E. Van Derlinden

Accurate estimation of cardinal growth temperatures of Escherichia coli from optimal dynamic experiments

Prediction of the microbial growth rate as a response to changing temperatures is an important aspect in the control of food safety and food spoilage. Accurate model predictions of the microbial evolution ask for correct model structures and reliable parameter values with good statistical quality. Given the widely accepted validity of the Cardinal Temperature Model with Inflection (CTMI) [Rosso, L., Lobry, J. R., Bajard, S. and Flandrois, J. P., 1995. Convenient model to describe the combined effects of temperature and pH on microbial growth, Applied and Environmental Microbiology, 61: 610-616], this paper focuses on the accurate estimation of its four parameters (T(min), T(opt), T(max) and micro(opt)) by applying the technique of optimal experiment design for parameter estimation (OED/PE). This secondary model describes the influence of temperature on the microbial specific growth rate from the minimum to the maximum temperature for growth. Dynamic temperature profiles are optimized within two temperature regions ([15 degrees C, 43 degrees C] and [15 degrees C, 45 degrees C]), focusing on the minimization of the parameter estimation (co)variance (D-optimal design). The optimal temperature profiles are implemented in a computer controlled bioreactor, and the CTMI parameters are identified from the resulting experimental data. Approximately equal CTMI parameter values were derived irrespective of the temperature region, except for T(max). The latter could only be estimated accurately from the optimal experiments within [15 degrees C, 45 degrees C]. This observation underlines the importance of selecting the upper temperature constraint for OED/PE as close as possible to the true T(max). Cardinal temperature estimates resulting from designs within [15 degrees C, 45 degrees C] correspond with values found in literature, are characterized by a small uncertainty error and yield a good result during validation. As compared to estimates from non-optimized dynamic experiments, more reliable CTMI parameter values were obtained from the optimal experiments within [15 degrees C, 45 degrees C].

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the systems dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy). This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.

On the critical evaluation of growth/no growth assessment of Zygosaccharomyces bailii with optical density measurements: Liquid versus structured media

Growth/no growth (G/NG) studies that include the effect of medium structure have typically been performed for (pathogenic) bacteria and on the basis of gelatin/agar as a gelling agent. In this study, the growth potential of the spoilage yeast Zygosaccharomyces bailii was investigated in two model systems that resemble the macroscopic physicochemical and rheological properties of acidic sauces. In a Carbopol model system, the effect of pH (3.5-4.5), glycerol concentration (17-32%), acetic acid concentration (1.5-2.0%) and medium structure (3 levels) was investigated. In xanthan gum, the behavior of the yeast was studied at different levels of pH (3.5-4.5), NaCl concentration (0.5-13.5%), acetic acid concentration (0-2.0%) and medium structure (2 levels). Rheologically, viscoelastic moduli failed to discriminate between different forms of microbial growth, whereas yield stress data appeared to provide a better indication. In general, G/NG results revealed an unexpected increase of growth probability as a function of medium structure, both at 22 and 30 °C. Whether this behavior is the result of an underlying growth-promoting mechanism could not be explained from a macroscopic point of view (e.g., macrorheology, a(w)), but may be more related to the local microscopic properties of the gels. In a second part of this study, the potential use and information content of optical density measurements for G/NG data collection in structured media were critically evaluated and confronted with their practical relevance to the food industry.

Towards the quantification of the effect of acid treatment on the heat tolerance of Escherichia coli K12 at lethal temperatures.

The aim of this work is to investigate the effect of acid treatment -before and during heat inactivation- on the heat resistance of Escherichia coli K12 MG1655 cells at lethal temperatures. E. coli cells were grown in Brain Heart Infusion broth until they reached the stationary phase (≈10(9) cfu/mL). Approximately 30 min before thermal inactivation the early stationary phase cells were added in Brain Heart Infusion broth with a specific pH value, achieved with addition of either acetic (50% (v/v)), lactic (50% (v/v)) or hydrochloric acid (30% (v/v)), and inactivation experiments took place at 54 °C and 58 °C. The inactivation dynamics are analysed using the inactivation model of Geeraerd et al. (2000). This enables to define the induced thermotolerance of E. coli as a prolongation of the shoulder and/or a reduction of the inactivation rate. Generally, addition of acids increased the heat resistance of E. coli. The induced resistance depends on the type of acid and on the quantity added, i.e. different levels of acidification lead to a different level of heat resistance. This work provides additional knowledge on the reaction of bacterial cultures to heat after acid treatment -before and during heat treatment- and, therefore, it contributes to an improved understanding of the effect of acid exposure on the bacterial heat resistance.

Quantifying the heterogeneous heat response of Escherichia coli under dynamic temperatures

Aims:  Non‐sigmoid growth curves of Escherichia coli obtained at constant temperatures near the maximum growth temperature (Tmax) were previously explained by the coexistence of two subpopulations, i.e. a stress‐sensitive and a stress‐resistant subpopulation. Mathematical simulations with a heterogeneous model support this hypothesis for static experiments at 45°C. In this article, the behaviour of E. coli, when subjected to a linearly increasing temperature crossing Tmax, is studied.

Modeling growth rates as a function of temperature: model performance evaluation with focus on the suboptimal temperature range.

Secondary models, describing the microbial growth rate as a function of temperature, are evaluated with focus on model performance in the suboptimal temperature region. Escherichia coli K12 MG1655 is considered as the case study. A large set of square root of μ(max)(T)-estimates is fitted with (1) the cardinal temperature model with inflection (CTMI, Rosso et al., 1993), (2) the square root model (SQRT, Ratkowsky et al., 1983), and (3) the CTMI adapted to describe the particular behavior of Listeria at suboptimal temperatures (aCTMI, Le Marc et al., 2002). Compared to the CTMI and the SQRT, a more accurate description of the μ(max)(T)-relation is obtained with the aCTMI, certainly at temperatures below 30 °C. Also, the T(min) estimate is more realistic, i.e., ≈6 °C, compared to 8-8.5 °C for the CTMI and SQRT. Use of the aCTMI improved square root of μ(max)(T)-data description which points at the existence of two phases in the suboptimal temperature region of E. coli K12. The alternation of the square root of μ(max)(T) is most likely related to the cold shock response. These results reveal a possible shortcoming of the model structure of commonly used secondary models describing the temperature effect on the microbial growth rate.

Behavior of Escherichia coli in a heterogeneous gelatin-dextran mixture

ABSTRACT In a gelatin-dextran mixture, changing the (relative and/or absolute) concentration of the components leads to the formation of different microstructures. Confocal laser scanning microscopy illustrated that the nature of the microstructure determines the location and morphology of Escherichia coli colonies. Observations indicate that bacterial growth preferentially occurs in the dextran phase, regardless of the microstructure.

Escherichia coli population heterogeneity: subpopulation dynamics at super-optimal temperatures.

In the past years, we explored the dynamics of Escherichia coli K12 at super-optimal temperatures under static and dynamic temperature conditions (Van Derlinden et al. (2008b, 2009, 2010). Disturbed sigmoid growth curves, i.e., a sequence of growth, inactivation and re-growth, were observed, especially close to the maximum growth temperature. Based on the limited set of experiments (i.e., 2 static temperatures and 2 dynamic temperature profiles), the irregular growth curves were explained by postulating the co-existence of two subpopulations: a more resistant, growing population and a temperature sensitive, inactivating population. In this study, the dynamics of the two subpopulations are studied rigorously at 11 constant temperature levels in the region between 45°C and 46°C, with at least five repetitions per temperature. At all temperatures, the total population follows a sequence of growth, inactivation and re-growth. The sequence of different stages in the growth curves can be explained by the two subpopulations. The first growth phase and the inactivation phase reflect the presence of the sensitive subpopulation. Hereafter, the populations dynamics are dominated by the growth of the resistant subpopulation. Generally, cell counts are characterized by a large variability. The dynamics of the two subpopulations are carefully analyzed using a heterogeneous subpopulation type model to study the relation between the kinetic parameters of the two subpopulations and temperature, and to evaluate if the fraction d of resistant cells varies with temperature. Results indicate that the growth rate of the sensitive subpopulation decreases with increasing temperature within the range of 45-46°C. Furthermore, results point in the direction that the duration of this initial growth phase is approximately constant, i.e., around 2h. Possibly, the stress resistance of the cells decreases after a certain period because the metabolism is fully adapted to exponential growth. Also, the growth rate of the resistant subpopulation decreases with increasing temperature. Due to the extreme variability in the cell density data, derivation of accurate relations was not possible. From the heterogeneous model implementations, given the experimental set-up, both a constant d value and a temperature dependent d value seem plausible.

Design of an Experimental Viscoelastic Food Model System for Studying Zygosaccharomyces bailii Spoilage in Acidic Sauces

ABSTRACT Within the field of predictive microbiology, the number of studies that quantify the effect of food structure on microbial behavior is very limited. This is mainly due to impracticalities related to the use of a nonliquid growth medium. In this study, an experimental food model system for studying yeast spoilage in acid sauces was developed by selecting a suitable thickening/gelling agent. In a first step, a variety of thickening/gelling agents was screened, with respect to the main physicochemical (pH, water activity, and acetic acid and sugar concentrations) and rheological (weak gel viscoelastic behavior and presence of a yield stress) characteristics of acid sauces. Second, the rheological behavior of the selected thickening/gelling agent, Carbopol 980, was extensively studied within the following range of conditions: pH 4.0 to 5.0, acetic acid concentration of 0 to 1.0% (vol/vol), glycerol concentration of 0 to 15% (wt/vol), and Carbopol concentration of 1.0 to 1.5% (wt/vol). Finally, the applicability of the model system was illustrated by performing growth experiments in microtiter plates for Zygosaccharomyces bailii at 0, 0.5, 1.0, and 1.5% (wt/vol) Carbopol, 5% (wt/vol) glycerol, 0% (vol/vol) acetic acid, and pH 5.0. A shift from planktonic growth to growth in colonies was observed when the Carbopol concentration increased from 0.5 to 1.0%. The applicability of the model system was illustrated by estimating μmax at 0.5% Carbopol from absorbance detection times.

Heat stress adaptation of Escherichia coli under dynamic conditions: effect of inoculum size*

Aims:  When subjected to dynamic temperatures surpassing the expected maximum growth temperature, Escherichia coli K12 MG1655 shows disturbed growth curves. These irregular population dynamics were explained by considering two subpopulations, i.e. a thermoresistant and a thermosensitive one ( Van Derlinden et al. 2010a ). In this paper, the influence of the initial cell concentration on the subpopulations’ dynamics is evaluated.