AMBER Archive (2004)

Subject: Re: AMBER: performance of periodic vs. non-periodic simulation

From: Thomas E. Cheatham, III (
Date: Wed May 12 2004 - 15:17:33 CDT

> I am have tried to speed up my simulations by switching from a periodic
> system with PME to a non-periodic system with a cap of ~300 water
> I first used a non bonded cutoff of 12A for the non-periodic system.
> This lead to fluctuations of ~1000 to 2000 kcal/mol of the electrostatic
> energy (corresponding to 10% of the total energy) preventing equilibration.
> Using a cutoff larger than my system and switching off the update of the
> non-bonded pairlist solved this problem - but now the simulations are
> significantly slower than for the periodic system (details below).

This is primarily why most of the AMBER developers focus on improving PME
simulation rather than finite representations. The cutoff is really what
is killing you in terms of performance since it leads to a large number of
pair interactions. There is a big difference between 8/12/15 angstroms in
terms of the number of pairs; basically a 12 A cutoff is roughly 2x the
cost of a 8 A, and a 15 is > 3x more expensive. With PME, we typically
use a fixed cutoff in the 8-10 angstrom range and then the reciprocal part
of the calculation only adds an additional 50% (depending on the size of
the charge grid and FFT performance). Whereas PME scales as roughly
NlogN, you cap simulation scales more like N**2.

If you could get stable cap simulations with an 8 angstrom cutoff, it may
be ok, however as you see, even with a larger cutoff there is tremendous
instability. This is likely due to the vacuum-water interface; earlier work
by BR Brooks on such systems estimated that the effective pressure on the
center of such a system (due to the interfacial order) was in the range of
~1000's of atmospheres ( dP ~ 15000/R where R is the radius in angstroms)
[Theor. Chem. Acc. 99, 279-288 (1998)]. In addition (if the cap force
constant is not high) water may drift away; if the force constant is high,
this only exacerbates the pressure issues.

What you ideally would like is a finite representation that properly
treats the outside as a continuum; there are many approaches in the
literature ranging from stochastic boundary conditions (CL Brooks, etc.),
finite representations (B. Roux, etc), reactions fields (W. van Gunsteren,
etc.), to Poisson-Boltzmann (R. Luo, etc.). Jorgensen's group published a
paper trying to develop a boundary potential that could fix the artifacts
[J Comp Chem 16, 951-972 (1995)]; this is shown to be an incredibly
complex process. The better the cap representation, the greater the cost.
In my experience, PME has simply proven more efficient than most other
approaches. Furthermore, the reaction field approaches likely have
problems in non-homogeneous environments (like lipid bilayers); a recent
paper shows that although the reaction fields work better than truncation,
PME appears to perform the best [J Chem Phys B 108, 4485-4494 (2004)].
Furthermore, the periodicity artifacts, while present, do not seem to be
overly large (on the order of kT for a water solvated system) [Hunenberger
and co-workers; J Chem Phys B 108, 774-788 (2004)].

If you want to stick with current versions of AMBER, it is likely best to
run with PME or possibly future versions that may include PB. Otherwise,
CHARMM can do stochastic boundaries and other finite representations.

Good luck,


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