Richards, A. (2004) MOAC
Biomolecular Dynamical Simulation: An Investigation Comparing the Effect
of Ewald and Reaction Field Electrostatic Treatments on a Small Peptide.
Adair D. Richards*
*
Molecular Organisation and Assembly in Cells Doctoral Training Centre, University of Warwick, Coventry, CV4
7AL, UK. Email: A.D.Richards@warwick.ac.uk
Biomolecular dynamical simulations can provide a wealth of useful information on the
structural behaviour of peptides. One of the largest approximations used in molecular
dynamics simulations is the treatment of long-range electrostatics forces and this study
analyses parallel simulations of the five-residue twin-arginine translocase peptide treating
long-range electrostatics either with Ewald or reaction field methods. It was found that the
simulations produced very similar results although the approach using reaction field
equations resulted in a slightly more vibrationally active peptide. For the peptide in
question, the choice between Ewald and reaction field electrostatic treatment has no
significant effect on the results of the simulation.
system† including quantum-mechanical treatment of all nuclei
and electrons for both solute and solvent molecules.
In recognition of this, concessions are made in the detail of
description eg. number of degrees of freedom, in the length of
time simulated, the system size and the accuracy of the relevant
forces. Even with a reduced set of explicitly treated degrees of
freedom, it is computationally impossible to simulate a system
large enough to avoid surface effects at the boundary of the box
with a vacuum or a dielectric continuum representing the mean
effect of solvent outside the system2. This boundary is
eliminated by infinitely replicating periodically the system box
although this introduces a crystalline order which can lead to
periodicity-induced artefacts.
Given this periodic microscopic system set-up, an appropriate
algorithm is required to treat the pairwise non-bonded
interactions, the number of which grows with N2, where N is the
number of particles in the system. These can be divided into the
Introduction
Molecular dynamics (MD) simulations provide an atomicresolution depiction of molecular systems which can elicit
valuable information about the structure and function of systems
of interest. In biomolecular science we can obtain from MD
simulations both physico-chemical properties through statistical
sampling of a system in equilibrium and an understanding of
pathways and mechanisms of, for example, peptide folding, by
following individual particle motions.
Since 1977 when the first MD simulation of biological interest
was published1, interdisciplinary research enveloping chemistry,
physics and biology, both theoretical and experimental, has
developed with a view to understanding the processes involved
with protein and peptide folding. Comparing simulation results
with experimental data is essential because the experimental data
can be used to validate the simulations and the simulations may
Fig. 1 Tat signal peptide, RRQGI, at the beginning (left) and end (right) of simulation under precision Ewald electrostatic treatment.
help to interpret the experiments correctly or guide future
experiments. The simulations are limited however by the
necessity for an accurate description of the in vivo situation and
the computational power needed to accurately describe the
forces and motions involved.
There is currently insufficient computational power to provide a
complete description of all degrees of freedom for a macroscopic
Van der Waals interactions which decay rapidly with distance
and are generally truncated after an appropriate cut off distance
to avoid interactions with more than one periodic copy of other
atoms, and the long-range electrostatic forces. There are two
†
Macroscopic in this sense means that the system size should be
sufficiently large to avoid any type of unwanted surface artefacts.
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Richards, A. (2004) MOAC
Fig. 2 Tat signal peptide, RRQGI, at the beginning (left) and end (right) of simulation under reaction field electrostatic treatment with the peptide
backbone highlighted in blue.
approaches to treating the long-range electrostatic interactions
and both include severe approximations which may lead to
unreliable simulations in some cases.
The first approach truncates the Coulombic interactions beyond
a cut-off distance using a reaction field (r.f.) method to
approximate the mean effect of the outside medium. The other
method utilises the exact periodicity of the system and includes
all periodic copies of all electrostatic interactions using latticesum techniques based upon Ewald summation. A third option,
currently in its infancy is the use of continuum electrostatics to
permit a systematic analysis or cut-off linked finite-size effects,
although this approach ignores the discrete nature of the solvent.
In the reaction field method, each charge is considered
individually as the origin of a particular spherical coordinate
system. Surrounding it is a cut-off sphere containing explicit
neighbouring particles, which itself is placed within a
homogeneous dielectric continuum of permittivity matching that
of the solvent. Continuum electrostatic equations are then solved
using spherical symmetry to estimate the reaction-field force
from the continuum onto the particle. This long-range correction
is then added to the short-range contribution which is computed
via explicit summation over the neighbouring atoms within the
cut-off sphere3.
As with the reaction-field method, the Ewald approximation
methods rely on splitting particle interactions into a short-range
component which is computed by pairwise particle-particle
summation, and a long-range component computed here by
evaluating Fourier series directly. This is based on the
assumption of exact periodicity within the simulated system.
Previous investigations have questioned the application of
artificial periodicity in biomolecular simulations4, suggesting
that it may perturb conformational equilibrium resulting in
smaller fluctuations and an artificial stabilisation of the most
compact state. The short-range component of non-bonded
electrostatic interactions is calculated by explicit particle-particle
summation with minimum-image spherical truncation.
The purpose of this work was to investigate the effect, if any, of
applying either a reaction field or Ewald method in simulating a
small peptide. The peptide chosen to work with is the fiveresidue signal peptide involved in the twin-arginine translocase
system5. Previous research indicates that the secondary structure
of this peptide alternates depending on the hydrophobicity of the
environment between helical and unstructured conformations6.
Preliminary in-house results indicate a sensitivity in the folding
behaviour of the peptide to the way in which the simulations are
constructed. The way the long-range electrostatics are treated
provides a possible explanation for this. The aim of this study is
to establish to what extent the choice between reaction-field and
Ewald methods of treating electrostatics affect the behaviour of
this small peptide.
Experimental procedures
An atomistic model of the twin-arginine translocase signal
peptide, RRQFI, was set up and energy minimisation
calculations were performed in a cubic box of length 20Å using
the molecular graphics analysis program QUANTA (Accelerys
Inc., Cambridge UK) and the CHARMM united atom force field
(Vs. 28.1, Accelerys Inc., Cambridge UK) in combination with
the DL_POLY7 molecular dynamics package (Vs. 3, CCLLC,
Daresbury UK). The peptide was surrounded by 306 molecules
(918 atoms) of TIP3P water8 and exported and converted to
Fig. 3 Ramachandran snapshot plot of an Ewald simulation of the Tat
signal peptide.
DL_POLY format using in-house software.
The Berendson9 ensemble was chosen to ensure constant
pressure at 30 atmospheres and constant temperature at 310K
throughout the simulations. For the non-bonded interactions a
twin-range method of calculation with cut-off radii of 9Å and a
Verlet neighbour-list width of 0.5Å were used. The long-range
electrostatics were either treated using the reaction field method
or a precision Ewald method explicitly solving all appropriate
Fourier series. Bond lengths were constrained using the SHAKE
algorithm10 to a geometric tolerance of 10-4.
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Richards, A. (2004) MOAC
The simulation ran using a single timestep of 1fs were
equilibrated for 5.5ns and then run for 5ns with the trajectory
coordinates being recorded every 250fs. The simulations were
run using an IBM cluster provided by the Centre for Scientific
Computing of the University of Warwick with support from
Joint Research Equipment Initiative grant JR00WASTEQ.
In-house software was then used to reconstruct the output files to
avoid abnormal bonds across the box boundary and to convert
the files to a VMD compatible format.
The molecular visualisation program VMD (CBG, University of
Illinois USA) was then used in conjunction with Excel
(Microsoft, Redmond USA) to analyse and compare the output
files. In addition to this, some secondary structural analysis was
conducted using DSSPcont11 (CUBIC, New York USA).
Discussion and Conclusion
The theoretical backgrounds of reaction field and Ewald
electrostatics are very different, with the Ewald methods relying
on the precise calculation of electrostatic interactions in an
infinite periodic system constructed by making replicas of the
unit box, and the reaction field method relying on the truncating
of Coulombic interactions within the periodic system and
treating the medium outside the cut off sphere of each atom as a
dielectric continuum with the same permittivity as the solvent. It
would be reasonable to expect that structural and energetic
properties obtained from MD simulations will differ as a result
of these dissimilar models.
It is accepted that Ewald methods in general evaluate the
8
Results
7
Figures 1 and 2 are snapshots taken at the beginning and end of
the simulations using each electrostatic treatment method and
visualised in VMD. The residues are colour coded for ease of
recognition.
Figure 3 shows a Ramachandran plot of the peptide under an
Ewald simulation with the three interior residues represented by
dots in the upper-left quadrant and the outer resides represented
by dots on the x and y axes.
Figures 4 and 5 demonstrate the inter-atomic distance between
Distance between atoms (Angstroms)
6
5
4
3
2
1
0
1
825
16
1649 2473 3297 4121 4945 5769 6593 7417 8241 9065 9889 10713 11537 12361 13185 14009 14833 15657 16481 17305 18129 18953 19777
Time (fs)
Fig. 6 Chart comparing the distance between two carbon atoms on
residues 2 and 4 over time under a reaction field electrostatic treatment.
14
Distance between atoms (Angstroms)
12
electrostatic interactions more accurately than reaction field
methods, giving a slightly lower electrostatic energy than the
reaction field12. This results in an expectation that there will be
more structural flexibility in reaction field simulations leading to
a greater amount of peptide backbone movement over time13.
A visualisation of the degree of structural change experienced
over 5ns is displayed (Figures 1 and 2) and there is little change
evident to the naked eye. The five residue peptide is too small to
use secondary structure prediction and analysis programs such as
Stride and DSSPcont effectively. When DSSPcont was applied,
it indicated a turn structure for both simulations but the size of
error due to the small number of atoms involved renders the
result unreliable. Ramachandran plots (snapshot given in Figure
3), predict a combination of a β-sheet and unstructured regions
in the peptide but again the large error due to the size of the
molecule invalidates that conclusion.
Figures 4 and 5 display a more useful reflection of the peptide’s
vibrations and movement over the 5ns simulation time. With an
average distance of 13.37Å and 13.00 Å and standard deviation
of 0.199 and 0.247 for the Ewald and reaction field experiments
respectively, the peptide’s conformation undergoes small
fluctuations. Evident from the displayed graphs and the standard
10
8
6
4
2
0
1
831
1661 2491 3321 4151 4981 5811 6641 7471 8301 9131 9961 10791 11621 12451 13281 14111 14941 15771 16601 17431 18261 19091 19921
Time (fs)
Fig. 4 Chart comparing the distance between two carbon atoms on
residues 1 and 5 over time under an Ewald electrostatic treatment.
16
14
Distance between atoms (Angstroms)
12
10
8
6
4
7
2
6
0
831
1661 2491 3321 4151 4981 5811 6641 7471 8301 9131 9961 10791 11621 12451 13281 14111 14941 15771 16601 17431 18261 19091 19921
Distance between atoms (Angstroms)
1
Time (fs)
Fig. 5 Chart comparing the distance between two carbon atoms on
residues 1 and 5 over time under a reaction field electrostatic treatment.
two carbon molecules in residues 1 and 5 over the 20 000
timesteps and Figures 6 and 7 display similar information
regarding two carbons in residues 2 and 4.
5
4
3
2
1
0
1
825
1649 2473 3297 4121 4945 5769 6593 7417 8241 9065 9889 10713 11537 12361 13185 14009 14833 15657 16481 17305 18129 18953 19777
Time (fs)
Fig. 7 Chart comparing the distance between two carbon atoms on
residues 2 and 4 over time under an Ewald electrostatic treatment.
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Richards, A. (2004) MOAC
deviations, there is meaningfully greater structural change
experienced under the reaction field method in line with
expectations, although this difference is small. Figures 6 and 7
compare the distance between a residue 2 carbon and a residue 4
carbon and provide results in line with those derived from
Figures 4 and 5. The evidence from Figures 6 and 7 add weight
to the conclusions drawn above and help to eliminate the
possibility of the two chosen atoms in Figures 4 and 5 being an
anomalous pair.
An advantage of MD simulations over Monte Carlo simulations
is that each successive iteration of the system is connected to the
previous states of the system, which allows us to consider a
property of the system, in this case inter-atom distances, as a
function of time. Thus we can produce a time correlation
coefficient as a measure of correlation between the Ewald and
reaction field simulations over time. The normalised version of
the time correlation coefficient is given below in equation 1
where x and y represent the inter-atomic distance, i represents the
index covering each timestep and M represents the total number
of timesteps (20,000). This correlation coefficient was calculated
to be 0.9997 in relation to the Ewald and reaction field
simulations for inter-atomic distances between residue 1 and
residue 5. This is a high correlation, (the maximum correlation is
1
C xy 
M
 1

M

i
yi
i 1
 1
 x i2  M
i 1

M
1
2
3
4
5
6
7
8
9
(1)
M
x
References


 y i2 
i 1

M
10
xi yi
x i2
11
y i2
12
one), and indicates that the simulations produce very similar
results. Therefore it can be said that the choice of long-range
electrostatic treatment between precision Ewald and reaction
field methods has no significant bearing on the outcome of
simulations.
Future investigations into this area may include conducting
longer simulations to establish the existence, if any, of artificial
artefacts and dynamics with long time periods. Additionally, MD
simulations could be run using a larger peptide to aid data
analysis and counter-ions added to the solvent to provide a more
realistic ionic environment. A third type of electrostatic
treatment could also be considered, namely one of the popular
particle-particle particle-mesh Ewald methods such as
P3ME/RESPA214.
In conclusion, it appears that there is no major difference
between using Ewald or reaction field methods for simulating
small peptides. There is slightly more peptide flexibility whilst
using the reaction field methods as they lead to higher
electrostatic energy values in comparison to Ewald simulations.
There is currently insufficient evidence to rule out the possibility
that different electrostatic treatments will have a significant
effect on larger or charge-neutral systems. For the system in
question in this study however, any effect due to the choice of
electrostatic interactions is negligible.
13
14
Acknowledgements
The author would like to thank the following for their guidance
and help: Mark Rodger and Rob Hawtin at the University of
Warwick, Syma Khalid at Oxford University, Philip Carter at
Imperial College London and Miguel San Miguel at
Universidad de Sevilla. This work was funded by the
Experimental and Physical Sciences Research Council Life
Sciences Initiative.
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Richards, A. (2004) MOAC
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