Differential Scanning Calorimetry of Proteins and the Two-State Model: Comparison of Two Formulas

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I have read the manuscript and I am perplexed because the authors have simply shown that two relationships, both coming from the so-called reversible two-state transition model, are able to fit with the same accuracy experimental DSC curves for the temperature-induced denaturation of 33 different globular proteins. Actually, the two formulas, equations (5b) and (6b) in the manuscript, are not really different because the second one is obtained by a series expansion of a part of the first one. So there should be no real surprise in the obtained results. In addition, the points of the experimental DSC peaks have been extracted from the figures of published articles of other authors; this means that they could be affected by significant errors, shedding doubts on the two-state analysis performed.

 

On this basis, I cannot support publication of such an investigation.

Comments on the Quality of English Language

The quality of English Language is satisfactory.

Author Response

Dear Reviewer,

Thank you for the comments. We think there is some level of misunderstanding though. You said:

"... Actually, the two formulas, equations (5b) and (6b) in the manuscript, are not really different because the second one is obtained by a series expansion of a part of the first one. So there should be no real surprise in the obtained results. "

Indeed, the square formula is obtained from truncation of the series expansion on linear term. As we have explained in lines 46-54, the expansion is justified only under the assumption of smallness of transition interval. It is not given, that this condition will be valid for all proteins. Each particular protein has different transition interval. It is a question, how this approximation affects fitted values. We have shown, on the example of a set of randomly collected 33 proteins, that both exact and approximate formulas give almost identical results in terms of statistical distributions of fitted parameters. It is not a paradigm-changing result, however, we find such validation obligatory to be done before the application of approximate formula to treat arrays of data.

You said:

" In addition, the points of the experimental DSC peaks have been extracted from the figures of published articles of other authors; this means that they could be affected by significant errors, shedding doubts on the two-state analysis performed."

In Results and Discussion, we have added the following text, explaining how the digitization was done. The procedure allows to digitize the printed graphs with very high precision, taking into account the point size of selected pattern.

"For digitization we took the graphs from the original papers and uploaded to online digitization tool system [13] that is an opensource software leveraging computer vision technology to assist in extracting numerical data from images, including plots, maps, and various other visual materials. WebPlotDigitizer ensures an accurate data extraction of information by employing a combination of computer vision algorithms and manual techniques."

We hope that you will reconsider our submission taking into account our responses and explanations.

Thank you!

 

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

The paper addresses an interesting topic, but further clarification is needed on some aspects before considering it for publication in the journal Biophysica.

 

My general objection is the following:

The main results and conclusions derived from the work should be presented in the Abstract.

It is necessary to better emphasize the scientific contribution and novelties of the paper, highlighting what has been done in the paper that is not already available in the literature.

 

 

Specific remarks:

In equation 7a, define what the label θ represents

Line 77: Specify which software was used for fitting.

Line 85: Please explain better how the data digitization was done.

Line 95: Explain how you obtained these histograms or provide a reference.

Author Response

Dear Reviewer,

We are grateful for your attention towards our submission and constructive criticism you have provided. Let us answer below to all of your comments point-by-point.

You said:

"The main results and conclusions derived from the work should be presented in the Abstract."

We have thankfully accepted your comment and added the following text to the abstract:

"We discuss here the application of exact two-state formula with its  approximation and process the DSC experimental data on protein folding in water. The approximate formula relies on smallness of transition interval, which is different for each protein. On the example of the set of 33 different proteins we show the practical validity of the approximation and the equivalence of exact and approximate two-state formulas for processing DSC data."

You said:

"It is necessary to better emphasize the scientific contribution and novelties of the paper, highlighting what has been done in the paper that is not already available in the literature."

We have accepted the comment. Changes are made throughout the manuscript in order to highlight the novelty.

You said:

"In equation 7a, define what the label θ represents"

Accepted. We have completed the description after Eq 7 to read:

"...where θU is the degree of denaturation and K NU represents the equilibrium constant between the native (N) and unfolded (U) states."

You said:

"Line 77: Specify which software was used for fitting."

Accepted. We have amended the text as:

"Least-square fit was performed with the domestic code in Python, using the
`optimize.curve_fit` function of the `scipy` library."

You said:

"Line 85: Please explain better how the data digitization was done."

Accepted. We have amended the text as:

"For digitization we took the graphs from the original papers and uploaded to online digitization tool system [13] that is an opensource software leveraging computer vision technology to assist in extracting numerical data from images, including plots, maps, and various other visual materials. WebPlotDigitizer ensures an accurate data extraction of information by employing a combination of computer vision algorithms and manual techniques."

You said:

"Line 95: Explain how you obtained these histograms or provide a reference."

Accepted. We have amended the text as:

"However, it is not clear, what would be the statistical consequences
of using the approximate formula while processing a dataset of experimental points. In order to study the statistical quantitative similarity, in Fig. 2 we compare the histograms of fitted parameters and their mean values for 33 proteins in Table 1. Histograms were constructed with a domestic code in Python, with the help of `histogram` function of the `numpy` library."

We are grateful for your constructive criticism, which we believe improved the quality and readability of our manuscript.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I understand the replies of the authors, and I agree that the investigation has its own merit. Nevertheless, the authors should be well aware that the transition interval (I would say the width in temperature of a DSC peak), for a reversible two-state process, depends on the value of the denaturation temperature and the value of the denaturation enthalpy change. So, the authors could add something on this point to the present version of the ms.

Comments on the Quality of English Language

The quality of the English Language is satisfactory for me.

Author Response

Dear Reviewer,

Thank you for the useful comment!

Following your suggestion, we have performed the estimate of transition intervals and can show now that although they are different (from 0.02 to 0.1), they remain small and thus justify the application of series expansion. We have added a paragraph at the end of Discussion and results section, and a figure.

Thanks for your comment once more.

Sincerely,

A. Badasyan

Reviewer 2 Report

Comments and Suggestions for Authors

The paper now has a satisfactory quality to be accepted for publication in the journal Biophysica.

Author Response

Dear Reviewer,

Many thanks for your useful comments which we believe improved the quality of our paper.

Sincerely,

A. Badasyan