Review Reports - The Finite Size Effects and Two-State Paradigm of Protein Folding

Round 1

Reviewer 1 Report

The authors nicely revisit concepts of protein folding, and its modelling. The paper well descibes what the authors did and a clear and concise manner. The only general point that I would like to raise is in relation to the applications of their revised model: addition of examples derived from literature or from specific collections would largely extend the interest towards the paper

A second (not necessary) point is to implement a folding prediction web server that would again greatly increase the exploitation of this work

Author Response

Dear Reviewer 1,

We have carefully considered and replied to your comments below and in the text of the manuscript.

Thank you!

Authors

--------------------------

Reviewer 1 says:
The authors nicely revisit concepts of protein folding, and its modelling. The paper well descibes what the authors did and a clear and concise manner.

AUTHORS: We appreciate the positive opinion of the Reviewer 1, thank you!

Reviewer 1 says:
The only general point that I would like to raise is in relation to the applications of their revised model: addition of examples derived from literature or from specific collections would largely extend the interest towards the paper

AUTHORS: We appreciate and accept the opinion of Reviewer 1. With respect to the point raised, we would like to stress once more, that we had done exactly what the respectful Reviewer 1 has mentioned. We took the dataset of Ref. [17] and performed its analysis using our approach. The whole text after Eq. 19 discusses the results of Lee et al in view of our finding.
In order to address the comment of the Reviewer 2 we have essentially re-written the text and figure captions to increase the readability and to stress:
a) the use of the dataset from Ref[17];
b) the statements of Ref[17] we oppose, and
c) the meaning of Figure 1.

Reviewer 1 says:

A second (not necessary) point is to implement a folding prediction web server that would again greatly increase the exploitation of this work.

AUTHORS: We are thankful to the Reviewer 1 for an interesting suggestion we might consider in the future.
However, the implementation of a web server will postpone the publication, and we will miss the deadlines for this Special Issue. Since Reviewer 1 has kindly mentioned the comment as "(not necessary)", we would consider it as such at this moment.

FINAL STATEMENT OF THE AUTHORS:
You can follow the changes colored green in the text.
We are grateful to the Reviewer for useful comments and hope that the manuscript will be found suitable for publication.

Reviewer 2 Report

Document attached.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 2,

We have carefully considered and replied to your comments below and in the text of the manuscript.

Thank you!

Authors

--------------------------

Reviewer 2 says:

In this paper, Badasyan et al., explain theoretically how the size of a protein (i.e.,
the number of residues comprising the polypeptide chain) is mathematically linked to
two cooperativity measures, and the derived physical consequences. The topic of the
paper is interesting, and it is well focused. There are some minor points to the opinion
of this reviewer that should be addressed for publication in IJMS

AUTHORS: We appreciate the positive opinion of the Reviewer 2 and address all the points. Details below.

Reviewer 2 says:

1. There are some parts that have to be better self-explanatory to a non-
accustomed reader of the field. I would suggest:
- In the abstract the Ω c is just written, without any explanation of what is the
magnitude about. Also, k 2 may be also defined for the reader.

AUTHORS:

Accepted. In the Abstract we have added the definition of k2 measure and mention the magnitude of Omega as growing with system sizes.
Changed part of text in Abstract reads now:

"We conclude that the $k_2$ measure, defined as the ratio of vant Hoff
and calorimetric enthalpy is related to the degeneracy of the
denatured state and describes the number of cooperative units involved in
the transition; additionally is found that the widely discussed $k_2=1$
is just the necessary condition to classify the protein as the
two-state folder. We also find that $\Omega_c$, a quantity not limited from above and growing with system sizes, is simply proportional
to the square of the transition interval."

Reviewer 2 says:

- f Dappr (Eq. 2) is simply not explained.

AUTHORS:

Accepted. Just before Eq. 2 we have changed the sentence to "Using the Taylor expansion
cut at first order, it is possible to approximate the order parameter as $f_D^{appr}$ with
the help of the tangent at transition point..."

Reviewer 2 says:
- In page 3, line just previous to 19, the authors state: “Excluding log g D from the
last expression...”. Why do the authors exclude that parameter in the expression?

AUTHORS:

Accepted. In order to clarify we have re-written the sentence to:
"The last expression can be rewritten as
\begin{equation} \label{priv}
E_D=\frac{4 {T_D}^2}{\Delta T},
\end{equation}
\noindent resulting in the famous expression for the energetic price of transition between the two states."

Reviewer 2 says:

- The plot in Figure 1 should be better described: it is replotted from Ref. 17, but
there is nothing of what is in Ref. 17, and the current manuscript should be readable
by itself, and not needing to see what is on one of the references. [This point might be
considered even as a major issue, since Figure 1 is critical for the manuscript,
according to this reviewer]

AUTHORS:

The whole text after Eq. 19 discusses the results of Lee et al in view of our finding.
We have essentially re-written the text and figure captions to increase the readability and to stress:
a) the use of the dataset from Ref[17];
b) the statements of Ref[17] we oppose, and
c) the meaning of Figure 1.

Reviewer 2 says:

2. There are a couple of formal aspects that should be taken care of:
- The disposition of the equations (5) to (10) is misleading. They should be
formatted in a better way.
- In page 5, 4 th paragraph, the authors write “Ist” and “IInd” in a sort of weird or
at least uncommon way. I would suggest to write “first” and “second”.

AUTHORS: Accepted and corrected.

Round 2

Reviewer 1 Report

The manuscript was revised according to my major criticisms