Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions
Round 1
Reviewer 1 Report
The paper is very interesting and organized in a very professional way. The way it is written and organized, I really enjoyed. The paper is a nice contribution to the field and deserves to be published. However, I have a few minor comments, which I believe will further improve the paper.
Define the terms "d" and "k" in Eq. (1)
Eq. (6), a complete range of the term "alpha" should be mentioned.
The sources or references of the data sets should be given.
The references are too old. To show the appropriateness of the topic, relevant references from recent years should be cited.
Author Response
The authors thank the referee for his careful reading, interesting remarks, and suggestions. We truly appreciate the effort taken to help us improve the manuscript in terms of content and presentation. We made a detailed review of the text to correct the remaining mistakes. It was removed some information in the introductory section. Finally, we are firmly convinced of the utility and impact of our results and predictions and that the present findings fit within the scope of Stats.
Below, we provide our answers to each concern:
- “Define the terms "d" and "k" in Eq. (1).”
Our comment: d is the digit(s), while k is all integers. We included these definitions in the text.
- “Eq. (6), a complete range of the term "alpha" should be mentioned”.
Our comment: We already inserted the validity range.
- “The sources or references of the data sets should be given”.
Our comment: All data was collected in our laboratory and at this time, we have chosen not to make the data publicly available. We hope to do this in the future.
- “The references are too old. To show the appropriateness of the topic, relevant references from recent years should be cited”.
Our comment: We understand and appreciate the reviewer's opinion. To provide a chronological overview of the state of the art of research involving the statistical basis of neurotransmitter release at the neuromuscular junction, we gave the deserved credit for all authors and their pioneering work in the field. However, we also cite several current studies, presenting the most recent results, including from our recent research. In particular, we included several recent articles and three books on the subject (Berger, A.; Hill, T. An Introduction to Benford’s Law; Princeton University Press; Princeton, NJ, USA, 2015; Kossovsky, A.E. Benford’s Law: Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications; World 399 Scientific: Singapore, 2014; Nigrini, M.J. Benford’s Law: Applications for Forensic Accounting, Auditing, and Fraud Detection; JohnWiley & Sons: Hoboken, NJ, 434, USA, 2012.), which contain the state of the art involving the theory and applications of the Newcomb-Benford Law.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The manuscript entitled “Newcomb-Benford Law in Neuromuscular Transmission: Validation at Hyperkalemic Conditions” by Adriano Silva et al., is under consideration for publication in this journal. While the research article shows promise, it requires some minor revisions and additional details to meet our publication standards.-
1. The abstract provides a clear overview of the study's objectives and findings. It effectively summarizes the key points of the research. However, it could be further improved by briefly mentioning the methodology used and the sample size.
2. The introduction provides a comprehensive background on the neuromuscular junction, neurotransmission, and the historical context of research in this field. It effectively sets the stage for the study. However, I suggest condensing certain sections to maintain focus on the primary research question.
3. The manuscript briefly mentions the results but lacks specific details. Reviewer would likely request a more comprehensive presentation of the results, including statistical measures and graphical representations. The discussion section could benefit from a more in-depth analysis of the findings and their implications.
4. The conclusion summarizes the study's main findings and mentions potential future research directions. However, it could be enhanced by restating the primary findings explicitly and their significance in the context of the broader field.
5. Ensure that any figures and tables are clear and effectively support the text. I request revisions or additions to figures and tables for better illustration of the data.
6. Read the following articles for reference and cite accordingly, DOI: 10.3390/su11123284;10.1016/B978-0-323-90784-2.00007-1; 10.1080/07391102.2021.1924263
7. The manuscript is generally well-written, but it is suggested minor language and clarity improvements to enhance readability.
Must be Improved.
Author Response
The authors thank the referee for his careful reading, interesting remarks, and suggestions. We truly appreciate the effort taken to help us improve the manuscript in terms of content and presentation. We made a detailed review of the text to correct the remaining mistakes. It was removed some information in the introductory section. Finally, we are firmly convinced of the utility and impact of our results and predictions and that the present findings fit within the scope of Stats.
Below, we provide our answers to each concern.
- “The abstract provides a clear overview of the study's objectives and findings. It effectively summarizes the key points of the research. However, it could be further improved by briefly mentioning the methodology used and the sample size.”
Our comment: We added information by mentioning the specific methodology adopted used and sample size.
- “The introduction provides a comprehensive background on the neuromuscular junction, neurotransmission, and the historical context of research in this field. It effectively sets the stage for the study. However, I suggest condensing certain sections to maintain focus on the primary research question”.
Our comment: In the introductory section, we have provided a detailed presentation of the topics involved in this investigation. This strategy certainly implied a slightly longer but very instructive section. However, we have summarized some parts of the text without compromising the satisfactory understanding of this section.
- “The conclusion summarizes the study's main findings and mentions potential future research directions. However, it could be enhanced by restating the primary findings explicitly and their significance in the context of the broader field.”.
Our comment: We discussed in detail how to expand the present research, considering new possibilities for verifying the law in other vital situations. In fact, in the discussion and conclusion sections, we emphasize the importance of considering electrophysiological recordings at different temperatures and tissues in pathological situations. In addition, we offered a more general biophysical context besides a biological scenario. We also suggested conducting theoretical studies investigating the possible connection between thermodynamic aspects and Newcomb-Benford´s law based on non-extensive statistical mechanics. If successful, this study could show more precisely the relationship between the level of membrane potential fluctuation and the law. These observations were included in the conclusion section.
- “The manuscript briefly mentions the results but lacks specific details. Reviewer would likely request a more comprehensive presentation of the results, including statistical measures and graphical representations. The discussion section could benefit from a more in-depth analysis of the findings and their implications”.
Our comment: We understand and appreciate the reviewer's opinion, but the presentation of the results is very concise and robust. We present figures and tables with precise results obtained using NBL and gNBL. Besides that, it presented sufficient arguments for adopting a more generalized version of the law and what biophysical implications would be involved. In addition, we justified why we used the three reliable methods for quantifying the conformity between experimental data and frequencies predicted by Newcomb-Benford's law. The SSD and MAD methods are commonly used in Newcomb-Benford´s law analyses. However, to increase the rigor and reliability of our results, we delved into the data analysis, including the severe test, to understand better the role of sample size in the MAD test. We discuss in detail the implications of our findings for each result, offering a plausible biophysical scenario for the dynamics of miniature potentials, connecting the results obtained with morphological and electrophysiological arguments. Furthermore, we describe a possible biological scenario and its implications for the observed conformity oscillations.
- “Ensure that any figures and tables are clear and effectively support the text. I request revisions or additions to figures and tables for better illustration of the data.”.
Our comment: All figures and tables presented provide a detailed overview of our findings.
6.“Read the following articles for reference and cite accordingly, DOI: 10.3390/su11123284;10.1016/B978-0-323-90784-2.00007-1; 10.1080/07391102.2021.192426”.
Our comment: The suggested references do not refer to Newcomb-Benford's Law applications. Therefore, although they seem to be essential works in their fields of knowledge, they do not fit into the present work. We appreciate the suggestions offered by the reviewer, but we do not include them as references as they are not within the scope of our article.
- Effect of structural variation on enzymatic activity in tetranuclear (Cu4) clusters with defective cubane core (https://doi.org/10.1080/07391102.2021.1924263).
- Water Environment Policy and Climate Change: A Comparative Study of India and South Korea. (doi:10.3390/su11123284).
- Synthesis of metal-organic frameworks (MOFs): Routes to various MOF topologies, morphologies, and composites (https://doi.org/10.1016/B978-0-323-90784-2.00007-1).
7.The manuscript is generally well-written, but it is suggested minor language and clarity improvements to enhance readability”
Our comment: We carefully read once more the manuscript and removed minor errors that remained.
Author Response File: Author Response.pdf
