Mathematical Modeling of Inhibitory Microbial Lethality Synergistic: Secondary Phytocompounds from Purple Toronjil, Temperature, and Harvest Stress Effects on Escherichia coli

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General Comments

The manuscript presents a comprehensive study on the inhibitory activity of secondary phytocompounds from Agastache mexicana subsp. mexicana (Amm) against Escherichia coli, integrating a mathematical modeling approach to evaluate bacterial growth inhibition. The investigation is of significant relevance to the field of food safety and microbial stress response, as it introduces a model incorporating temperature and starvation stresses to quantify bacterial inhibition. The study is backed by a thorough experimental design and the use of mathematical models that aid in the interpretation of data. However, the manuscript has several issues that need to be addressed to enhance clarity, scientific rigor, and overall readability. The main concerns revolve around the depth of data interpretation, the organization of the methodology, and the justification of certain experimental choices.

Major Concerns

#1 The derivation and justification of the proposed model (Equations 1-13) require clearer explanation. The reasoning behind using the specific exponential decay model should be elaborated further.

#2 The manuscript would benefit from a more robust comparison with existing models in the field to highlight the novelty of this approach.

#3 Clarify the number of repetitions for CFU measurements and their statistical treatment. Were data averaged, and how was variability accounted for?

#4 The preparation of the E. coli inoculum (e.g., 24-hour incubation at 35°C) should be justified for its relevance to the experiment’s goals.

#5 The mechanisms of action for saponins, flavonoids, tannins, etc., need to be more critically discussed with references to recent findings.

#6 Provide more detail on the ‘standard account technique’ for CFU measurement and how it ensures accuracy and reproducibility.

#7 Address why E. coli exhibited survival behavior at lower temperatures and how this finding aligns with literature.

Minor Concerns

#1 Correct minor typographical errors throughout the manuscript.

#2 Expand on the equipment calibration procedures (e.g., rotary evaporator).

#3 Provide more details on the sourcing and preparation of the plant material used.

#4 Adjust the title and abstract to better reflect the focus on the mathematical model and inhibition mechanisms.

Author Response

Reviewer 1

Major Concerns

#1 The derivation and justification of the proposed model (Equations 1-13) require a clearer explanation. The reasoning behind using the specific exponential decay model should be elaborated further.

4. We have done a justification and we improve the equations due to mistakes, please see the section 4.4.

#2 The manuscript would benefit from a more robust comparison with existing models in the field to highlight the novelty of this approach.

1. Done, please see section 3

#3 Clarify the number of repetitions for CFU measurements and their statistical treatment. Were data averaged, and how was variability accounted for?

4. Done. Please, see section 4.3.3. Also, see the note to the final of this document.

#4 The preparation of the E. coli inoculum (e.g., 24-hour incubation at 35°C) should be justified for its relevance to the experiment’s goals.

4. Done. Please, see section 4.3.1.

#5 The mechanisms of action for saponins, flavonoids, tannins, etc., need to be more critically discussed with references to recent findings.

1. We have included and improved the explanation of inhibition with new recent references. Besides, we eliminated some wrong mechanisms.

 

#6 Provide more detail on the ‘standard account technique’ for CFU measurement and how it ensures accuracy and reproducibility.

4. The standard account technique really is called “Agar-Plate Method” so we have changed the name. Besides, we have included the specific methodology especially in the emptying temperature before accounting the CFU that is key to reproducibility. Please, see section 4.3.3.

 

#7 Address why E. coli exhibited survival behavior at lower temperatures and how this finding aligns with literature.

3. Done. Please, see the last two paragraphs in section 3. We added references.

 

Minor Concerns

#1 Correct minor typographical errors throughout the manuscript.

1. Done

#2 Expand on the equipment calibration procedures (e.g., rotary evaporator).

1. Rotary evaporator does not calibrate, but in this issue, we are confused because in Laboratory only we do internal calibrations. The more important tests are the CFU account, temperature and weight measurements. Do you want calibration procedures about these instruments?

#3 Provide more details on the sourcing and preparation of the plant material used.

4. Done, please see section 4.1

#4 Adjust the title and abstract to better reflect the focus on the mathematical model and inhibition mechanisms.

1. Done. Please, see the new title

In the statistical results we have done some models. Statistically the rules for CFU measurements was explained in section 4.3.3.

• The model in Equation 2 can be rewritten as a statistical model as * by using the following substitutions: ,  ,  ,    and  can be seen as the following linear regression model
•  
• where the are identical and independent random variables with distribution . The independence assumption was verified using the Durbin-Watson test, the homogeneus variance assumption was checked using the non-constant variance score test and the normality assumption was assessed using the Shapiro-Wilk test. The linear regression model was fitted using the R statistical software (R Core Team, 2020). The Durbin-Watson and non-constant variance score tests are implemented in the car library (Fox and Weisberg S (2019) and the Shapiro-Wilk test is implemented in the stats library (R Core Team, 2020). 
• The goodness of fit of a linear regression model is measured by the coefficient of determination, , which measures the proportion of the variance in the response variable explained by the model. A model with good fit is one with close to 1. Another way to assess the fit of a model is with the root mean sum of squares of the residuals (RMSSR). The RMSSR was calculated with equation

 

• where n is the number of observations in the sample, is the observed CFU and  is the CFU estimated by the model. A good model is one with the lowest RMSCR. This statistic is cited by Wang et al. (2018) and named root mean square deviation.
• Because linear regression models were fitted for , to determine the estimated value of the CFU, , the inverse function of the logarithm was used, that is, the exponential function to return to the original values.
• For the case Amm at 35.5 °C the equation of the model is:
• The fitted model fulfill the assumption of independence (p=0.16), homogeneity of variances (p=0.06) and normal distribution (p=0. 29). The fitted model has a very high goodness of fit given by a . In the original variables the model has the equation
•  
• The fit goodness of this model is 4.
•  
• For the case Amm at 8.12 °C the equation of the model is:
• The fitted model fulfill the assumption of independence (p=0.41), homogeneity of variances (p=0.38) and normal distribution (p=0.13). The fitted model has a very high goodness of fit given by a . In the original variables the model has the equation
•  
• The fit goodness of this model is 9.
• For the case of food-grade paper at 35.5 °C the equation of the model is: . The fitted model fulfill the assumption of independence (p=0.91), homogeneity of variances (p=0.65) and normal distribution (p=0. 90). The fitted model has a very high goodness of fit given by a . In the original variables the model has the equation
•  
• The fit goodness of this model is 1.
• For the case of food-grade paper at 8.12 °C the equation of the model is: . The fitted model fulfill the assumption of independence (p=0.29), homogeneity of variances (p=0.37) and normal distribution (p=0. 99). The fitted model has a high goodness of fit given by a . In the original variables the model has the equation
•  
• The goodness of fit of this model is 0.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

    I have reviewed the manuscript entitled "Mathematical modelling and inhibitory activity of secondary phytocompounds from “purple toronjil” on Escherichia coli: a food safety alternative" and found it generally well-written and of intererest for the scientific community. However, there are some small observations to be taken into account to improve the quality of the manuscript, that are mentioned below:

1. Please write all Latin names of plant species and bacterial species using italics, throughout the entire manuscript.

2. There is no need for quotation marks when writing the names of plants and bacteria.

3. In most cases the reference citation in the text are placed between stop points. The stop points before the citations should be eliminated.

4. Lines 50 and 51: There is no need to use italics for "and" and "stand out".

5. Please write "mL" instead of "ml" throughout the entire manuscript.

6. Lines 61-65: Why is the phrase put between question marks?

7. Line 83: I believe "antimicrobial activity" would be more suitable than "microbial activity" in this context.

8. Line 120: I suggest the following change: "substrate of Amm, and...".

9. Line 124: Please change "Aerial" to "aerial" as it is not the first word of the sentence.

10. Line 136: I suggest the following change: "from the aerial parts that were macerated".

11. Please correct "HCL" to "HCl" (for hydrochloric acid) throughout the entire manuscript.

12. Lines 185-186: I suggest the following rephrasing to increase the readability: "If there is a blue/green color change, the reaction is considered positive for the presence of steroids, and a red to purple coloring indicates the presence of triterpenes."

13. Line 194: I suggest the following changes: "The proposal ungrowth equation that fits the experimental results is:".

14. Line 195: Please correct "eavluated" to "evaluated".

15. Line 198: I suggest the following modification: "different than zero".

16. Line 199: I suggest the following change: "decreasing through time".

17. Equations 4, 5 and 6: Shouldn't it be "e^-kt" instead of "e^kt". Please verify and correct if appropriate.

18. Line 204: Please correct "fist" to "first".

19. Lines 218 and 219: Please corect "intervale" to "interval".

20. Line 221: Please correct to "Table 3 displays...".

21. Lines 230 and 231: Please correct "y" to "and".

22. Line 256: Please correct "Inhibición" to "Inhibition".

23. Line 258: Please use "bacterial growth" instead of "bacterian growth".

24. Line 268: I suggest the following change: "which contribute to penetration".

25. Line 302-303: I suggest the following modifications: "across the substrated, which was the highest on Amm and at 35.5^oC.

26. The Conclusion section could be a little bit more detalied to better underline the scientific value of the research conducted.

 

Author Response

Reviewer 2

Comments and Suggestions for Authors

Dear Authors,

    I have reviewed the manuscript entitled "Mathematical modelling and inhibitory activity of secondary phytocompounds from “purple toronjil” on Escherichia coli: a food safety alternative" and found it generally well-written and of intererest for the scientific community. However, there are some small observations to be taken into account to improve the quality of the manuscript, that are mentioned below:

1. Please write all Latin names of plant species and bacterial species using italics, throughout the entire manuscript.

Done

There is no need for quotation marks when writing the names of plants and bacteria.

3. In most cases the reference citation in the text are placed between stop points. The stop points before the citations should be eliminated.
4. Lines 50 and 51: There is no need to use italics for "and" and "stand out".
5. Please write "mL" instead of "ml" throughout the entire manuscript.
6. Lines 61-65: Why is the phrase put between question marks?
7. Because it had been copied exactly the same as the quote but in the end, it was modified and the quotation marks were not removed.

Quotation marks have already been removed

7. Line 83: I believe "antimicrobial activity" would be more suitable than "microbial activity" in this context.
8. Thank you, done
9. Line 120: I suggest the following change: "substrate of Amm, and...".
10. Done
11. Line 124: Please change "Aerial" to "aerial" as it is not the first word of the sentence. R. Done.
12. Line 136: I suggest the following change: "from the aerial parts that were macerated".
13. Text was chaged by “From the aerial parts, 46.2 g were separated for 48 h in a 1 L amber flask, using distilled water as a solvent by covering the plant’s material”
14. Please correct "HCL" to "HCl" (for hydrochloric acid) throughout the entire manuscript.
15. Corrected.
16. Lines 185-186: I suggest the following rephrasing to increase the readability: "If there is a blue/green color change, the reaction is considered positive for the presence of steroids, and a red to purple coloring indicates the presence of triterpenes."
17. Thank you, Done
18. Line 194: I suggest the following changes: "The proposal ungrowth equation that fits the experimental results is:".
19. Thank you. Done
20. Line 195: Please correct "eavluated" to "evaluated".
21. Thank you. Done
22. Line 198: I suggest the following modification: "different than zero".
23. Thank you. Done
24. Line 199: I suggest the following change: "decreasing through time".
25. Thank you. Done.
26. Equations 4, 5 and 6: Shouldn't it be "e^-kt" instead of "e^kt". Please verify and correct if appropriate.
27. Thank you very very much. There were many shameful mistakes, so we corrected them. Please see the correct equations.
28. Line 204: Please correct "fist" to "first".
29. Thank you. Done.
30. Lines 218 and 219: Please corect "intervale" to "interval".
31. We have corrected by “In the same way, to know the relationship between CFU and its survival time by every experimental time interval was proposed an integrating operation. To calculate the area under the curve by every time interval or gradient; is the initial amplitude for . Besides is the final time in according to the interval selected as follow:”
32. Line 221: Please correct to "Table 3 displays...".
33. Thank you. We have changed by “Table 1 displays” because there was a change in the sections order.
34. Lines 230 and 231: Please correct "y" to "and".
35. Thank you. Done.
36. Line 256: Please correct "Inhibición" to "Inhibition".
37. Thank you. Done.
38. Line 258: Please use "bacterial growth" instead of "bacterian growth".
39. Thank you. Done.
40. Line 268: I suggest the following change: "which contribute to penetration".
41. Thank you. Done.
42. Line 302-303: I suggest the following modifications: "across the substrated, which was the highest on Ammand at 35.5^oC.
43. Thank you. Done.
44. The Conclusion section could be a little bit more detalied to better underline the scientific value of the research conducted.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have provided detailed responses to your major and minor concerns, and their revisions are comprehensive. Thus, this paper can be accepted.