# Quantification of the Effects of Salt Stress and Physiological State on Thermotolerance of *Bacillus cereus* ATCC 10987 and ATCC 14579

## ABSTRACT

*Bacillus cereus*can acquire enhanced thermal resistance through multiple mechanisms. Two

*Bacillus cereus*strains, ATCC 10987 and ATCC 14579, were used to quantify the effects of salt stress and physiological state on thermotolerance. Cultures were exposed to increasing concentrations of sodium chloride for 30 min, after which their thermotolerance was assessed at 50°C. Linear and nonlinear microbial survival models, which cover a wide range of known inactivation curvatures for vegetative cells, were fitted to the inactivation data and evaluated. Based on statistical indices and model characteristics, biphasic models with a shoulder were selected and used for quantification. Each model parameter reflected a survival characteristic, and both models were flexible, allowing a reduction of parameters when certain phenomena were not present. Both strains showed enhanced thermotolerance after preexposure to (non)lethal salt stress conditions in the exponential phase. The maximum adaptive stress response due to salt preexposure demonstrated for exponential-phase cells was comparable to the effect of physiological state on thermotolerance in both strains. However, the adaptive salt stress response was less pronounced for transition- and stationary-phase cells. The distinct tailing of strain ATCC 10987 was attributed to the presence of a subpopulation of spores. The existence of a stable heat-resistant subpopulation of vegetative cells could not be demonstrated for either of the strains. Quantification of the adaptive stress response might be instrumental in understanding adaptation mechanisms and will allow the food industry to develop more accurate and reliable stress-integrated predictive modeling to optimize minimal processing conditions.

*Bacillus cereus*is a spore-forming gram-positive rod causing both food spoilage and food poisoning. The organism is ubiquitous in soil, in spices, on grass, in dairy cattle feed, and in dung and is an inevitable low-grade contaminant of pasteurized milk products (15). Toxins produced by vegetative cells of

*B. cereus*can be the causative agents of two types of gastrointestinal disease, i.e., emesis and diarrhea. The diarrheal type is caused by heat-labile enterotoxins produced in the intestine, whereas emetic outbreaks are associated with the heat-stable cereulide toxin produced in the food product (8).

*B. cereus*has been investigated previously (4, 22, 28). However, in most investigations, thermotolerance was assessed in exponentially growing cultures after preexposure to just one condition per stress-inducing factor, and the end-point method was used to evaluate the effect of stress preexposure on thermotolerance. The main disadvantage of the end-point method is that it does not provide information on the thermal death kinetics, which could provide valuable knowledge for quantitative risk assessment studies and might reflect the mechanisms by which stress preexposure influences thermotolerance. In the last decades, a number of mathematical primary models have been developed to quantitatively describe microbial inactivation. Primary kinetic models describe microbial survival as a function of time. An important aspect of modeling is the possibility of reliable estimation of the effects of various stress conditions on the number of surviving microorganisms. Therefore, in this study we evaluated the fitting performance of different primary models, which cover a wide range of inactivation curvatures for vegetative cells. The most suitable models were selected in order to identify the survival curvature characteristics in more detail and to quantify the effects of the adaptive stress response and physiological state on the inactivation kinetics.

## MATERIALS AND METHODS

### Bacterial strains and culture conditions.

*Bacillus cereus*ATCC 10987, isolated from a study on cheese spoilage in Canada in 1930 (24), and

*Bacillus cereus*ATCC 14579, isolated from the air in a cow shed in the United Kingdom (9), were used in this study. The cultures were stored frozen (−80°C) in brain heart infusion (BHI) broth (Becton Dickinson, France) supplemented with 25% glycerol (Sigma). The bacteria were cultivated before each experiment in 10 ml BHI broth and incubated in a water bath at 30°C with aeration at 200 rpm (Julabo SW20; Julabo Labortechnik GmbH, Germany) for 16 to 24 h.

### Thermal inactivation experiments with and without preexposure of cells to salt.

*g*, 5 min, 20°C) (Mistral 3000i; MSE, United Kingdom), and the supernatant was removed immediately after centrifugation. To preexpose the harvested cells to salt, the cells were resuspended in 20 ml BHI broth containing sodium chloride (VWR-International, France) at various concentrations (final concentrations of sodium chloride were as follows: for exponential-phase cells, 1%, 2.5%, and 5%; and for transition- and stationary-phase cells, 2.5% [wt/vol]) and incubated for 30 min in a water bath (30°C, 200 rpm). After preexposure to salt, the cells were spun down and resuspended in 2 ml BHI broth. When cells were not preexposed to sodium chloride, 20 ml of culture was centrifuged and concentrated in 2 ml BHI broth.

_{10}CFU ml

^{−1}(detection limit of the method, 1.3 log

_{10}CFU ml

^{−1}). For all experimental conditions, three experiments were performed on different days.

### Microbial survival models.

*D*is the decimal reduction time, which is the time needed for 1 log

_{10}reduction of the population (min);

*N*(0) is the initial population (log

_{10}CFU ml

^{−1}); and

*N*(

*t*) is the population at time

*t*(log

_{10}CFU ml

^{−1}).

*δ*is the first decimal reduction time (min) and

*β*is a fitting parameter which defines the shape of the curve.

*β*values of <1 correspond to concave upward survival curves,

*β*values of >1 correspond to concave downward curves, and a

*β*value of 1 corresponds to a straight line (same as equation 1).

*f*) and

*f*are the fractions of the heat-sensitive and heat-resistant populations, respectively, and

*D*and

_{sens}*D*are the decimal reduction times of the two populations, respectively (min).

_{res}*t*is the duration of the shoulder (min), (1 −

_{s}*f*) and

*f*are the fractions of the heat-sensitive and heat-resistant populations, respectively, and

*k*and

_{sens}*k*are the maximum specific inactivation rates for the heat-sensitive and heat-resistant populations, respectively (min

_{res}^{−1}). The respective decimal reduction times can be calculated from the inactivation rates by the equation

*D*= ln(10)/

*k*. When no shoulder or second population is present, then

*t*= 0 or

_{s}*f*= 0, respectively.

*a*,

*b*, and

*c*are fitting parameters.

*t*is the duration of the shoulder (min),

_{s}*k*is the maximum specific inactivation rate (log

_{10}min

^{−1}), and

*A*is the difference between the population at the end of the inactivation period and the initial population (log

_{10}CFU ml

^{−1}).

*m*= 1 and υ = μ) (2):

*μ*is the maximum specific growth rate (min

^{−1}),

*N*(

*final*) is the final population (log

_{10}CFU ml

^{−1}), and

*A*(

*t*) is as defined by Baranyi et al. (2).

*t*is the duration of the lag period of the growth curve (min).

_{lag}*N*equals the sum of two subpopulations, with one of them having more heat resistance (

*N*=

*N*+

_{sens}*N*) (11). Inactivation of cells ensues when a critical component (

_{res}*C*) is inactivated or destructed. The following equations define the model:

_{c}*C*(0) = exp(

_{c}*k*·

_{sens}*t*) − 1.

_{s}*t*is the duration of the shoulder (min), (1 −

_{s}*f*) and

*f*are the fractions of the heat-sensitive and heat-resistant populations, respectively, and

*k*and

_{sens}*k*are the maximum specific inactivation rates of the heat-sensitive and heat-resistant populations, respectively (min

_{res}^{−1}).

### Model fitting and model selection.

_{model},

*r*

^{2},

*A*, and

_{f}*F*test), biological meaning of the parameters, and reflection of a proposed inactivation mechanism.

### (i) MSE_{model}.

_{model}) is the residual sum of squares (sum of the squared differences between the observed values and the fitted values) divided by the degrees of freedom. The lower the MSE

_{model}is, the better is the adequacy of the model to describe the data. It was calculated by the following equation:

*n*is the number of data points,

*s*is the number of parameters of the model,

*N*

_{observed}

^{i}is the observed population level (log

_{10}CFU ml

^{−1}), and

*N*

_{fitted}

^{i}is the fitted population level (log

_{10}CFU ml

^{−1}).

### (ii) *r*^{2}.

*r*

^{2}) is the proportion of the total variation of the data explained by the model. The value can range between 0 and 1, and the higher the value, the better the fit of the model.

*r*

^{2}was calculated by the following equation:

### (iii) *A*_{f}.

_{f}

*A*) shows the accuracy of the model and indicates how close the fitted values are, on average, to the observed values. The larger the value, the less accurate the model, and when

_{f}*A*is equal to 1, there is perfect agreement between the fitted and the observed values. An

_{f}*A*of 2 indicates that the fitted values are, on average, different by a factor of 2 from the observed values (i.e., either half as large or twice as large). The

_{f}*A*was calculated by the following equation:

_{f}*n*is the number of data points.

### (iv) *F* test.

*F*test was used to decide if the fitting performance of a model was statistically accepted. The

*f*value was calculated by the following equation:

_{model}is the mean square error of the model and MSE

_{data}is the mean square error of the data for replicate values, which indicates the measuring error. MSE

_{data}was determined by the deviation of the observed values from the mean value at one time point,

*i*, and was calculated as follows:

*n*is the number of data points,

*m*is the number of time points (sampling times),

*k*is the number of replicates at each time point, average

*N*is the mean value of the population at time point

^{i}*i*(log

_{10}CFU ml

^{−1}), and

*N*is the population at time point

^{ij}*i*for specific replicate

*j*(log

_{10}CFU ml

^{−1}).

*f*value was tested against an

*F*table value (95% confidence). If the

*f*value was smaller than the

*F*table value (

*F*

_{DFdata}

^{DFmodel}), then the

*F*test was accepted, and this indicated that the model described the observed data well.

### Reduction of model parameters.

*F*test was applied each time after the exclusion of one nonsignificant parameter to evaluate if the reduction of parameters was still statistically acceptable (33). If the

*F*test was not accepted, the model reduction was not performed regardless of whether a nonsignificant parameter was included in the model. The

*f*value to test if a parameter could be excluded was calculated by the following equation:

_{1}is the residual sum of squares of the full model, RSS

_{2}is the residual sum of squares of the reduced model, and DF

_{1}and DF

_{2}are the degrees of freedom for the full and reduced models, respectively, calculated by the formula DF

*=*number of data points − number of parameters.

*f*value was tested against an

*F*table value (95% confidence, \( \(F_{\mathrm{DF}_{1}}^{\mathrm{DF}_{2}{-}\mathrm{DF}_{1}}\) \)). If the

*f*value was smaller than the

*F*table value, the

*F*test was accepted and the nonsignificant parameter was excluded from the model.

### Statistical analysis of model parameters.

*t*tests (one-sided) were performed in order to compare the average parameter estimates for the different conditions and to investigate if there were any significant effects of preexposure to salt and of physiological state on the inactivation kinetic parameters (SPSS, version 11.5.0).

## RESULTS

*B. cereus*ATCC 10987 and ATCC 14579 was determined in BHI broth supplemented with 1%, 2.5%, 5%, and 10% sodium chloride (wt/vol) for 300 min. The two

*B. cereus*strains were able to grow in the presence of salt in the growth medium (1% and 2.5%), although exposure to 2.5% sodium chloride resulted in an initial decline in the number of cells. Higher salt concentrations (5% and 10%) proved to be lethal for the bacterial cells (data not shown). The concentrations of 1%, 2.5%, and 5% sodium chloride were chosen in order to investigate the effects of preexposure to nonlethal and lethal salt conditions on thermotolerance.

### Effects of salt stress and physiological state on thermotolerance: strain diversity and population heterogeneity.

*B. cereus*ATCC 10987 (panel a) and ATCC 14579 (panel b). The thermotolerance of exponential-phase cells of both strains was highly increased by preexposure to 1%, 2.5%, and 5% sodium chloride, resulting in a lower inactivation rate for strain ATCC 10987 compared to the experimental condition without preexposure to salt and an additional shoulder period for strain ATCC 14579. Preexposure to 1% and 2.5% salt seemed to be most effective. The observed shoulder for strain ATCC 14579 after preexposure to salt could not be dismissed as an experimental artifact of cell clumping. Wet mounts of cell suspensions collected at the start of the inactivation showed no aggregation.

### Assessment of model adequacy and model selection.

*B. cereus*strains studied were further analyzed by fitting eight microbial survival models to the experimental data. The fitting performances of these models were assessed statistically and evaluated in order to select the most suitable model(s) to quantify in more detail specific curvature characteristics and to quantify the effects of preexposure to salt and of growth phase on thermotolerance.

_{model},

*r*

^{2},

*A*, and the

_{f}*f*value were calculated (Table 1). Comparison of the indices of the models showed that overall, the first-order model and the Weibull model did not describe the inactivation data for strains ATCC 10987 and ATCC 14579 acceptably, and neither did the biphasic linear model for the latter strain, which could be confirmed by the

*F*test. When the

*F*test was accepted (bold values), this indicated that the model described the observed inactivation data well. The rejection of the biphasic linear model for strain ATCC 14579 was caused by the inability of this model to describe the shoulder curvature. The Baranyi model was statistically acceptable for most of the experimental conditions, except for transition-phase cells of strain ATCC 10987 with preexposure to 2.5% salt and exponential-phase cells of strain ATCC 14579 without preexposure to salt. One of the noticeable differences between the Baranyi model and other sigmoid curves, such as the modified Gompertz model, is that the mid-phase of the model curvature is very close to linear. This property of the Baranyi model was not applicable for exponential-phase cells of strain ATCC 14579 without preexposure to salt, as this condition showed a nonconstant inactivation rate in the mid-phase.

*Bacillus cereus*strains ATCC 10987 and ATCC 14579

Strain, growth phase, and % NaCl | Statistical index | Statistical index value (no. of model parameters) | |||||||
---|---|---|---|---|---|---|---|---|---|

Linear (2) | Weibull (3) | Biphasic linear (4) | Biphasic logistic (5) | Modified Gompertz (4) | Reparameterized Gompertz (4) | Baranyi (4) | Geeraerd (5) | ||

ATCC 10987 | |||||||||

Exponential | |||||||||

0 | r^{2} | 0.2284 | 0.9022 | 0.9798 | 0.9796 | 0.9756 | 0.9753 | 0.9751 | 0.9798 |

A_{f} | 1.62 | 1.34 | 1.11 | 1.11 | 1.13 | 1.13 | 1.13 | 1.11 | |

MSE_{model} | 2.5136 | 0.3746 | 0.0689 | 0.0712 | 0.0832 | 0.0842 | 0.0849 | 0.0706 | |

F | 28.32 | 4.22 | 0.78 | 0.80 | 0.94 | 0.95 | 0.96 | 0.80 | |

F table | 1.78 | 1.78 | 1.78 | 1.79 | 1.78 | 1.78 | 1.78 | 1.79 | |

1 | r^{2} | 0.6788 | 0.8696 | 0.9816 | 0.9818 | 0.9809 | 0.9809 | 0.9789 | 0.9819 |

A_{f} | 1.44 | 1.33 | 1.09 | 1.09 | 1.09 | 1.09 | 1.10 | 1.09 | |

MSE_{model} | 1.1110 | 0.4555 | 0.0648 | 0.0648 | 0.0673 | 0.0673 | 0.0744 | 0.0645 | |

F | 12.52 | 5.13 | 0.73 | 0.73 | 0.76 | 0.76 | 0.84 | 0.73 | |

F table | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | |

2.5 | r^{2} | 0.6826 | 0.8546 | 0.9448 | 0.9449 | 0.9409 | 0.9409 | 0.9455 | 0.9458 |

A_{f} | 1.43 | 1.29 | 1.14 | 1.13 | 1.14 | 1.14 | 1.13 | 1.13 | |

MSE_{model} | 0.9873 | 0.4567 | 0.1750 | 0.1771 | 0.1875 | 0.1875 | 0.1728 | 0.1737 | |

F | 5.16 | 2.39 | 0.91 | 0.93 | 0.98 | 0.98 | 0.90 | 0.91 | |

F table | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | 1.41 | |

5 | r^{2} | 0.5024 | 0.7907 | 0.8489 | 0.8488 | 0.8550 | 0.8551 | 0.8592 | 0.8590 |

A_{f} | 1.43 | 1.24 | 1.17 | 1.17 | 1.17 | 1.17 | 1.16 | 1.16 | |

MSE_{model} | 0.9242 | 0.3947 | 0.2895 | 0.2944 | 0.2777 | 0.2776 | 0.2697 | 0.2743 | |

F | 2.91 | 1.24 | 0.91 | 0.93 | 0.88 | 0.87 | 0.85 | 0.86 | |

F table | 1.55 | 1.56 | 1.56 | 1.56 | 1.56 | 1.56 | 1.56 | 1.56 | |

Transition | |||||||||

0 | r^{2} | 0.7368 | 0.8654 | 0.9662 | 0.9680 | 0.9717 | 0.9717 | 0.9661 | 0.9682 |

A_{f} | 1.42 | 1.35 | 1.14 | 1.14 | 1.13 | 1.13 | 1.13 | 1.14 | |

MSE_{model} | 1.2524 | 0.6458 | 0.1638 | 0.1560 | 0.1369 | 0.1369 | 0.1640 | 0.1554 | |

F | 9.18 | 4.73 | 1.20 | 1.14 | 1.00 | 1.00 | 1.20 | 1.14 | |

F table | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | |

2.5 | r^{2} | 0.7990 | 0.9045 | 0.9820 | 0.9823 | 0.9853 | 0.9853 | 0.9808 | 0.9824 |

A_{f} | 1.42 | 1.21 | 1.07 | 1.07 | 1.06 | 1.06 | 1.07 | 1.07 | |

MSE_{model} | 0.8106 | 0.3887 | 0.0738 | 0.0731 | 0.0605 | 0.0605 | 0.0787 | 0.0728 | |

F | 15.22 | 7.30 | 1.39 | 1.37 | 1.14 | 1.14 | 1.48 | 1.37 | |

F table | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | 1.38 | |

Stationary | |||||||||

0 | r^{2} | 0.7946 | 0.8926 | 0.9548 | 0.9570 | 0.9569 | 0.9569 | 0.9481 | 0.9572 |

A_{f} | 1.35 | 1.19 | 1.11 | 1.11 | 1.11 | 1.11 | 1.13 | 1.11 | |

MSE_{model} | 0.7952 | 0.4188 | 0.1775 | 0.1703 | 0.1692 | 0.1692 | 0.2041 | 0.1696 | |

F | 4.58 | 2.41 | 1.02 | 0.98 | 0.97 | 0.97 | 1.18 | 0.98 | |

F table | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 | |

2.5 | r^{2} | 0.7037 | 0.8355 | 0.9462 | 0.9590 | 0.9572 | 0.9572 | 0.9499 | 0.9592 |

A_{f} | 1.34 | 1.22 | 1.12 | 1.11 | 1.11 | 1.11 | 1.12 | 1.11 | |

MSE_{model} | 1.1115 | 0.6219 | 0.2051 | 0.1575 | 0.1632 | 0.1632 | 0.1910 | 0.1566 | |

F | 6.80 | 3.81 | 1.26 | 0.96 | 1.00 | 1.00 | 1.17 | 0.96 | |

F table | 1.36 | 1.36 | 1.36 | 1.36 | 1.36 | 1.36 | 1.36 | 1.36 | |

Goodness of fit^{a} | 0/8 | 1/8 | 7/8 | 8/8 | 8/8 | 8/8 | 7/8 | 8/8 | |

ATCC 14579 | |||||||||

Exponential | |||||||||

0 | r^{2} | 0.8821 | 0.9413 | 0.9615 | 0.9621 | 0.9575 | 0.9576 | 0.9407 | 0.9622 |

A_{f} | 1.18 | 1.11 | 1.09 | 1.09 | 1.10 | 1.09 | 1.12 | 1.09 | |

MSE_{model} | 0.3326 | 0.1671 | 0.1105 | 0.1096 | 0.1221 | 0.1218 | 0.1703 | 0.1095 | |

F | 2.83 | 1.42 | 0.94 | 0.93 | 1.04 | 1.04 | 1.45 | 0.93 | |

F table | 1.37 | 1.37 | 1.37 | 1.37 | 1.37 | 1.37 | 1.37 | 1.37 | |

1 | r^{2} | 0.9455 | 0.9496 | 0.9455 | 0.9869 | 0.9870 | 0.9870 | 0.9829 | 0.9869 |

A_{f} | 1.12 | 1.11 | 1.12 | 1.06 | 1.06 | 1.06 | 1.07 | 1.06 | |

MSE_{model} | 0.2436 | 0.2274 | 0.2489 | 0.0604 | 0.0592 | 0.0592 | 0.0781 | 0.0604 | |

F | 4.46 | 4.17 | 4.56 | 1.11 | 1.08 | 1.08 | 1.43 | 1.11 | |

F table | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | |

2.5 | r^{2} | 0.9459 | 0.9647 | 0.9459 | 0.9833 | 0.9833 | 0.9833 | 0.9831 | 0.9833 |

A_{f} | 1.10 | 1.09 | 1.10 | 1.06 | 1.06 | 1.06 | 1.06 | 1.06 | |

MSE_{model} | 0.1761 | 0.1163 | 0.1800 | 0.0563 | 0.0556 | 0.0556 | 0.0561 | 0.0563 | |

F | 3.16 | 2.09 | 3.24 | 1.01 | 1.00 | 1.00 | 1.01 | 1.01 | |

F table | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | |

5 | r^{2} | 0.9612 | 0.9613 | 0.9740 | 0.9886 | 0.9890 | 0.9890 | 0.9862 | 0.9886 |

A_{f} | 1.12 | 1.12 | 1.07 | 1.05 | 1.05 | 1.05 | 1.06 | 1.05 | |

MSE_{model} | 0.1346 | 0.1358 | 0.0919 | 0.0408 | 0.0390 | 0.0390 | 0.0490 | 0.0408 | |

F | 3.59 | 3.63 | 2.45 | 1.09 | 1.04 | 1.04 | 1.31 | 1.09 | |

F table | 1.42 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | 1.43 | |

Transition | |||||||||

0 | r^{2} | 0.9412 | 0.9445 | 0.9412 | 0.9744 | 0.9753 | 0.9753 | 0.9712 | 0.9744 |

A_{f} | 1.17 | 1.15 | 1.17 | 1.10 | 1.10 | 1.10 | 1.11 | 1.10 | |

MSE_{model} | 0.3456 | 0.3297 | 0.3530 | 0.1556 | 0.1485 | 0.1485 | 0.1728 | 0.1556 | |

F | 2.23 | 2.12 | 2.28 | 1.00 | 0.96 | 0.96 | 1.11 | 1.00 | |

F table | 1.44 | 1.44 | 1.44 | 1.44 | 1.44 | 1.44 | 1.44 | 1.44 | |

2.5 | r^{2} | 0.9307 | 0.9764 | 0.9307 | 0.9792 | 0.9809 | 0.9809 | 0.9801 | 0.9792 |

A_{f} | 1.09 | 1.05 | 1.09 | 1.05 | 1.04 | 1.04 | 1.04 | 1.05 | |

MSE_{model} | 0.2679 | 0.0923 | 0.2739 | 0.0856 | 0.0754 | 0.0754 | 0.0786 | 0.0844 | |

F | 3.06 | 1.06 | 3.13 | 0.98 | 0.86 | 0.86 | 0.90 | 0.97 | |

F table | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | 1.45 | |

Stationary | |||||||||

0 | r^{2} | 0.8956 | 0.9176 | 0.8956 | 0.9303 | 0.9307 | 0.9307 | 0.9277 | 0.9303 |

A_{f} | 1.14 | 1.15 | 1.14 | 1.12 | 1.12 | 1.12 | 1.13 | 1.12 | |

MSE_{model} | 0.4492 | 0.3587 | 0.4596 | 0.3106 | 0.3051 | 0.3051 | 0.3181 | 0.3106 | |

F | 1.42 | 1.13 | 1.45 | 0.98 | 0.96 | 0.96 | 1.00 | 0.98 | |

F table | 1.47 | 1.47 | 1.47 | 1.47 | 1.47 | 1.47 | 1.47 | 1.47 | |

2.5 | r^{2} | 0.9173 | 0.9340 | 0.9173 | 0.9597 | 0.9560 | 0.9560 | 0.9475 | 0.9597 |

A_{f} | 1.14 | 1.11 | 1.14 | 1.09 | 1.09 | 1.09 | 1.10 | 1.09 | |

MSE_{model} | 0.3495 | 0.2819 | 0.3572 | 0.1761 | 0.1902 | 0.1902 | 0.2268 | 0.1761 | |

F | 1.82 | 1.46 | 1.86 | 0.91 | 0.99 | 0.99 | 1.18 | 0.91 | |

F table | 1.45 | 1.45 | 1.45 | 1.46 | 1.45 | 1.45 | 1.45 | 1.46 | |

Goodness of fit^{a} | 1/8 | 2/8 | 2/8 | 8/8 | 8/8 | 8/8 | 7/8 | 8/8 |

^{a}

*F*test was accepted.

*a*· exp[−exp(

*b*)] is disregarded in the reparameterized modified Gompertz model, and the effect of this model reduction on the statistical indices was negligible. Parameter

*A*of the reparameterized Gompertz model represents the difference between the population at the end of the observation and the initial population and might reflect a highly resistant subpopulation present in the tail of the sigmoid curvature. The latter phenomenon was applicable for strain ATCC 10987 since the presence of spores was confirmed. The reparameterized Gompertz model did not reflect the population heterogeneity for strain ATCC 14579 suitably, as this strain did not show distinct tailing caused by a subpopulation of cells for which the inactivation rate was equal to zero. In addition, description of a curvature without a tail (linear inactivation or linear inactivation with shoulder) using the reparameterized Gompertz model resulted in a nonrealistic estimation of parameter

*A*. Therefore, the two sigmoid models were not regarded as adequate, although the number of parameters was less (four parameters) than that for the biphasic logistic model and the Geeraerd model (five parameters). The biphasic logistic model and the Geeraerd model assume the presence of a primary heat-sensitive and a secondary heat-resistant population, and both models include a shoulder period (

*t*). The parameters of the biphasic logistic and Geeraerd model can be given biological meaning, have clear significance, and can be recognized easily in the inactivation curvature. Moreover, both models are flexible, allowing a decrease in the number of parameters when certain phenomena are not present. The biphasic logistic model is derived from a logistic-based model. The Geeraerd model is based on the interesting features of a dynamic model and addresses the hypothesis of the presence of a pool of protective or critical components (

_{s}*C*) around or in each cell (10, 11). Gradually, this pool is destroyed, undergoing first-order inactivation, and becomes approximately zero. Towards this time, the heat-sensitive and heat-resistant populations are inactivated following first-order kinetics. Taking into account these aspects, the Geeraerd model was considered the most adequate model. The dynamic properties of this model and the underlying hypothesis about the occurrence of a shoulder in an inactivation curve were preferred over the logistic-based properties of the biphasic logistic model. However, both the biphasic logistic and Geeraerd models were used to quantify the effects of salt stress and growth phase on thermotolerance, as both models were able to fit the inactivation characteristics occurring for strains ATCC 10987 and ATCC 14579 suitably.

_{c}### Reduction of model parameters.

*F*test was used to determine whether the reduction of parameters was acceptable. Because the tailing fraction for the three physiological growth phases of strain ATCC 10987 corresponded to a minor population of spores, the inactivation rate of the heat-resistant subpopulation (

*k*) was set at zero, resulting in a four-parameter model before the stepwise procedure was applied for this strain. It should be noted that the fixation of parameter

_{res}*k*at zero resulted in a nonaccepted

_{res}*F*test for one experimental condition (transition phase with preexposure to 2.5% salt) for the biphasic logistic and Geeraerd models. The measuring error for this experimental condition was very small (MSE

_{data}= 0.05), as replicate experiments produced small variation. Visual inspection of the fitting performances of the biphasic logistic and Geeraerd models showed that the adequacies of both models were sufficient, although the

*F*test was not accepted due to the low MSE

_{data}. Tables 2 and 3 show the parameter estimates obtained with the reduced biphasic logistic and reduced Geeraerd models. The numbers of parameters of the reduced biphasic logistic and reduced Geeraerd models were similar, except for one experimental condition for strain ATCC 10987 (transition phase without preexposure to salt). For this condition, parameter

*t*was not significant for the biphasic logistic model (

_{s}*P*= 0.12) but was significant for the Geeraerd model (

*P*= 0.01).

Strain | Growth phase | % NaCl | Parameter value^{c} | ||||
---|---|---|---|---|---|---|---|

log_{10}N(0) | f | k_{sens} | t_{S} | k_{res} | |||

ATCC 10987 | Exponential | 0 | 6.85 | 5.94 × 10^{−6} | 6.00 | NS | 0^{a} |

1 | 6.84 | 6.10 × 10^{−6} | 0.74 | NS | 0^{a} | ||

2.5 | 6.48 | 1.54 × 10^{−5} | 0.65 | NS | 0^{a} | ||

5 | 5.04 | 4.59 × 10^{−4} | 1.18 | NS | 0^{a} | ||

Transition | 0 | 7.74 | 9.42 × 10^{−7} | 0.69 | NS | 0^{a} | |

2.5 | 7.61 | 2.48 × 10^{−6} | 0.57 | NS | 0^{a} | ||

Stationary | 0 | 7.56 | 3.94 × 10^{−6} | 0.43 | NS | 0^{a} | |

2.5 | 7.39 | 1.72 × 10^{−5} | 0.61 | 5.63 | 0^{a} | ||

ATCC 14579 | Exponential | 0 | 6.96 | 1.65 × 10^{−3} | 0.84 | NS | 0.22 |

1 | 6.92 | 1.19 × 10^{−3}^{b} | 0.91 | 8.86 | 0.27 | ||

2.5 | 6.70 | 2.89 × 10^{−4}^{b} | 0.57 | 9.05 | 0.14^{b} | ||

5 | 6.49 | 5.66 × 10^{−4}^{b} | 0.63 | 5.84 | 0.17 | ||

Transition | 0 | 7.86 | 6.30 × 10^{−5}^{b} | 0.47 | 6.66 | 0.12 | |

2.5 | 7.95 | NS | 0.35 | 13.50 | NS | ||

Stationary | 0 | 8.04 | 3.63 × 10^{−4}^{b} | 0.38 | NS | 0.12 | |

2.5 | 8.07 | 1.41 × 10^{−3}^{b} | 0.49 | 5.02 | 0.15 |

^{a}

*k*was 0 for the heat-resistant population of spores at 50°C.

_{res}^{b}

*F*test showed that the phenomenon of two populations was significant.

^{c}

Strain | Growth phase | % NaCl | Parameter value^{d} | ||||
---|---|---|---|---|---|---|---|

log_{10}N(0) | f | k_{sens} | t_{S} | k_{res} | |||

ATCC 10987 | Exponential | 0 | 6.85 | 5.94 × 10^{−6} | 5.65 | NS | 0^{a} |

1 | 6.99 | 4.30 × 10^{−6} | 0.71 | NS | 0^{a} | ||

2.5 | 6.63 | 1.07 × 10^{−5} | 0.62 | NS | 0^{a} | ||

5 | 5.11 | 3.76 × 10^{−4} | 1.06 | NS | 0^{a} | ||

Transition | 0 | 7.62 | 1.25 × 10^{−6} | 0.71 | 1.73^{c} | 0^{a} | |

2.5 | 7.77 | 1.65 × 10^{−6} | 0.55 | NS | 0^{a} | ||

Stationary | 0 | 7.73 | 2.60 × 10^{−6} | 0.41 | NS | 0^{a} | |

2.5 | 7.39 | 1.72 × 10^{−5} | 0.61 | 5.68 | 0^{a} | ||

ATCC 14579 | Exponential | 0 | 7.05 | 2.10 × 10^{−3} | 0.77 | NS | 0.21 |

1 | 6.92 | 1.22 × 10^{−3}^{b} | 0.91 | 8.87 | 0.27 | ||

2.5 | 6.70 | 3.30 × 10^{−4}^{b} | 0.57 | 9.07 | 0.14^{b} | ||

5 | 6.49 | 6.89 × 10^{−4}^{b} | 0.63 | 5.88 | 0.17 | ||

Transition | 0 | 7.86 | 8.40 × 10^{−5}^{b} | 0.47 | 6.76 | 0.12 | |

2.5 | 7.95 | NS | 0.35 | 13.52 | NS | ||

Stationary | 0 | 8.13 | 1.27 × 10^{−4}^{b} | 0.35 | NS | 0.09 | |

2.5 | 8.07 | 1.94 × 10^{−3}^{b} | 0.49 | 5.20 | 0.15 |

^{a}

*k*was 0 for the heat-resistant population of spores at 50°C.

_{res}^{b}

*F*test showed that the phenomenon of two populations was significant.

^{c}

*P*= 0.01) when the model was fitted to all the replicate data together for this experimental condition. When replica curves were fitted individually, the average parameter estimate was not statistically significant (

*P*= 0.14).

^{d}

*f*, of heat-resistant cells for the various experimental conditions, and this fraction could be attributed to the presence of spores at the start of inactivation. Further heterogeneity within the vegetative cell population of strain ATCC 10987 could not be statistically validated, as the biphasic logistic and Geeraerd models were sufficient to describe the data acceptably and further model complexity could not be substantiated. The presence of spores at the start of inactivation was not observed for strain ATCC 14579. The existence of a heat-sensitive and a heat-resistant vegetative population was statistically acceptable for strain ATCC 14579 under most of the experimental conditions, although the parameter

*f*was not significant. Reduction of the nonsignificant parameter

*f*also resulted in redundancy of the parameter

*k*, which was not statistically acceptable according to the

_{res}*F*test. The presence of a mutated heat-resistant subpopulation of vegetative cells for strain ATCC 14579 was evaluated by collecting colonies at the time points corresponding to the end of the inactivation curvatures. Cell suspensions obtained from these colonies did not exhibit enhanced thermotolerance compared to the original inactivation curves, indicating that the biphasic curvature was not caused by the presence of a genetically more resistant vegetative subpopulation. Furthermore, in addition to the presence of a fraction of spores, a stable heat-resistant subpopulation of vegetative cells could not be demonstrated experimentally for strain ATCC 10987 either.

### Quantification of effects of salt stress and physiological state on thermotolerance.

*t*tests. The results of the

*t*tests are shown in Tables 4 and 5.

*P*values shown refer to statistical analyses using the Geeraerd model.

*Bacillus cereus*ATCC 10987, using

*P*values

Growth phase (% NaCl)^{a} | P value for difference in k values_{sens}^{b} | |||||||
---|---|---|---|---|---|---|---|---|

Exp (0) | Exp (1) | Exp (2.5) | Exp (5) | Trans (0) | Trans (2.5) | Stat (0) | Stat (2.5) | |

Exp (0) | ||||||||

Exp (1) | 0.00 | |||||||

Exp (2.5) | 0.00 | 0.22 | ||||||

Exp (5) | 0.00 | 0.08 | 0.07 | |||||

Trans (0) | 0.00 | 0.44 | 0.26 | 0.09 | ||||

Trans (2.5) | 0.00 | 0.03 | 0.15 | 0.05 | 0.11 | |||

Stat (0) | 0.00 | 0.01 | 0.02 | 0.04 | 0.03 | 0.01 | ||

Stat (2.5) | 0.00 | 0.48 | 0.34 | 0.08 | 0.44 | 0.18 | 0.06 |

^{a}

^{b}

*t*test (one-sided).

*Bacillus cereus*ATCC 14579, using

*P*values

Growth phase (% NaCl) and parameter^{a} | P value for difference in parameter values^{b} | |||||||
---|---|---|---|---|---|---|---|---|

Exp (0) | Exp (1) | Exp (2.5) | Exp (5) | Trans (0) | Trans (2.5) | Stat (0) | Stat (2.5) | |

k_{sens} | ||||||||

Exp (0) | ||||||||

Exp (1) | 0.12 | |||||||

Exp (2.5) | 0.11 | 0.01 | ||||||

Exp (5) | 0.11 | 0.00 | 0.43 | |||||

Trans (0) | 0.01 | 0.00 | 0.04 | 0.01 | ||||

Trans (2.5) | 0.00 | 0.00 | 0.00 | 0.00 | 0.01 | |||

Stat (0) | 0.01 | 0.00 | 0.02 | 0.01 | 0.17 | 0.20 | ||

Stat (2.5) | 0.15 | 0.04 | 0.48 | 0.45 | 0.18 | 0.04 | 0.10 | |

t_{s} | ||||||||

Exp (0) | NS | |||||||

Exp (1) | NS | |||||||

Exp (2.5) | NS | 0.42 | ||||||

Exp (5) | NS | 0.01 | 0.02 | |||||

Trans (0) | NS | 0.11 | 0.10 | 0.43 | ||||

Trans (2.5) | NS | 0.01 | 0.01 | 0.00 | 0.00 | |||

Stat (0) | NS | NS | NS | NS | NS | NS | NS | |

Stat (2.5) | NS | 0.00 | 0.00 | 0.50 | 0.41 | 0.00 | NS |

^{a}

^{b}

*t*test (one-sided). NS, one of the two compared parameter estimates was a nonsignificant model parameter and was excluded from the model.

*P*= 0.01) and a similar inactivation rate to that of stationary-phase cells.

*P*= 0.05). Strain ATCC 14579 showed an adaptive response in both the transition and stationary phases, as a significantly enhanced shoulder period was observed in both phases (

*P*= 0.00).

*P*= 0.97). Spores were formed further at the end of the growth cycle, as the transition- and stationary-phase cultures exhibited significantly larger amounts of spores than the exponential-phase cultures (

*P*= 0.00), with the highest level of spores found in the stationary-phase cultures.

## DISCUSSION

### Experimental design and fitting performances of survival models.

*f*value. The higher the measuring error, the less complex a model has to be to describe the data acceptably. It is important to include this biological variation in the quantification, and therefore reproductions have to be performed to provide valuable information for quantitative risk assessment studies. In addition, the experimental procedure influences the inactivation curvatures, which necessitates an unambiguous description of the experimental process in order to compare the data to those in other studies and to evaluate the findings.

_{10}

*N*(0). When the shoulder period

*t*was not significant in both models, the parameter log

_{s}_{10}

*N*(0) was estimated to be lower by the biphasic logistic model than by the Geeraerd model. Both models can fit a curvature without a shoulder period by selecting a

*t*of 0. However, the shoulder curvature is not completely eliminated from the biphasic logistic model when

_{s}*t*= 0, resulting in a lower estimation of log

_{s}_{10}

*N*(0).

*f*of the biphasic logistic and Geeraerd models was not significant for most of the experimental conditions tested for strain ATCC 14579 but was not excluded from the models because the

*F*test showed that the biphasic inactivation was significant (Tables 2 and 3). Also, the parameter

*k*was not significant for one experimental condition for strain ATCC 14579 (exponential-phase cells with preexposure to 2.5% salt) but was not excluded. The confidence intervals of both parameters were large when the parameters were not significant but not excluded (data not shown). Zwietering et al. mentioned that parameters which are strongly correlated are difficult to estimate and have large confidence intervals (32). The correlation matrices of the experimental conditions revealed that parameters

_{res}*f*and

*k*were strongly correlated (>0.99) when both parameters were not significant and not excluded (exponential-phase cells with preexposure to 2.5% salt). The correlation between both parameters was lower (>0.94) when only parameter

_{res}*f*was nonsignificant and not excluded. Parameters were less correlated (<0.90) when both parameters were significant (exponential-phase cells without preexposure to salt).

### Effect of salt preexposure on thermotolerance.

_{10}

*N*(0)]. When cells are exposed to lethal salt stress conditions, two phenomena can take place, namely, the inactivation of bacterial cells and the induction of an adaptive response in the surviving cells, and this agrees with observations in

*Listeria monocytogenes*(19, 20). In our study, differences in the heat sensitivities of cells after preexposure to nonlethal and lethal salt stress conditions could not be confirmed, indicating that cells which are able to survive lethal stress conditions are still capable of demonstrating an adaptive stress response that might be comparable to the adaptive stress response of cells which are exposed to nonlethal stress conditions.

*B. cereus*ATCC 14579 (22) and

*B. cereus*NCIMB 11796 (4). Periago et al. showed an overlap in proteins induced by heat shock and salt stress exposure as well as induction of non-heat-shock-specific proteins during salt stress exposure (22). Several heat shock proteins induced during salt stress exposure belong to the group of chaperones and proteases, and these proteins act together to maintain quality control of cellular proteins (1). Increased production of heat shock proteins after salt stress exposure in

*B. cereus*was also demonstrated by Browne and Dowds (4) and was observed in other bacilli as well (21, 23, 29). In addition to de novo protein synthesis during preexposure to salt, Periago et al. mentioned an increase in thermotolerance after preexposure to salt in the presence of chloramphenicol, indicating an alternative and complementary mechanism (22). It has been shown that compatible solutes such as glycine betaine can function as thermoprotectants in

*Bacillus subtilis*(12).

### Thermotolerance and adaptive stress response are affected by strain diversity, physiological state, and population heterogeneity.

*B. cereus*NCIMB 11796 (4) and for other bacteria (see, e.g., reference 18). Induction of a generalized stress response and additional physiological changes provide enhanced resistance for cells toward the end of the growth cycle (25). Moreover, the transient decline in pH of the culture during the growth cycle, reaching pH values of 7.2 and 6.5 in the exponential phase for

*B. cereus*ATCC 10987 and the transition phase for

*B. cereus*ATCC 14579, respectively (data not shown), may have contributed in the latter case to the enhanced stress resistance of these cells. As shown by Browne and Dowds (3), 40 min of exposure of exponential-phase cells of

*B. cereus*NCIMB 11796 to pH 6.3 resulted in enhanced stress resistance. Our study has shown that the effect of physiological state on heat resistance was comparable to the maximum adaptive response to salt demonstrated in exponential-phase cells. This indicates that two different stresses may provide similar increased resistance levels.

*B. cereus*strains. These results are consistent with other studies, which examined differences in heat shock-induced thermotolerance for exponential- and stationary-phase cells (14, 19). In the current study, we quantified the adaptive stress response in three different growth phases in more detail and demonstrated that the significance of the adaptive stress response was strain and growth phase dependent.

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