[gmx-users] REMD: average potential energy as a function of temperatue

[Mark Abraham]

Robert Johnson wrote:
> Hello Pascal,
> I'm not sure I can really comment on (1), but the reason why your
> energy gap decreases in (2) is because the energy fluctuations in your
> system increase as you raise the temperature. For example, at low
> temperatures your potential energy distributions will be sharply
> peaked about the average value. However, as you increase the
> temperature, the peak will broaden because of the increased thermal
> fluctuations. As a result, you will have more overlap between your
> potential energy distributions at higher temperature.

What Bob says is true, but Pascal was talking about

> the gap between average potential energies

which is not directly dependent of the shape of the distribution.

> On Tue, May 6, 2008 at 9:50 AM,  <pascal.baillod at epfl.ch> wrote:
>> Dear community,
>>
>>  I am performing some REMD tests with the trp-cage peptide. In order to figure
>>  out the optimal temperature distribution ensuring similar exchange probabilities
>>  at every temperature, I have performed short MD runs at increasing temperatures,
>>  with a run every 5K from 300K to 500K. If I plot the average potential energy as
>>  a function of temperature, I obtain the following trend:
>>
>>  1) For NPT, the gap between average potential energies progressively increases
>>  with equal increments of temperature.
>>
>>  2) For NVT, the gap between average potential energies progressively decreases
>>  with equal increments temperature.

You seem to be in qualitative agreement with Figure 1 of

M Marvin Seibert, Alexandra Patriksson, Berk Hess and David van der 
Spoel (2005).
Reproducible Polypeptide Folding and Structure Prediction using 
Molecular Dynamics Simulations.
Journal of Molecular Biology, 354(1):173-183

Figures 4 and 5 of

Daniel Sindhikara, Yilin Meng and Adrian E Roitberg (2008).
Exchange frequency in replica exchange molecular dynamics.
Journal of Chemical Physics, 128(2):024103.

show linearity for a wide range of temperatures, however they use a GB 
solvent model.

>>  I also read a very interesting paper on this issue:
>>  Alexandra Patriksson and David van der Spoel, A temperature predictor for
>>  parallel tempering simulations Phys. Chem. Chem. Phys., 10 pp. 2073-2077 (2008)
>>
>>  The temperature predictor works with a set of parameters obtained from a number
>>  of simulations of different proteins at different temperatures. Among the test
>>  proteins, the Trp-cage peptide is also used, but the authors describe a linear
>>  function for average potential energy as a function of temperature. However,
>>  this result was obtained in the 284 to the 330K range, and my results also
>>  appear linear in this domain.
>>
>>  As far as I understand, potential energy should scale with the number of degrees
>>  of freedom f and temperature T:
>>
>>  Epot_{avg} ~= f k_B T    (k_B is Boltzmann's constant)
>>
>>  Could anybody explain to me why the relation I obtain in 1) and 2) here above
>>  are not linear? Is the linearity broken from a higher threshhold temperature,
>>  for which force field parameters are not designed, onwards?

How non-linear are they? I'd expect that such non-linearity is useful 
evidence of the non-transferability of force fields to high 
temperatures. All of my REMD simulations use a maximum T around 
350-360K, so I figure my average energies won't say much of anything.

I'd expect some serious distortion in Epot_{avg} for NVT at high T, 
because now the pressure is far too large to match the parameterization 
conditions. This forms much of the argument for doing NPT-REMD, as made 
in Seibert, et al. above.

Mark