Macroscopic modeling of the growth and substrate consumption of wild type and genetically modified Pichia pastoris

Pichia pastoris is a popular yeast platform to generate several industrially relevant products which have applications in a wide range of sectors. The complexities in the processes due to the addition of a foreign gene are not widely explored. Since these complexities can be dependent on the strain characteristics, promoter, and type of protein produced, it is vital to investigate the growth and substrate consumption patterns of the host to facilitate customized process optimization. In this study, the growth rates of P. pastoris GS115 wild type (WT) and genetically modified (GM) strains grown on glycerol and methanol in batch cultivation mode were estimated and the model providing the best representation of the true growth kinetics based on substrate consumption was identified. It was observed that the growth of P. pastoris exhibits Haldane kinetics on glycerol rather than the most commonly used Monod kinetics due to the inability of the latter to describe growth inhibition at high concentrations of glycerol. Whereas, the cardinal parameter model, a newly proposed model for this application, was found to be the best fitting to describe the growth of P. pastoris on methanol due to its ability to describe methanol toxicity. Interestingly, the findings from this study concluded that in both substrates, the genetically engineered strain exhibited a higher growth rate compared to the WT strain. Such an observation has not been established yet in other published works, indicating an opportunity to further optimize the carbon source feeding strategies when the host is grown in fed-batch mode.

The effect of ultrasound treatment in combination with nisin on the inactivation of Listeria innocua and Escherichia coli

Ultrasound, alone or in combination with natural antimicrobials, is a novel food processing technology of interest to replace traditional food decontamination methods, as it is milder than classical sterilisation (heat treatment) and maintains desirable sensory characteristics. However, ultrasound efficacy can be affected by food structure/composition, as well as the order in which combined treatments are applied. More specifically, treatments which target different cell components could result in enhanced inactivation if applied in the appropriate order. The microbial properties i.e. Gram positive/Gram negative can also impact the treatment efficacy. This work presents a systematic study of the combined effect of ultrasound and nisin on the inactivation of the bacteria Listeria innocua (Gram positive) and Escherichia coli (Gram negative), at a range of cavitation conditions (44, 500, 1000 kHz). The order of treatment application was varied, and the impact of system structure was also investigated by varying the concentration of Xanthan gum used to create the food model systems (0 - 0.5% w/v). Microbial inactivation kinetics were monitored, and advanced microscopy and flow cytometry techniques were utilised to quantify the impact of treatment on a cellular level. Ultrasound was shown to be effective against E. coli at 500 kHz only, with L. innocua demonstrating resistance to all frequencies studied. Enhanced inactivation of E. coli was observed for the combination of nisin and ultrasound at 500 kHz, but only when nisin was applied before ultrasound treatment. The system structure negatively impacted the inactivation efficacy. The combined effect of ultrasound and nisin on E. coli was attributed to short-lived destabilisation of the outer membrane as a result of sonication, allowing nisin to penetrate the cytoplasmic membrane and facilitate cell inactivation.

The impact of food model system structure on the inactivation of Listeria innocua by cold atmospheric plasma and nisin combined treatments

Novel processing methods such as cold atmospheric plasma (CAP) and natural antimicrobials like nisin, are of interest to replace traditional food decontamination approaches as, due to their mild nature, they can maintain desirable food characteristics, i.e., taste, texture, and nutritional content. However, the microbial growth characteristics (planktonic growth/surface colonies) and/or the food structure itself (liquid/solid surface) can impact the inactivation efficacy of these novel processing methods. More specifically, cells grown as colonies on a solid(like) surface experience a completely different growth environment to cells grown planktonically in liquid, and thus could display a different response to novel processing treatments through stress adaptation and/or cross protection mechanisms. The order in which combined treatments are applied could also impact their efficacy, especially if the mechanisms of action are complementary. This work presents a fundamental study on the efficacy of CAP and nisin, alone and combined, as affected by food system structure. More specifically, Listeria innocua was grown planktonically (liquid broth) or on a viscoelastic Xanthan gum gel system (1.5% w/v) and treated with CAP, nisin, or a combination of the two. Both the inactivation system, i.e., liquid versus solid(like) surface and the growth characteristics, i.e., planktonic versus colony growth, were shown to impact the treatment efficacy. The combination of nisin and CAP was more effective than individual treatments, but only when nisin was applied before the CAP treatment. This study provides insight into the environmental stress response/adaptation of L. innocua grown on structured systems in response to natural antimicrobials and novel processing technologies, and is a step towards the faster delivery of these food decontamination methods from the bench to the food industry.

Food Microstructure and Fat Content Affect Growth Morphology, Growth Kinetics, and Preferred Phase for Cell Growth of Listeria monocytogenes in Fish-Based Model Systems

Food microstructure significantly affects microbial growth dynamics, but knowledge concerning the exact influencing mechanisms at a microscopic scale is limited. The food microstructural influence on Listeria monocytogenes (green fluorescent protein strain) growth at 10°C in fish-based food model systems was investigated by confocal laser scanning microscopy. The model systems had different microstructures, i.e., liquid, xanthan (high-viscosity liquid), aqueous gel, and emulsion and gelled emulsion systems varying in fat content. Bacteria grew as single cells, small aggregates, and microcolonies of different sizes (based on colony radii [size I, 1.5 to 5.0 μm; size II, 5.0 to 10.0 μm; size III, 10.0 to 15.0 μm; and size IV, ≥15 μm]). In the liquid, small aggregates and size I microcolonies were predominantly present, while size II and III microcolonies were predominant in the xanthan and aqueous gel. Cells in the emulsions and gelled emulsions grew in the aqueous phase and on the fat-water interface. A microbial adhesion to solvent assay demonstrated limited bacterial nonpolar solvent affinities, implying that this behavior was probably not caused by cell surface hydrophobicity. In systems containing 1 and 5% fat, the largest cell volume was mainly represented by size I and II microcolonies, while at 10 and 20% fat a few size IV microcolonies comprised nearly the total cell volume. Microscopic results (concerning, e.g., growth morphology, microcolony size, intercolony distances, and the preferred phase for growth) were related to previously obtained macroscopic growth dynamics in the model systems for an L. monocytogenes strain cocktail, leading to more substantiated explanations for the influence of food microstructural aspects on lag phase duration and growth rate.IMPORTANCEListeria monocytogenes is one of the most hazardous foodborne pathogens due to the high fatality rate of the disease (i.e., listeriosis). In this study, the growth behavior of L. monocytogenes was investigated at a microscopic scale in food model systems that mimic processed fish products (e.g., fish paté and fish soup), and the results were related to macroscopic growth parameters. Many studies have previously focused on the food microstructural influence on microbial growth. The novelty of this work lies in (i) the microscopic investigation of products with a complex composition and/or structure using confocal laser scanning microscopy and (ii) the direct link to the macroscopic level. Growth behavior (i.e., concerning bacterial growth morphology and preferred phase for growth) was more complex than assumed in common macroscopic studies. Consequently, the effectiveness of industrial antimicrobial food preservation technologies (e.g., thermal processing) might be overestimated for certain products, which may have critical food safety implications.

Inactivation of Single Strains of Listeria monocytogenes and Salmonella Typhimurium Planktonic Cells Biofilms With Plasma Activated Liquids

Recent research has proven the ability of cold atmospheric plasma (CAP) for assuring food safety. A more flexible and transportable alternative is the use of plasma activated liquids (PAL), which are also known to have antimicrobial properties. However, within the context of food safety, little is known on its potential regarding decontamination. This research therefore focusses on identifying the impact of (i) the microbial species and its cell type (planktonic cells or biofilms), (ii) the CAP settings (i.e., gas composition and generation time) and (iii) PAL related factors (treatment time and PAL age) on the technologies efficacy. Cell densities were monitored using the plate counting technique for which the results were analyzed by means of predictive inactivation models. Moreover, the pH and the concentrations of long-lived species (i.e., hydrogen peroxide, nitrite, and nitrate) were measured to characterize the PAL solutions. The results indicated that although the type of pathogen impacted the efficacy of the treatment, mainly the cell mode had an important effect. The presence of oxygen in the operating gas ensured the generation of PAL solutions with a higher antimicrobial activity. Moreover, to ensure a good microbial inactivation, PAL generation times needed to be sufficiently long. Both CAP related factors resulted in a higher amount of long-lived species, enhancing the inactivation. For 30 min. PAL generation using O2, this resulted in log reductions up to 3.9 for biofilms or 5.8 for planktonic cells. However, loss of the PAL activity for stored solutions, together with the frequent appearance of a tailing phase in the inactivation kinetics, hinted at the importance of the short-lived species generated. Different factors, related to (i) the pathogen and its cell mode, (ii) the CAP settings and (iii) PAL related factors, proved to impact the antimicrobial efficacy of the solutions and should be considered with respect to future applications of the PAL technology.

Modelling the microbial dynamics and antimicrobial resistance development of Listeria in viscoelastic food model systems of various structural complexities

Minimal processing for microbial decontamination, such as the use of natural antimicrobials, is gaining interest in the food industry as these methods are generally milder than conventional processing, therefore better maintaining the nutritional content and sensory characteristics of food products. The aim of this study was to quantify the impact of (i) structural composition and complexity, (ii) growth location and morphology, and (iii) the natural antimicrobial nisin, on the microbial dynamics of Listeria innocua. More specifically, viscoelastic food model systems of various compositions and internal structure were developed and characterised, i.e. monophasic Xanthan gum-based and biphasic Xanthan gum/Whey protein-based viscoelastic systems. The microbial dynamics of L. innocua at 10 °C, 30 °C and 37 °C were monitored and compared for planktonic growth in liquid, or in/on (immersed or surface colony growth) the developed viscoelastic systems, with or without a sublethal concentration of nisin. Microscopy imaging was used to determine the bacterial colony size and spatial organisation in/on the viscoelastic systems. Selective growth of L. innocua on the protein phase of the developed biphasic system was observed for the first time. Additionally, significant differences were observed in the colony size and distribution in the monophasic Xanthan gum-based systems depending on (i) the type of growth (surface/immersed) and (ii) the Xanthan gum concentration. Furthermore, the system viscosity in monophasic Xanthan gum-based systems had a protective role against the effects of nisin for immersed growth, and a further inhibitory effect for surface growth at a suboptimal temperature (10 °C). These findings give a systematic quantitative insight on the impact of nisin as an environmental challenge on the growth and spatial organisation of L. innocua, in viscoelastic food model systems of various structural compositions/complexities. This study highlights the importance of accounting for system structural composition/complexity when designing minimal food processing methods with natural antimicrobials.

A tutorial on uncertainty propagation techniques for predictive microbiology models: A critical analysis of state-of-the-art techniques

Building mathematical models in predictive microbiology is a data driven science. As such, the experimental data (and its uncertainty) has an influence on the final predictions and even on the calculation of the model prediction uncertainty. Therefore, the current research studies the influence of both the parameter estimation and uncertainty propagation method on the calculation of the model prediction uncertainty. The study is intended as well as a tutorial to uncertainty propagation techniques for researchers in (predictive) microbiology. To this end, an in silico case study was applied in which the effect of temperature on the microbial growth rate was modelled and used to make simulations for a temperature profile that is characterised by variability. The comparison of the parameter estimation methods demonstrated that the one-step method yields more accurate and precise calculations of the model prediction uncertainty than the two-step method. Four uncertainty propagation methods were assessed. The current work assesses the applicability of these techniques by considering the effect of experimental uncertainty and model input uncertainty. The linear approximation was demonstrated not always to provide reliable results. The Monte Carlo method was computationally very intensive, compared to its competitors. Polynomial chaos expansion was computationally efficient and accurate but is relatively complex to implement. Finally, the sigma point method was preferred as it is (i) computationally efficient, (ii) robust with respect to experimental uncertainty and (iii) easily implemented.

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.

Salmonella Typhimurium and Staphylococcus aureus dynamics in/on variable (micro)structures of fish-based model systems at suboptimal temperatures

The limited knowledge concerning the influence of food (micro)structure on microbial dynamics decreases the accuracy of the developed predictive models, as most studies have mainly been based on experimental data obtained in liquid microbiological media or in/on real foods. The use of model systems has a great potential when studying this complex factor. Apart from the variability in (micro)structural properties, model systems vary in compositional aspects, as a consequence of their (micro)structural variation. In this study, different experimental food model systems, with compositional and physicochemical properties similar to fish patés, are developed to study the influence of food (micro)structure on microbial dynamics. The microbiological safety of fish products is of major importance given the numerous cases of salmonellosis and infections attributed to staphylococcus toxins. The model systems understudy represent food (micro)structures of liquids, aqueous gels, emulsions and gelled emulsions. The growth/inactivation dynamics and a modelling approach of combined growth and inactivation of Salmonella Typhimurium and Staphylococcus aureus, related to fish products, are investigated in/on these model systems at temperatures relevant to fish products' common storage (4°C) and to abuse storage temperatures (8 and 12°C). ComBase (http://www.combase.cc/) predictions compared with the maximum specific growth rate (μ_max) values estimated by the Baranyi and Roberts model in the current study indicated that the (micro)structure influences the microbial dynamics. Overall, ComBase overestimated microbial growth at the same pH, a_w and storage temperature. Finally, the storage temperature had also an influence on how much each model system affected the microbial dynamics.

Influence of food intrinsic complexity on Listeria monocytogenes growth in/on vacuum-packed model systems at suboptimal temperatures

Food intrinsic factors e.g., food (micro)structure, compositional and physicochemical aspects, which are mutually dependent, influence microbial growth. While the effect of composition and physicochemical properties on microbial growth has been thoroughly assessed and characterised, the role of food (micro)structure still remains unravelled. Most studies on food (micro)structure focus on comparing planktonic growth in liquid (microbiological) media with colonial growth in/on solid-like systems or on real food surfaces. However, foods are not only liquids or solids; they can also be emulsions or gelled emulsions and have complex compositions. In this study, Listeria monocytogenes growth was studied on the whole spectrum of (micro)structure, in terms of food (model) systems. The model systems varied not only in (micro)structure, which was the target of the study, but also in compositional and physicochemical characteristics, which was an inevitable consequence of the (micro)structural variability. The compositional and physicochemical differences were mainly due to the presence or absence of fat and gelling agents. The targeted (micro)structures were: i) liquids, ii) aqueous gels, iii) emulsions and iv) gelled emulsions. Furthermore, the microbial dynamics were studied and compared in/on all these model systems, as well as on a compositionally predefined canned meat, developed in order to have equal compositional level to the gelled emulsion model system and represent a real food system. Frankfurter sausages were the targeted real foods, selected as a case study, to which the canned meat had similar compositional characteristics. All systems were vacuum packed and incubated at 4, 8 and 12°C. The most appropriate protocol for the preparation of the model systems was developed. The pH, water activity and resistance to penetration of the model systems were characterised. Results indicated that low temperature contributes to growth variations among the model systems. Additionally, the firmer the solid system, the faster L. monocytogenes grew on it. Finally, it was found that L. monocytogenes grows faster on canned meat and real Frankfurters, as found in a previous study, followed by liquids, aqueous gels, emulsions and gelled emulsions. This observation indicates that all model systems, developed in this study, underestimated L. monocytogenes growth. Despite some limitations, model systems are overall advantageous and therefore, their validation is always recommended prior to further use.

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.

Effect of cell immobilization on the growth dynamics of Salmonella Typhimurium and Escherichia coli at suboptimal temperatures

Predictive microbiology has recently acknowledged the impact of the solid(like) food structure on microbial behavior. The presence of this solid(like) structure causes microorganisms to grow as colonies and no longer planktonically as in liquid. In this paper, the growth dynamics of Salmonella Typhimurium and Escherichia coli were studied as a function of temperature, considering different growth morphologies, i.e., (i) planktonic cells, (ii) immersed colonies and (iii) surface colonies. For all three growth morphologies, both microorganisms were grown in petri dishes. While E. coli was grown under optimal pH and water activity (aw), for S. Typhimurium pH and aw were adapted to 5.5 and 0.990. In order to mimic a solid(like) environment, 5% (w/v) gelatin was added. All petri dishes were incubated under static conditions at temperatures in the range [8.0°C-22.0°C]. Cell density was determined via viable plate counting. This work demonstrates that the growth morphology (planktonic vs. colony) has a negligible effect on the growth dynamics as a function of temperature. The observation of almost equal growth rates for planktonic cultures and colonies is in contrast to literature where, mostly, a difference is observed, i.e., μplanktonic cells≥μimmersed colonies≥μsurface colonies. This difference might be due to shaking of the liquid culture in these studies, which results in a nutrient and oxygen rich environment, in contrast to the diffusion-limited gel system. Experiments also indicate that lag phases for solid(like) systems are similar to those for the planktonic cultures, as can be found in literature for similar growth conditions. Considering the maximum cell density, no clear trend was deducted for either of the microorganisms. This study indicates that the growth parameters in the suboptimal temperature range do not depend on the growth morphology. For the considered experimental conditions, models previously developed for liquid environments can be used for solid(like) systems.

The effect of medium structure complexity on the growth of Saccharomyces cerevisiae in gelatin-dextran systems

As most food systems are (semi-)solid, the effect of food structure on bacterial growth has been widely acknowledged. However, studies on the growth dynamics of yeasts have neglected the effect of food structure. In this paper, the growth dynamics of the spoilage yeast Saccharomyces cerevisiae was investigated at 23.5 °C in broth, singular, homogeneous biopolymer systems and binary biopolymer systems with a heterogeneous microstructure. The biopolymers gelatin and dextran were used to introduce the different levels of structure. The metabolizing ability of gelatin and dextran by S. cerevisiae was examined. To study microbial behavior in the binary systems at the micro level, mixtures were imaged with confocal laser scanning microscopy (CLSM). Growth dynamics and microscopic images of S. cerevisiae were compared with those obtained for Escherichia coli in the same model system (Boons et al., 2014). Different phase-separated, heterogeneous microstructures were obtained by changing the amount of added gelatin and dextran. Regardless of the microstructure, S. cerevisiae was preferentially located in the dextran phase. Metabolizing ability-tests indicated that gelatin could be consumed by S. cerevisiae but in the presence of glucose, no change in gelatin concentration was observed. No indication of dextran metabolizing ability was observed. When supplementing broth with gelatin or dextran alone, an enhanced growth rate and maximum cell density were observed. This enhancement was further increased by adding a second biopolymer, introducing a heterogeneous microstructure and hence increasing the medium structure complexity. The results obtained indicate that food structure complexity plays a significant role in the growth dynamics of S. cerevisiae, an important food spoiler.

Effect of microstructure on population growth parameters of Escherichia coli in gelatin-dextran systems

Current literature acknowledges the effect of food structure on bacterial dynamics. Most studies introduce this "structure" factor using a single gelling agent, resulting in a homogeneous environment, whereas in practice most food products are heterogeneous. Therefore, this study focuses on heterogeneous protein-polysaccharide mixtures, based on gelatin and dextran. These mixtures show phase separation, leading to a range of heterogeneous microstructures by adjusting relative concentrations of both gelling agents. Based on confocal microscope observations, the growth of Escherichia coli in gelatin-dextran systems was observed to occur in the dextran phase. To find a relation between microscopic and population behavior, growth experiments were performed in binary and singular gelatin-dextran systems and culture broth at 23.5°C, with or without adding 2.9% (wt/vol) NaCl. The Baranyi and Roberts growth model was fitted to the experimental data and parameter estimates were statistically compared. For salted binary mixtures, a decrease in the population maximum cell density was observed with increasing gelatin concentration. In this series, for one type of microstructure, i.e., a gelatin matrix phase with a disperse dextran phase, the maximum cell density decreased with decreasing percentage of dextran phase. However, this relation no longer held when other types of microstructure were observed. Compared to singular systems, adding a second gelling agent in the presence of NaCl had an effect on population lag phases and maximum cell densities. For unsalted media, the growth parameters of singular and binary mixtures were comparable. Introducing this information into mathematical models leads to more reliable growth predictions and enhanced food safety.

Effect of immobilization and salt concentration on the growth dynamics of Escherichia coli K12 and Salmonella typhimurium

Up to now, it is generally observed that (i) the microbial growth domain is confined by structure-induced stress, or (ii) a solid(-like) environment can enhance microbial survival/growth. In most studies in solid(-like) systems, structure is induced by the addition of gelatin. The aim of this study was to evaluate the effect of other structure-inducing components on the growth dynamics. Both single and binary gel systems are used. Growth is studied when simultaneously exposed to salt stress. Experiments are performed in spectrophotometer tubes, filled with 1 mL of liquid, or structured inoculated brain heart infusion. Four different (combinations of) gelling agents are tested, that is, gelatin, xanthan gum, a 50% combination of xanthan gum and gelatin, and a 50% combination of carrageenan and gelatin. Experiments determine the growth behavior of both Escherichia coli (0% to 0.5% and 1%, 2%, 3%, 4%, and 5% NaCl) and Salmonella Typhimurium (0%, 1%, 2%, 3%, 4%, and 5% NaCl) at 23.5 and 27 °C. By means of plate counting, the growth dynamics are determined. At the studied conditions, growth of E. coli and Salmonella Typhimurium seems independent of the type of structure-inducing component. However, at higher concentrations of salt (>2%), lag phases are typically shorter in solid(-like) systems than in liquid media. For the conditions tested, the effect of a structured environment on growth rate and maximal cell density can be neglected.

Genome-scale metabolic flux analysis of Streptomyces lividans growing on a complex medium

Constraint-based metabolic modeling comprises various excellent tools to assess experimentally observed phenotypic behavior of micro-organisms in terms of intracellular metabolic fluxes. In combination with genome-scale metabolic networks, micro-organisms can be investigated in much more detail and under more complex environmental conditions. Although complex media are ubiquitously applied in industrial fermentations and are often a prerequisite for high protein secretion yields, such multi-component conditions are seldom investigated using genome-scale flux analysis. In this paper, a systematic and integrative approach is presented to determine metabolic fluxes in Streptomyces lividans TK24 grown on a nutritious and complex medium. Genome-scale flux balance analysis and randomized sampling of the solution space are combined to extract maximum information from exometabolome profiles. It is shown that biomass maximization cannot predict the observed metabolite production pattern as such. Although this cellular objective commonly applies to batch fermentation data, both input and output constraints are required to reproduce the measured biomass production rate. Rich media hence not necessarily lead to maximum biomass growth. To eventually identify a unique intracellular flux vector, a hierarchical optimization of cellular objectives is adopted. Out of various tested secondary objectives, maximization of the ATP yield per flux unit returns the closest agreement with the maximum frequency in flux histograms. This unique flux estimation is hence considered as a reasonable approximation for the biological fluxes. Flux maps for different growth phases show no active oxidative part of the pentose phosphate pathway, but NADPH generation in the TCA cycle and NADPH transdehydrogenase activity are most important in fulfilling the NADPH balance. Amino acids contribute to biomass growth by augmenting the pool of available amino acids and by boosting the TCA cycle, particularly when using glutamate and aspartate. Depletion of glutamate and aspartate causes a distinct shift in fluxes of the central carbon and nitrogen metabolism. In the current work, hurdles encountered in flux analysis at a genome-scale level are addressed using hierarchical flux balance analysis and uniform sampling of the constrained solution space. This general framework can now be adopted in further studies of S. lividans, e.g., as a host for heterologous protein production.

A novel method for high-throughput data collection in predictive microbiology: optical density monitoring of colony growth as a function of time

Recently, the focus of predictive food microbiology has shifted towards more mechanistically-inspired modelling. Together with this trend, the need for methods that allow rapid data collection at the (intra)cellular level, as well as the intermediate subpopulation/colony level, has emerged. Although several experimental techniques are currently available to study colony dynamics in/on solid media, their widespread implementation as high-throughput methods remains a challenge. In this research, a novel method is presented to study colony growth based on optical density measurements performed in microtiter plates. An area scan procedure was applied to monitor individual Escherichia coli colonies in 48-well plates at 30 °C. Based on a fixed threshold value to separate the object (colony) from the background, the colony area was determined as a function of time. With this technique, expansion of the colony in radial direction could be monitored. Practical limitations (i.e., maximum achievable resolution and colony size) of the proposed method were investigated. A comparison was made with existing methods at the level of hardware requirements, data acquisition and data processing. Overall, the novel optical density method proved to be a flexible, high-throughput tool for monitoring (the mechanisms of) microbial colony growth in solid(like) systems.

Sensitivity analysis of a two-dimensional quantitative microbiological risk assessment: keeping variability and uncertainty separated

The aim of quantitative microbiological risk assessment is to estimate the risk of illness caused by the presence of a pathogen in a food type, and to study the impact of interventions. Because of inherent variability and uncertainty, risk assessments are generally conducted stochastically, and if possible it is advised to characterize variability separately from uncertainty. Sensitivity analysis allows to indicate to which of the input variables the outcome of a quantitative microbiological risk assessment is most sensitive. Although a number of methods exist to apply sensitivity analysis to a risk assessment with probabilistic input variables (such as contamination, storage temperature, storage duration, etc.), it is challenging to perform sensitivity analysis in the case where a risk assessment includes a separate characterization of variability and uncertainty of input variables. A procedure is proposed that focuses on the relation between risk estimates obtained by Monte Carlo simulation and the location of pseudo-randomly sampled input variables within the uncertainty and variability distributions. Within this procedure, two methods are used-that is, an ANOVA-like model and Sobol sensitivity indices-to obtain and compare the impact of variability and of uncertainty of all input variables, and of model uncertainty and scenario uncertainty. As a case study, this methodology is applied to a risk assessment to estimate the risk of contracting listeriosis due to consumption of deli meats.

Efficient Tracking of the Dominant Eigenspace of a Normalized Kernel Matrix

Various machine learning problems rely on kernel-based methods. The power of these methods resides in the ability to solve highly nonlinear problems by reformulating them in a linear context. The dominant eigenspace of a (normalized) kernel matrix is often required. Unfortunately, the computational requirements of the existing kernel methods are such that the applicability is restricted to relatively small data sets. This letter therefore focuses on a kernel-based method for large data sets. More specifically, a numerically stable tracking algorithm for the dominant eigenspace of a normalized kernel matrix is proposed, which proceeds by an updating (the addition of a new data point) followed by a downdating (the exclusion of an old data point) of the kernel matrix. Testing the algorithm on some representative case studies reveals that a very good approximation of the dominant eigenspace is obtained, while only a minimal amount of operations and memory space per iteration step is required.

Optimal fed batch experiment design for estimation of monod kinetics of Azospirillum brasilense: from theory to practice

In this paper the problem of reliable and accurate parameter estimation for unstructured models is considered. It is illustrated how a theoretically optimal design can be successfully translated into a practically feasible, robust, and informative experiment. The well-known parameter estimation problem of Monod kinetic parameters is used as a vehicle to illustrate our approach. As known for a long time, noisy batch measurements do not allow for unique and accurate estimation of the kinetic parameters of the Monod model. Techniques of optimal experiment design are, therefore, exploited to design informative experiments and to improve the parameter estimation accuracy. During the design process, practical feasibility has to be kept in mind. The designed experiments are easy to implement in practice and do not require additional monitoring equipment. Both design and experimental validation of informative fed batch experiments are illustrated with a case study, namely, the growth of the nitrogen-fixing bacteria Azospirillum brasilense.

Modeling individual cell lag time distributions for Listeria monocytogenes

The food industry faces two paradoxical demands: on the one hand, foods need to be microbiologically safe for consumption and on the other hand, consumers want fresh, minimally processed foods. To meet these demands, more insight into the mechanisms of microbial growth is needed, which includes, among others, the microbial lag phase. This is the time needed by bacterial cells to adapt to a new environment (for example, after food product contamination) before starting an exponential growth regime. Since food products are often contaminated with low amounts of pathogenic microorganisms, it is important to know the distribution of these individual cell lag times to make accurate predictions concerning food safety. More precisely, cells with the shortest lag times (i.e., appearing in the left tail of the distribution) are largely decisive for the outgrowth of the population. In this study, an integrated modeling approach is proposed and applied to an existing data set of individual cell lag time measurements of Listeria monocytogenes. In a first step, a logistic modeling approach is applied to predict the fraction of zero-lag cells (which start growing immediately) as a function of temperature, pH, and water activity. For the nonzero-lag cells, the mean and variance of the lag time distribution are modeled with a hyperbolic-type model structure. This mean and variance allow identification of the parameters of a two-parameter Weibull distribution, representing the nonzero-lag cell lag time distribution. The integration of the developed models allows prediction of a global distribution of individual cell lag times for any combination of environmental conditions in the interpolation domain of the original temperature, pH, and water activity settings. The global fitting quality of the model is quantified using several measures indicating that the model gives accurate predictions, erring slightly on the fail-safe side when predicting the shortest lag times.

Concepts and tools for predictive modeling of microbial dynamics

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

Linearization of the activated sludge model ASM1 for fast and reliable predictions

In this paper a strategy is proposed to reduce the complexity of the activated sludge model no. 1 (ASM1) which describes the biotransformation processes in a common activated sludge process with N-removal. The key feature of the obtained reduced model is that it combines high predictive value (all state variables keep their biological interpretation) with very low computation time. Therefore, this model is a valuable tool in a risk assessment environment (designed for the evaluation of wastewater treatment plants facing stricter effluent norms) as well as in on-line (MPC) control strategies. The complexity reduction procedure consists of four steps. In the first step representative input/output data sets are generated by simulating the full ASM1 model. In the second step the ASM1 model is rewritten in state space format with linear approximations of the nonlinear (kinetic) terms. In the third step the unknown parameters in the linear terms are identified based on the generated input/output data. To reduce the amount of parameter sets that have to be identified (to cover the full operation range of the plant), a Multi-Model interpolation procedure is introduced as a last step.

Feedback stabilization of fed-batch bioreactors: non-monotonic growth kinetics

This paper deals with the design of a feedback controller for fed-batch microbial conversion processes that forces the substrate concentration C(S) to a desired setpoint, starting from an arbitrary (initial) substrate concentration when non-monotonic growth kinetics apply. This problem is representative for a lot of industrial fermentation processes, with the baker's yeast fermentation as a well-known example. It is assumed that the specific growth rate mu is function of the substrate concentration only. A first approach exploits the availability of on-line measurements of both the substrate and biomass concentration. A second approach is merely based on on-line measurements of the biomass concentration, which provide an estimate for the specific growth rate. After a reformulation of the substrate concentration setpoint into a specific growth rate setpoint, it is demonstrated that the fed-batch process can still be stabilized around any desired operating point along the non-monotonic kinetics.

Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions

As part of the model building process, parameter estimation is of great importance in view of accurate prediction making. Confidence limits on the predicted model output are largely determined by the parameter estimation accuracy that is reflected by its parameter estimation covariance matrix. In view of the accurate estimation of the Square Root model parameters, Bernaerts et al. have successfully applied the techniques of optimal experiment design for parameter estimation [Int. J. Food Microbiol. 54 (1-2) (2000) 27]. Simulation-based results have proved that dynamic (i.e., time-varying) temperature conditions characterised by a large abrupt temperature increase yield highly informative cell density data enabling precise estimation of the Square Root model parameters. In this study, it is shown by bioreactor experiments with detailed and precise sampling that extreme temperature shifts disturb the exponential growth of Escherichia coli K12. A too large shift results in an intermediate lag phase. Because common growth models lack the ability to model this intermediate lag phase, temperature conditions should be designed such that exponential growth persist even though the temperature may be changing. The current publication presents (i) the design of an optimal temperature input guaranteeing model validity yet yielding accurate Square Root model parameters, and (ii) the experimental implementation of the optimal input in a computer-controlled bioreactor. Starting values for the experiment design are generated by a traditional two-step procedure based on static experiments. Opposed to the single step temperature profile, the novel temperature input comprises a sequence of smaller temperature increments. The structural development of the temperature input is extensively explained. High quality data of E. coli K12 under optimally varying temperature conditions realised in a computer-controlled bioreactor yield accurate estimates for the Square Root model parameters. The latter is illustrated by means of the individual confidence intervals and the joint confidence region.

Analysis and practical implementation of a model for combined growth and metabolite production of lactic acid bacteria

Next to the traditional application of lactic acid bacteria (LAB) as starter cultures for food fermentations, the use of LAB as protective cultures against microbial pathogens and spoilage organisms in other food production processes gains more and more interest. The inhibitory effect of LAB is mainly accomplished through formation of antimicrobial metabolites. In this paper, the model of Nicolaï et al. [Food Microbiol. 10 (1993) 229.], describing cell growth and production of lactic acid, which is the major end-product of LAB metabolism, is investigated. In contrast to classical predictive models, the transition of the exponential growth phase to the stationary phase is obtained through the increasing concentrations of undissociated lactic acid [LaH] and decreasing pH in the environment. To describe the variation in time of [LaH] and pH, a novel, robust calculation method is introduced. The model of Nicolaï et al. in combination with the novel method of [LaH] and pH computation is then further applied to an experimental data set of Lactococcus lactis SL05 grown in a rich medium. An accurate description of the measured values of cell concentration, total lactic acid concentration and pH is obtained.