University of Groningen
Characterization of oil/water interfaces
van Buuren, Aldert Roelf
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1995
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van Buuren, A. R. (1995). Characterization of oil/water interfaces: a molecular dynamics study Groningen:
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Chapter 4
Structural Properties of
1,2-Diacyl-sn-glycerol in Bulk and at the
Water Interface
Aldert R. van Buuren, Jacob de Vlieg and Herman J.C. Berendsen
Langmuir, in press (1995).
We performed four different Molecular Dynamics (MD) simulations of 1,2-dilauroyl-sn-glycerol
(DLG) systems at 300 and 360 K: a crystal simulation, a pure DLG oil phase, a DLG oil phase
in contact with a water layer and an oil/monolayer/water simulation. All these systems were
simulated for several nanoseconds in total. We describe the behaviour of the DLG molecules
in the lipid phase as well as at the aqueous interface. The crystal and pure oil phase tend to
converge to the same overall structure (i.e., an isotropic liquid), as do the systems with an aqueous
interface, although equilibrium for the crystal and monolayer system has not yet been reached
compared to their counterpart. The presence of an aqueous interface induces layering of the
lipid molecules. The overall properties like density, hydrogen bonding and rdf’s converge at the
different temperatures. We can conclude that the rearrangement of the DLG molecules in these
DLG systems is a slow process, but we estimate that the equilibrium for these systems at 360 K,
the liquid phase, will be reached within a few nanoseconds, for the DLG molecules diffuse over
nanometers on a nanosecond time scale.
4.1 Introduction
1,2-Diacyl-sn-glycerol (DLG) is involved in anabolic reactions in that it participates in the biosynthesis of monoacylglycerols, triacylglycerols, other phospholipids, and phosphatidic acid. Furthermore, DLG is a substrate for lipases which cleave a fatty acid off DLG, leaving monoacylglycerol.
To understand the mechanism and the role of lipases which act predominantly at an oil-water
interface, a thorough understanding and characterization of the diglycerides is required. The latter
statement initiated this project and therefore in this paper, we try to describe the behaviour of
DLG molecules in the lipid phase as well as at the aqueous interface.
In the literature there are almost no reports on physical studies on pure 1,2-diacyl-glycerols.
Pascher et al. [88] determined the crystal structure of DLG, whereas Kodali et al. [89] examined
the polymorphic behaviour of saturated monoacid 1,2-diacyl-sn-glycerols by differential scanning
calorimetric and X-ray powder diffraction. Theoretical studies were performed by Williams and
49
50
Structural Properties of DLG in Bulk and at the Water Interface
Stouch [90] who developed a force field for lipid molecules to apply to simulations of crystal
structures, as did Vanderkooi [91]. Peters et al. [92, 93] used molecular dynamics to simulate
diglyceride Langmuir monolayers at the air-water interface (without taking into account water
explicitely, but using a continuous medium).
We describe four different Molecular Dynamics (MD) simulations of DLG systems: a crystal
simulation (CRYS), a pure DLG oil phase (OIL), a DLG oil phase in contact with a water layer
(GLYC) and an oil/monolayer/water simulation (MONO), where for the latter two simulations
we included the water molecules explicitly. We performed the simulations at 300 K and 360 K
because for the glycerides it is observed that the melting point of the crystal is 19.5 C for the phase and 47.5 C for the 0 -phase (to isotropic liquid), whereas the temperature of crystallization
is 15.5 C [89]. We started with the crystal structure and pure oil system to test our models (force
field) and use these systems for comparison with the other two oil/water systems. The other two
simulations were designed to characterize an oil-water interface. The GLYC simulation was set
up as an “extreme” starting configuration, using randomly distributed DLG molecules attached to
a water layer. This system did not have any appreciable structure in the oil phase, i.e., no layering
of the DLG molecules like in the crystal system. The MONO simulation was the other “extreme”
starting configuration. By starting with a monolayer, i.e., one layer of crystal-like DLG at the water
interface, one of the goals of the GLYC and MONO simulations was to see whether these systems
would converge to the same overall structure in time, an overall structure of which not much is
known, only guessed. By comparing the four models (at different temperatures), we are able to see
the difference in behaviour of DLG molecules in the pure oil phase, as well as in contact with water.
We performed the simulations on a parallel computer that was constructed in our laboratory with
corresponding parallel MD software [3]. Simulations of one nanosecond of a system with around
8.000 atoms take about four days, and therefore computer time was not the limiting factor and long
time effects on the nanosecond scale could be investigated. We simulated a total time of 15 ns.
By comparing density profiles, density in time, order parameters, hydrogen bonding, clustering
of the DLG molecules, radial distribution functions (rdf) and diffusion, we describe the physical
behaviour of the DLG molecules in the pure oil phase as well as at the oil/water interface. The
behaviour of water molecules at lipid interfaces was the subject of a previous study [94].
o7
c9
o5
c1
c6
c4
h3
o2
o 20
c 19
c 21
c8
c 11
c 10
c 13
c 12
c 15
c 14
o 22
c 23 c 24 c 25
c 26
c 28
c 27
c 17
c 16
c 30
c 29
c 18
c 32
c 31
c 33
Figure 4.1: Schematic representation of the lipid molecule 1,2-dilauroyl-sn-glycerol (DLG) with all
the atoms numbered.
4.2 Methods
4.2 Methods
4.2.1
Model
For 1,2-dilauroyl-sn-glycerol, or 2,3-dilauroyl-D-glycerol (DLG), we used the crystal structure [88]. See Figure 4.1 for the structure, as well as for the numbering of the carbon and
oxygen atoms. The molecule was energy minimized (steepest descent) in 25 steps.
4.2.2
Method of simulation
The energy of a molecular system is described by simple potential energy functions which include
stretch, bend, torsional, Lennard-Jones, and electrostatic interactions. We used the GROMACS
package [3], a parallel GROMOS [4] like implementation, which uses the GROMOS force field,
with the latest modifications for the C-OW interaction [75, 95]. This software runs on a multiprocessor parallel computer, which was constructed in our laboratory. Atomic detail is used
except for hydrogen atoms bound to carbon atoms, which we treated as united atoms and no
special hydrogen-bond term is included. The water is modeled according to the single point
charge (SPC) [5] model. For the proper dihedrals CH2 -CH2 -CH2 -CH2 and CH2 -CH2 -CH2 -CH3
the Ryckaert-Bellemans potential [25] was used (which gives better statistics on trans/gauche
behaviour). The methylene and methyl Lennard-Jones parameters were taken from ref [22].
4.2.3
The simulations
In Figure 4.2 we present the four performed simulations schematically, whereas in the next four
subsections we describe the setup conditions for these simulations. The general first steps for all
the simulations are listed below.
We energy minimized all the constructed systems for 250 steps (conjugate gradient). The initial
velocities were taken from a Maxwellian distribution at 300 K. The temperature was coupled to
an external temperature bath [27] of 300 K (time constant 0.1 ps). Periodic boundary conditions
were performed in all three spatial dimensions. All covalent bond lengths as well as the water
angle were constrained by using SHAKE [28] (tolerance 10 5 nm), and a time step of 2 fs was
used. The intermediate structures generated during MD were saved every 0.5 ps and a single
cutoff for the non-bonded forces of 1.0 nm was used. If an aqueous interface was involved (GLYC
and MONO), we position restrained the non-aqueous phase for 10 ps during the start-up of the
simulation, followed by an equilibration run without restraints (see below). For all the simulations
we performed an equilibration run at constant volume (NVT) for 1 ns. The last ns of all the runs
was performed at 360 K, to investigate the behaviour of the systems above the melting point of
the ’ phase. This temperature was reached by coupling to a temperature bath of 360 K with a
time constant of 0.01 ps for 2 ps followed by 1 ns with a time constant of 0.1 ps. Most of the
analyses were performed on the last 2 ns: 1 ns at 300 K and 1 ns at 360 K.
NPT simulation
It is desirable to allow the bulk pressure to adjust automatically to a preset value while the surface
area per head group remains fixed when simulating aqueous interfaces (GLYC and MONO). The
pressure scaling was thus only performed in the z -direction (perpendicular to the interface) by
51
52
Structural Properties of DLG in Bulk and at the Water Interface
coupling to a pressure bath [27] of 1 bar (time constant 0.5 ps). This procedure allowed the length
of the box in the z -direction to change, while keeping the box lengths in x- and y -direction fixed
to their initial value in order to conserve a stable interface. Due to long relaxation times of the
structural adjustments of the interface if the lateral box lengths change, this method was chosen.
Without an aqueous interface, we performed the pressure scaling in all three spatial dimensions.
CRYS
OIL
crystal
random
144 lipids
100 lipids
GLYC
"split"
after 1 ns
100 lipids
1419 water
MONO
monolayer
72 lipids monolayer
50 lipids in oil phase
1264 water
NPT
300 K
NPT
300 K
0.3 ns
0.3 ns
NVT
300 K
NVT
300 K
NVT
300 K
NVT
300 K
1 ns
1 ns
1 ns
1 ns
NPT
300 K
NPT
300 K
NPT
300 K
NPT
300 K
2 ns
2 ns
1 ns
1 ns
NPT
360 K
NPT
360 K
NPT
360 K
1 ns
1 ns
NPT
360 K
1 ns
1 ns
Figure 4.2: Scheme of the four different simulations.
CRYS
By making use of the crystal symmetry P 21 [88], we constructed a crystal structure of 144 DLG
molecules in a box (664, i.e., in z -direction there are 4 DLG molecules, forming two bilayers)
with the Cerius2 package [96]. Although the crystal structure describes a monoclinic box with
= 93.1, we made use of periodicity and put the molecules in a rectangular box with box lengths
3.284.566.86 nm, resulting in a density of 1.1 g/cm3. This is somewhat different to the density
4.3 Results and discussion
of 1.07 g/cm3 as was reported for the crystal structure [88], but the system had the tendency to
converge to this latter density after a long equilibration run. By making use of a rectangular box,
we are able to compare the CRYS simulation with the other simulations.
OIL
We constructed a box which contained 100 DLG molecules, randomly oriented. To reach a density
of around 1.0 g/cm3 , we performed a short run of 15 ps coupling to a pressure bath of 10 bar (time
constant 0.05), followed by a 15 ps run with coupling to 1 bar, which resulted in a box with box
lengths 5.363.713.71 nm and a density of 0.99 g/cm3.
GLYC
The above mentioned OIL box was “split” in two halves after 1 ns (by removing PBC in z -direction
only) with a distance of 3 nm between the two halves (and restoring PBC). This gap was filled
with SPC water [5], using a cubic box containing 216 equilibrated SPC water molecules as a
building block. The water molecules were kept at a minimum distance of 0.23 nm from the DLG
atoms. This led to a number of 1419 water molecules in the GLYC model (5.363.716.71
nm). This system was equilibrated for 10 ps using position restraints on the lipids, followed by
an equilibration run of 290 ps (constant temperature = 0:1 ps, and constant pressure of 1 atm in
all three spatial directions = 0:5 ps).
MONO
From the minimized molecule two opposite monolayers were constructed with a distance of
2.0 nm in between. Each monolayer contained 36 (66) surfactants, randomly rotated around
their head-to-tail axis, with an area of 16.81 nm2 (with lateral box lengths of 4.14.1 nm).
The distance between the layers was filled with SPC water [5], using a cubic box containing 216
equilibrated SPC water molecules as a building block. The water molecules were able to penetrate
the monolayers by 0.3 nm and were kept at a minimum distance of 0.23 nm from the surfactant
atoms. This led to a number of 1264 water molecules in the MONO model (4.234.235.73
nm). After an equilibration run of 200 ps at constant pressure in all three spatial directions (1 bar,
time constant 0.5 ps), an equilibrated box of 25 DLG molecules was placed at each side of the
monolayer and the system was equilibrated for 100 ps at constant pressure in only the z -direction
(1 bar, time constant 0.5 ps resulting in a box with dimensions 3.943.948.55 nm).
4.3 Results and discussion
4.3.1
Density profiles
In Figure 4.3 the density profiles of CRYS, OIL, GLYC and MONO are presented at the two
different temperatures. The density profiles of CRYS and OIL become more smooth after the
temperature rise, which is to be expected for these systems, for 360 K is above the melting point. It
is also obvious from this figure that the water slab (GLYC and MONO) expands upon temperature
increase, what results in a box expansion only in the z -direction due to the method of pressure
scaling as mentioned above. Also the widening of the lipid/water interface at higher temperature
can be observed. The interface is arbitrarily defined at the point where the water density equals
53
54
Structural Properties of DLG in Bulk and at the Water Interface
the lipid density, i.e., at 2 nm for GLYC and at 3 nm for MONO. For MONO it is also obvious
that upon temperature increase, the monolayer looses its structure, for the curve at 360 K becomes
more smooth and the “dip” around 1.2 and 7.2 nm (where the tails of the monolayer glycerides
are in contact with the oil phase glycerides) is less profound. For all the plots we used the data of
the full 1 ns trajectory; if the last 250 ps of the trajectories were used, the plots at 360 K would
even be more smooth. This will become evident in a next figure (Figure 4.5).
150.0
CRYS (300K)
CRYS (360K)
OIL (300K)
OIL (360K)
100.0
50.0
2.0
4.0
6.0
GLYC (300K)
H2O (300K)
GLYC (360K)
H2O (360K)
3
ρ (atoms/nm )
0.0
0.0
300.0
200.0
100.0
0.0
0.0
300.0
1.0
2.0
3.0
4.0
5.0
6.0
MONO (300K)
H2O (300K)
MONO (360K)
H2O (360K)
200.0
100.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
z (nm)
Figure 4.3: Density profiles against z-position in the box at 300 and 360 K for the four systems.
In Figure 4.4 the total density of the systems are given as a function of simulation time. For
CRYS the density reaches a value of 1.081 g/cm3 (instead of 1.07 g/cm3 as in ref. [88]) after 3 ns
of simulation time, although it is not yet completely equilibrated. Because the trend towards the
correct density (it appears to be a linear drift) for CRYS was observed with our force field, despite
the use of united atoms, we are confident that the densities reached in the other systems are correct
too. Moreover, similar simulations on a decane/water system resulted in correct densities [75].
The (total) densities of OIL, GLYC and MONO differ somewhat (around 0.98 to 1.0 g/cm3), but
are stable over the whole course of the 300 K trajectory. After heating up the system a rapid
drop in density can be observed for all systems. CRYS levels off slowest, as is to be expected for
Density profiles
55
the rearrangement of a crystal system. Also obvious is that the densities of CRYS and OIL are
converging to approximately the same value, which suggests that the melting process of CRYS
was completed after 0.8 ns. From Figure 4.3 it was clear, that the drop in density for GLYC and
MONO is mainly caused by the expansion of the aqueous layer. The tendency for GLYC and
MONO to converge to the same density is obvious. We also note that in Figure 4.4 the water layer
is included in the total density and the difference in total density between GLYC and MONO is
due to a different number of DLG and water molecules.
1.10
3
ρ (g/cm )
1.05
CRYS
OIL
GLYC
MONO
1.00
0.95
0.90
1.0
2.0
3.0
4.0
time (ns)
Figure 4.4: Total density of all the systems as a function of time. The arrows indicate the points
where the temperature was increased.
Figure 4.5 presents the density profiles for all oxygen atoms in the systems against simulation
time. At 300 K the systems do not show much diffusion, since the oxygen densities do not change
much in time. At 360 K however, the peaks do change in time. CRYS shows less sharp peaks in
the plot at 360 K (legend IV), which implies melting of the crystal. For OIL the oxygen atoms
are more randomly distributed after 4 ns: a liquid like oil phase has been reached. GLYC shows
an increase in number of oxygen atoms near the water interface after 3.3 ns (360 K, legend IV),
which implies that the DLG molecules diffuse towards the water phase with the oxygen atoms
in contact with water, so the oxygen atoms can make hydrogen bonds with the water molecules.
MONO shows an overall more smeared out distribution after 3.3 ns, but is still not completely
comparable with GLYC. A similar density pattern is obvious, however.
In Figure 4.6 snapshots are shown at the end of the 300 K and 360 K runs for CRYS. After 3 ns
of simulation time, the crystal did not loose its structure. The density reached the correct value
of 1.07 g/cm3 (Figure 4.4), but did not start to melt (the melting temperature is at 47.5 ). Clearly
the snapshot at 360 K shows the melting of the crystal, but the simulation time of 1 ns at this
56
Structural Properties of DLG in Bulk and at the Water Interface
temperature is not long enough to reach equilibrium (isotropic liquid) comparable to the structure
of OIL as shown in Figure 4.7. This figure shows clusters of the oxygen atoms at 300 K, whereas
at 360 K it appears to be a more isotropic liquid. From Figure 4.5 the “movement” of the oxygen
atoms in time was already clear, and is also obvious from these snapshots. One has to bear in
mind though, that these two snapshots are 2D-projections.
Figures 4.8 and 4.9 show snapshots after 2.3 (300 K) and 3.3 ns (360 K) for GLYC and MONO.
For GLYC a rearrangement of the oxygens can be observed, so a tendency of the oxygen atoms to
be more in contact with water (as was also shown in Figure 4.5). As a result of this rearrangement,
the area next to the oxygen atoms is almost solely occupied by lipid tails and alayering induced
by water is apparent. However, the simulation box is too small to be able to observe the number
of layers that are induced. From Figure 4.9 this layering can also be seen at both temperatures:
300 K
360 K
100.0
CRYS
I
II
III
IV
CRYS
0.0
20.00.0
2.0
4.0
6.0 0.0
2.0
4.0
OIL
3
ρ (atoms/cm )
50.0
6.0
OIL
10.0
0.0
30.00.0
2.0
4.0
0.0
2.0
GLYC
4.0
6.0
I
II
III
IV
GLYC
0.0
60.00.0
2.0
4.0
6.0 0.0
2.0
MONO
3
ρ (atoms/cm )
15.0
4.0
6.0
MONO
30.0
0.0
0.0
2.0
4.0
z (nm)
6.0
8.0 0.0
2.0
4.0
6.0
8.0
z (nm)
Figure 4.5: Density profiles of all the oxygen atoms against z-position in the box for CRYS, OIL,
GLYC and MONO. The data is averaged over 4 0.25 ns, I to IV, respectively, at 300 K and 360 K.
Density profiles
57
300 K
360 K
1 nm
Figure 4.6: Snapshot of CRYS after 3 ns (at 300 K, top) and 4 ns (at 360 K, bottom); a 2-D projection
on the yz plane. The oxygen atoms are represented in bold.
58
Structural Properties of DLG in Bulk and at the Water Interface
300 K
360 K
1 nm
Figure 4.7: Snapshot of OIL after 3 ns (at 300 K, top) and 4 ns (at 360 K, bottom); a 2-D projection
on the yz plane. The oxygen atoms are represented in bold.
Density profiles
59
300 K
360 K
1 nm
Figure 4.8: Snapshot of GLYC after 2.3 ns (at 300 K, top) and 3.3 ns (at 360 K, bottom); a 2-D
projection on the yz plane. The oxygen atoms are represented in bold. Water molecules are omitted
for clarity.
60
Structural Properties of DLG in Bulk and at the Water Interface
300 K
360 K
1 nm
Figure 4.9: Snapshot of MONO after 2.3 ns (at 300 K, top) and 3.3 ns (at 360 K, bottom); a 2-D
projection on the yz plane. The oxygen atoms are represented in bold, monolayer in solid, and the
oil phase is dotted. Water molecules are omitted for clarity.
Order parameters of lipid tails
61
where the tails are in contact with the oil phase, the oxygen atoms are directed away from these
monolayer tails. This same figure shows that the monolayer looses its structure at 360 K. The layer
on the right shows more disorder than the layer at the left. This latter layer shows an “inverted
micelle” structure, i.e., in the middle of the layer is curved with the oxygens in close contact
and the tails forming an open structure. However, due to the periodic boundary conditions, this
micelle cannot be closed. Some lipids of the monolayer already diffused towards the oil phase,
which means they “left” the monolayer and moved over more than the length of a molecule in 1 ns.
The lipids that were part of the oil phase (dotted) are not yet mixed with the monolayer. So also
for this simulation we need longer equilibration runs to reach similar structure as in GLYC. But a
tendency to converge to the same overall structure is obvious, as was also observed in Figures 4.4
and 4.5.
4.3.2
Order parameters of lipid tails
0.8
CRYS (300K)
CRYS (360K)
OIL (300K)
OIL (360K)
0.6
S
0.4
0.2
0.0
–0.2
0.0
0.8
2.0
4.0
6.0
GLYC (300K)
GLYC (360K)
MONO (300K)
MONO (360K)
0.6
S
0.4
0.2
0.0
–0.2
–0.4
0.0
1.0
2.0
z (nm)
3.0
Figure 4.10: Order parameters per CH2 segment of the alkyl tails of CRYS and OIL (top) and GLYC
and MONO (bottom) as a function of z-position in the box. The plot of GLYC has been translated
+1 nm to be able to compare the data with respect to the interface of MONO at 3 nm, i.e., where the
density of the glycerides equals the density of water.
For the orientational preference of the alkyl tails we calculated the order parameters of a designated
62
Structural Properties of DLG in Bulk and at the Water Interface
molecular axis with respect to the simulation box:
S = 32 hcos2 i
1
;
2
:1)
(4
where is the angle between the z -axis of the simulation box and the molecular axis under
consideration. The molecular axis at Cn is defined as the vector from Cn 1 to Cn+1 . Brackets
imply averaging over time and molecules.
In Figure 4.10 the order parameters per CH2 segment of the alkyl tails of the systems as a function
of z-position in the box are given at the two temperatures. For CRYS it gives information on
where the crystal starts to melt: around the glycerol backbone (around postition 1.7 and 5.3 nm)
and where the tails of one layer are in contact with the opposite layer (around 3.5 nm). OIL
shows an almost isotropic orientation at both temperatures. These results are consistent with
figures 4.3, 4.5, 4.6 and 4.7. The plots of GLYC and MONO show towards the interface a more
lateral orientation of the diglycerides with respect to the interface, as was observed for other
hydrophobic surfaces as well [75, 94]. This can also nicely be observed from the snapshots in
Figure 4.8 and 4.9. The order in both GLYC and MONO decreases with increasing temperature.
For MONO this shows that when the temperature is raised, the “monolayer” is loosing its structure.
The oil phase that is attached to the monolayer forms an slmost isotropic liquid phase comparable
to OIL (see also Figures 4.8 and 4.9). For MONO a layering of the lipids (as in GLYC) can be
observed. However, the tails of the lipids for GLYC at 360 K do not show a significant preferential
orientation in the region next to the oxygens, so the layer of tails behaves liquid like.
0.6
CRYS (300K)
CRYS (360K)
OIL (300K)
OIL (360K)
GLYC (300K)
GLYC (360K)
MONO (300K)
MONO (360K)
0.5
0.4
S
0.3
0.2
0.1
0.0
–0.1
8
10
12
14
16
18
atom #
Figure 4.11: Order parameters per CH2 segment of the alkyl tails per Carbon atom for CRYS, OIL,
GLYC and MONO. The data for both tails is averaged in one plot.
In Figure 4.11 the order parameters per CH2 segment of the alkyl tails per carbon atom for the four
systems are given with respect to the reference axis, the z -axis. This figure shows that the order in
Hydrogen bonding
CRYS is the highest which is to be expected for the crystal structure. The order in MONO is also
high, due to the monolayer, where the carbon tails are in a perpendicular orientation with respect
to the z -axis. At 300 K OIL is already almost isotropically oriented, whereas GLYC shows some
order, which is due to the orientation of the lipids at the aqueous interface, as shown in Figure 4.10.
So at 300 K GLYC is not an isotropic liquid yet. Upon temperature increase, for CRYS it is clear
that the crystal looses its structure around the glycerol backbone (the carbon atoms connected to
the ester linkage show a decrease in order) and at the end of the tails, but it is also clear that the
melting process is not completed. OIL and GLYC show a more isotropic orientation at 360 K,
and MONO shows less structure as the monolayer looses its structure. These observations are in
agreement with the observations in Figure 4.10.
4.3.3
Hydrogen bonding
The criteria used for a hydrogen bond being present is that the distance between the donor (D)
and acceptor (A) is less than 0.35 nm and the angle H-D-A is less than 60 [4].
In Figure 4.12 the hydrogen bonds that are present between different lipid molecules (inter),
within a lipid molecule (intra) as well as between lipid and water molecules are given. For CRYS
the number of inter and intra hydrogen bonds does not change very much over the course of
the simulation, also not upon temperature increase. So the crystal structure is melting, but the
hydrogen bond network is not disturbed, although the total number of hydrogen bonds decreases
slightly. For OIL there is a small decrease in number of inter hydrogen bonds, which is somewhat
compensated by an increase of intra hydrogen bonds. GLYC shows a rapid increase in the number
of lipid-water hydrogen bonds, which even increases more at 360 K. This is due to the fact that
oxygen atoms are located preferentially at the water interface (see Figure 4.5), so there are more
possible hydrogen bond donors/acceptors at the aqueous interface. The number of inter hydrogen
bonds decrease. MONO shows a decrease in the number of lipid-water hydrogen bonds due to the
loss of structure of the monolayer. The number of intra hydrogen bonds increases for GLYC and
MONO. Also obvious from the figure is the fact that the number of hydrogen bonds for CRYS
and OIL converge to similar values, as do the values for GLYC and MONO. Despite the fact
that not all systems have reached equilibrium yet, overall properties like density (Figure 4.4) and
hydrogen bonding, seem to have converged.
63
64
Structural Properties of DLG in Bulk and at the Water Interface
CRYS
OIL
# H-bonds/lipid
2.0
2.0
1.5
1.5
total
1.0
1.0
inter
inter
0.5
0.5
intra
0.0
2.0
3.0
GLYC
# H-bonds/lipid
2.5
2.0
0.5
intra
4.0
0.0
2.0
3.0
MONO
4.0
2.5
total
total
2.0
1.5
1.0
total
1.5
GLYC-H2O
1.0
inter
inter
intra
0.0
1.3
MONO-H2O
0.5
intra
2.3
time (ns)
0.0
3.3
1.3
2.3
3.3
time (ns)
Figure 4.12: Ratio of hydrogen bonds between lipid-lipid (inter, intra) and lipid-water, normalized
to the number of lipids in the system, as a function of simulation time. The arrows indicate the point
were the temperature was increased
4.3.4
Clustering
One way of looking at the process of rearrangement of lipid molecules in time, is following
the hydrogen bonding charateristics as was described in a previous section. Another way is by
looking at the clustering of atoms or groups. For example, if the lipids are in a liquid phase,
there will be on average less clustering than when the lipids are in a solid phase, due to the
larger disorder in the liquid phase. We investigated the clustering of the systems by looking at
random overlapping spheres [97] of the five oxygen atoms and the hydroxyl hydrogen of the DLG
molecules. The oxygen atoms were taken as reference points, for if clustering appears, it is likely
that these hydrophilic groups are involved (e.g., for hydrogen bonding). A periodic grid (with the
largest box length set to 100 grid points) was put over the simulation box, in which the radii of
oxygen atoms and hydroxyl hydrogens was set to be 0.15 and 0.1 nm, respectively; the rest of the
radii was set to 0.0 nm. The size of the atoms was taken this large to account for the distance in
which hydrogen bonding can occur (see previous section on hydrogen bonding). The volume of
the overlapping spheres can be evaluated by counting the grid points that are occupied by these
spheres.
Clustering
65
In Figure 4.13 the total number of clusters per lipid molecule, whereas in Figure 4.14 the size
of the largest cluster is plotted. From these plots it is clear that the number of clusters per lipid
molecule for GLYC and MONO does not differ much at 300 K. At 360 K the number of clusters
per lipid increases for GLYC, but not that drastically for MONO. This is due to the fact that the
monolayer in MONO does not loose its structure so fast, but the oil phase (i.e., 50 DLG molecules
in total) shows the same trend as OIL, in that the number of clusters per lipid go up. OIL shows
less clusters per lipid, which is due to periodicity: the lipids are in contact with lipids only,
whereas in GLYC the same amount of lipids is also in contact with water. This clearly results in
more/larger clusters for OIL compared to GLYC.
1.0
GLYC
# of clusters/lipid
0.8
MONO
0.6
0.4
OIL
0.2
0.0
1.0
2.0
3.0
4.0
time (ns)
Figure 4.13: Number of clusters per lipid molecule as a function of simulation time for OIL, GLYC
and MONO. The arrows indicate the points where the temperature was increased.
When we compare the largest cluster for the three systems (Figure 4.14), we can conclude that
for OIL this cluster is slightly larger than for GLYC and MONO, again due to the periodicity and
absence of a water layer. Upon a temperature increase, the largest cluster decreases more for OIL
and GLYC than for MONO, which is in agreement with the observation that the monolayer (the
largest cluster in MONO) does not loose its structure very fast. While the largest cluster decreases
for OIL and GLYC, the number of cluster per lipid (Figure 4.13) increases. This can be explained
by the fact that these systems behave like liquids at 360 K. And although the lipids in GLYC orient
in layers, this does not result in large clusters. So a monolayer is not formed as in MONO, due to
the higher temperature and corresponding mobility.
Another observation from Figure 4.14 is that the fluctuation in the largest cluster size decreases for
OIL and GLYC, whereas for MONO the fluctuation increases, again indicating that the monolayer
is loosing its structure, which is a result of fluctuating lipids. Longer simulations will probably
show the full convergence of MONO to GLYC. We note that we did not plot the distribution of
clusters, because of poor statistics.
66
Structural Properties of DLG in Bulk and at the Water Interface
6.0
OIL
4.0
3
largest cluster (nm )
2.0
0.0
2.0
6.0
2.5
3.0
3.5
4.0
GLYC
4.0
2.0
0.0
1.3
6.0
1.8
2.3
2.8
3.3
MONO
4.0
2.0
0.0
1.3
1.8
2.3
time (ns)
2.8
3.3
Figure 4.14: The largest cluster per system as a function of simulation time for OIL, GLYC and
MONO. The arrows indicate the points where the temperature was increased.
4.3.5
Radial distribution functions (rdf)
Another way of investigating the movement and clustering of the DLG molecules, is by calculating
the rdf’s of the oxygen molecules of DLG. We did this in two different ways: “normal” rdf’s
(g (r)) for CRYS and OIL, and angular dependent rdf’s (g (r; )) for GLYC and MONO. The last
method was used, because GLYC and MONO are non-homogeneous systems and the plots are
not converging to 1. G(r; ) was calculated by using 12 equally sized slices (0 to ), which were
later averaged into 6 slices (0 to 1/2 ), thereby using the symmetry of the system with respect to
reflection about the xy plane.
In Figure 4.15 we present the rdf’s of the five oxygen atoms of DLG with surrounding DLG
molecules for CRYS and OIL. At 300 K it is obvious that CRYS has more structure than OIL.
At higher temperatures, the plots become more smooth, indicating less structure. The difference
at 360 K between CRYS and OIL is not that profound, indicating convergence towards the same
overall structure, although CRYS has not yet reached its equilibrium as was observed in previous
sections.
The plots of g (r; ) of the hydroxyl oxygen (O2 ) with water for GLYC and MONO (data not
shown here) gave similar results as g (r ), in that the differences between GLYC and MONO were
not that profound. The data was averaged over 0.25 ns to see the evaluation of the rdf peaks in
Diffusion
67
time. Also different slices were compared. However, the differences between GLYC and MONO
were not obvious from these figures, as the movement of the oxygen atoms towards the interface
was not. This indicates, as for CRYS and OIL, convergence towards the same overall structure,
although MONO is not equilibrated yet.
4.0
g (r)
3.0
3.0
2.0
2.0
1.0
1.0
0.0
0.0
4.0
3.0
g (r)
4.0
CRYS O2 (300K)
CRYS O2 (360K)
OIL O2 (300K)
OIL O2 (360K)
0.5
1.0
1.5
CRYS O7 (300K)
CRYS O7 (360K)
OIL O7 (300K)
OIL O7 (360K)
0.0
0.0
4.0
3.0
CRYS O5 (300K)
CRYS O5 (360K)
OIL O5 (300K)
OIL O5 (360K)
0.5
1.0
1.5
CRYS O20 (300K)
CRYS O20 (360K)
OIL O20 (300K)
OIL O20 (360K)
4.0
3.0
2.0
2.0
2.0
1.0
1.0
1.0
0.0
0.0
0.5
1.0
1.5
0.0
0.0
0.5
1.0
1.5
0.0
0.0
CRYS O22 (300K)
CRYS O22 (360K)
OIL O22 (300K)
OIL O22 (360K)
0.5
1.0
1.5
r (nm)
Figure 4.15: Radial distribution functions of the five oxygen atoms as shown in Figure 4.1 with the
other diglycerides for CRYS and OIL at different temperatures. The plots at 360 K are shifted +1
on the y -axis for clarity.
4.3.6
Diffusion
From the slope of the mean square displacement (MSD) curve of (the center of mass of the)
particles versus time the diffusion constant D can be evaluated:
E
1 D
2
D = tlim
[r (t)
r
(0)] ;
!1 2dt
:2)
(4
where r(t) stands for the position vector of a particle at time t, and the brackets denote an ensemble
average. The number of dimensions is given by the factor d: d=1 for linear, d=2 for lateral, and
d=3 for bulk diffusion.
In Table 4.1 D is presented for CRYS, OIL, GLYC and MONO at the two temperatures. The data
for CRYS at 300 K shows that for the crystal there is no long time diffusion at this temperature,
and therefore CRYS is still in the crystal (-)phase. D does not vary much for the three other
68
Structural Properties of DLG in Bulk and at the Water Interface
Table 4.1: Apparent diffusion constants per lipid as a whole at different temperatures for CRYS,
OIL, GLYC and MONO, and for water (GLYC and MONO).
system
CRYS
OIL
GLYC
H2 O (GLYC)
MONO
H2 O (MONO)
D (cm2/s) at 300 K D (cm2 /s) at 360 K
2:6 (0:1) 10 8 2:4 (0:1) 10 6
7:4 (0:5) 10 7 3:2 (0:2) 10 6
1:2 (0:1) 10 6 5:4 (0:4) 10 6
2:9 (0:1) 10 5 6:3 (0:1) 10 5
1:0 (0:1) 10 6 3:0 (0:2) 10 6
2:6 (0:1) 10 5 5:9 (0:1) 10 5
2.5
2.5
CRYS (300K)
CRYS (360K)
OIL (300K)
OIL (360K)
2.0
2
MSD (nm )
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
4.0
0.2
0.6
0.8
1.0
GLYC (300K)
GLYC (360K)
3.0
0.0
0.0
2.5
0.2
0.4
0.6
0.8
1.0
0.8
1.0
MONO (300K)
MONO (360K)
2.0
2
MSD (nm )
0.4
1.5
2.0
1.0
1.0
0.0
0.0
0.5
0.2
0.4
0.6
time (ns)
0.8
1.0
0.0
0.0
0.2
0.4
0.6
time (ns)
Figure 4.16: Mean square displacement in time for CRYS, OIL, GLYC and MONO at the two
different temperatures.
systems at 300 K. From this table it is also obvious that upon temperature increase, D increases
by about a factor of three in all “liquid” systems. D for CRYS at 360 K is comparable with
OIL, so CRYS is also in the liquid phase at 360 K, although not yet equilibrated (see figure 4.6).
Furthermore, at both temperatures OIL has a lower D than GLYC, which can only be due to the
water layer in GLYC.
Diffusion
69
D for the water molecules in GLYC and MONO are also listed in Table 4.1, and it is obvious that
the water molecules show a higher diffusion compared to the lipid molecules at both temperatures.
When these values are compared with values of pure SPC systems [98], lower diffusion constants
are observed in our systems at both temperatures. This is due to the DLG molecules, because it
is observed that near interfaces the diffusion of the water molecules is slowed down by a factor of
two to three [24, 26, 94]. The higher motion for water is probably the cause of the higher motion
of the lipid molecules in GLYC compared to the lower D of the lipids in OIL at both temperatures.
In Figure 4.16 the MSD of all the DLG molecules (center of gravity) of the four systems is plotted
against time. From this figure it is clear that the lipid molecules diffuse on a nm scale within 1 ns
(except for CRYS at 300 K), so real diffusion is observed in these systems. This diffusion is more
profound for GLYC than for OIL and MONO. CRYS, OIL and MONO do not show constant
slopes at 360 K, indicating that these systems still behave inhomogeneously. The diffusion in
x; y; and z-direction is of the same order, so, e.g., no higher lateral diffusion is observed.
2 –1
D (cm s )
2.0e–05
OIL (300K)
OIL (360K)
1.5e–05
1.0e–05
5.0e–06
2 –1
D (cm s )
0.0e+00
GLYC (300K)
GLYC (360K)
1.5e–05
1.0e–05
5.0e–06
2 –1
D (cm s )
0.0e+00
MONO (300K)
MONO (360K)
1.5e–05
1.0e–05
5.0e–06
0.0e+00
0
20
40
60
80
100
120
molecule #
Figure 4.17: Diffusion per lipid molecule for OIL, GLYC and MONO at different temperatures.
In Figure 4.17 D is plotted for all DLG molecules, to be able to locate the molecules that show
a possible higher diffusion. From this figure it is clear that there is no significant difference in
behaviour between the lipid molecules. However, upon temperature increase the lipid molecules
70
Structural Properties of DLG in Bulk and at the Water Interface
show a wider spread in D . Also in this figure the higher diffusion of GLYC diglyceride molecules
compared to OIL is obvious. Another observation from this figure is the fact that the molecules
in the monolayer (MONO, lipid number 1 to 72) show similar diffusion behaviour with respect to
the oil phase (number 73 to 122), which is comparable to OIL. So there is almost no difference in
behaviour between lipids in contact with water, in the monolayer or in the oil phase.
4.4 Conclusion
We have described four different Molecular Dynamics (MD) simulations of 1,2-dilauroyl-snglycerol (DLG) systems: a crystal simulation (CRYS), a pure DLG oil phase (OIL), a DLG oil
phase in contact with a water layer (GLYC) and an oil/monolayer/water simulation (MONO).
All these systems were simulated for several nanoseconds in total. The behaviour of the DLG
molecules in the lipid phase as well as at the aqueous interface is described.
The overall properties like density, hydrogen bonding and rdf’s converged at the different temperatures. CRYS and OIL tend to converge to the same overall structure, as do GLYC and MONO,
although equilibrium for CRYS and MONO has not yet been reached compared to their counterpart. We can conclude that the rearrangement of the DLG molecules in these DLG systems is a
slow process, but we estimate that the equilibrium for these systems at 360 K, the liquid phase,
will be reached within a few nanoseconds. This is supported by the calculated diffusion rates of
the lipid molecules: the DLG molecules diffuse over nanometers on a nanosecond time scale.
The presence of an aqueous interfaces in GLYC resulted in a layering of the DLG molecules: the
oxygen atoms moved towards the water phase, where they preferred to be hydrogen bonded to
the water molecules. Due to this movement, a “hydrophobic” layer of lipid tails is formed next
to this “hydrophilic” layer. This layering is not observed in the pure oil phase (OIL) at the same
temperature.
Also noted is the fact that the melting of the crystal (at 360 K) can be simulated with our force
field, although we made use of united atoms, and not of reported better force fields for densily
packed systems, e.g., anisotropic united atoms (AUA) [99] or all atoms.
Gezien
dr. J.T.W.M. Tissen