AMBER Archive (2008)Subject: Re: AMBER: comparison of MD trajectories recorded with pmemd and sander
From: Robert Duke (rduke_at_email.unc.edu)
Date: Wed Dec 17 2008  11:18:46 CST
Regarding changing the seed in langevin dynamics runs  this is very
important. One should absolutely be careful to do this to get valid
results, and this is not yet automated in pmemd (next release). Please see
Cerutti, Duke, et al, J Chem Theor Comp 4, 166980 (2008).
Regards  Bob
 Original Message 
From: "Ross Walker" <ross_at_rosswalker.co.uk>
To: <amber_at_scripps.edu>
Sent: Wednesday, December 17, 2008 12:01 PM
Subject: RE: AMBER: comparison of MD trajectories recorded with pmemd and
sander
> 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 forcefield, 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
>
> /\
> \/
> \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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