Reviewer #2 (Comments to the Author):
 
The authors describe some simple modifications for accelerating the mixing of
thermodynamic states during replica exchange and expanded ensemble
simulations. They show that swapping thermodynamic states at random leads to a
better sampling compared to standard swapping approaches such as nearest
neighbor swaps in replica exchange simulations. Model-systems on which they
demonstrate this include a large Lennard-Jones sphere and an alanine
dipeptide. The manuscript is well written and both sections reflect a deep
understanding of the problem.
 
(1) Several alternative modifications to improve mixing are suggested. Even if
the authors describe in details two methods easy to implement (Independence
Sampling and Metropolized Indep.), they also show the equivalence with a third
method that does not require any modification at all to the common algorithm
('nearest neighbor' repeated many times in a row). The simplest (third)
proposed modification will probably be more appealing to users of replica
exchange for example. In addition the reader may not understand, still after
the method section, why/how Independence Sampling could ever increase the
acceptance rate for exchanges of thermodynamic states compared to consecutive
passes of the neighbor exchange algorithm since the latter was set up (4-10,
74) for a maximum acceptance rate. On larger systems, users of replica
exchange will know that random swaps (exchange attempts between non-neighbors)
lead to unacceptably small acceptance rate. The authors should investigate or at 
least discuss this issue.
 
(2) The fundamental problem with the approach proposed in this manuscript is
that it has not been tested on complex systems with real application in
biology. The authors mention that typical correlation time for water
orientation is a few picoseconds, but this becomes much longer for non-trivial
coordinates that result from collective moves during molecular dynamics. The
authors mention that these collective moves might be disrupted by too frequent
changes in state space. It would be great to know if/when this is the case.
Systematic jumps from one thermodynamic state to the other should prevent some
key biomolecular processes to ever happen if (i) they have a slow relaxation
time and (ii) they occur in a narrow range of values of the thermodynamic
variables in question. The authors should investigate or carefully discuss
this issue. 
 
(3) "In the cases that proposal probabilities are based on past history
however, the algorithm will not preserve the equilibrium distribution" (p.4,
column 2): 
Later (p.5) the Metropolized Indep. scheme is described as a particular case
of Independence Sampling where the current state is removed from the subset of
allowed states for the next move. What then prevents from removing some
previously visited states in addition to the current one? Some recent work
(Bussi 2006, Roitberg 2007) indicates that history-based generalized ensemble
algorithms can be in equilibrium under particular setting (e.g.
infinitesimally small bias combined with stochastic replica exchanges, Bussi
2006). It might be better to remove this statement or else develop better the
conditions of ergodicity under which Metropolized Indep. works.
 
Bussi G, Gervasio FL, Laio A, Parrinello M (2006) Free-energy landscape for
β hairpin folding from combined parallel tempering and metadynamics. J.
Am. Chem. Soc. 128: 13435-41.
 
Roitberg AE, Okur A, Simmerling C (2007) Coupling of replica exchange
simulations to a non-Boltzmann structure reservoir. J. Phys. Chem. 111:
2415-18. 
 
(4) Typos :
- p.3, column 2 : closing bracket
after « walker » not opened.
- p.4, column 2 : (...) to sample in k or x depending according to
(...). 
- p.4, column 2 : closing bracket after ref. 71 not opened.
- p.5, column 2 : This scheme has the surprisingly property that,
(...). 
- p.6, column 1 : (...) even something simple as application of (...).
- p.7, column 2 : (...) an expanded ensembles (...).
- p.7, column 2 : « Nij is the number of times
(...) » should be « Nik is the number of times
(...) ».