\documentclass[10pt]{letter}
\address{
John D. Chodera\\
QB3 Institute\\
260J Stanley Hall \#3220\\
University of California\\
Berkeley, CA 94720-3220, USA \\
phone: 415.867.7384\\
email: \href{mailto:jchodera@berkeley.edu}{jchodera@berkeley.edu}\\
\name{John D. Chodera}
}

\signature{
\resizebox{2.5in}{!}{\includegraphics{JDC-signature}} \\
John D.~Chodera, corresponding author
} 

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\begin{document}
\begin{letter}{Marsha I. Lester, Editor\\
\emph{The Journal of Chemical Physics}\\
Department of Chemistry\\
University of Pennsylvania\\
231 S.~34th St.\\
Philadelphia, PA 19104-6323, USA}

\opening{Dear Editor,}

We are submitting a revised form of the following manuscript for publication as a {\bf full length article} in the Journal of the Chemical Physics:

{\bf Dynamical reweighting: Improved estimates of dynamical properties from simulations at multiple temperatures} by John D.~Chodera, William C.~Swope, Frank No\'{e}, Jan-Hendrik Prinz, Michael R.~Shirts, and Vijay S.~Pande.

We thank referee \#2 for his helpful optional comments.  
We have made revisions in response to these requests.
Changes in the manuscript are colored red for convenience of review.

We ask that this manuscript be considered for back-to-back publication in the same issue with another manuscript concurrently in review at JCP [{\bf Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics}, by Jan-Hendrik Prinz, John D.~Chodera, Vijay S.~Pande, William C.~Swope, Jeremy C.~Smith, and Frank No\'{e}], since the included manuscript provides the theoretical groundwork for the estimator used in this companion paper.

We describe our changes in response to referee comments below.

\color{blue}
Reviewer \#2 (Comments to the Author): 

The authors have addressed carefully most questions raised by the original manuscript. The manuscript is now suitable for publication in JCP. A few minor/optional suggestions: 

1.- The two panels for the bias and variance in Fig 3 are plotted too small. 

\color{black}
We have made this figure (actually numbered Figure 4) a full-page figure in order to enlarge the bias and variance panels.

\color{blue}
2.- The authors are explaining now how are their replicas geometrically-spaced in T (page 9), but they may also wish to explain why did they make this specific choice. Is this better than other possible optimized T-spacing methods proposed for replica exchange? 

\color{black}
We make no claims as to the optimality of this choice of temperature spacing, and have modified the manuscript to make this clear, adding citations to published algorithms to adapt the temperatures to achieve more optimal spacing.
The geometric choice is motivated by a simple argument based on the heat capacity of an ideal gas, but the optimal spacing of temperatures for complex systems may very well differ from this choice; it was simply a convenient initial choice.

\color{blue}
3.- Fig 5 seems confusing. According to its interpretation in the text (page 12): "After the target temperature, neighboring temperatures contribute the most trajectory weight to averages at the target temperature, with the contribution rapidly falling off for more distant temperatures." This statement/result seems to be against the typical motivation of using simulations at different temperatures (i.e., to use data from temperatures as distant as possible from the target temperature in order to improve the estimates at the target temperature). The authors may wish to clarify this apparent contradiction. 

\color{black}
The usual motivation for using a parallel tempering simulation spanning a large range of temperatures either (1) to extract temperature-dependent properties across a range of temperatures, or (2) to couple in very high temperatures where correlations are short, so as to artificially reduce the correlation time for sampling lower temperatures of interest. 
However, in reweighting the data collected from all temperatures, samples from thermodynamic states closest to the temperature of interest contribute the most statistical weight.  
There is no conflict or contradiction here.  
We have added a note to clarify this issue in the manuscript.

\closing{Kind regards,}
\end{letter}
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