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The stochastic growth of homogeneous bacterial populations in the wells of a microtiter plate was studied as a function of the random initial cell number and their random individual lag times. These significantly affected the population growth in the well, while the maximum specific growth rate of the population was constant (or its variance was negligible) for each well. We showed the advantages of the mathematical assumption that a transformation of the single cell lag time, called the single cell physiological state (or, more accurately, that of the sub-population generated by the single cell) follow the Beta distribution. Simulations demonstrated what patterns would such assumption generate for the distribution of the detection times observed in the wells. An estimation procedure was developed, based on the beta-assumption, that resulted in an explicit expression for the expected value of the single cell physiological state as a function of measured "time to detection" values using turbidity experiments. The method was illustrated using laboratory data with Escherichia coli, Salmonella enterica subsp. enterica strains. The results gave a basis to quantify the difference between the studied organisms in terms of their single-cell kinetics.

Using turbidity measurements to quantify bacterial growth is a common and well-established practice in microbiology. Automated devices offering high throughput analyses have largely contributed to the increase of its use. A main difficulty of this method is that it detects growth only at late exponential phase, making turbidity measurements limited for studies focussing on low cell numbers. This work proposes an improved estimator for the probability of growth of individual cells using turbidity-based measurements, when the initial number of cells is low and random. We modify the currently used estimator for the expected cell number per well, a Poisson-parameter, and show that an optimal scenario is when ca 20% of the wells do not become turbid, resulting in improved accuracy and precision.

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.

The z -value concept, commonly used in thermal death kinetics of bacteria, is generalized for growth and for the situation when the modelled growth parameter is a non-linear function of several environmental variables. The (harmonic) mean of the generalized z -value in the region of interest is applied to quantify the ‘average’ effect of an environmental variable. This mean is used to compare the effect of temperature and atmospheric carbon dioxide on the growth of Listeria monocytogenes.

In the present study, the effect of modified atmospheres ranging from 0–90% CO 2 (balance 10% H 2 and N 2 ) was evaluated on growth from spores of non-proteolytic Clostridium botulinum (types B, E and F), at different pH and NaCl concentrations, over the temperature range 5–12°C. Growth tests were carried out using a model broth system, PYGS (peptone, yeast, glucose, starch). In general terms, a CO 2 concentration of 5% enhanced growth, 50% CO 2 showed a moderate inhibition and 90% had a considerable inhibitory effect. A predictive model has been developed that describes the effect of CO 2 , in combination with other mild preservative factors, on growth from spores of non-proteolytic C. botulinum . The model provides a good description of the experimental data.

A growth/no growth boundary model based on interpolated probabilities is presented in this paper. The boundary is defined as the loci where the probability of growth for a sample is equal to its chance of no growth, P (growth)= P (no growth). Brochothrix thermosphacta was used as a test micro-organism to collect data near the boundary of growth/no growth, in a pH/NaCl grid. Results showed a dramatic change in the probability of growth at the boundary with minor changes of pH or NaCl, and that the location of the boundary was affected by the inoculum level. A quadratic polynomial was used to describe the boundary of the growth region (interpolated P =0·5). The importance of growth/no growth boundary models as limits for the application of kinetic models is discussed.

Two aspects of the addition of new environmental factors to predictive microbiology models are discussed. The concept of risk of extrapolation is introduced to characterize the probability that a prediction is outside the model interpolation region. For an empirical model, the interpolation region is defined by the data which are used to estimate the parameters of the model. It is shown that the risk of extrapolation can become unexpectedly high during extending a model to describe the effect of newer factors, if the extension is supported by insufficient data. A convenient method of extending predictive models is also presented to accommodate observations on the effect of additional environmental factors. New factors can be added to a basic common model, in such a way that the basic model will be a special case of the extended models. Conditions under which this approach is useful are discussed. Published data are used to illustrate both points.

Growth data from three isolates of each of four species belonging to Aspergillus sect. Flavi ( Aspergillus flavus , Aspergillus oryzae , Aspergillus parasiticus and Aspergillus nomius ) were modelled to describe the effect of a w on colony growth rate for each species. The model coefficients were used in a novel way to quantify the ‘relatedness’ of the four species in terms of how their growth rate varies with a w . This ‘relatedness’ can be described by a linear model where A. oryzae and A. parasiticus are very close to each other, placed between A. nomius and A. flavus and closer to the latter species.

The use of primary mathematical models with curve fitting software is dramatically changing quantitative food microbiology. The two most widely used primary growth models are the Baranyi and Gompertz models. A three-phase linear model was developed to determine how well growth curves could be described using a simpler model. The model divides bacterial growth curves into three phases: the lag and stationary phases where the specific growth rate is zero (μ=0), and the exponential phase where the logarithm of the bacterial population increases linearly with time (μ=constant). The model has four parameters: N O i (Log 10 of initial population density), NMAX (Log 10 of final population density), tLAG (time when lag phase ends), and tMAX (time when exponential phase ends). A comparison of the linear model was made against the Baranyi andGompertz models, using established growth data for Escherichia coli 0157:H7. The growth curves predicted by the three models showed good agreement. The linear model was more 'robust' than the others, especially when experimental data were minimal. The physiological assumptions underlying the linear model are discussed, with particular emphasis on assuring that the model is consistent with bacterial behavior both as individual cells and as populations. It is proposed that the transitional behavior of bacteria at the end of the lag phase can be explained on the basis of biological variability.

Empirical models fitted to measured data should be used only in the region within which measurements were made, the so-called interpolation region. In cases in which many variables are involved, the determination of the interpolation region is not self-evident and the region is sometimes unexpectedly small. A definition of the interpolation region is presented, to enable some consequences of the use of models with high numbers of parameters to be exemplified. In particular, unreliability close to the boundary of the interpolation region is highlighted by comparison of the predictions of models with different numbers of parameters.

It is recognised that inoculum size affects the rate and extent of bacterial spore germination. It has been proposed that this is due to spores interacting: molecules released from germinated spores trigger germination of dormant neighbours. This study investigated whether changes to the total number of spores in a system or proximity to other spores (local spore density) had a more significant effect on interaction between spores of non-proteolytic Clostridium botulinum strain Eklund 17B attached to defined areas of microscope slides. Both the number of spores attached to the slides and local spore density (number of spores per mm(2)) were varied by a factor of nine. Germination was observed microscopically at 15 °C for 8 h and the probability of, and time to, germination calculated from image analysis measurements. Statistical analysis revealed that the effect of total spore number on the probability of germination within 8 h was more significant than that of proximity to neighbours (local spore density); its influence on germination probability was approximately four-times greater. Total spore number had an even more significant affect on time to germination; it had a nine-fold greater influence than proximity to neighbours. The applied models provide a means to characterise, quantitatively, the effect of the total spore number on spore germination relative to the effect of proximity to neighbouring spores.

The growth of Salmonella from different osmotic histories was studied in low water activity conditions. Cell cultures were successively diluted and grown in batch, in minimal medium, without and then with added NaCl, several times and from different inoculum levels. The viable count curves obtained in low water activity conditions showed an initial decline after which the culture either died out or recovered and entered the exponential phase. After the first batch with NaCl added, the subsequent curves at low water activity showed progressively smaller initial decline and shorter lag time as the number of transfers from high to low water activity conditions increased. The observed curves were analyzed by F -tests applying an extension of the model of Baranyi and Roberts (1994) . The results suggest that periodic, systematic “training” can improve the adaptation capability of the organism without resulting in higher specific growth rate.

In order to describe the dynamics of growing bacterial cultures a non-autonomous differential equation is applied. The model describes the lag phase as an adjustment period and for the lag-parameter a new definition is introduced. Some mathematical aspects of the model are described and, on the basis of more than 500 growth curves, its statistical properties are compared with the Gompertz-approach commonly used in food microbiology.