# Simplified Approach to Predict Food Safety through the Maximum Specific Bacterial Growth Rate as Function of Extrinsic and Intrinsic Parameters

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{w}), hydrogen potential (pH), oxidation-reduction potential, chemical composition and biological structure of the food as well as its anti-microbial substances, microbial development, among others [5].

- $y\left(t\right)\text{}$ is the same as $\mathrm{ln}\left(x\left(t\right)\right)$ where $x\left(t\right)$ is the number of colony-forming unit (CFU)/g;
- ${y}_{0}$ is the initial value of CFU/g (scaled logarithmically) and its value derived from Tables 1–6 is shown as result in Table 7;
- ${y}_{max}$ is the maximum value of CFU/g (scaled logarithmically) and its value is also defined in Table 7;
- µmax is the maximum specific growth rate and its value is affected by intrinsic and extrinsic factors;
- ${h}_{0}$ is a constant defined by ${h}_{0}=-\mathrm{ln}\left({\propto}_{0}\right)$, where ${\propto}_{0}$ is the physiological state; It is also related with $\lambda $ (lag phase), where $\lambda =\frac{{h}_{0}}{{\mu}_{max}}$;
- $m$ is the parameter that define the curvature between the exponential and stationary phase;
- ${n}_{c}$ is the parameter that define the curvature between the initial and exponential phase through the equation ${n}_{c}=\frac{v}{{\mu}_{max}}$;
- $t$ is the time since the beginning of the bacteria growth.

^{®}(COX Technologies), Sensorq

^{®}(DSM NV and Food Quality Sensor International), among others [11].

_{max}, represents, in the bacterial growth curve, how intrinsic and extrinsic factors affect the bacterial development, being manifested in distinct ways for each bacteria.

_{max}with temperature (T), pH and water activity (a

_{w}), the Masana & Baranyi model will be used, presented in Equation (2) [20]:

_{i}are the coefficients to be estimated, T and pH are respectively the values of temperature (°C) and pH, and b

_{w}is calculated through [21]:

## 2. Materials and Methods

_{i}values, will be used the online tool available in www.ComBase.com (accessed on 3 March 2021). This way will only be considered some bacteria presented on the referred tool:

- Aeromonas hydrophila;
- Bacillus cereus;
- Bacillus licheniformis;
- Bacillus subtilis;
- Clostridium botulinum;
- Clostridium perfringens;
- Escherichia coli;
- Listeria monocytogenes;
- Salmonella;
- Shigella flexneri;
- Staphylococcus aureus;
- Yersinia enterocolitica;
- Brochothrix thermosphacta;
- Pseudomonas.

#### 2.1. Determination of the Maximum Specific Growth Rate

_{max}.

#### 2.2. Calculation of Coefficients

_{i}to the Brochothrix thermosphacta bacteria will be estimated. To do that, with Combase, Table 1 with different combinations of values of temperature, pH and a

_{w}(and b

_{w}) is constructed and, after, with those conditions the maximum specific growth rate is verified.

_{i}. factors. This table will be used as a matrix, Matrix A, with 10 rows and 10 columns. Another matrix, Matrix B, with 10 rows and 1 column, is made with the values of ln(µ

_{max}), which also included in Table 2.

_{0}to a

_{9}, through the Equation (4).

_{w}for any bacteria, in this case for the Brochothrix thermosphacta. Once all these values start to be calculated with an estimation, when compared with Combase Predictor there is a small error associated. Table 4 represents that error for randomly obtained environments.

_{i}coefficients, Table 5 was formulated, which contains these coefficients to the bacteria.

- Relative error below 5%, e
_{r}< 5%; - Relative error between 5% and 10%, 5% < e
_{r}< 10%; - Relative error between 10% and 15%, 10% < e
_{r}< 15%; - Relative error above 15%, e
_{r}> 15%.

#### 2.3. Graphic Generating

_{max}in order of the intrinsic and extrinsic factors that define a specific bacterial growth environment. This way it is possible to analyze how the temperature, pH and water activity affects the maximum specific growth rate. Since there are no graphics that represent this, a code in MatLab was created that presents a tridimensional graphic with the predictive value of µ

_{max}when changing the three parameters referred. Because is only possible to build graphics until 3 variables, and in this case there is a requirement to see the changes in four parameters, the temperature and the pH were represented in the axes x and y and µ

_{max}in z. To represent how a

_{w}changing affects the maximum specific growth rate, the graphic with the lowest value of a

_{w}was constructed. Then, this value was increased and built the graphic, in the same figure, to this new value. This process was repeated until the maximum value of a

_{w}is reached. This way it is possible to visualize the changing of the four variables in the same graphic. As a complement, a graphic was also created that represents the maximum value of µ

_{max}obtained to each value of a

_{w}. In this figure is also represented the maximum specific growth rate value for the studied bacteria and the conditions that make it happen.

## 3. Results

#### 3.1. Aeromonas hydrophila

_{w}= 0.999), respectively. The decrease of temperature causes a quit decrease in µ

_{max}value, the same that happens for pH and water activity, but, in this last case, not so abruptly. The maximum value of µ

_{max}= 0.6.

#### 3.2. Bacillus cereus

_{w}affect this bacteria growth is different to all the others analyzed. To Bacillus cereus as represented in Figure 4, the maximum specific growth rate is maximum to the maximum value of temperature and pH, meanwhile for water activity only decreases when its value is greater than a

_{w}= 0.999, which can be ignored in a practical situation. The maximum µ

_{max}= 1.8 log(CFU/g)/h, which is the greatest between the microorganisms analyzed. It is also relevant to mention that the values for µ

_{max}are relatively low (about 0.5 log(CFU/g)/h) while the temperature is lower than 25 °C, pH below 5.5 and a

_{w}until 0.97. A small increase of these values triggers a quit increase of the maximum specific growth rate.

#### 3.3. Bacillus licheniformis

_{max}similar to the one presented for Aeromonas hydrophila. The main difference is that while in the first case the maximum specific growth rate increases until 73% of the temperature value range of growth, in this case the maximum value happens to the maximum value of temperature (T = 34 °C). The values to pH and water activity to get the maximum value of µ

_{max}are pH = 6.6 and a

_{w}= 0.995, respectively, which is between the same range defined in the first bacteria commented, with values of 72% and 94%.

#### 3.4. Bacillus subtilis

_{max}, in Bacillus subtilis the reaction is the opposite. The optimal growth condition is achieved with a

_{w}= 0.933, and, after that point, the maximum specific growth rate decreases with the rise of a

_{w}and increases again only between 0.993 and 1, thus not being relevant. While the rise of the temperature value creates an increase in µ

_{max}, the pH simply does this until half of the range of growth of this bacteria, which causes a decrease with the same rhythm.

#### 3.5. Clostridium botulinum

_{max}are in the range defined previously: 78% (T = 24.5 °C), 70% (pH = 6.8) and 88% (a

_{w}= 0.997) respectively for the range of values of temperature, pH and water activity.

#### 3.6. Clostridium perfringens

_{max}which becomes bigger as it approaches the maximum temperature range of growth, T = 41.5 °C. When this value is achieved, the decrease of µ

_{max}, caused by the rise of the temperature, happens at a slow pace. However, pH is mainly responsible for the odd curve created. While, in the other bacteria, the increase of pH causes a greater raise of µ

_{max}until the optimal value of pH is reached, for Clostridium perfringens, the rise of pH causes the same increase of µ

_{max}along all the range of growth. Therefore, the pH value that causes the maximum value of µ

_{max}= 8. Water activity also has a distinct growth curve, since its minimum value corresponds to a specific growth rate value of 0.6, which increases with the increase of a

_{w}until a

_{w}= 0.989, that represents the maximum µ

_{max}= 1.24. These characteristics are described in Figure 6.

#### 3.7. Escherichia coli

_{max}occurs with temperature at 76% (T = 34.5 °C) of its range of growth and 66.7% (pH = 6.5) of the same range of pH. The maximum µ

_{max}is obtained with the maximum value of water activity, this is, a

_{w}= 1, Escherichia coli being the only bacteria where this happens.

#### 3.8. Listeria monocytogenes

_{max}is maximum, are, respectively, pH = 6.9 and a

_{w}= 0.994 that, in percentage, represents 80% and 90% of its correspondent range of growth.

#### 3.9. Salmonella

_{max}value, where Listeria monocytogenes achieved a maximum value of µ

_{max}= 0.63 and Salmonella went beyond 0.93. This value is reached with both temperature (T = 37.5 °C) and water activity at a

_{w}= 90% of its range of growth, while the optimal pH = 6.4 happens around 70%.

#### 3.10. Shigella flexneri

_{max}value that justifies the growth curve shape. Water activity almost has a symmetrical growth curve, once the minimum value of µ

_{max}is achieved to a

_{w}

_{,min}, but also to a

_{w}

_{,max}, where a

_{w}= 0.993 represents the maximum value of µ

_{max}= 0.76.

#### 3.11. Staphylococcus aureus

_{w}between 80% and 90% of water activity growth range. In this specific case, these percentages are respectively 67.7% (pH = 6.5) and 89% (a

_{w}= 0.99), that, with a temperature of 30 °C, result in µ

_{max}= 0.58.

#### 3.12. Yersinia enterocolitica

_{w}= 0.996. The value of µ

_{max}for these parameters is equal to 0.66.

#### 3.13. Brochothrix thermosphacta

_{w}for which µ

_{max}is maximum, because of its proximity to the maximum value (a

_{w}= 0.999). Both values of temperature and pH are close to 80% (T = 23.5 °C; pH = 6.7) of their growth range and contribute to a maximum µ

_{max}= 0.38.

#### 3.14. Pseudomonas

_{max}is maximum when the temperature achieves its maximum value (T = 20 °C), while pH is around 60% (pH = 6.5) of its growth range and the water activity is slightly lower than the other bacteria, 82% (a

_{w}= 0.993). The largest value of µ

_{max}= 0.28 is the lowest between the bacteria analyzed.

## 4. Discussion

_{max}, between bacteria, they can be put together in groups defined by their growth curve relation of these 4 parameters.

_{%opt}= [70%, 80%] and pH

_{%opt}= [65%, 80%] and are put together in one group. The other group is composed of bacteria where T

_{%opt}= T

_{max}, this is, T

_{%opt}= 100% and pH

_{%opt}= [50%, 70%]. This occurs in bacteria like Bacillus licheniformis, Bacillus subtilis, Staphylococcus aureus, Yersinia enterocolitica and Pseudomonas.

_{%opt}is bigger than 90%, on the other, pH

_{%opt}has bigger values than the ones considered in the second group, pH

_{%opt}= [70%, 80%]. One example of this category is the bacteria Shigella flexneri, which maintains the value of T

_{%opt}= 100% but has pH

_{%opt}> 90%. Bacillus cereus is an extreme case of the last example, once T

_{%opt}= pH

_{%opt}= 100%. Beyond this microorganism, Clostridium perfringens also presents a unique case where T

_{%opt}= 70%, like the first group, but with pH

_{%opt}= 100%.

_{max}. With the particular case of Escherichia coli, where the increase happens until the water activity maximum value, in all of the others the growth of a

_{w}represents an increase of µ

_{max}but only until a certain value. The increase after that value represents a decrease of the maximum specific growth rate. That value will be denoted as a

_{w,opt}. The different water activity limits are due to the diverse mechanisms of water movements between bacteria and their environment. This conditions the way different microorganisms deal with osmotic stress, that is, the impossibility of absorbing more water into the cells, and, thus, becoming unable to grow. In Table 7 all the values obtained with this study are presented, represented as minimum, maximum and optimal values of the temperature, pH and water activity for each bacteria, and also the values of initial, final and infective dose of CFU/g for each microorganism already described [22,24].

## 5. Conclusions

_{max}). Through the Massana and Baranyi model, that allows the calculation of the referred growth rate, and the data provided in Combase Predictor, the coefficients that define the bacterial growth were estimated. Obtaining the value of these coefficients was possible to create tridimensional graphics that represent the relation between four parameters—temperature, pH, water activity and maximum specific growth rate—and conclude that the 14 bacteria studied can be divided in different groups characterized by the way that µ

_{max}is affected by the described factors.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{i} | Coefficients that define the maximum specific growth rate; |

a_{w} | Water activity; |

b_{w} | Constant (b_{w} = $\sqrt{1-{a}_{w}}$); |

e | Euler’s number (e = 0.5772); |

e_{r} | Relative error [%]; |

h_{0} | Logarithmic value of a bacteria physiological state (h_{0} = -ln α_{0}); |

m | Parameter that define the curvature between the exponential and stationary phase; |

n_{c} | Parameter that define the curvature between the initial and exponential phase; |

pH | Potential of hydrogen; |

t | Time [h]; |

T | Temperature [°C]; |

X_{%opt} | Percentage of the value range in which bacteria grow, for which bacterial growth is optimal (with X = Temperature or X = pH); |

X_{opt} | Value for which bacterial growth is optimal (with X = Temperature or X = pH); |

X_{min} | Minimum value for which a bacteria grows (with X = Temperature or X = pH); |

X_{max} | Maximum value for which a bacteria grows (with X = Temperature or X = pH); |

y | Logarithmic value of the number of colony forming unit by gram; |

y_{0} | Initial number of colony forming unit by gram; |

y_{max} | Maximum number of colony forming unit by gram; |

α_{0} | Bacteria physiological state; |

λ | Lag [h]; |

µ_{max} | Maximum specific growth rate [log(CFU/g)/h]. |

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**Figure 1.**Relation between the growth curve and the Baranyi and Roberts model variables (Reprinted from ref. [19]).

**Figure 2.**Example of ComBase Predictor (available online in www.ComBase.com, accessed on 3 March 2021).

**Figure 3.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Aeromonas hydrophila.

**Figure 4.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Bacillus cereus.

**Figure 5.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Bacillus licheniformis.

**Figure 6.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Clostridium perfringens.

**Figure 7.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Escherichia coli.

**Figure 8.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Listeria monocytogenes.

**Figure 9.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Shigella flexneri.

**Figure 10.**Influence of intrinsic and extrinsic factors in the maximum specific growth rate of Staphylococcus aureus.

**Table 1.**Maximum specific growth rate to different values of temperature (T), pH and water activity (a

_{w}), to the bacteria Brochothrix thermosphacta.

Input | |||
---|---|---|---|

T [°C] | pH | a_{w} | µ_{max} |

1 | 5.50 | 0.950 | 0.012 |

1 | 6.25 | 0.975 | 0.027 |

1 | 7.00 | 0.95 | 0.011 |

15 | 5.50 | 1.000 | 0.132 |

15 | 6.25 | 1.000 | 0.247 |

30 | 5.50 | 0.950 | 0.028 |

30 | 6.25 | 0.950 | 0.061 |

30 | 7.00 | 0.950 | 0.066 |

30 | 7.00 | 0.975 | 0.145 |

30 | 7.00 | 1.000 | 0.313 |

**Table 2.**Matrix A and Matrix B to the bacteria Brochothrix thermosphacta, using the values of Table 1.

Matrix A | Matrix B | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

T | pH | b_{w} | T·pH | T·b_{w} | pH^{.}b_{w} | T^{2} | pH^{2} | b_{w}^{2} | ln(µ_{max}) | |

1 | 1 | 5.50 | 0.223607 | 5.50 | 0.2236068 | 1.229837388 | 1 | 30.2500 | 0.050 | −4.42285 |

1 | 1 | 6.25 | 0.158114 | 6.25 | 0.1581139 | 0.988211769 | 1 | 39.0625 | 0.025 | −3.61192 |

1 | 1 | 7.00 | 0.223607 | 7.00 | 0.2236068 | 1.565247584 | 1 | 49.0000 | 0.050 | −4.50986 |

1 | 15 | 5.50 | 0 | 82.5 | 0 | 0 | 225 | 30.2500 | 0 | −2.02495 |

1 | 15 | 6.25 | 0 | 93.75 | 0 | 0 | 225 | 39.0625 | 0 | −1.39837 |

1 | 30 | 5.50 | 0.223607 | 165.00 | 6.7082039 | 1.229837388 | 900 | 30.2500 | 0.050 | −3.57555 |

1 | 30 | 6.25 | 0.223607 | 187.5 | 6.7082039 | 1.397542486 | 900 | 39.0625 | 0.050 | −2.79688 |

1 | 30 | 7.00 | 0.223607 | 210.00 | 6.7082039 | 1.565247584 | 900 | 49.0000 | 0.050 | −2.71810 |

1 | 30 | 7.00 | 0.158114 | 210.00 | 4.7434165 | 1.106797181 | 900 | 49.0000 | 0.025 | −1.93102 |

1 | 30 | 7.00 | 0 | 210.00 | 0 | 0 | 900 | 49.0000 | 0 | −1.16155 |

a_{i} | Value |
---|---|

a_{0} | −28.3244 |

a_{1} | 0.0976 |

a_{2} | 7.8197 |

a_{3} | 8.0746 |

a_{4} | 0.0217 |

a_{5} | −0.1346 |

a_{6} | −0.5496 |

a_{7} | −0.0051 |

a_{8} | −0.6221 |

a_{9} | −31.9812 |

Input | µ_{max} | |||||
---|---|---|---|---|---|---|

T [°C] | pH | a_{w} | µ_{max} | µ_{max (estimated)} | Absolute Error | Relative Error |

4.65 | 5.7 | 0.960 | 0.031 | 0.0313837 | 3.837 × 10^{−4} | 1.2% |

17.00 | 6.8 | 0.962 | 0.129 | 0.1302418 | 12.418 × 10^{−4} | 1.0% |

28.00 | 6.5 | 0.990 | 0.257 | 0.2611274 | 41.274 × 10^{−4} | 1.6% |

1.50 | 6.5 | 0.990 | 0.036 | 0.0360317 | 0.317 × 10^{−4} | 0.1% |

1.50 | 5.8 | 0.960 | 0.020 | 0.0199184 | 0.816 × 10^{−4} | 0.4% |

3.50 | 6.0 | 0.990 | 0.051 | 0.0520164 | 10.164 × 10^{−4} | 2.0% |

5.40 | 6.0 | 0.997 | 0.074 | 0.0746830 | 6.83 × 10^{−4} | 0.9% |

20.00 | 7.0 | 0.997 | 0.323 | 0.3226309 | 3.691 × 10^{−4} | 0.1% |

3.00 | 5.9 | 0.960 | 0.027 | 0.0271576 | 1.576 × 10^{−4} | 0.6% |

10.00 | 6.8 | 0.960 | 0.070 | 0.0702477 | 2.477 × 10^{−4} | 0.4% |

23.00 | 6.0 | 0.962 | 0.114 | 0.1167338 | 27.338 × 10^{−4} | 2.4% |

Microorganism | a_{i} | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

a_{0} | a_{1} | a_{2} | a_{3} | a_{4} | a_{5} | a_{6} | a_{7} | a_{8} | a_{9} | |

Aeromonas hydrophila | −28.0530 | 0.2469 | 7.2505 | 3.1783 | 0.0067 | −0.0561 | 1.3009 | −0.0054 | −0.5609 | −125.5860 |

Bacillus cereus | −2.7330 | 0.1622 | −0.8614 | 1.5969 | 0.0122 | −0.1831 | 1.2199 | −0.0025 | 0.0720 | −59.3343 |

Bacillus licheniformis | −29.1238 | 0.4592 | 6.4417 | −12.1128 | −0.0053 | 0.0649 | 2.7058 | −0.0055 | −0.4889 | −54.4646 |

Bacillus subtilis | −20.5091 | 0.2066 | 4.7178 | 2.1808 | 0.0075 | 0.0456 | −1.1555 | −0.0025 | −0.3835 | 19.8195 |

Clostridium botulinum | −32.7539 | 0.4803 | 7.6414 | 26.4667 | 0 | −0.0939 | −1.0452 | −0.0096 | −0.5609 | −163.932 |

Clostridium perfringens | −7.4775 | 0.2831 | 0.0580 | 8.6498 | 0.0068 | 0.1154 | 2.3642 | −0.0042 | −0.0195 | −153.4672 |

Escherichia coli | −20.3231 | 0.4115 | 4.1261 | 2.2349 | 0.0002 | −0.2249 | −0.0415 | −0.0060 | −0.3162 | −31.9882 |

Listeria monocytogenes | −18.2070 | 0.2029 | 3.9028 | 6.0167 | 0.0024 | 0.0408 | −0.1241 | −0.0028 | −0.2886 | −43.1797 |

Salmonella | −12.9739 | 0.3529 | 1.8967 | 6.4026 | −0.0048 | 0.0224 | −0.0118 | −0.0043 | −0.1336 | −62.1296 |

Shigella flexneri | −17.2012 | 0.4993 | 1.7936 | 21.6882 | −0.0044 | 0.3454 | −0.5534 | −0.0065 | −0.1091 | −182.8641 |

Staphylococcus aureus | −18.4275 | 0.3267 | 3.8293 | −4.5893 | 0.0029 | 0.1031 | 0.9995 | −0.0050 | −0.3105 | −25.0405 |

Yersinia enterocolitica | −15.3130 | 0.2159 | 3.2613 | 4.7524 | −0.0118 | 0.1356 | 0.4380 | −0.0016 | −0.2312 | −93.5564 |

Brochothrix thermosphacta | −28.3244 | 0.0976 | 7.8197 | 8.0746 | 0.0217 | −0.1346 | −0.5496 | −0.0051 | −0.6221 | −31.9812 |

Pseudomonas | −14.0267 | 0.1571 | 3.2135 | 0.4892 | 0.0005 | −0.0371 | 2.9697 | −0.0021 | −0.2671 | −117.0019 |

Microorganism | Relative Error, e_{r} | Total Number of Tests | |||
---|---|---|---|---|---|

e_{r} < 5% | 5% < e_{r} < 10% | 10% < e_{r} < 15% | e_{r} > 15% | ||

Aeromonas hydrophila | 45% | 23% | 7% | 25% | 60 |

Bacillus cereus | 64% | 19% | 14% | 3% | 36 |

Bacillus licheniformis | 62% | 24% | 10% | 5% | 21 |

Bacillus subtilis | 100% | 0% | 0% | 0% | 21 |

Clostridium botulinum | 86% | 10% | 5% | 0% | 21 |

Clostridium perfringens | 95% | 5% | 0% | 0% | 20 |

Escherichia coli | 80% | 10% | 10% | 0% | 20 |

Listeria monocytogenes | 64% | 27% | 9% | 0% | 22 |

Salmonella | 83% | 4% | 8% | 4% | 24 |

Shigella flexneri | 86% | 5% | 10% | 0% | 21 |

Staphylococcus aureus | 62% | 14% | 24% | 0% | 21 |

Yersinia enterocolitica | 76% | 14% | 5% | 5% | 21 |

Brochothrix thermosphacta | 100% | 0% | 0% | 0% | 21 |

Pseudomonas | 95% | 5% | 0% | 0% | 20 |

Microorganism | T_{min}[°C] | T_{opt}[°C] | T_{max}[°C] | pH_{min} | pH_{opt} | pH_{max} | a_{w}_{,min} | a_{w}_{,opt} | a_{w}_{,max} | µ_{max,opt} | Initial Colony [UFC/g] | Infective Colony [UFC/g] | Final Colony [UFC/g] |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Aeromonas hydrophila | 2.0 | 27-0 | 37.0 | 4.6 | 6.7 | 7.5 | 0.974 | 0.998 | 1 | 0.60732 | 10^{3} | >10^{5} | 10^{7.39} |

Bacillus cereus | 5.0 | 34-0 | 34.0 | 4.9 | 7.4 | 7.4 | 0.94 | 0.999 | 1 | 1.83940 | 10^{1} | >10^{5} | 10^{7.61} |

Bacillus licheniformis | 13.0 | 34.0 | 34.0 | 4 | 6.6 | 7.6 | 0.907 | 0.995 | 1 | 1.56890 | 10^{3} | >10^{5} | 10^{7.83} |

Bacillus subtilis | 10.0 | 34.0 | 34.0 | 4.3 | 6.1 | 7.8 | 0.933 | 0.933 | 1 | 1.17800 | 10^{1} | >10^{5} | 10^{7.83} |

Clostridium botulinum | 4.0 | 24.5 | 30.0 | 5.1 | 6.8 | 7.5 | 0.974 | 0.997 | 1 | 0.75511 | 10^{0} | >10^{4} | 10^{7.04} |

Clostridium perfringens | 15.0 | 41.5 | 52.0 | 5.0 | 8.0 | 8.0 | 0.971 | 0.989 | 1 | 1.24150 | 10^{1} | >10^{6} | 10^{7.61} |

Escherichia coli | 10.0 | 34.5 | 42.0 | 4.5 | 6.5 | 7.5 | 0.961 | 1 | 1 | 1.26770 | 10^{2} | >10^{6} | 10^{8.7} |

Listeria monocytogenes | 1.0 | 40.0 | 40.0 | 4.4 | 6.9 | 7.5 | 0.934 | 0.994 | 1 | 0.63606 | 10^{1} | >10^{2} | 10^{8.52} |

Salmonella | 7.0 | 37.5 | 40.0 | 3.9 | 6.4 | 7.4 | 0.973 | 0.997 | 1 | 0.93591 | 10^{2} | >10^{5} | 10^{8.52} |

Shigella flexneri | 15.0 | 37.0 | 37.0 | 5.5 | 7.3 | 7.5 | 0.971 | 0.993 | 1 | 0.76419 | 10^{0} | >10^{2} | 10^{8.78} |

Staphylococcus aureus | 7.5 | 30.0 | 30.0 | 4.4 | 6.5 | 7.5 | 0.907 | 0.99 | 1 | 0.58302 | 10^{1} | >10^{5} | 10^{8.09} |

Yersinia enterocolitica | −1.0 | 37.0 | 37.0 | 4.4 | 6.2 | 7.2 | 0.957 | 0.996 | 1 | 0.66226 | 10^{2} | >10^{7} | 10^{8.3} |

Brochothrix thermosphacta | 0.0 | 23.5 | 30.0 | 5.5 | 6.7 | 7.0 | 0.950 | 0.999 | 1 | 0.38374 | 10^{2} | >10^{7} | 10^{7.83} |

Pseudomonas | 0.0 | 20.0 | 20.0 | 5.0 | 6.5 | 7.4 | 0.961 | 0.993 | 1 | 0.27746 | 10^{2} | >10^{7} | 10^{8.26} |

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**MDPI and ACS Style**

Gaspar, P.D.; Alves, J.; Pinto, P.
Simplified Approach to Predict Food Safety through the Maximum Specific Bacterial Growth Rate as Function of Extrinsic and Intrinsic Parameters. *ChemEngineering* **2021**, *5*, 22.
https://doi.org/10.3390/chemengineering5020022

**AMA Style**

Gaspar PD, Alves J, Pinto P.
Simplified Approach to Predict Food Safety through the Maximum Specific Bacterial Growth Rate as Function of Extrinsic and Intrinsic Parameters. *ChemEngineering*. 2021; 5(2):22.
https://doi.org/10.3390/chemengineering5020022

**Chicago/Turabian Style**

Gaspar, Pedro D., Joel Alves, and Pedro Pinto.
2021. "Simplified Approach to Predict Food Safety through the Maximum Specific Bacterial Growth Rate as Function of Extrinsic and Intrinsic Parameters" *ChemEngineering* 5, no. 2: 22.
https://doi.org/10.3390/chemengineering5020022