^{*}

Edited by: Francisco Noé Arroyo López, Consejo Superior de Investigaciones Científicas, Spain

Reviewed by: Konstantinos Papadimitriou, Agricultural University of Athens, Greece; Zhao Chen, University of California, Davis, United States

*Correspondence: Maria R. Corbo

This article was submitted to Food Microbiology, a section of the journal Frontiers in Microbiology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The fermentation of table olives relies on a complex microbiota of lactic acid bacteria (LAB), yeasts, and enterobacteria. Producers often add sugar to increase the growth rate of LAB, “but this practice could also increase the survival rate of some pathogens. Therefore, the main topic of this paper was to study the effect of sugar, salt and temperature on the survival of

The microbiota of table olives is composed by lactic acid bacteria (LAB), yeasts, enterobacteria, and some other minor groups (clostridia, propionibacteria, Micrococcaceae). Some authors reported that the high amount of salt and the low pH could assure the safety of the product (Medina et al.,

The fermentation of table olives is generally a homo-lactic fermentation and if the LAB prevail on the other microorganisms the pH is around 4.5 and the product is stable; however, in traditional fermentations, the process is uncontrolled, and olives might harbor undesirable microorganisms (Argyri et al.,

Several pathogens could be found in olives, like

Modeling microorganisms both in food and in real systems is an iterative process, usually starting with a preliminary hypothesis, followed by a step when the initial conjecture needs to be programmed (design of experiments), and then tested (experiments) (van Boekel and Zwietering,

It is not possible to find a perfect design; however, if the goal of the research is to study the effects of multiple factors on bacterial growth/death curve, the DoE approach (Design of Experiments) could be appropriate.

Different kinds of DoE can be recovered in the literature (full, fractional, or mixture designs); in this paper, three factors were combined through a simple mixture design (simplex-lattice design). In a mixture design, the ratio of the components and their levels are dependent on each other (Flores et al.,

The main goal of this paper was to study the effects of temperature and NaCl on the survival of two pathogens (

The bacteria were stored at −20°C in Nutrient broth (Oxoid, Milan, Italy), supplemented with 33% of sterile glycerol; before each assay, they were grown in Nutrient broth, incubated at 37°C for 24 h. The microorganisms were centrifuged at 3,000 g for 10 min and the pellet was suspended in a brine prepared with tap water and 4% NaCl. The viable count of these suspensions was 7 log cfu/ml.

The brines were prepared with tap water, salt (4.0–10.0%) and sugar (0–4 g/l), as reported in Table

Simplex centroid.

A | 1 | 0 | 0 | 10.0 | 0.0 | 5.0 |

B | 0 | 1 | 0 | 4.0 | 4.0 | 5.0 |

C | 0 | 0 | 1 | 4.0 | 0.0 | 25.0 |

D | 0.5 | 0.5 | 0 | 7.0 | 2.0 | 5.0 |

E | 0.5 | 0 | 0.5 | 7.0 | 0.0 | 15.0 |

F | 0 | 0.5 | 0.5 | 4.0 | 2.0 | 25.0 |

The brines were inoculated to 5 log cfu/ml with each strain separately and stored at the temperatures shown in Table

The viability of the strains was evaluated through the spread plate count three times per week (Nutrient Agar, incubated at 37°C for 24–48 h).

The design was repeated two times and each time the experiments were done on three independent batches (

The results of the viable count were fitted through the equation of Weibull, cast in the form of Mafart et al. (

where log _{0} the inoculum (log cfu/ml); FRT, the first reduction time (day), i.e., the time for a 1 log cfu/ml decrease of the bacterial population; p, the shape parameter (

The results were also fitted through the Weibull equation, modified by Bevilacqua et al. (

Where ^{2}.

FRT, p, and s.t. were used as dependent variables for a multiple regression analysis; salt, sugar, and temperature were the independent variables or categorical factors. The modeling was performed through the option DoE/mixture design of the software Statistica for Windows; salt, sugar, and temperature were used as independent variables and the fitting parameters of Weibull equation as dependent variables. The model was built by using the option “quadratic,” for the evaluation of both individual (“salt,” “sugar,” and “temperature”) and interactive effects (“salt^{*}sugar,” “salt^{*}temperature,” and “temperature^{*}sugar”).

The Most Important Output of the Modeling was a Polynomial Equation Reading as follows:

where, _{i}, and _{j} are respectively the dependent and the independent variables; _{i} and _{ij} are the coefficients of the model. This model assessed the effects of linear (_{i}), and interactive terms (Σ_{i}_{j}) of the independent variables on the dependent variable.

The significance of the model was evaluated through the R^{2} coefficient adjusted for a multiple regression and the residual mean square error (RMSE), as suggested by Chen and Zhu (

The effect of each independent variable (salt, temperature, sugar) on the fitting parameters of the death kinetic of Weibull (p, FRT, and s.t.) was evaluated through the individual desirability functions, estimated as follows:

Where y_{min} and y_{max} are the minimum and maximum values of the dependent variable, respectively.

The desirability was included in the range 0–1 (0 for the lowest value of p, FRT, and s.t. and 1 for their maximal values). The desirability profiles were built by setting a variable to the coded level 1 (25°C for the temperature, 12% for NaCl, and 4% for sugar) and the other two to their minimum values (5°C for the temperature, 4.0% NaCl, and 0.0% sugar).

The results of the viable count of

Significance of the factors of the simplex centroid on the first reduction time (FRT, days) and on the survival time (s.t., days) of

NaCl | 10.34 | 0.000 | 3.35 | 0.006 |

Temperature | – | – | – | – |

Sugar | 4.85 | 0.000 | 6.53 | 0.000 |

NaCl^{*}Temp. |
– | – | – | – |

NaCl^{*}Sugar |
2.25 | 0.044 | 2.68 | 0.020 |

Sugar^{*}Temp. |
– | – | 2.69 | 0.020 |

0.741 | 0.744 | |||

RMSE | 0.427 | 0.909 | ||

NaCl | 6.23 | 0.000 | 10.30 | 0.000 |

Temperature | – | – | – | – |

Sugar | 8.55 | 0.000 | 4.67 | 0.001 |

NaCl^{*}Temp. |
2.59 | 0.024 | 2.54 | 0.026 |

NaCl^{*}Sugar |
– | – | 4.55 | 0.001 |

Sugar^{*}Temp. |
– | – | – | – |

0.733 | 0.761 | |||

RMSE | 86.715 | 335.108 |

The equation could be used to build ternary plots; Figure

Ternary plot for the effects of sugar, salt, and temperature on the survival time of

A ternary plot is an important tool; however, it could not be used to analyze the quantitative effect of each individual term. Thus, the desirability approach was used to counteract this limit.

The desirability is a dimensionless parameter, ranging from 0 to 1 and is the answer to question: how much desired is an output? The reply is: 0 for the worst result and 1 for the best one. Moreover, a desirability profile is often completed by a prediction profile, which shows the predicted values of the dependent variable as a function of the coded values of the factors of the design.

Figure

Prediction (

Figure

Prediction

Finally, Figure

Prediction profile for the effect of NaCl on the survival time (s.t.) of

The first reduction time of

Figure

Ternary plot for the effects of sugar, salt, and temperature on the survival time of

As reported for

Prediction profiles for the effect of the temperature on the first reduction time (FRT)

Prediction profiles for the effect of sugar on the first reduction time (FRT)

Finally, the effect of salt was unexpected, as the model suggested a positive rather than a negative effect, with an increase of both the first reduction and survival time as a function of an increase of the concentration of salt (from 0.6 to 3.2 days-Figure

Prediction profiles for the effect of NaCl on the first reduction time (FRT)

The effects of the factors of the design on the shape parameter of

Ternary plot for the effects of sugar, salt, and temperature on the shape parameter of

Prediction profiles for the effect of temperature (0, temperature at 5°C; 1, temperature at 25°C)

The effect of the factors of the design on the shape parameter of

Ternary plot for the effects of sugar, salt, and temperature on the shape parameter of

Olives and other fermented vegetables are consumed worldwide (Medina et al.,

In Southern Italy the fermentation of table olives takes place from the end of September to December, with temperature ranging from 10 to 20–25°C; moreover, salt is in the range 6–12% (Bevilacqua et al.,

The effect of temperature on the survival of both pathogens confirms the data of some other authors: the survival in harsh conditions could be enhanced by refrigeration, as suggested by Medina et al. (

Sugar enhanced the survival of ^{+} import to H^{+} export, thus permitting

Concerning the positive effect of sugar, Casey and Condon (

In the second step of this research, the effects of the factors of centroid on the shape parameter (p) were assessed. When the shape parameter is 1, the death curve is a line and follow the first-order kinetic of Bigelow; on the other hand, when

In

In conclusion, this paper offers a structured statistical approach on the variables acting on the survival of pathogens in brines and represents the first step to set up and design a predictive approach for olive producers. Concerning the addition of sugar in brine, this practice could be a challenge as it could increase the survival of some pathogens and salt could not be able to counteract this effect. Some evidences suggested that the increased survival of

MC, MS, and AB conceived the study. AB and MC designed the experiments. BS and DC performed the experiments. AB, MS, and MC interpreted the results and modeling. All authors wrote and approved the manuscript. MC funded the research.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.