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\begin{center}
{\bf  Responses to reviewers:}
\end{center}


We would like to thank the referee for their additional constructive
comments.  We briefly address our changes in response to the referee
comments below.\\

{\color{blue} {\bf  Reviewer \#2}}

{\color{blue} (1) The current reviewer recommends publication in JCP
  mainly because the response to comment (1) is satisfactory. But the
  sentence in the response to comment (1) that is mentioned to have
  been introduced in the text is not the same as the one actually in
  red in the text. The first sentence is much clearer for the current
  reviewer so it is advised to use this one.
 
One concern of the current reviewer regarding ``many sweeps of
neighbor exchange'' was that the authors produce very interesting and
original results on this aspect, such that, if it is ``indeed
essentially identical'' to the new method, readers who already use
replica exchange may very well prefer to try this approach and not the
new method.  The term ``consecutive passes'' was correctly understood
by the authors.  } \\

We thank the referee for suggesting the phrasing in the response
letter rather than in the manuscript.  We have changed the manuscript
text to reflect the version of this sentence that the referee found
clearer.  We have also further edited this section to read more
clearly.  The use of multiple consecutive passes of standard neighbor
exchange could indeed be a more straightforward way to implement the
sampling improvement we describe into existing codebases, though the
rate of convergence may differ from the random swap algorithm we
initially suggest---we note this in our manuscript revision.  We hope
future theoretical work will be able to determine which approaches are
more efficient. \\

 
{\color{blue} (2) The results proposed in the current manuscript are
  of high value and sophisticated enough for a complete story
  indeed. Based on his own experience, the current reviewer believes
  that the story will be entirely different for complex biomolecular
  systems. The authors are in the process of examining the approach in
  the context of peptide folding. Serious candidates for using the new
  method will look forward such results.  } \\

We thank the referee for agreeing that the illustrations presented in
the current manuscript are sufficiently intriguing to warrant
publication. \\

{\color{blue} (3) The authors have replied satisfactorily to the
  comments concerning history dependence and made appropriate changes
  in the text (not marked in red though). } \\

We apologize for neglecting to highlight the changed text in red, but
are happy the reviewer liked our changes. \\
 
{\color{blue} (4) 
 Good (note the missing capital letter at the beginning of the sentence in red page 3). } \\

We have corrected this typo.

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