Improved Adaptive Resolution Molecular Dynamics
Simulation
Iuliana Marin1, Virgil Tudose2, Anton Hadar2, Nicolae Goga1,3, Andrei Doncescu4
Affiliation 1: Faculty of Engineering in Foreign Languages
University POLITEHNICA of Bucharest, Bucharest, Romania, n.goga@rug.nl
Affiliation 2: Department of Strength of Materials, University POLITEHNICA of Bucharest, Bucharest, Romania
Affiliation 3: Molecular Dynamics Group, University of Groningen, Groningen, Netherlands
Affiliation 4: Laboratoire d'analyse et d'architecture des systemes, Université Paul Sabatier de Toulouse, Toulouse, France

Abstract—Molecular simulations allow the study of properties
and interactions of molecular systems. This article presents an
improved version of the Adaptive Resolution Scheme that links two
systems having atomistic (also called fine-grained) and coarsegrained resolutions using a force interpolation scheme. Interactions
forces are obtained based on the Hamiltonian derivation for a given
molecular system. The new algorithm was implemented in
GROMACS molecular dynamics software package and tested on a
butane system. The MARTINI coarse-grained force field is applied
between the coarse-grained particles of the butane system. The
molecular dynamics package GROMACS and the Message Passing
Interface allow the simulation of such a system in a reasonable
amount of time.
Keywords—adaptive resolution scheme; molecular dynamics;
MPI; stochastic dynamics; coarse-grained; fine-grained.

INTRODUCTION
The traditional computational molecular modeling
indicates the general process of describing complex chemical
systems in terms of a realistic atomic model, with the goal of
understanding and predicting macroscopic properties based on
detailed knowledge at an atomic scale [1]. In literature, the
study of a system at atomistic level can be defined as finegrained (FG) modeling [2].
I.

Coarse-graining is a systematic way of reducing the
number of degrees of freedom for a system of interest.
Typically whole groups of atoms are represented by single
beads and the coarse-grained (CG) force fields describe their
effective interactions. Coarse-grained models are designed to
reproduce certain properties of a reference system. This can be
either a full atomistic model or a set of experimental data. The
coarse-grained potentials are state dependent and should be reparameterized depending on the system of interest and the
simulation conditions [1].
The main disadvantage of a coarse-grained model is that
the precise atomistic details are lost. In many applications it is
important to preserve atomistic details for some region of
special interest [2]. To combine the two systems, fine-grained
and coarse-grained, it was developed a so-called multiscale
simulation technique [3, 4, 5, 6, 7]. This method combines the
two resolutions by coupling them with a mixing parameter .
The multiscale interaction forces are computed as a weighted

sum of the interactions on fine-grained and coarse-grained
levels [2].
The adaptive resolution scheme (AdResS) couples two
systems with different resolutions by a force interpolation
scheme. The two resolutions are called atomistic and coarsegrained [3, 4]. The atomistic representation of system
describes the phenomena produced at the atomic level (noted
fine-grained or FG) and the other one, coarse-grained,
describes the system at molecular level (noted coarse-grained
or CG).
The AdResS scheme works in the following conditions:
•
the forces between molecules are scaled and the
potential energy is not scaled. Consequently, the Hamiltonian
cannot be used to obtain the energies;
•
just non-bonded interactions between molecules are
scaled. In this way, some computational resources are saved;
•
particles are kept together via bonded atomistic
forces that are computed everywhere, including the coarsegrained part (no pure coarse-grained in that part);
•
in the transition regions there is a potential which is
added (that takes into account the difference in chemical
potentials between the two representations). In this paper it is
denoted by .
In the current paper, it is proposed a method for obtaining
the interaction forces by applying the Hamiltonian derivation,
where potentials can be scaled. The advantage of this method
is that, derivation is based on the sound Hamiltonian model and
energies can be reported correctly. The improved algorithm
was implemented in GROMACS, a molecular dynamics
software, that runs in parallel using the Message Passing
Interface (MPI). Simulations have been done on butane. The
MARTINI coarse-grained force field which was implemented
by the Molecular Dynamics Group from the University of
Groningen was also applied.
The paper is organized as follows. In the next section the
improved AdResS multiscaling resolution scheme is presented.
Section 3 describes the implementation of AdResS in
GROMACS using MPI and its testing on a butane molecular
system. Section 4 outlines the obtained results. The last section
presents the final conclusions.

II. RELATION TO EXISTING THEORIES AND WORK
In this section it is presented the relevant theory for the
algorithm implemented in GROMACS – the improved
AdResS multiscaling resolution scheme [3,4].
A convention is made: for a coarse-grained molecule are
used capital letters for coordinates and for a fine-grained
molecule, small letters. For simplifying the presentation, it is
considered that the space factor is function only on the
coordinate of the reference system. On the and coordinate
axis, is constant.
It is denoted by
the
coordinate of a fine-grained
particle with the number
in the coarse-grained molecule
with number . The coarse-grained molecule is centered in
the center of mass ( ) of the ensemble of corresponding finegrained particles .
The relation between the two parameters is:
∑

(1)

∑

Fig. 2. The coordinates

is

for a coarse-grained particle

A. Multiscaling force
Starting from the Hamiltonian that scales the non-bonded
forces, it is added an extra potential in the transition region
that adjusts for the difference in chemical potentials between
the fine-grained and coarse-grained regions.
As explained above, fine-grained bonded interactions are
computed everywhere, including the coarse-grained region.
The potential energy in the multiscaling model
is a
function of coordinates only and it is chosen as: The
multiscaling factor is defined as follows:
"/

-.
4,

(2)

where
is the mass of the fine-grained particle and
the mass of the coarse-grained particle.

and

"∙

.
+,

-.
+,

/

.
4,

/ 01 2
" /

"3 ∙

(4)

The multiscaling factor is defined as follows:
#
!" $

In Figure 1 more coarse-grained molecules with
corresponding fine-grained particles and the parameters
and are represented.

%

∙ (
'

(5)

Using (4) in (5), it is obtained:

25

6

6

89
:7

∙

/

/

89
57

6 957
6

Because is function of
variable. Then

Fig. 1. The coordinates

and

<=

In AdResS, the space factor is function of the coordinate
of a coarse-grained particle ( ):
#
!" $

%

∙ (
'

(3)

where
is the coordinate in the reference system for the
center of fine-grained region, ) is half of the length of the
fine-grained region and * is the length of transition (hybrid
fine-grained - coarse-grained) region. In Figure 2 are
displayed these parameters.

6 89
57
6

6 9:7
6

/ 12

/

6 ;

6

∙

6 89
:7
6

2

6

6

∙
(6)

, it is necessary to change the

<=

<

for a coarse-grained particle

/

∙

<

∙

<

<

(7)

According to (1), it is obtained
<

<

(8)

Using (8) in (7), results
<=

<

∙ ′

where ′ is the derivative of (3) with respect
computed at the end of section (see formula (18)).

(9)
which is

Taking that into account
BC
<?@A

<

25 -.

(10)

25 .

(11)

C
<?@A

<

are the non-bonded, respectively bonded, forces in the atom
and
BC
<?DA

<

,

25 -.

(12)

25 .

(13)

C
<?DA

<

are the non-bonded, respectively bonded, force in the coarsegrained molecule , formula (6) becomes:

6

6

25
2

∙ ′∙

89
:7

∙

∙

′

89
57

2

6 9:7

2 59 /

6

By making the notation

∙

6

6

∙ 589 / 1 2
/

∙

6 ;

6

6 89
:7
6

The implementation of the new algorithm is based on MPI
parallelization (see Figure 3). MPI is used by dividing the
simulation box into several boxes. The number of processors
involved in computation is equal to the number of the smaller
simulation boxes. Data is passed between the neighboring
simulation boxes through the use of messages which is
constant. The MARTINI coarse-grained force field which is
applied on the particles of the system lowers the initial energy
of atoms until the reference temperature is reached and it is
maintained at that state [8].
The parallelization and the improved AdResS algorithm are
depicted in Figure 3.

∙

(14)

25

<?E

<

III. TECHNOLOGY APPROACH
The implementation of the improved AdResS is done in
GROMACS, a package specialized for running molecular
dynamics simulations. GROMACS was firstly developed at the
University of Groningen. Because the simulation time might
last for a long time, even in terms of months, the Message
Passing Interface (MPI) is used for parallelizing the
computations within the molecular system. The thermostat that
was used is stochastic dynamics.

(15)

it is obtained:

25
2

∙

′

∙

89
:7

∙

′

∙

89
57

2 59 2 59 ∙

2

∙ 589 2 1 2
2 5;

∙ 589 ∙

(16)

Then it results:

5

5

89
:7

2

/ 12

I ′∙

89
:7

∙

′

∙ 589 ∙

G2

/ 12

∙

89
57

∙

′

<=

K

'
%

∙ cos O

P

!

P

!

/ 59 ∙
89
57

/

/ 5;

%

# $

∙ Q ∙ sin O
'

∙

′

⇒

∙ 589 / 59 H /

with respect

!

#

∙ 589 / 59 /

∙ 589 / 59 J / 5;

Finally, the derivative of
formula (3):
<

∙

/

∙

(17)

is obtained from
P

!

%

# $

∙ Q∙
'

(18)

Fig. 3. The simulation box and its processes

Parallelization is done through MPI. The computation is
divided between the involved processors. Each processor will
follow the algorithm that starts by firstly computing the bonded
.
.
fine-grained and coarse-grained interactions +,
, 4,
. The next
step is the computation of the non-bounded fine-grained and
-.
-.
, 4,
. The multiscaling forces
coarse-grained interactions +,
are computed according to formula (17). The velocities and the
positions of the particles get after that updated.
IV.

FINDINGS

The simulation was done on an Asus ZenBook Pro
UX501VW computer having an Intel Core i7-6700HQ
processor with 8 threads and a frequency of 2.6 GHz. The
RAM has a capacity of 16 GB. The simulation box comprises
butane with 36900 atoms. The dimension of an atom is equal to
10 nm on each direction (x, y, z). The reference temperature is
set at 323 K. The system of atoms has been simulated on a
different number of processors for 10,000 simulation steps. For
each processor, a number of eight executions were made, each

of the reported values being an average of the eight execution
times.
The execution time expressed in ns/day and in hour/ns are
presented in Table 1.
TABLE I.

EXECUTION TIMES AND TEMPERATURE FOR A DIFFERENT
NUMBER OF PROCESSORS

Performance

Temperature

Test
No.

[ns/day]

[hour/ns]

[K]

1

7.421

3.234

326.487

2

15.326

1.566

326.497

3

20.146

1.191

326.440

4

26.127

0.919

326.481

5

19.328

1.242

326.543

6

28.193

0.851

326.498

7

23.697

1.013

326.525

8

35.591

0.674

326.466

In the table above the standard deviations are no larger than
0.036 for the execution time and 0.110 for the temperature.

Execution time [hour/ns]

A different number of processors was used to analyze how
parallelization evolves at run time for the butane system. The
execution time according to the number of processors is
presented in Fig. 4.
4

1.566 1.191

0
1

The reference temperature for the system was of 323 K.
The obtained value with a difference of around ± 3K is within
the statistical accepted errors for such simulations.
V. CONCLUSIONS
The article presents the improved AdResS through the MPI
parallelization implemented in the GROMACS molecular
dynamics software and its testing on a butane molecular
system, along with the experimental results. Usually the
simulation time is large. For this reason parallelization is used
for obtaining the results in a shorter period of time.
The algorithm depends on the hardware used and on the
number of processors on which it is run. There is a significant
difference in time for the simulation where only one processor
is involved as compared to the case when several processors
interact through the use of MPI - a speedup of about four times
more was obtained when six processors were used as compared
with the case of one processor. The temperature is kept within
the accepted statistical ranges for such simulations.
Further work include the testing of this implementation on
more systems, generalizing the theory for cylinder coordinates,
further improvements for AdResS algorithm.

3
2
3.234
1

Fig. 5. Temperature variation in time

2

3

0.919 1.242 0.851 1.013 0.674
4

5

6

7

REFERENCES
[1]

8

Processor No
Fig. 4. Execution time expressed in hour/ns as a function of the processor
number used

It can be observed that as the number of processors
increased, the execution time linearly decreased, after which a
plateau was obtained for the considered butane system with
36900 atoms.
There is a significant difference in time for the simulation
where only one processor is involved compared to the case
when several processors interact through the use of MPI - a
speedup of about four times more was obtained when six
processors were used as compared with the case of one
processor.
In Figure 5 is represented the variation of temperature in
time. By using the stochastic dynamics thermostat and the
improved AdResS, the temperature of the system is kept
around the value of 326 K as it can be observed in Table 1.

[2]

[3]

[4]

[5]

[6]

[7]
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