T.A. Roberts

A dynamic approach to predicting bacterial growth in food.

A new member of the family of growth models described by Baranyi et al. (1993a) is introduced in which the physiological state of the cells is represented by a single variable. The duration of lag is determined by the value of that variable at inoculation and by the post-inoculation environment. When the subculturing procedure is standardized, as occurs in laboratory experiments leading to models, the physiological state of the inoculum is relatively constant and independent of subsequent growth conditions. It is shown that, with cells with the same pre-inoculation history, the product of the lag parameter and the maximum specific growth rate is a simple transformation of the initial physiological state. An important consequence is that it is sufficient to estimate this constant product and to determine how the environmental factors define the specific growth rate without modelling the environment dependence of the lag separately. Assuming that the specific growth rate follows the environmental changes instantaneously, the new model can also describe the bacterial growth in an environment where the factors, such as temperature, pH and aw, change with time.

Predicting microbial growth: growth responses of salmonellae in a laboratory medium as affected by pH, sodium chloride and storage temperature

The growth responses of salmonellae (mixed inoculum of Salmonella thompson, S. stanley and S. infantis) as affected by NaCl concentration, pH level and storage temperature were studied in laboratory medium. Growth curves were obtained at 5 concentrations of NaCl (0.5-4.5%, w/v), 5 pH levels (5.6-6.8) and 5 storage temperatures (10-30 degrees C). Sigmoid curves (Gompertz form) were fitted to the data and the curve parameters used to produce a polynomial model from which predicted growth curves could be generated for any combination of NaCl, pH and storage temperature within the limits studied. From those growth curves values for growth rate, generation time, lag time and other values such as time to a 1000-fold increase in numbers were derived. Such a model offers a cost-effective approach to understanding the microbial growth response in foods, and forms a data-base against which other controlling factors could be evaluated. Some problems of fitting curves to microbial growth data and of modelling such data are discussed.

Mathematics of predictive food microbiology

Commonly encountered problems related to modelling bacterial growth in food are analysed from a mathematical point of view. Modelling techniques and terms, some misused, are discussed and an attempt is made to clarify how, and under what conditions, they may be used. A theoretical framework is given to provide a basis in which mathematical models having been used in predictive microbiology can be embedded. By using several simplifying idealizations as a compromise between the complexity of the biological system and the available data, a practically usable model becomes available.

Predicting fungal growth: the effect of water activity on Aspergillus flavus and related species

Growth of four species belonging to Aspergillus Section Flavi (A. flavus, A. oryzae, A. parasiticus and A. nomius) was studied at 30 degrees C at ten water activities (aw) between 0.995 and 0.810 adjusted with equal mixtures of glucose and fructose. Colony diameters were measured at intervals and plotted against time. A flexible growth model describing the change in colony diameter (mm) with respect to time was first fitted to the measured growth data and from the fitted curves the maximum colony growth rates were calculated. These values were then fitted with respect to aw to predict colony growth rates at any aw within the range tested. The optimum aw for each species and time to reach a colony diameter of 3 mm were also calculated.

Predictive modelling of growth of Listeria monocytogenes The effects on growth of NaCl, pH, storage temperature and NaNO2

The effect of NaCl concentration (5.0 115.0 g/l). pH value (4.0-7.2), temperature (1-35 degrees C) and NaNO2 concentration (0 200 mg/l) on the growth responses of Listeria monocytogenes, in laboratory medium was investigated. The growth curves generated within this matrix of conditions were fitted using the function of Baranyi and Roberts (1994) and the growth responses modelled using a quadratic polynomial to produce response surfaces. Growth curves could then be regenerated for any set of conditions within the experimental matrix and values predicted for the growth rate, doubling time, lag time and time to 1000-fold increase. The model was validated using data from published literature and was found to give realistic predictions for doubling times in foods, including meat and meat products, milk, dairy products and vegetables. Predictions from this model (Baranyi and Roberts. 1994) compared favourably with those from the models of Buchanan and Phillips (1990), Murphy et al. (1996) and the Food MicroModel.

A predictive model for the combined effect of pH, sodium chloride and storage temperature on the growth of Brochothrix thermosphacta

Growth of Brochothrix thermosphacta was observed under ranges of pH (5.6-6.8), NaCl (0.5-8.0% w/v) and incubation temperature (1-30 degrees C). In order to compare different approaches, two models were used to fit growth curves to viable count data, and to calculate parameters from those fitted curves. Growth responses as a function of pH, NaCl and temperature were described with a quadratic function which was then used to predict growth within the limits where growth was observed. The predictions of the model show good agreement with published observations from other laboratories.

The effects of temperature, pH, sodium chloride and sodium nitrite on the growth of Listeria monocytogenes

An automated turbidimetric system using multiwelled plates was used to examine the effects of different combinations of NaCl (0.5-8.0% w/v), NaNO2 (0-400 micrograms/ml) pH (4.6-7.4) and temperature (5-30 degrees C) on the growth of Listeria monocytogenes in tryptone soya broth. The data presented clearly illustrate the combinations that permit visible growth of the organism. The ability of L. monocytogenes to grow at low pH levels was strongly influenced by incubation temperature as well as NaNO2 concentration. At 20 degrees C and below, no visible growth was detected, even with 50 micrograms/ml NaNO2 at pH 5.3 (or below) within 21 days. At pH 6.0 and above, NaNO2 had little effect in delaying visible growth except at higher concentrations and also at lower incubation temperatures.

Evaluation of a monoclonal antibody-based immunoassay for detecting type B Clostridium botulinum toxin produced in pure culture and an inoculated model cured meat system

A monoclonal antibody-based amplified ELISA method for detecting Clostridium botulinum type B toxin was evaluated for its ability to detect the toxin in the supernatant fluid of pure cultures and after growth from Cl. botulinum spores inoculated into pork slurries. Slurries containing NaCl (1.5-4.5% w/v) and polyphosphate (0.3% w/v) were either unheated or heated 80 degrees C/5 min followed by 70 degrees C/2 h before incubation at 15 degrees, 20 degrees or 27 degrees C. Presence of specific toxin was confirmed by mouse bioassay and results were compared with those of the amplified ELISA method. A total of 48 strains, consisting of 38 Cl. botulinum and 10 Cl. sporogenes (putrefactive anaerobes), and 140 slurry samples were tested. Cultures of eight out of nine strains of type B Cl botulinum and 73 of 101 slurry samples containing type B toxin were positive by ELISA; the remaining 28 slurry samples contained type B toxin at levels below or close to the detection limit (20 LD50/ml) of the type B ELISA. No false-positive reactions occurred with Cl. botulinum types A, C, D, E or F, or with the 10 strains of Cl. sporogenes. Toxin produced by one strain of Cl. botulinum type B (NCTC 3807) was not detected by this single monoclonal antibody-based amplified ELISA. With a mixture of two monoclonal antibodies, however, the toxin from NCTC 3807 could be detected without reducing the sensitivity of the ELISA.

Modeling bacterial growth responses

SummaryThe main steps of modeling bacterial growth responses are summarized and a new model for growth curves is shown. Its advantages are analyzed from some theoretical and practical points of view. The new model fits better and has more advantageous statistical properties than the Gompertz curve.

The effect of ph water activity sodium nitrite and storage temperature on the growth of enteropathogenic escherichia coli and salmonellae in a laboratory medium

Abstract The effect of salt concentration (1–10% w/v) in combination with sodium nitrite (0–400 μg/ml) on growth of mixed strains of Salmonella and enteropathogenic E. coli at three pH values (5.6, 6.2, 6.8) and storage temperatures ranging from 10°C to 35°C is reported. E. coli tended to be more tolerant of salt and nitrite than Salmonella.