AMBER Archive (2008)

Subject: RE: AMBER: comparison of MD trajectories recorded with pmemd and sander

From: Ross Walker (ross_at_rosswalker.co.uk)
Date: Wed Dec 17 2008 - 11:01:37 CST

Hi Therese,

Bob and others can chime in some more here but I'll at least try to answer
your concerns.

> But, I am concerned by the following problem. Molecular modeling
> studies are often based on the comparison of MD trajectories run with
> several conditions. In that way, two sander trajectories are recorded
> with different conditions and compared. If one trajectory is recorded with
> pmemd, and the other with sander, is the comparison still meaningful?

Yes it is. PMEMD is designed to reproduce sander results by integrating the
AMBER equation over time. For approximately 500 steps or so it gets
identical results and then begins to diverge. However, this is NOT a problem
it is merely a limitation of computers not being exact in their
representation of floating point numbers. This is a function of Newton's
equations of motion being chaotic in nature. These equations are
deterministic which means that given the exact state of the particles in the
system at a given time one (in theory) can predict the position and momentum
of the particles at an arbitrary time t where t can be +ve or -ve. An
analytical solution to Newton's equations of motion for a many body system
does not exist and therefore one has to numerically integrate over time
which is what MD is doing. However, the key point is that given a starting
point that is infinitesimally different from the current starting point the
two trajectories will ultimately decorrelate - this is what it means to be
'chaotic'. So what this should tell you is that if computers cannot store
the initial condition (which actually has to be the condition after every
integration) to infinite precision then two trajectories will always
decorrelate. Neither is more wrong than the other they are just exploring
different regions of accessible phase space.

If you notice large differences between two simulations started from the
same conditions but run for example with different random seeds (or just
allowed to decorrelate through issues with numerical precision) then you
simply haven't sampled long enough.

Something to try. Run a sander simulation in parallel on 2 cpus. Then run
the exact same simulation on 8 cpus. You should see that the two
trajectories start to decorrelate after several thousand steps or so - this
is exactly the same thing that occurs with PMEMD, it is simply summing
things in different orders and this causes small changes (in the last
decimal place) due to the limited precision of computers and these small
changes propogate over time to give different trajectories.

The key point is that given a trajectory file there is no way you can
determine if it was run using sander or pmemd, they are essentially one and
the same thing.

Some groups, for example DE Shaw Research, have attempted to address the
issue of reproducibility by using fixed precision in their calculations,
this allows true time reversibility but also imposes a number of
restrictions on the types of calculations that can be done. For example the
number of particles, box size etc is limited by the range of your fixed
precision representation. Also some algorithms like shake, for example,
simply are not time reversible. The net result is that using this fixed
precision approach one can run the same simulation on different processor
counts (with different orders of summation) and get the same trajectory. It
is important to remember though that this has no impact whatsoever on the
'accuracy' of the simulation (or trajectory) it is simply an issue of
precision and the two are very different things. If you see a specific
movement in this 'reversible' trajectory it is no more meaningful than if
you did or did not see it in a trajectory that was not engineered to be
strictly reversible.

> Also, if one uses an additional trajectory recorded by CHARMM, GROMACS or
> NAMD with the AMBER force-field, will the pmemd trajectory be "closer" to
> the sander trajectory than the CHARMM, GROMACS or NAMD trajectory?

In theory they should all be the same - by which I mean if you have run long
enough the ensemble average properties should all be identical. Obviously
for the reasons discussed above the exact trajectories will not be
correlated! Now this of course raises the question of whether the AMBER
force field is correctly implemented in CHARMM, GROMACS or NAMD, I would
hope that it is but this of course is a completely different discussion...
 
> If two trajectories are recorded with pmemd and sander starting from the
> same input, should we consider that they are no more different than
> two trajectories recorded with the same program (sander or pmemd) but
> using different initial velocities?

Exactly!!! with the caveat that you can only really assume this (I believe)
beyond the correlation time of the system. How long does it take for the
velocities to 'forget' their initial values? This is the point at which you
can consider the trajectories to be independent as if they had been started
from different random seeds. To be honest though, you are safer using a
different random seed for every simulation you do. This is particularly true
with langevin dynamics, which for reasons too complex to go into here, it is
actually possible to do the reverse of above by using the same random number
stream in two simulations. That is you can potentially take two snapshots
from uncorrelated trajectories and then run them with Langevin and identical
random streams and cause them to correlate - obviously a totally artificial
situation.

> Another question is: let one suppose that a trajectory was recorded using
> alternatively sander and pmemd for different time intervals, in the
> following way: some ns with pmemd, then restart with keeping velocities
> and then additional ns with sander. Should the complete trajectory
> obtained with these different interval be considered as an "homogeneous"
> trajectory which can be analyzed as a whole?

Yes...
 
Good luck,
Ross

/\
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|\oss Walker

| Assistant Research Professor |
| San Diego Supercomputer Center |
| Tel: +1 858 822 0854 | EMail:- ross_at_rosswalker.co.uk |
| http://www.rosswalker.co.uk | PGP Key available on request |

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