# Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of Geotrichum candidum

^{*}

## Abstract

**:**

^{−1}h

^{−0.5}and T

_{min}= −0.72 °C showed better indices relating to goodness of fit based on a low root mean sum of square error (RMSE = 0.028 log CFU mL

^{−1}), a higher coefficient of determination (R

^{2}= 0.978), and the lowest value of AIC (AIC = −38.65). The present study provides a solution to the possible application of secondary predictive models to the death rate dependence on temperature during the microbial lag phase. Despite limited practical importance, under specific conditions, it is possible to consider its use, for example, in exposure assessment.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Microorganism and Preparation of Inoculum

^{2}CFU mL

^{−1}.

#### 2.2. Estimation of G. candidum Cell Viable Counts

^{−1}fat content (Rajo, Inc., Bratislava, Slovak Republic) with the addition of 1% NaCl (Centralchem Inc., Bratislava, Slovak Republic) was used in the experiments as cultivation medium for G. candidum growth. Three parallels of an inoculated milk medium were incubated at 8, 12, 15, 18, 21, and 25 ± 0.5 °C under static aerobic conditions. At 6 °C, three replicated cultivations in three parallels were performed due to an almost negligible decrease in G. candidum counts. The actual counts of viable G. candidum cells were determined at defined time intervals on DRBC agar (Biokar Diagnostics, Beauvais, France) in accordance with EN ISO 21527-1 [33] by a cultivation method using ten-fold dilution in a peptone–saline solution. Inoculated Petri dishes were cultivated in aerobic conditions at 25 ± 0.5 °C for 5 days.

#### 2.3. Modelling of Lag Death Rate of G. candidum

^{−1}) at different incubation temperatures, the selected primary data from the lag phase were fitted with Weibull’s model Equation (1) as derived by Mafart et al. [34]:

_{0}and N are the G. candidum cell viable counts (CFU mL

^{−1}) determined after inoculation and then during the lag phase in time t. The shape parameter p and the first decimal reduction δ (h) were estimated with non-linear regression performed with the Solver tool of Microsoft Excel 2013 (Microsoft, Redmond, WA, USA). δ, as the key output, was recalculated to the specific lag death rate LDR (k

_{max}; h

^{−1}) according to Equation (2):

_{max}is the specific LDR (h

^{−1}) and k* is the death rate (h

^{−1}) at reference temperature T

_{K}*. Both T

_{K}* and incubation temperature T

_{K}are in K, E

_{a}is the activation energy (kJ mol

^{−1}), R is the ideal gas constant (8.314.10

^{−3}kJ mol

^{−1}K

^{−1}), and C

_{0}is the coefficient to be estimated by non-linear regression. For the square root model, b is the coefficient (°C

^{−1}h

^{−0.5}), T

_{min}is the minimum temperature at which no decrease is expected, and T is the incubation temperature (°C).

#### 2.4. Statistical Evaluation

^{2}) according to Wells-Bennik et al. [38], with a root mean sum of square error (RMSE). Equation (6) characterized the experimental variability, and the variations between the observed values (y

_{obs}) and the fitted values (y

_{pred}) within the experiment with the replications.

_{p}is the number of parameters; and y

_{i}can include ln k

_{max}or square root of k

_{max}, dependent of the model equation used. For the variability between biologically independent reproductions (reproduction or biological variability), the same equations were used, although with a different number of observations. For example, there were three independent trials with two replicates (n = 46) and three parameters to be estimated at 6 °C.

## 3. Results and Discussion

#### 3.1. Lag Death Rate Primary Modelling

^{−1}and 0.13 log CFU mL

^{−1}at 6 °C and 8 °C, respectively (data not included in Table 1), while the biological variability was represented with higher RMSE values of 0.200 log CFU mL

^{−1}and 0.349 log CFU mL

^{−1}. The other values of RMSE in Table 1 represent only the biological variability that showed a maximum at 25 °C, the temperature at which the highest LDR or the lowest decimal reduction time of G. candidum was observed.

#### 3.2. Lag Death Rate Secondary Modelling

^{−1}was needed for G. candidum arthrospores to germinate. In our case, they formed a substantial part of the inoculums (microscopic observation not presented in this study). The modified Arrhenius equations also provided the identical graphical outputs presented in Figure 2a, with a high coefficient of determination (R

^{2}= 0.927). However, the application of the square root model presented in Figure 2b showed better indices relating to the goodness of fit involving RMSE (RMSE = 0.028 log CFU mL

^{−1}), a higher coefficient of determination (R

^{2}= 0.978), and the lowest value of AIC value (Table 2).

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Decrease in the cell numbers during the lag phases of G. candidum growth in milk, in the range of 6 °C to 12 °C.

**Figure 2.**Temperature dependence of G. candidum LDR modelled with the modified ARH models, identical for both equations (

**a**). Graphical presentation of G. candidum LDR as modelled with the square root model (

**b**).

**Table 1.**Parameters of the primary model and statistical indicators for the rate of decrease in G. candidum cell viable counts in dependence on the incubation temperature.

T (°C) | δ (h) | p | log N_{0} (log CFU mL^{−1}) | n | RMSE (log CFU mL^{−1}) | R^{2} |
---|---|---|---|---|---|---|

6 | 111.94 | 1.53 | 2.01 | 46 | 0.200 | 0.491 |

8 | 52.35 | 1.90 | 2.13 | 30 | 0.349 | 0.608 |

12 | 20.96 | 1.85 | 1.78 | 8 | 0.164 | 0.959 |

15 | 17.96 | 3.57 | 1.93 | 6 | 0.086 | 0.989 |

18 | 9.91 | 5.91 | 1.97 | 8 | 0.052 | 0.972 |

21 | 7.71 | 2.03 | 1.93 | 8 | 0.087 | 0.984 |

25 | 6.14 | 1.27 | 1.97 | 7 | 0.377 | 0.788 |

_{0}—initial cell counts of G. candidum, n—number of observations, RMSE—root mean sum of square error, R

^{2}—coefficient of determination.

**Table 2.**The statistical indices and parameters of secondary models for rate of decrease in G. candidum cell viable counts.

Model Parameters | ln k* | C_{0} | E_{a}(kJ mol ^{−1}) | T_{K}*(K) | b (°C ^{−1} h^{−0.5}) | T_{min}(°C) | RMSE (log CFU mL ^{−1}) | R^{2} | AIC |
---|---|---|---|---|---|---|---|---|---|

Modified ARH (Equation (3)) | −4.453 | − | 100.88 | 273.02 | − | − | 0.346 | 0.927 | 9.20 |

Modified ARH (Equation (4)) | − | 39.988 | 100.88 | − | − | − | 0.309 | 0.927 | −4.80 |

RTK | − | − | − | − | 0.016 | −0.720 | 0.028 | 0.978 | −38.65 |

_{K}*, C

_{0}—the coefficient estimated by non-linear regression, E

_{a}—activation energy, b—coefficient of RTK model estimated by non-linear regression, T

_{min}—minimum temperature, RMSE—root mean sum of square error, R

^{2}—coefficient of determination, AIC—Akaike´s Information Criterion, ARH—Arrhenius equation, RTK—square root model.

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**MDPI and ACS Style**

Valík, Ľ.; Šipošová, P.; Koňuchová, M.; Medveďová, A.
Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of *Geotrichum candidum*. *Appl. Sci.* **2021**, *11*, 7344.
https://doi.org/10.3390/app11167344

**AMA Style**

Valík Ľ, Šipošová P, Koňuchová M, Medveďová A.
Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of *Geotrichum candidum*. *Applied Sciences*. 2021; 11(16):7344.
https://doi.org/10.3390/app11167344

**Chicago/Turabian Style**

Valík, Ľubomír, Petra Šipošová, Martina Koňuchová, and Alžbeta Medveďová.
2021. "Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of *Geotrichum candidum*" *Applied Sciences* 11, no. 16: 7344.
https://doi.org/10.3390/app11167344