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% Title:    A LaTeX Template For Responses To a Referees' Reports
% Author:   Petr Zemek <s3rvac@gmail.com>
% Homepage: https://blog.petrzemek.net/2016/07/17/latex-template-for-responses-to-referees-reports/
% License:  CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
\documentclass[10pt]{article}
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\usepackage[margin=1in]{geometry}
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% Allow Unicode input (alternatively, you can use XeLaTeX or LuaLaTeX)
\usepackage[utf8]{inputenc}

\usepackage{microtype,xparse,tcolorbox}
\newenvironment{reviewer-comment }{}{}
\tcbuselibrary{skins}
\tcolorboxenvironment{reviewer-comment }{empty,
  left = 1em, top = 1ex, bottom = 1ex,
  borderline west = {2pt} {0pt} {black!20},
}
\ExplSyntaxOn
\NewDocumentEnvironment {response} { +m O{black!20} } {
  \IfValueT {#1} {
    \begin{reviewer-comment~}
      \setlength\parindent{2em}
      \noindent
      \ttfamily #1
    \end{reviewer-comment~}
  }
  \par\noindent\ignorespaces
} { \bigskip\par }

\NewDocumentCommand \Reviewer { m } {
  \section*{Comments~by~Reviewer~#1}
}
\ExplSyntaxOff
\AtBeginDocument{\maketitle\thispagestyle{empty}\noindent}

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\title{Appeal to the decision on ``The necessary emergence of structural complexity in self-replicating RNA populations''}
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\author{C. Oliver \and V. Reinharz \and J. Waldisp\"{u}hl}
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\date{\today}

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% Customizations
\usepackage[super,comma,numbers]{natbib}
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\usepackage{xcolor}
\usepackage{xspace}
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\usepackage{tikz}
\usetikzlibrary{shadows}

%% tags

\tikzstyle{bluetagstyle} = [rectangle, fill = blue!30, draw = black, drop shadow, font={\sffamily\bfseries}, text=black]
\tikzstyle{greentagstyle} = [rectangle, fill = green!30, draw = black, drop shadow, font={\sffamily\bfseries}, text=black]
\tikzstyle{redtagstyle} = [rectangle, fill = red!30, draw = black, drop shadow, font={\sffamily\bfseries}, text=black]
\tikzstyle{yellowtagstyle} = [rectangle, fill = yellow!30, draw = black, drop shadow, font={\sffamily\bfseries}, text=black]

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\newcommand{\claimstag}{\tikz{\node[bluetagstyle] {Claims};}\xspace}
\newcommand{\hypothesistag}{\tikz{\node[greentagstyle] {Hypothesis};}\xspace}
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\newcommand{\experimentstag}{\tikz{\node[redtagstyle] {Experiments};}\xspace}
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\newcommand{\methodstag}{\tikz{\node[yellowtagstyle] {Methods};}\xspace}
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\newcommand{\maternal}{\texttt{MateRNAl}\xspace}
\newcommand{\rnamutants}{\texttt{RNAmutants}\xspace}
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\newcommand{\rnafold}{\texttt{RNAfold}\xspace}
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\begin{document}

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First of all, we would like to thank the reviewers for their careful review of our manuscript and precise comments. We do appreciate the time invested in reviewing our manuscript and quality of their remarks.\\
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However, we believe that misunderstandings of our methodologies and claims may have negatively altered the editorial decision. We take full responsibility for any ambiguity. Although, we would like to stress that \textbf{our hypothesis and findings are already strikingly inline with most of the reviewer comments}. For this reason, we believe that a clarification of our methodology and claims could motivate a positive re-evaluation of the impact of our work, and the possibility to re-submit a revised version of our manuscript.\\
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In this letter, we clarify these misunderstandings and highlight key arguments that might have been missed in our original manuscript. Before addressing all comments, we remind the scenarios explored in our study:
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\begin{enumerate}
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\item \textbf{Search:} A natural selection process eliciting sequences with stable structures. This model has been implemented in a software called \maternal. Our simulation shows that this model does not have desired properties and importantly \textbf{we do not support this hypothesis}. 
\item \textbf{Discovery:} A random replication model that is shown to favor the emergence of complex structures at specific GC content regimes. \textbf{Our simulations support this hypothesis}.
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\end{enumerate}
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Importantly, we did not investigate natural selection scenarios based on the fitness of a population to target(s) phenotype(s). It has been extensively studied in the past \cite{???}, and we justified this choice in the introduction (page ???).\\ 

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We identified four major misunderstandings that likely resulted in a low appreciation of our work.\\
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\claimstag There is a misunderstanding of the claims made in this manuscript. In particular, as stated on page~5, we do not advocate for an energy-based natural selection model (i.e. \maternal). Instead, we support the hypothesis that RNA were randomly replicated and that stable complex structures have been spontaneously discovered (See page~4).\\
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\experimentstag Results and discussions of experiments conducted with an uniform sampling model appears to have been (unintentionally) overlooked (See Fig.~6).\\
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\hypothesistag The principles of the evolutionary scenario supported in this study have not been correctly interpreted. It might results from a misunderstanding of the \rnamutants algorithm \cite{Waldispuhl:2008aa} used in this study.\\
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\methodstag The principles and output of \rnamutants \cite{Waldispuhl:2008aa}, which has been used to characterized the energy landscape, are misundertood.\\
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We strongly believe that the misunderstandings cited above can be easily clarified in a revised version of the manuscript. Please, find below our detailed answers to the reviewers.
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%%% REVIEWER 1

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\Reviewer{\#1}

\begin{response}{
It is assumed that there is selection to favour sequences with a low folding energy. There is no biological motivation for this. Maybe thermodynamically stable folders are supposed to be more stable against hydrolysis, and therefore have a longer life time? But what about replication - maybe too stable a structure prevents replication. It is not clear that fitness always increases when the folding gets more stable.}
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\claimstag We do not advocate for a natural selection scenario selecting sequences with low energy structure simulated with \maternal (See page~5). We included it to show that this model struggles to generate complex structures. Hence, we do agree with the remark: ``It is not clear that fitness always increases when the folding gets more stable''. By contrast, we suggest that under GC content bias random replications (with errors) are likely to \textbf{discover} complex structures with low folding energy (See page 4). Our claims are thus in agreement with this comment. We will emphasize our claims. 
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\end{response}


\begin{response}{
One of the main conclusions (Discussion, p14) is that intermediate GC content allows for generation of sequences with the highest frequency of complex structures. This sounds reasonable, but these sequences would arise anyway if the mutation GC frequency was 0.5 and there was no selection for low folding energy. It is only because the authors select for low folding energy that the GC frequency goes up, and it is then necessary to put an additional constraint to maintain the GC frequency close to 0.5. Thus it is not clear whether this property in the real world arises by mutation or selection (see my comment below related to section 4.1.3).}
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\claimstag As in the previous comment, we respectfully believe that the reviewer misinterpreted our claims. Our proposed model of evolution does not select low energy structures. Instead, as suggested by the reviewer, we propose that RNA got randomly replicated and that stable complex structures have been spontaneously discovered. We believe that our claims are in agreement with this remark.
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\end{response}


\begin{response}{
The effect of GC is seen in Fig 4a, for example, where the yellow curve for GC = 0.5 is the highest. But this could have been shown much more simply by just generating many random sequences with a given GC content and measuring what fraction of these sequences has a multi-branched structure. I am not clear why the number of mutations k is important for this point.}
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\experimentstag We already performed the experiment suggested by the reviewer in Figure~6 (dotted lines). There, we uniformly sampled sequences and separately plotted the MFE of structures with and without multi-loops (first row), and frequency of multi-branched structures (second row). We note that the average MFEs are comparable and high (i.e. less stable). Moreover, multi-branched structures also appear to not be uncommon in uniform samples.\\
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However, it was not clear if the same phenomenon holds true when we focus our analysis to low energy structures (i.e. the ones that are stable enough to carry functions). For this reason, we used \rnamutants to show that sampling shows that the ensemble of low energy structures is enriched with multi-branched structures at GC content bias of 0.3-0.5. Interestingly, it is not the case in the immediate vicinity of random sequences. Instead, mutants have to significantly move away from the initial seed to increase the likelihood to discover stable multi-branched structures.\\
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Variations of the number of mutations k is used to study properties of the local and global neighbourhoods. 
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\end{response}


\begin{response}{
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In general, I am confused by the concentric ring structure for the sampling. I agree that if we take one starting sequence w0, then the properties of the sequences at distance k from this point will depend on w0. However, if we average over many starting points, it is not clear why the distance k should matter. Every sequence will contribute to every ring after averaging over the starting points. So why are the results in 3a 3b 4a etc not independent of k? The answer to this question has something to do with the fact there is a different normalizing Z for each ring and for each starting point. I am not sure of the validity of normalizing these rings separately for every starting point. I cannot understand this either from the statistical physics viewpoint (this is not really a proper thermodynamic ensemble) or from the biological viewpoint (there is not a true model of mutation and selection). This needs to be justified or motivated better, because many of the results depend on the way this is done.}
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\hypothesistag Variations of the number of mutations k is used to study properties of the local and global neighbourhoods. The impact of varying sizes of the neighbourhoods is discussed in Section~2.4 and eventually illustrated in Figure~5. At large mutational distances, the occurrence of stable multi-loops could be attributed to larger diversity of available RNA architectures (defined as shape coverage in \cite{??}). Figure~6 (second row) does not support this claim in the uniform model (dotted lines). By contrast, the frequency of stable multi-loops increases with the growth of structural diversity (plain lines). Although, we are puzzled by this comment because we do not normalize rings as suggested by the reviewer. \\
We hypothesize that this misunderstanding may originate from the description of \rnamutants in Section~2.1 and Section~4.2, which has been used to identify stable structures available in the energy landscape. Eventually, this misunderstanding appears to be related to typos in Section~4.2 that were kindly reported by the reviewer (see below), and most likely prevented a complete understanding of our techniques. We believe that improving the clarity of  Section~2.1 and fixing typos in Section~4.2 will address these concerns.
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\end{response}


\begin{response}{
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It is said that selection for low folding energy drives sequences towards high GC content and low frequency of multi-branched loops. So what if you select for high folding energy (i.e. less negative)? Is this sufficient on its own to generate large numbers of multi-branched loops?\\
I would suggest the following simple sampling method would be useful:\\
- generate many sequences at random with GC content in each of the five bins from 0.1 to 0.9.\\
- find the MFE for each sequence and then bin them according to MFE using 5 bins.\\
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- Now measure properties as a function of MFE and GC content and plot frequencies of multibranched loops on this 5 x 5 array of bins. Does this depend on both properties or just on MFE?}
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\claimstag We do not apply or suggest that any selection mechanism is at play. On the contrary, we showed with \maternal that it would result in lower structural diversity and most importantly prevent the discovery of multi-branched structures. We also believe that experiences on random sequences (uniformly sampled) in Figure~6 already address these comments. 
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\end{response}


\begin{response}{
Section 4.1.1 - The notation S\_t+1 appears at the end of this section without definition. Should this be P\_t+1?}
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The reviewer is correct. It is has been fixed in the manuscript. 
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\end{response}


\begin{response}{
Section 4.1.2 - R has units of kcal mol-1 K-1 (which are not stated). Then RT = 0.06 kcal/mol. Although it seems reasonable to use this RT in the selection function, there is of course no reason why fitness has to depend on the Boltzmann factor. Use of beta in this equation is potentially confusing because often beta = 1/kT, and you have a 1/RT already. Maybe call beta something else, or just miss beta out of the equation. Later in this paragraph - shouldn't it be beta = +1 not -1, because more negative E means higher fitness? There is already a minus sign in the equation.}
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The units of R are stated in the paragraph following the fitness function. The use of RT in the fitness function was to scale fitness in a way that could be readily compared with \texttt{RNAmutants}. The use of $\beta=-1$ is necessary as energy values are either zero or negative. If $\beta = +1$ then the exponent would remain negative and a more negative energy would then result in a lower fitness structure. 
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\end{response}


\begin{response}{
Section 4.1.3 - GC content is maintained by an algorithm associated with mutation. However, this is more similar to selection than mutation. It would be possible to generate new mutant bases with probability controlled by the target GC (theta in the Tamura matrix later in the paper). Then mutation defines the GC content and selection may cause a bias away from theta. The extent to which the observed GC content moves away from theta is a measure of how strong selection is relative to mutation rate. In population genetics it is often interesting to know whether a property arises as the result of mutation or selection. In this model, mutation and selection are not clearly distinguished.
Another funny thing about the algorithm is the while loop. This means that no sequences outside the GC range are ever born. It would be more natural to create sequences by random mutation (for example by the Tamura matrix) and then assign them zero fitness if they are outside the range, so that they cannot be parents for the next generation. The latter seems more reasonable biologically - natural selection cannot tell if something is fit until it exists.}
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\claimstag This comment appears to discuss the properties of \maternal, which is not the hypothesis supported in our study. Nonetheless, we remind that we adapted our algorithm from techniques previously used by other groups \cite{???}.
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\end{response}


\begin{response}{
Section 4.2 - Should it be "where w is also a k-mutant of w0" not "where s' is also a k-mutant of w0"?}
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The reviewer is correct. It is has been fixed in the manuscript. 
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\end{response}


\begin{response}{
Section 4.2 A few lines down - "the structure sampled is not in general the MFE". I have not understood what the structure is when it is not the MFE structure of the sequence. How are the suboptimal structures of the sequence determined? The same question applies for the definition of Z on p19. In the sum for Z, are there many structures s' for each w'? What set of structures is allowed?}
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\methodstag It comes to the root of the \rnamutants algorithm \cite{Waldispuhl:2008aa}, which generalizes the \texttt{mfold} algorithm \cite{Zuker:1981aa} to mutant searches. Using dynamic programming techniques, mutants are mapped to all valid nested secondary structures (i.e. without pseudo-knot). Then, using a similar backtracking procedure as the one introduced in \texttt{Sfold} \cite{Ding:1999aa}, we sample pairs of mutant sequences and structures $(s,S)$ with a probability determined by the folding energy of $S$ on $s$. Sampling only MFE structures would require to guarantee their optimality, and require an exhaustive enumeration of all pair of sequences and MFE structures that breaks the dynamic programming scheme. Brute-force approaches are impossible to conduct on sequences of size 50, which is why previous exhaustive studies were limited to small sequences.
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\end{response}

\begin{response}{
Just after the Z equation it says a pair (l,w), but the equation is for P(w,s). Is this a mistake?}
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Yes. We thank the reviewer for this observation that has been fixed in the revised manuscript.
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\end{response}

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%%% REVIEWER 2
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\Reviewer{\#2}

\begin{response}{
In this work the authors explore the space of RNA sequences of length 50 through random sampling and through an evolutionary algorithm. They characterize some structural properties of the corresponding secondary structures paying attention in particular to the folding energy and to the GC content. This is a computationally intensive work that relies on efficient algorithms previously developed by the senior author of this work and other co-workers. While I do not have any technical objection to this study, I have found have major conceptual issues regarding the context and motivation of the study and the interpretation of the results.}
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\methodstag We believe that a misunderstanding of the purpose and output of \rnamutants~\cite{Waldispuhl:2008aa} led to misinterpretation of the results and impact of our work. First, in order to remove any ambiguity, we emphasize that \rnamutants does not sample mutants from a uniform distribution. Instead it extracts in priority mutants folding into stable structures (See Section~4.2). This enabled us to characterize the distribution of stable structure in the mutational landscape.
\end{response}

\begin{response}{
My main criticism regards the ``distinct region of the sequence landscape enriched with multi-branched structures''. I do not see in which sense is this ``region'' special, and in my opinion the ms does not clarify this point. To begin with, the authors probably know that the abundance of structural motifs in (minimum free energy) RNA secondary structures varies with the length of the sequence. This is why short sequences are rich in hairpins and poor in multi-loops, which start to be frequent and lengths about 50, and become unavoidable for longer RNA sequences.}
\experimentstag We do agree. In fact, the data presented in Figure~6 (uniformly sampled sequences represented in dotted lines) already illustrates this claim.
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\begin{response}{
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The discussion in the ms is confusing at several points because different lengths are mixed to discuss what is typical and what is not. In the absence of energetic considerations, the abundance of any structural motif converges to a Gaussian distribution for sufficiently long sequences (50 is already sufficiently long), and therefore typical shapes exist and can be defined. Check for instance Nebel, M.E., 2002. Combinatorial properties of RNA secondary structures. J. Comp. Biol. 9, 541?573 or Poznanovi?, S., Heitsch, C.E., 2014. Asymptotic distribution of motifs in a stochastic context-free grammar model of RNA folding. J. Math. Biol. 69, 1743?1772. In the light of those results the main question is: in which sense do structures in the "distinct region" differ from typical structures at those lengths? Can be those differences, if present at all, be ascribed to selection for low-energy folds? How are those results related to the apparent lack of structural selection identified by other authors (their ref. [18]), where most abundant structures seem to be the ones found in non-coding RNA databases? This main criticism takes different forms along the ms and in the light of a number of statements and interpretations, as follows.}
\methodstag 
We agree with the reviewer that if the sampling was random then those results would hold. But as discussed previously it is not random but instead a weighted sampling.
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\end{response}

\begin{response}{
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Page 1. "Non-coding RNAs acquire functions through complex structures." What is the basis for this claim? Do viroids have complex structures?}
\hypothesistag While definition of complex structure is still vague, we argue that multiloops are one of the important and easily identifiable features. 
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The basis is how quickly and often they appear in consensus structure of RFAM families at short lengths, as shown in Fig.1. 
Viroids by themselves are an interesting example which have different  replication mechanisms depending of relatively subtle changes in structures (Structural differences within the loop E-motif imply alternative mechanisms of viroid processing, RNA 2007. 13: 824-834).
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\begin{response}{
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Page 2, last paragraph: In which sense are nucleic acids with complex shapes supporting essential molecular functions? Are these structures really complex (in relation to typical or 1-sigma structures of their size)? Is the existence of a multi-loop a signature of complexity?}
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\hypothesistag From an energetic point of view, multiloops ~\cite{???} have a much weaker contribution than other conformations. 
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We can  consider their conservation as a signature of complexity  given their destabilizing effect.
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\begin{response}{
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Page 3. Comparison with shorter structures has to be done consistently, it is not acceptable to justify the interest of looking for multi-branched structures referring to works that analyzed shorter sequences  and in consequence did not find them. Also, the statement on how size and connectivity of neutral networks decreases with the complexity of the structure has to be related not to complexity, but to abundant or rare structures at a given length.}
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\hypothesistag Due to the lack of experiments and theoretical results for sequences of  size 50 we can only extrapolate from previous results. 
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At the same time, there is a clear conservation of multiloops in rfam families starting at lengths of around 50 nts.   
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\begin{response}{
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Page 4 to 5. I am puzzled by this region located at a distance of 30 to 40 mutations from a random sequence?. Where is it located, in terms of the space of sequences? Is this region not constituted itself by random sequences as a result of the very process to generate them? If they are not, which is the special property that cause their deviation from randomness? This would be essential to know.}
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\methodstag As mentioned the sampled sequences are not random but sampled given the energy of all pairs sequence-structure at hamming distance exactly $k$ from the random wild type. 
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\end{response}

\begin{response}{
Page 5. Exhaustive folding of sequences longer than 20 nucleotides has been achieved by the Vienna group with two-letter alphabets, probably more recently by other people. Provide references and be precise.}
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Additional citations as \cite{???} will be included
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\begin{response}{
Page 7. A fixed number of sequence-structure pairs is sampled at each mutational distance. How can we be sure that results do not depend on the relative size of the sample with respect to the total number of available sequences? Is it just a coincidence that the largest number of sequences occurs for a GC content of 50\% and at a distance of 35 mutations from any sequence (figure S7)? Though extremely intensive, the exploration performed here is very far from being exhaustive, so results could be easily biased (there are multiple examples of such deviations in the literature due to the vastness of the genotype space).}
Voila
\end{response}

\begin{response}{
End of first paragraph in section 2.2 and later: This statement repeats a well-known effect in evolution: it has a much higher canalization of the search process, is much faster and, unavoidably, discards most alternatives when compared to random sampling.}
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We agree with this comment. However, we do not understand the request. We could obviously add a reference if that is the purpose of this comment.
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\begin{response}{
Page 8 and all through the ms. Higher GC content has the straight implication of yielding more stable structures. It seems to me that at certain points it is presented as a surprising observation, while, the other way round, I think it helps understanding the results. Later, ?This sudden and unexpected change of regime...?. What would be the expectation? End of page: again, results for RNAs of different lengths are being compared, and that is nonsense.}
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\experimentstag The expectation would be a slow increase in the diversity roughly with not as much difference in the mutational distance between the different GC contents. 
As of page 8, we are showing length 50 seems to be critical for this increase of diversity which have not been observed in experiments of smaller size. 
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Page 9. ?... at distances at a mutational distance of about 35.?, and later ?We revealed that multi- branched structures reside in specific regions of the mutational landscape at fixed mutational distances...?. Beyond the ?randomness? (or not) of that region, I fear it could be a result of the number of sequences/structures sampled at each mutational distance. To demonstrate this is not the case, the authors must better explore the correlation between energy of folding and multi-branched structures. For example, at a fixed mutation of ten substitutions from the random sequence, how is the multi-loop content depending on the number of sequences sampled, and therefore on the chosen set of low- energy structures (as in Fig. 4)? Figure 4 is also confusing. Are panels b), c) and d) including all sequences probed, at any mutational distance? How can the complete set of multi-branched structures be compared? Again, it is essential to demonstrate that the quantitative results in Figure 4 are independent of the number of sequence-structure pairs sampled.}
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\experimentstag This is shown in Fig.6. where comparaisons between \rnamutants and random sampling is done.
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Page 10. "The selected structures are therefore by-products of intrinsic adaptive forces." I would say they are by-products of selection for low-energy folds, which is more precise and less involved.}
We agree with the suggested change and will update the sentence.
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Page 11. Here there are some very general statements based on very few simulations: ... variation to overcome energy barriers and obtain energies reached by RNAmutants.? The population used was quite small in comparison to natural ones, and no effort to study other population sizes has been made. It is known that, despite the canalization of evolutionary dynamics, the ability to overcome energy barriers is strongly dependent on the product of the population size times the mutation rate. The barrier disappears when this product is large enough.
Last paragraph. It is stated that their algorithm fails to generate the structural complexity found in real populations?. Which real populations are the authors comparing with? A single one? The complete database? Is this comparison sensible at sufficiently long evolutionary times (natural versus synthetic populations)? Why should selection for stability be the only pressure determining the observed natural structures?}
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\experimentstag We are confronted with technical limitations were length 50 is the upper limit for which we can conduct such an extensive search, which we compare with smaller size as seen in other papers~\cite{???}.
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typos    
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\claimstag We are comparing with the abundance of families with length around 50 which contain multiloops as shown in Fig.1. And we do not support the hypothesis that selection for stability is a good model since it does not correlate well with observations.   
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Page 12, end of first paragraph. Same objection as previously. Is the quantitative observation really surprising? I miss all across the ms a clear characterization of the "region of the sequence landscape enriched with multi-branched structures". As it stands, the easiest interpretation is that the region corresponds to the most abundant structures at length 50, and this region would not be generic for other parameters (as length or sampling size).}
Voila
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Page 14. Two interpretations are given to the presence of these structures, and here finally the authors converge to the simplest (and likely correct) explanation. First, they should know that rod-shaped folds are the most resilient architecture to point mutations (check the literature on viroids). The second option (that they are just observing the typical structure at a given length) is much more plausible ?also less fancy.}
Voila
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Page 15. I definitely disagree with the conclusion that ?Variations of the sizes of populations or lengths of RNA sequences (...) we do not expect any major impact on our conclusions? for all the reasons exposed.
Summarizing, I guess that the region of structural complexity (according to the definition of the authors) identified in these very large simulations does not depart from typical (understood as abundant) structures for RNA sequences of length 50. If this is so, this study does not contribute any advance with respect to previous works where typical structures have been analytically characterized for all lengths or where it has been demonstrated that non-coding natural RNA structures do belong to abundant folds and are, in this respect, dominated by entropic principles and not functional selection. The results here presented agree with previous findings and I cannot see its relevance in the context of the early stages of life. Therefore, I cannot recommend publication of this work.}
Voila
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add bib    
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\bibliographystyle{unsrtnat}
\bibliography{appeal.bib}
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\end{document}