@@ -32,7 +32,7 @@ Sequences in the initial population, i.e. generation $t=0$, are generated by sam

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@@ -32,7 +32,7 @@ Sequences in the initial population, i.e. generation $t=0$, are generated by sam

\subsubsection{Fitness Function}

\subsubsection{Fitness Function}

\label{sec:replication_selection}

\label{sec:replication_selection}

In order to obtain subsequent generations, we iterate through $S_{t}$ and sample 1000 sequences with replacement according to their relative fitness in the population. Selected sequences generate one offspring that is added to the next generation's population $S_{t+1}$. Because we are sampling with replacement, higher fitness sequences on average contribute more offspring than lower fitness sequences. The relative fitness, or reproduction probability of a sequence $\omega$ is defined as the probability $F(\omega, s)$ that $\omega$ will undergo replication and contribute one offspring to generation $t +1$. In previous studies, $F(\omega_{i}, s_i)$ has been typically defined as a function of the base pair distance between the MFE structure of $\omega$ and a given target structure$T$. However, in our model, this function is proportional to the free energy of the sequence-structure pair, $E(\omega, s)$ as computed by \texttt{RNAfold}.

In order to obtain subsequent generations, we iterate through $P_{t}$ and sample 1000 sequences with replacement according to their relative fitness in the population. Selected sequences generate one offspring that is added to the next generation's population $P_{t+1}$. Because we are sampling with replacement, higher fitness sequences on average contribute more offspring than lower fitness sequences. The relative fitness, or reproduction probability of a sequence $\omega$ is defined as the probability $F(\omega, s)$ that $\omega$ will undergo replication and contribute one offspring to generation $t +1$. In previous studies, $F(\omega_{i}, s_i)$ has been typically defined as a function of the base pair distance between the MFE structure of $\omega$ and a given target structure. However, in our model, this function is proportional to the free energy of the sequence-structure pair, $E(\omega, s)$ as computed by \texttt{RNAfold}.

@@ -139,7 +139,8 @@ The reviewer is correct. It is has been fixed in the manuscript.

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@@ -139,7 +139,8 @@ The reviewer is correct. It is has been fixed in the manuscript.

\begin{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.}

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.}

This algorithm has been routinely implemented by multiple groups that studied RNA evolution \cite{???}.

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.