-35°C). A meta-analysis of published T. radiata development datasets, together with the results of this study, indicated convergence in degree-days and theoretical minimum developmental thresholds among geographically distinct parasitoid populations. These findings demonstrate the significant effects of temperature on T. radiata life history and have important implications for optimization of mass-rearing and release efforts, improvement of predictions from climate modeling, and comparison of T. radiata population performance across climatic gradients and geographic regions.

Temperature sensitivity of soil microbial activity modeled by the square root equation as a unifying model to differentiate between direct temperature effects and microbial community adaptation

Numerous models have been used to express the temperature sensitivity of microbial growth and activity in soil making it difficult to compare results from different habitats. Q10 still is one of the most common ways to express temperature relationships. However, Q10 is not constant with temperature and will differ depending on the temperature interval used for the calculation. The use of the square root (Ratkowsky) relationship between microbial activity (A) and temperature below optimum temperature, √A = a × (T-T_min ), is proposed as a simple and adequate model that allow for one descriptor, T_min (a theoretical minimum temperature for growth and activity), to estimate correct Q10-values over the entire in situ temperature interval. The square root model can adequately describe both microbial growth and respiration, allowing for an easy determination of T_min . Q10 for any temperature interval can then be calculated by Q10 = [(T + 10 - T_min )/(T-T_min )]² , where T is the lowest temperature in the Q10 comparison. T_min also describes the temperature adaptation of the microbial community. An envelope of T_min covering most natural soil habitats varying between -15°C (cold habitats like Antarctica/Arctic) to 0°C (tropical habitats like rain forests and deserts) is suggested, with an 0.3°C increase in T_min per 1°C increase in mean annual temperature. It is shown that the main difference between common temperature relationships used in global models is differences in the assumed temperature adaptation of the soil microbial community. The use of the square root equation will allow for one descriptor, T_min , determining the temperature response of soil microorganisms, and at the same time allow for comparing temperature sensitivity of microbial activity between habitats, including future projections.

Mechanistic modelling of the inhibitory effect of pH on microbial growth

Modelling and simulation of microbial dynamics as a function of processing, transportation and storage conditions is a useful tool to improve microbial food safety and quality. The goal of this research is to improve an existing methodology for building mechanistic predictive models based on the environmental conditions. The effect of environmental conditions on microbial dynamics is often described by combining the separate effects in a multiplicative way (gamma concept). This idea was extended further in this work by including the effects of the lag and stationary growth phases on microbial growth rate as independent gamma factors. A mechanistic description of the stationary phase as a function of pH was included, based on a novel class of models that consider product inhibition. Experimental results on Escherichia coli growth dynamics indicated that also the parameters of the product inhibition equations can be modelled with the gamma approach. This work has extended a modelling methodology, resulting in predictive models that are (i) mechanistically inspired, (ii) easily identifiable with a limited work load and (iii) easily extended to additional environmental conditions.

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 Novel Approach to Predict the Growth of Staphylococcus aureus on Rice Cake

This study aimed to investigate the growth kinetics of Staphylococcus aureus on rice cake and to determine the shelf life based on the probability model of the increase in S. aureus contamination on rice cake. Secondary models were developed based on the growth parameters derived from the Baranyi model at constant temperatures (15, 25, 35, and 45°C). External validation was then conducted using additional data under experimental conditions not used in development of the models to verify the performance and reliability of the developed model through different goodness-of-fit indices. Furthermore, the growth of S. aureus on rice cake under dynamic temperature was obtained with the root mean square error (RMSE) of 0.218 and the 90.9% acceptable prediction rate. In addition, probability models of the 1-, 2-, 3-, and 4-log increases of S. aureus on rice cake were also developed from the data, which could provide the probability and the time to a certain log increase. The results of validation demonstrated that the developed predictive model and the obtained growth parameters could be used for evaluating the growth behavior of S. aureus on rice cake under different conditions, and qualified to supply sufficient information for microbiological risk assessment studies of S. aureus on rice cake in Korea.

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.

Risk management of viral infectious diseases in wastewater reclamation and reuse: Review

Inappropriate usage of reclaimed wastewater has caused outbreaks of viral infectious diseases worldwide. International and domestic guidelines for wastewater reuse stipulate that virus infection risks are to be regulated by the multiple-barrier system, in which a wastewater treatment process composed of sequential treatment units is designed based on the pre-determined virus removal efficiency of each unit. The objectives of this review were to calculate representative values of virus removal efficiency in wastewater treatment units based on published datasets, and to identify research topics that should be further addressed for improving implementation of the multiple-barrier system. The removal efficiencies of human noroviruses, rotaviruses and enteroviruses in membrane bioreactor (MBR) and conventional activated sludge (CAS) processes were obtained by a systematic review protocol and a meta-analysis approach. The log10 reduction (LR) of norovirus GII and enterovirus in MBR were 3.35 (95% confidence interval: 2.39, 4.30) and 2.71 (1.52, 3.89), respectively. The LR values of rotavirus, norovirus GI and GII in CAS processes were 0.87 (0.20, 1.53), 1.48 (0.96, 2.00) and 1.35 (0.52, 2.18), respectively. The systematic review process eliminated a substantial number of articles about virus removal in wastewater treatment because of the lack of information required for the meta-analysis. It is recommended that future publications should explicitly describe their treatment of left-censored datasets. Indicators, surrogates and methodologies appropriate for validating virus removal performance during daily operation of wastewater reclamation systems also need to be identified.

Real versus Artificial Variation in the Thermal Sensitivity of Biological Traits

Whether the thermal sensitivity of an organism's traits follows the simple Boltzmann-Arrhenius model remains a contentious issue that centers around consideration of its operational temperature range and whether the sensitivity corresponds to one or a few underlying rate-limiting enzymes. Resolving this issue is crucial, because mechanistic models for temperature dependence of traits are required to predict the biological effects of climate change. Here, by combining theory with data on 1,085 thermal responses from a wide range of traits and organisms, we show that substantial variation in thermal sensitivity (activation energy) estimates can arise simply because of variation in the range of measured temperatures. Furthermore, when thermal responses deviate systematically from the Boltzmann-Arrhenius model, variation in measured temperature ranges across studies can bias estimated activation energy distributions toward higher mean, median, variance, and skewness. Remarkably, this bias alone can yield activation energies that encompass the range expected from biochemical reactions (from ~0.2 to 1.2 eV), making it difficult to establish whether a single activation energy appropriately captures thermal sensitivity. We provide guidelines and a simple equation for partially correcting for such artifacts. Our results have important implications for understanding the mechanistic basis of thermal responses of biological traits and for accurately modeling effects of variation in thermal sensitivity on responses of individuals, populations, and ecological communities to changing climatic temperatures.

Colonial vs. planktonic type of growth: mathematical modeling of microbial dynamics on surfaces and in liquid, semi-liquid and solid foods

Predictive models are mathematical expressions that describe the growth, survival, inactivation, or biochemical processes of foodborne bacteria. During processing of contaminated raw materials and food preparation, bacteria are entrapped into the food residues, potentially transferred to the equipment surfaces (abiotic or inert surfaces) or cross-contaminate other foods (biotic surfaces). Growth of bacterial cells can either occur planktonically in liquid or immobilized as colonies. Colonies are on the surface or confined in the interior (submerged colonies) of structured foods. For low initial levels of bacterial population leading to large colonies, the immobilized growth differs from planktonic growth due to physical constrains and to diffusion limitations within the structured foods. Indeed, cells in colonies experience substrate starvation and/or stresses from the accumulation of toxic metabolites such as lactic acid. Furthermore, the micro-architecture of foods also influences the rate and extent of growth. The micro-architecture is determined by (i) the non-aqueous phase with the distribution and size of oil particles and the pore size of the network when proteins or gelling agent are solidified, and by (ii) the available aqueous phase within which bacteria may swarm or swim. As a consequence, the micro-environment of bacterial cells when they grow in colonies might greatly differs from that when they grow planktonically. The broth-based data used for modeling (lag time and generation time, the growth rate, and population level) are poorly transferable to solid foods. It may lead to an over-estimation or under-estimation of the predicted population compared to the observed population in food. If the growth prediction concerns pathogen bacteria, it is a major importance for the safety of foods to improve the knowledge on immobilized growth. In this review, the different types of models are presented taking into account the stochastic behavior of single cells in the growth of a bacterial population. Finally, the recent advances in the rules controlling different modes of growth, as well as the methodological approaches for monitoring and modeling such growth are detailed.

Integrated kinetic and probabilistic modeling of the growth potential of bacterial populations

When bacteria are exposed to osmotic stress, some cells recover and grow, while others die or are unculturable. This leads to a viable count growth curve where the cell number decreases before the onset of the exponential growth phase. From such curves, it is impossible to estimate what proportion of the initial cells generates the growth because it leads to an ill-conditioned numerical problem. Here, we applied a combination of experimental and statistical methods, based on optical density measurements, to infer both the probability of growth and the maximum specific growth rate of the culture. We quantified the growth potential of a bacterial population as a quantity composed from the probability of growth and the “suitability” of the growing subpopulation to the new environment. We found that, for all three laboratory media studied, the probability of growth decreased while the “work to be done” by the growing subpopulation (defined as the negative logarithm of their suitability parameter) increased with NaCl concentration. The results suggest that the effect of medium on the probability of growth could be described by a simple shift parameter, a differential NaCl concentration that can be accounted for by the change in the medium composition. Finally, we highlighted the need for further understanding of the effect of the osmoprotectant glycine betaine on metabolism.

Bacterial economics: adaptation to stress conditions via stage-wise changes in the response mechanism

Common features of microbial adaptation are analysed with mathematical models and extended to stress conditions when the bacterial population declines before growing again. A parallel is drawn between bacterial and human communities in terms of non-mutation-based adaptation (acclimation) to stress. For a case study, the behaviour of Escherichia coli under osmotic stress, is detailed. It is suggested that stress modelling adaptation should be the focus of further developments in predictive food microbiology.

Modeling of Bacillus cereus growth in brown rice submitted to a combination of ultrasonication and slightly acidic electrolyzed water treatment

The combined effects of ultrasonication and slight acidic electrolyzed water were investigated to improve the microbial safety of brown rice against Bacillus cereus infection and to evaluate the growth kinetics of these bacteria during storage of untreated and treated rice at various temperatures (5, 10, 15, 20, 25, 30, and 35°C). The results indicate that this combination treatment was bactericidal against B. cereus, resulting in an approximately 3.29-log reduction. Although B. cereus can be efficiently reduced by treatment, temperature abuse during storage can allow B. cereus to recover and grow. A primary growth model (Baranyi and Roberts equation) was fitted to the raw growth data from untreated (control) and treated samples to estimate growth rate, lag time, and maximum population density, with a low standard error of the residuals (≤0.140) and high adjusted coefficient of determination (>0.990). The growth curves obtained from the Baranyi and Roberts model indicated that B. cereus grew more slowly on treated brown rice than on untreated brown rice. Secondary models predicting the square root of the maximum growth rate and the natural logarithm of the lag time as a function of temperature were satisfactory (bias factor = 0.993 to 1.013; accuracy factor = 1.290 to 1.352; standard error of prediction = 18.828 to 36.615%). Inactivation results and the model developed and validated in this study provided reliable and valuable growth kinetics information for quantitative microbiological risk assessment studies of B. cereus on brown rice.

Scaling laws governing stochastic growth and division of single bacterial cells

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈ 1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

Filament formation by foodborne bacteria under sublethal stress

A number of studies have reported that pathogenic and nonpathogenic foodborne bacteria have the ability to form filaments in microbiological growth media and foods after prolonged exposure to sublethal stress or marginal growth conditions. In many cases, nucleoids are evenly spaced throughout the filamentous cells but septa are not visible, indicating that there is a blockage in the early steps of cell division but the mechanism behind filament formation is not clear. The formation of filamentous cells appears to be a reversible stress response. When filamentous cells are exposed to more favorable growth conditions, filaments divide rapidly into a number of individual cells, which may have major health and regulatory implications for the food industry because the potential numbers of viable bacteria will be underestimated and may exceed tolerated levels in foods when filamentous cells that are subjected to sublethal stress conditions are enumerated. Evidence suggests that filament formation under a number of sublethal stresses may be linked to a reduced energy state of bacterial cells. This review focuses on the conditions and extent of filament formation by foodborne bacteria under conditions that are used to control the growth of microorganisms in foods such as suboptimal pH, high pressure, low water activity, low temperature, elevated CO2 and exposure to antimicrobial substances as well as lack a of nutrients in the food environment and explores the impact of the sublethal stresses on the cell's inability to divide.