From: Jason Swails (jason.swails_at_gmail.com)
Date: Thu Sep 19 2013 - 11:19:24 CDT
On Thu, Sep 19, 2013 at 11:53 AM, Francesco Pietra <chiendarret_at_gmail.com>wrote:
> Absolutely no. Each individual replica samples from the same pool.
> Therefore, if you do not get the same from each individual replica, this
> means no convergence. It might be difficult to get convergence but, if not
> obtained, it would be non scientific to go to "sortreplicas" to compute
> properties at the temperature of your interest.
>
> This is the way I understand T-remd. But I am prone to reeducate myself in
> the light of compelling reasoning. This was not the case so far.
>
Convergence is a tricky(ier) issue in REMD simulations (I'll direct my
discussion toward T-REMD, although it is generally applicable to other
variations).
REMD samples from an expanded ensemble composed of the typical
6N-dimensions of phase space (the standard statistical ensembles; I'll call
this conformation space), plus one or more thermodynamic state parameters
(for instance, the temperature; I'll call this state space). "Good"
replica exchange simulations will completely sample both state space and
conformation space. As Niklaus pointed out, converging conformation space
is difficult to do and impossible to prove. Converging state space is a
bit easier, since it is much smaller (typically not more than a couple
hundred states). [Of course, they are not completely independent, but
roughly speaking you can consider them to be separate sampling problems]
You can compare the properties of individual replicas (as they move through
state space) as one 'convergence' metric. Since all replicas sample from
the same expanded ensemble, their answers should all be the same (e.g., the
same RMSD distributions, the same average structure, same residence time in
at each thermodynamic state, etc.). If you see convergence here, however,
I would claim this is more of an indication that you converged in state
space, since each replica could be equally limited in its conformational
sampling at all temperatures. All the equivalence of the replicas shows is
that each replica is spending the same amount of time in the same
configurations at each temperature as every other replica.
You can use other metrics (like comparing chunks of the total simulation
and comparing properties from those) in order to support your claims of
conformational convergence (e.g., does the average structure from the first
half of the simulation match that of the second?). You can do these types
of analyses in the pre-sorted replicas (in which case the average
structures of all replicas for all time chunks should match), or the
post-sorted replicas if you want to talk about conformational convergence
within a particular sub-ensemble.
For certain REMD methods like T-REMD where 'higher' replicas can sample
more space (REXAMD is another example), it is much easier to converge the
conformational ensembles (to a satisfactory degree) of the sub-ensemble of
interest (e.g., low T or no boost factor) than it is to converge the (much
larger) conformational ensembles of the high-T or high-boost sub-ensembles.
So even if you do not see global conformational convergence in the
expanded ensemble, you can still be satisfied with what you see in the
subensemble of interest.
And thus ends my ramblings,
Jason
-- Jason M. Swails BioMaPS, Rutgers University Postdoctoral Researcher
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