Subject: Ewald sums

From: [email-masked] (Howard Alper)
Date: Tue, 4 Apr 1995 19:08:38 -0500 (DT )

Dear Dr. Brown,

  I saw your post concerning the use of Ewald sums in liquid simulations,
as a response to the question of Pieter Stouten (sorry if I have misspelled
the name).  Since the issue of long-range electrostatic forces is of central
importance in simulations, and I have spent much time studying this issue, I
thought I would add my own responses to your dialog.

  The Ewald sum is one of several commonly used methods to include long-range
electrostatic interactions in a computationally tractable manner (the other
main approach is the continuum-based Reaction Field model, besides, of course,
using VERY large cutoffs.)  The reason for even considering such methods is
that the truncation of molecular interactions commonly employed in simulations 
gives rise to problems.  Many in the simulation community, some for lack of
understanding but most for lack of infinite computational resources, tend to
downplay or outright ignore the effects of truncating potential and forces.
Briefly, for polyatomic systems with regions of significant charge or polarity,
use of abrupt truncation (meaning the potential and forces between entities
are instantly set to zero when some representative distance between the
entities crosses the preset cutoff distance) leads to the development
of "hot spots" at those places in the system where truncation of strongly
polar/charged interactions is being done.  This means that some parts of the
system have a temperature much higher than the target temp. (say, 300K)
while other regions may have a temp. much lower than the target (since it is
common to force the temp. of the whole system to equal the target temp.).
This maldistribution of temperature will significantly affect dynamics
properties (such as the diffusion coefficient) but will also affect structural
quantities as well.  Also briefly (well, sort of), the use of so-called
switching functions also leads to an unnatural distribution of kinetic energy
(ie, temperature), but of a different kind.  Switching functions lead to a
decrease in the kinetic energy in regions where they are applied, or to "cold
spots" of a sort.  The reasons for this behavior are discussed more fully
in K. F. Lau, H. E. Alper, T. Thacher, and T. R. Stouch, J. Phys. Chem. 
98, 8785 (1994).  (I and Terry Stouch are from Bristol-Myers Squibb, by
the way (or I was until 1994), so the paper is a joint effort between 2
researchers from Biosym and 2 from BMS, and does not necessarily represent the
contention of Biosym as a company).  Given the deleterious effects of the 2
most common methods for truncating interactions (and similar effects have
been observed for a variety of systems (I will provide some references below)),
it seems necessary to consider methods for including long-range electrostatic
interactions more explicitly.

  I do not mean to say that for all simulations of any system that failure
to use very large cutoffs, or methods such as Ewald sums for a Reaction Field,
will lead to totally wrong results.  It is a matter of how large a perturbation
in the results (from that which would obtain if all interactions were
included) one is willing to tolerate, or can tolerate, before one cannot
obtain chemically meaningful results.  But in the case of systems with highly
polar or charged regions, the effects of truncation will be more significant
than in more nonpolar systems.  This situation will obtain for many
biochemical systems of importance.

  Since the use of infinite cutoffs is impossible, much effort has gone into
methods that closely approximate the effect of including all interactions,
but in an affective manner.  It is true that the Ewald sum was originally
developed for use in crystalline/periodic systems, and that its use in liquid
systems represents an approximation.  The accuracy of that assumption must
be tested empirically through simulations on relevant systems.  It turns out
that the use of Ewald sums on water and many biochemical systems (solvated
proteins/nucleic acids) is a very good approximation.  Simulations of water
have shown that the Ewald sum does not introduce significant "crystallinity"
into the behavior of liquid water, and that many properties (such as the
orientational structure/dielectric constant and the diffusion coefficient)
are produced most accurately/meaningfully only when Ewald sums (or Reaction
Fields) are used.  For simulations of solvated biomolecules, some care must
taken, but when that is done the Ewald sum produced results that are more
physically consistent and in better agreement with experiment than results
obtained with abrupt truncation or switching functions.  Generally similar
conclusions are seen when the Reaction Field is used.

  The Ewald sum can be expensive to use, though how much more depends on how
well your code is written, how large your system is, and the values you choose
for the relevant Ewald summation parameters.  Again, one has to decide how much
perturbation in one's results is tolerable.

  Some references:

H. E. Alper and R. M. Levy, J. Chem. Phys. 91, 1242 (1989) - shows the effects
of switching functions on the orientational/dielectric properties of water.

P. E. Smith and B. M. Pettitt, J. Chem. Phys. 95, 8430 (1991) - simulations
of a pentapeptide in water with ions, which shows clearly the differences 
between using an Ewald sum and truncating with switching functions.

H. E. Alper, D. Bassolino-Klimas, and T. R. Stouch, J. Chem. Phys. 98, 9798
(1993) - a simulation of water above a phosphlipid monolayer which demonstrates
the necessity of using large cutoffs in simulations of charged or polar
systems, if artifacts are to be avoided.

H. E. Alper, D. Bassolino-Klimas, and T. R. Stouch, J. Chem. Phys. 99, 5547
(1993) - simulations of water above the monolayer which describe the properties
of this system when the artifacts due to truncation are essentially eliminated,
but also showing in more detail the effects of truncation.  This paper
complements the previous one.

H. Schreiber and O. Steinhauser, Biochemistry 31, 5856 (1992) - this paper
shows how the treatment of the long-range electrostatic forces affects
simulations of protein stability in water.

  Many more references could be listed, but this should serve as a good start.
Please forgive the length of this note; I hope it is informative.  Please
feel free to share it with anyone you consider relevant .  Also feel free
to contact me ([email-masked]) if you want to discuss this further.

  Sincerely,

  Howard Alper

-- 

  Dr. Howard Alper
  Moldyn Inc.
  1033 Massachusetts Avenue
  Cambridge, MA 02138
  617-354-3124 x19

- helping molecules find happiness for over a 10th of a century.

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