# [gmx-users] REMD Statistics

Mark Abraham mark.j.abraham at gmail.com
Mon May 6 01:05:04 CEST 2013

```On Sun, May 5, 2013 at 5:14 PM, Kong xq <xqkong776 at gmail.com> wrote:

> Dear GMX users,
>
>     I have some concerns about the statistics analysis of REMD which do
>
>     I performed a 50ns isothermal-isobaric REMD simulation with 64 replicas
> spaning from 300K to 390K. Then I want to do some statistics analysis for
> the results. First, I calculated the acceptance ratio for the adjacent
> pairs of temperatures (showing below). It seems that most of the values are
> uniform ( 0.25 +/- 0.11) .

That is an abnormally high variation in my experience. That could suggest
lack of generalized equilibrium on this time scale.

> Second, I  followed the track of replica 1 in
> the temperature space with the information from replica_temp.xvg  generated
> by demux.pl(demux.pl md0.log) scipt. However, the histogram（table below)
> indicated that the distribution of replica 1 in temperature space is not
> very uniform. So my question is why did the nonuniform temperature
> distribution of replica 1 occur given the fact that the acceptance ratio
> indicated a free random walk in temperature space ?

The acceptance ratio is only a proxy for the existence of a random walk. It
would be an amusing exercise to construct a toy system with replicas that
would only exchange over a few adjacent temperatures. With suitable overlap
of replicas constrained-temperature subranges, you could synthesise uniform
exchange rates with no interesting replica flow. For example, if
* state A is possible in the lower two-thirds of your temperature range, and
* state B is possible in the upper two-thirds of your temperature range, and
* no other states are possible, and
* your initial configurations include examples of both A and B, and
* A and B have no available interconversion pathways,
then you can see apparently uniform neighbour exchange rates, and the REMD
simulation is probably not being very useful in the normal case of trying
to enhance statistics at the lowest temperature.

The possibility of this kind of kinetic trapping is discussed in the REMD
literature (including some rather old mentions). The extreme challenge of
actually achieving replica flow efficiently is discussed in a series of
papers from Nadler and Hansmann. Even spacing the temperatures for even
replica flow for met-enkephalin is not trivial.

What's more, whether a
> longer simulation was needed to make a more flatter temperature
> distribution for each replica?
>

Probably, but as above, not necessarily meaningful. It might be instructive
to construct some random walks following the GROMACS REMD protocal with
acceptance rate 0.25 and see whether your intuition is valid :-)

By the way, I want to double check that each column except the first in
> replica_temp.xvg represents a constant temperature corresponding to that
> specified in tpr file, we may need to follow the replica index (such as 0
> for the first replica) among different coloumns (or temperatures). Does
> this make sense?
>

Look at the first row and column, and back at the .log files to see what
exchanges take place. That's much better than trying a written description!

Mark

>
>    Best regards!
>
>    Xiangqian Kong
>
> *The frequency of replica 1 in temperature space *
> TemperatureFrequency31016.91%32011.58%33013.68%34013.79%35012.64%36011.60%
> 3704.38%3805.26%39010.16%
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```