# [gmx-users] HREX simulation

Michael Shirts mrshirts at gmail.com
Fri Aug 28 17:02:23 CEST 2015

```> I am new to doing replica exchange simulations.
> I am trying to understand the empirical transition matrix printed in the
> log files. I tried exchange intervals 2 ps and 0.2 ps. However, later I
> read gromacs recommends exchange interval not to be under 1ps.

I don't know that there are firm rules for this.  It seems like faster
exchange is generally better, up to a point (if there are specific
code reasons one might thing this is not the case, anyone else on the
list, speak up).

> the system is protein in water and I am only showing parts of the matrix:
>
> Exchange interval: 0.2 ps
> Repl            1            2            3            4             5
>
> Repl  0.9528  0.0472  0.0000  0.0000  0.0000
> Repl  0.0472  0.9017  0.0511  0.0000  0.0000
> Repl  0.0000  0.0511  0.8946  0.0543  0.0000
> Repl  0.0000  0.0000  0.0543  0.8898  0.0558
>
> 1. If I look at line 3 ""Repl  0.0472  0.9017  0.0511" does this mean
> exchange between replica 1, 2 is accepted 4.72 %  and exchange between 2,3
> is accepted 5.11 % ?

Yes.

> Repl            1            2            3            4             5
>
>
> Repl  0.9504  0.0496   0.0000  0.0000  0.0000
>
> Repl  0.0496  0.8982  0.0522   0.0000  0.0000
>
> Repl  0.0000  0.0522  0.8942  0.0536   0.0000
>
> Repl  0.0000  0.0000  0.0536  0.8888  0.0576
>
> 2. With exchange interval 2 ps, I am getting slightly better acceptance
> rate. For example, again looking at line 3 "Repl  0.0496  0.8982  0.0522"
> the acceptance rate for exchange 1 to 2 is 4.96 %, and he acceptance rate
> for exchange 2 to 3 is 5.22 %

Those are statistically insignificant results.  The success rate
exchange should not change as the interval changes, which is what you
are seeing, which is good.

You probably want to make your spacing narrower in order to improve
the exchange rate; otherwise, replicas move too slowly in state space.

The optimal rate depends on a few factors, but generally you want to
keep the diagonal around 0.60 to 0.70. not 0.9.  One minus the second
smallest eigenvalue of the transition matrix expressed the rate at
which the system moves in state space (see
http://scitation.aip.org/content/aip/journal/jcp/135/19/10.1063/1.3660669).
```