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Biophys J, October 2000, p. 1718-1730, Vol. 79, No. 4
and
*Faculty of Biology, University of Bucharest, 76201 Bucharest,
Romania; and Lehrstuhl für Biocomputing, IWR,
Universität Heidelberg, D-69120 Heidelberg, Germany
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
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Molecular dynamics simulations have been performed of the
sequence-symmetric cyclic decapeptide antibiotic gramicidin S (GS), in
interaction with a hydrated dimyristoylphosphatidylcholine (DMPC)
bilayer, and the results compared with a "control" simulation of
the system in the absence of GS. Following experimental evidence, the
GS was initially set in a single antiparallel 
-sheet conformation with two Type II' -turns in an amphiphilic interaction with the membrane. This conformation and position remained in the 6.5 ns simulation. Main-chain dihedrals are on average ~26° from those determined by NMR experiment on GS in dimethylsulfoxide (DMSO) solution. Sequence-symmetric main-chain and side-chain dihedral angle
pairs converge to within ~5° and ~10°, respectively. The area
per lipid, lipid tail order parameters, and quadrupole spin-lattice relaxation times of the control simulation are mostly in good agreement
with corresponding experiments. The GS has little effect on the
membrane dipole potential or water permeability. However, it is found
to have a disordering effect (in agreement with experiment) and a
fluidifying effect on lipids directly interacting with it, and an
ordering effect on those not directly interacting.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
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There is much interest in understanding the interaction of peptides with lipid bilayers at atomic detail. This requires characterization of the position, orientation, structure, and dynamics of the peptide in the lipid bilayer and its effects on surrounding lipids. Although molecular dynamics (MD) simulation can in principle furnish complete structural and dynamical information, considerable obstacles exist to obtaining accurate results, due partly to inexact force fields and other approximations in simulation methodology, and partly to the relaxation times of some important dynamical phenomena being of the order of or longer than those presently accessible to MD.
Gramicidin S,
[cyclo-(Leu-D-Phe-Pro-Val-Orn)2,
(GS)] is a cyclic decapeptide that is of particular interest for
pursuing peptide/membrane MD studies. The sequence and structure of the
peptide are relatively simple. NMR, x-ray, and MD studies indicate that
the backbone adopts an antiparallel -sheet with two Type II'
-turns in various solutions of different polarity and in the
crystalline form (Jones et al., 1978
; Hull et al., 1978; Mihailescu and
Smith, 1999). One consequence of this is that the GS structure is
amphipathic, with the hydrophobic side chains on one side of the
molecule and the hydrophilic ones on the other, and this provides a
logical geometry for interaction with a lipid membrane, with the polar side of GS at the lipid/water interface and the nonpolar side interacting with the lipid tails. Considerable experimental evidence exists that this is indeed the case and a variety of biophysical studies on the interaction of GS with model lipid membranes have confirmed that it interacts primarily with the headgroup and
interfacial polar/apolar regions (Datema et al., 1986; Zidovetzki et
al., 1988; Prenner et al., 1997; Higashijima et al., 1986). The
sequence symmetry also provides a natural test of convergence of
certain properties in the simulation which, when time-averaged, should be identical for the two halves of the molecule.
Also of interest is that GS has antibiotic action via membrane ion
permeability change (Katsu et al., 1989; Portlock et al., 1990). For
this reason over 200 analogs have been synthesized with the aims of
better-defining its structure-activity properties and extending the
activity of the compound to produce a more potent and specific
antibiotic. The presence of the amphipathy (or "sidedness") and the
-turns appears to be required for activity (Katsu et al., 1987).
Although a complete description of how GS induces ion permeability is
probably beyond the capability of present-day simulation methods, they
can be used to provide information on how GS interacts with and
perturbs lipid bilayers under simple controlled conditions. In initial
simulation work we performed a 5-ns MD calculation of GS in DMSO
solution, enabling detailed comparison with NMR results in the same
solvent (Mihailescu and Smith, 1999). Here we extend this work to an
analysis of the interaction of GS with a hydrated DMPC membrane
bilayer. DMPC was chosen as a well-studied model system, and because
NMR data exist on the disordering effect of GS on DMPC lipid bilayers.
We report on two MD simulations, one of GS in interaction with a hydrated DMPC bilayer and a "control" simulation of a hydrated DMPC bilayer in the absence of GS. The control simulation is used to check the validity of the simulation method with respect to spectroscopic and diffraction data, and to use for comparison of the lipid molecule structure and dynamics in the presence and absence of GS.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
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Two simulations were performed, one of GS interacting with a hydrated DMPC bilayer (subsequently called the "GS/DMPC" simulation) and one of a hydrated pure DMPC bilayer (subsequently called the "control" simulation).
The effect of GS on membranes varies with lipid composition, and
13P-NMR and x-ray diffraction have provided
evidence for lipid polymorphism in gramicidin S-lipid systems (Prenner
et al., 1997). However, both in the gel and liquid-crystalline states
hydrated DMPC doped with GS exists exclusively as a bilayer (Prenner et
al., 1997). In the present GS/DMPC simulation the microscopic system is
a single GS molecule interacting with a hydrated DMPC bilayer with 38 molecules of DMPC (17 in the layer containing GS (the "GS" layer)
and 21 in the layer not containing GS (the "non-GS" layer) and 1666 water molecules, i.e., a total of 9656 atoms. The resulting lipid/GS
ratio (38:1) is far higher than that at which GS destroys bilayers:
total bilayer disruption occurs only at ratios of <3:1 (Zidovetzki et
al., 1988). At 25:1 the DMPC membranes are still in bilayer form
(Prenner et al., 1997).
A "control" simulation, of DMPC without the peptide, was also performed. The control system consisted of 42 DMPC molecules and 1734 water molecules i.e., a total of 10,158 atoms. For consistency, both simulations started with the same primary box dimensions: 37 × 37 × 70.6 Å3. Consequently, the number of water molecules is slightly different in the two systems.
System size effects must be considered. Although these may influence
bilayer and peptide insertion properties, there is some indication that
the system size chosen is reasonable for the present purposes. First,
MD simulation studies on hydrated DMPC bilayers with different numbers
of lipid molecules per monolayer have indicated that a bilayer of 18 DMPC molecules per monolayer is sufficient for characterizing many
bilayer properties (Stouch, 1993). Moreover, the water/lipid ratio in
the present work is 44:1, well above the ratio of 20.5:1, above which
the bilayer structure does not noticeably change with hydration
(Marrink et al., 1993). X-ray experiments suggest that the basic
structural characteristics of the dipalmitoyl phosphatidylcholine
(DPPC) bilayer are maintained even at 15.3 waters/lipid (Nagle et al.,
1996).
In what follows the membrane normal is oriented along the z axis and the center of the bilayer is at z = 0. The x and y axes are therefore parallel to the membrane plane. Periodic rectangular boundary conditions were applied in the x and y directions to simulate an infinite planar layer and in the z direction to simulate a multilayer system.
The program used was CHARMM Version 26 (Brooks et al., 1983). The
all-atom CHARMM force field version 22.0 was used for the lipids
(Schlenkrich et al., 1996) and all peptide (MacKerell et al., 1998)
residues except Orn. The force field for Orn, which is the same as Lys
except that it has one less CH2 group, was published in Mihailescu and Smith (1999). The water model was TIP3P
(Jorgensen et al., 1983) modified as in current use in CHARMM. The
electrostatic interactions were smoothed using the SWITCH method
(Brooks et al., 1983), which involves multiplication by a cubic
function, in this case between 8 and 12 Å. During the NVE and NPT
dynamics bond lengths involving hydrogen atoms were constrained with
the SHAKE algorithm, thus allowing the use of a time step of 2 fs.
There are various ways of treating macroscopic boundary conditions in
MD, discussed in the case of lipid bilayer systems by Tieleman et al.,
1997. Two of the most frequently used are N (number of
molecules) V (volume) E (energy), and
N (number of molecules) P (pressure) T
(temperature) in which the named parameters are kept constant during
the simulation. Constant pressure algorithms allow the surface area per
lipid to vary, and thus be compared with experiment. Another property
to be considered is the surface tension. It has been pointed out that
if the surface tension of the bilayer membrane is not zero the
membrane, if free to compress or expand, will adopt a state in which
the attractive and repulsive interactions balance each other
(Jähnig, 1996). In this situation the free energy is minimal with
respect to the area of the membrane, and the derivative of the free
energy with respect to the area, the surface tension, will vanish.
However, long wavelength undulations, intrinsically associated with the
value of the macroscopic surface tension, are absent in a simulation
cell that is constrained by periodic boundary conditions. To reduce the
consequences of this system size effect, a small surface tension might
therefore be appropriate, even if the macroscopic tension should be
zero (Feller and Pastor, 1996). However, direct comparison of membrane
simulations with (28 mN/m) and without surface tension revealed no
significant differences in the results (Tieleman and Berendsen, 1996).
In the present work no surface tension was applied.
We choose here NPT conditions, allowing the box dimensions to vary. The
Langevin piston algorithm was used (Feller et al., 1995). This method
is appropriate for inhomogeneous systems such as aqueous biopolymers,
liquid/liquid interfaces, and lipid bilayers containing peptides, for
two reasons. First, for such systems no large temperature difference
between the components of the system is created, and therefore it is
not necessary to couple the different components to separate heat
baths. Second, the method has the advantage of not being critically
dependent on the choice of the piston parameters.
The method for constructing the initial configuration of the GS/DMPC
system and the equilibration mostly follows that used in the simulation
of Gramicidin A/DMPC (Woolf and Roux, 1994, 1996) and described in Roux
and Woolf (1996). The main steps were as follows.
GS/DMPC simulation
Initial system geometry
An initial equilibration was performed at 330 K, higher than the final simulation temperature (305 K) to allow increased exploration of the local conformational space. To derive an initial geometry for this simulation the area per lipid was taken as 64 Å2, estimated by extrapolation from the experimental values of 59.6 ± 0.5 Å2 at for DMPC at 30° (Petrache et al., 1998; König et al., 1997) and
62.9 ± 1.3 Å2 for DPPC at 50°C (Nagle et
al., 1996). The cross-sectional area of the GS was calculated using the
method of Lee and Richards (1971) to be ~258
Å2 and, using the value of 64 Å2 for the DMPC cross-section, the layer
containing GS should then contain four lipids fewer than the layer
without GS.
The starting conformation of GS was chosen as one of the most
C2-symmetric geometries obtained in the
preliminary MD study of GS in DMSO (Mihailescu and Smith, 1999). This
conformation was positioned with the Orn 
N atoms at
z = 17 Å, with the plane defined by the heavy atom
backbone of GS placed parallel to the membrane plane and the associated
symmetry axis parallel to the z axis. This insertion
geometry is consistent with a variety of biophysical experiments on
GS/membrane interactions and satisfies the amphiphilicity of the
molecule, with the Orn residue side chains at the polar interface and
the hydrophobic side chains interacting with the lipid hydrophobic
tails (Davis et al., 1983; Katsu et al., 1987). Moreover, in this way
both phenylalanines are also at the lipid/water interface. The presence
of aromatic amino acids such as tryptophan, tyrosine, and phenylalanine
near the interfacial region is a feature of several membrane proteins (see Woolf and Roux, 1996 and references therein; and Woolf, 1998).
To determine the position of each of the 17 lipids in the GS-containing
layer and 21 lipids in the non-GS layer, the polar headgroups were
represented as spheres of cross-sectional area 64 Å2. The positions of the spheres were
constrained at z = 17 Å (the same level as the Orn N atoms) for the upper layer and z = 
17 Å for the
lower layer. Short energy minimization and Langevin dynamics runs were
used to arrange the spheres around the peptide and to obtain the
desired dimensions of the system. The van der Waals parameters of the
spheres approximated the polar group of the lipid molecule.
The spheres were substituted by all-atom DMPC molecules, randomly
chosen from a library of 2000 preequilibrated and prehydrated (with
~20 water molecules) lipids, obtained by empirically adjusting the
force field parameters to reproduce experimental deuterium quadrupolar
splitting order parameters and 13C-NMR relaxation
times of the acyl chains (Venable et al., 1993). The center of any
given sphere was used to place the center of mass of the phosphorus and
nitrogen atoms of the corresponding lipid polar head.
Rigid-body rotations of the lipids around the z axis and
translations in the xy plane were performed to minimize the
number of unfavorable contacts and atomic overlaps. The remaining bad contacts were removed by energy minimization.
The system was then fully hydrated by overlaying a preequilibrated
water box of the appropriate dimensions in the x and
y directions. The resulting starting conformations for the
DMPC/GS and control primary simulation boxes are shown in Fig.
1.
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Initial all-atom equilibration
A number of position constraints were used at the beginning of the ensuing equilibration period to ensure a smooth relaxation of the system toward an equilibrated configuration. Harmonic constraints were initially applied to all the atoms of GS to prevent its changing position and orientation in the bilayer, and the polar headgroups of the lipids were kept around z = ±17 Å using planar harmonic constraints of the form V = k(d do)2, where
k is the force constant (5.0 kcal/mol/Å2), d is the distance from
the plane to each atom at a given time, and
do is the same distance in the initial
frame. A similar planar potential was applied to the water atoms to
prevent their penetration into the bilayer region.
The above constraints were gradually reduced during 125 ps of Langevin
dynamics equilibration, performed with a friction coefficient of 3.0 ps
1 applied to all
non-hydrogen atoms. A further 25 ps of equilibration was performed
without the Langevin bath.
NVE equilibration
Following the constrained equilibration, a 3 ns NVE equilibration at 330 ± 4 K was performed. During this equilibration step a cylindrical potential was applied to all the atoms of DMPC and GS to prevent drift of the lipids and peptide. This was of the form k(r ro)2 with
k = 5.0 kcal/mol/Å2, and where
r is the distance of any given atom from an axis parallel to
z.
NPT equilibration
After the NVE equilibration an NPT equilibration was performed and the dimensions of the orthorhombic cell were monitored. The constraints on the lipids were removed but those on the peptide were kept to prevent it drifting. For this simulation step the parameters were the following: the mass of the pressure piston was 100.0 amu, the Langevin piston collision frequency was 10.0 ps1, and the thermal
piston mass was 250.0 kcal ps2. An isotropic
pressure of 1 atm was applied. The temperature was kept constant at 305 K, above the gel-to-fluid phase transition midpoint temperature of the
system (297 ± 0.2 K) and at the same temperature as in the DMPC + GS NMR study to which certain results are compared (Zidovetzki et al.,
1988). After 0.5 ns of NPT equilibration the simulation box dimensions
appeared to have equilibrated (see Results).
NPT production
Three ns of NPT production dynamics were run, with no constraints. This production was used for the analysis.Control simulation
For the control simulation the same steps as above were
performed apart from the NVE dynamics, which was not needed because the
lipids were chosen from an already preequilibrated library (Venable et
al., 1993). After equilibration at 330 K an NPT dynamics run at 305 K
was performed. Again, the dimensions of the dynamic cell were
monitored. After 0.75 ns these dimensions had reached approximate
plateaus (Fig. 2, right
panels). The equilibration was continued until 0.9 ns. The NPT was
continued for another 2.0 ns production, which was used for the
subsequent analysis.
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The coordinates were saved every 50 steps. A total of 9.55 ns were run, taking approximately 4320 Central Processing Unit hours on a cluster composed of four dual Pentium II/450 MHz nodes, running in parallel, using the LINUX operating system. The analysis of the non-bonded interaction energies between GS and each DMPC molecule required a further 240 h of CPU.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
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GS structure and dynamics
Position and orientation of GS
The position and orientation of GS relative to the bilayer during the equilibration and production periods are shown in Fig. 2, A and B. Fig. 2 A presents the projections of the normal to the plane fitted to the backbone heavy atoms of GS. This plane can be described by the equation lx + my + nz = p. If n is the vector normal directed through the plane from the origin of the Cartesian axes (x, y, z), then l, m, n are the axis projections of n and p is the projection of r on n, where r is the position vector of a point on the plane relative to the origin of the axis. During the NVE equilibration GS diffused into the bilayer, with its center of mass 3-4 Å deeper into the hydrophobic core than at the beginning of the equilibration (Fig. 2 B). A tilt of the GS backbone plane relative to the z axis (the n projection) was also observed during this phase. After ~1 ns of NVE equilibration the GS molecule regained its initial membrane/water interfacial position with the backbone and membrane planes parallel to each other (n projection
1). During the 3.0 ns NPT
production dynamics the average position of GS relative to the membrane
remained practically unchanged.
Backbone structure and H-bonding
Experiments using x-ray diffraction (Hull et al., 1978), circular
dichroism (Balasubramanian, 1967), and NMR (Stern et al., 1968) and MD
of GS in DMSO solution (Mihailescu and Smith, 1999) have shown that GS
adopts a robust antiparallel -sheet with two Type II' -turns both
in the crystalline form and in various solutions. This was also the
case throughout the present simulation. Both experimentally and in the
present and previous simulations two pairs of backbone hydrogen bonds
for GS were found, involving O-Leu-1 ... NH-Val-4, O-Leu-6 ... NH-Val-9, O-Val-4 ... NH-Leu-1, and O-Val-9 ... NH-Leu-6.
During the GS/DMPC simulation the O ... N (Leu-1 ... Val-4 and
Leu-6 ... Val-9) distances were = 3.5 ± 0.5 Å and
3.4 ± 0.4 Å, respectively, and those for N ... O (Leu-1
... Val-4 and Leu-6 ... Val-9) were 2.8 ± 0.1 Å and
3.0 ± 0.2 Å. The values for the two members of each pair of
distances are remarkably close, suggesting that this aspect of the
structural symmetry of the system has converged.
Main-chain dihedrals
The main-chain dihedral angle averages are given in Fig. 3 A together with the corresponding NMR values of GS in DMSO solution (Xu et al., 1995). The
average standard deviation between the NMR and MD values is 26°, and
most dihedrals are in the same minimum as in the NMR experiment. In
comparison, in the simulation of GS in DMSO solution this value was
18°, slightly closer to experiment (Mihailescu and Smith, 1999),
consistent with the use of the experimental solvent, DMSO. The slightly
larger deviation from the experiment in the present work may therefore
be an environmental effect. As in the previous solution simulation, the
backbone remains in one potential minimum during the simulation, and no
conformational transitions were found for any of the backbone
dihedrals. This is consistent with experimental findings for GS, which
indicate that the pleated sheet structure is an extremely rigid
conformation found in the crystalline form (Hull et al., 1978) and
retained in solvents differing widely in their polarity (Ovchinnikov
and Ivanov, 1975). 2H-NMR data are
consistent with this conformation of GS in DPPC bilayers (Datema et
al., 1986).
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) is plotted in Fig. 3 B. Improving
convergence with time is apparent. After 3 ns the sequence-symmetric main-chain dihedrals are the same to within ~5°, indicating a high
degree of corresponding structural symmetry and approximate convergence
of this aspect of the simulation. The side-chain pairs of the two
halves of the molecule converge to within ~10°, indicating that the
side-chain rotameric states are reasonably well-sampled.
In the MD simulation of GS in DMSO it was found that the fluctuations
of 
i and 
i+1 are
anticorrelated (Mihailescu and Smith, 1999). Fig.
4 indicates that similar short-range
correlation effects are present for and angles of GS in the
DMPC bilayer.
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Side-chain H-bonds
The interactions of the Orn side-chain ammonium groups are of particular interest. It has been suggested that they form salt linkages with phospholipid headgroups (Pache et al., 1972). Another possibility
is the existence of hydrogen bonding between the
N
of Orn and the CO of Phe (Hull et al., 1978;
Krauss and Chan, 1982; Xu et al., 1996). If the latter hydrogen bonding
exists it may be of order i 
I + 2 or i
I 3, where i is the residue number. In the previous simulation work of GS in DMSO a hydrogen bond
was found for one-half of the molecule, between
N of Orn and the CO group of the D-Phe that
follows it, i.e., i I + 2 (Mihailescu and Smith, 1999).
This was only partially occupied, as was found in an NMR investigation
of GS in methanol (Krauss and Chan, 1982).
In the present GS/DMPC simulation the Orn side chains again interact
with Phe. The donor ( N of Orn)-acceptor (O of Phe) distances are
Orn-5-Phe-2, 8.3 ± 1.1 Å; Orn-5-Phe-7, 4.8 ± 1.1 Å;
Orn-10-Phe-2, 5.4 ± 1.2 Å, Orn-10-Phe-7, 8.1 ± 0.8 Å.
Again, the symmetry-related partners show similar distance values.
Although none of the above four average values appear consistent with
hydrogen-bonding, time series of the distances between N Orn-5
... O Phe-7 and N Orn-10 ... O Phe-2 show the existence of a
conformational equilibrium between hydrogen-bonded and
non-hydrogen-bonded geometries (Fig. 5, A and B). The
corresponding population distributions are shown in Fig. 5,
C and D, together with fitted Gaussians for each
of the two populated states. The Gaussians are at 4.33 ± 0.03 Å, 6.31 ± 0.02 Å, and 3.73 ± 0.03 Å, 5.59 ± 0.05 Å for the two pairs indicating the existence of very weak i
I + 2 hydrogen-bonding populations. The potentials
of mean force, U, determined from the probability
distributions are given in Fig. 5, E and F. These exhibit two shallow wells with barriers between them of ~0.1-0.2 kcal/mol, i.e., significantly lower than
kBT.
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Lipid structure and dynamics
Area per lipid
Time series of the dimensions of the dynamic cells for the GS/DMPC and control simulations are shown in Fig. 6. During the NPT equilibration the system sizes relax to approximate plateaus, and in the subsequent NPT production drift only slightly. For the control system the area per lipid passes from 64 Å2 at 330 K (the temperature of the NVE equilibration) to 60 Å2 at 305 K (the temperature of the NPT equilibration) in 0.75 ns. For the entire 305 K control NPT production the area per lipid is 60.03 ± 0.78 Å2, in good agreement with the corresponding experimental value of 59.6 ± 0.5 Å2, which was obtained at a slightly lower temperature, 303 K (König et al., 1997; Petrache et al., 1998).
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) in 1-Å-thick
slabs normal to the z axis, and the maximal value of the
area was kept. The time-averaged maximal cross-sectional area of GS was
272 ± 11 Å2. Subtracting this from the
xy area of the system and dividing the result by 17, the
number of lipids in the GS layer, gives a value of 54 ± 2 Å2, which is again smaller than in the control
system. However, if the volume under the peptide, which is also
occupied by lipid chains, is included then the area per lipid increases
to ~70 Å2 in non-GS layer. Averaging over
lipids in both layers then gives 63 Å2,
indicating an apparent increase in the area per lipid relative to the control.
Headgroup atom distributions
Headgroup atom distributions along the bilayer normal (z axis) are shown for both monolayers in the GS/DMPC and control simulations in Fig. 7. Following Essemann and Berkowitz (1999) to quantify the degree of symmetry
between the two layers of the membrane, the distribution functions
obtained for each layer were fitted with Gaussian functions and the
positions and widths of the Gaussians compared. For the control
simulation the widths were 3.88 ± 0.20 Å and 3.67 ± 0.29 Å for O, 3.61 ± 0.31 Å and 4.44 ± 0.45 Å for N, and
3.83 ± 0.25 Å and 3.72 ± 0.30 Å for P. Although the
N-distributions in the two halves of the bilayer are slightly
asymmetric, those for O and P are not significant.
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Interaction energies
Thermograms of GS/DMPC mixtures have been graphically resolved into components attributed to "free" lipids and those "perturbed" by the interaction with GS (Wu et al., 1978). To find
an approximate simulation equivalent the non-bonded interaction
energies between GS and the individual lipid molecules were examined
(Fig. 8). A continuous range of
interaction energies is seen. Nine lipids from the GS-layer have
average interaction energies greater than kBT, and in what follows these
are considered as "bound" to the GS. The remaining eight GS-layer
lipids are "free," as are the 21 from the non-GS layer.
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6.2 ± 2.2 kcal/mol) comes from the interaction with Orn-10 (4.4 ± 1.2 kcal/mol) and this
contribution is larger than the electrostatic component, which is
3.3 ± 1.8 kcal/mol. The average electrostatic interaction
energy between GS and DMPC 1 is positive, 2.9 ± 1.0 kcal/mol.
Solvation of GS
In Fig. 9 are plotted the numbers of lipid groups (head or tail) and water molecules that are in the proximity of each amino acid residue of GS. Leu and Val are the only residues with no headgroup interactions, consistent with their nonpolar nature. The number of nonpolar tail groups close to the polar Orn-10 is maybe surprisingly large. However, this complex environment found for Orn-10 is similar to that observed for a Lys residue during the MD simulation of melittin in a DMPC bilayer (Berneche et al., 1998). The
nitrogen atoms of Orn are involved in flickering intramolecular H-bonds
with Phe (Fig. 5).
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; Halladay et al., 1990;
Huster et al., 1999). This may in principle reflect either close
approach of protons in space (i.e.,. molecular disorder) or spin
diffusion (Halladay et al., 1990; Volke and Pampel, 1995), although it
appears to be unlikely that the latter effect contributes (Huster et
al., 1999; Huster and Gawrisch, 1999). In the present simulations only
one lipid terminal methyl group, in the non-GS-layer of the DMPC/GS
simulation, came transiently within 6 Å of a headgroup, the latter
belonging to another group in the same layer, suggesting that this type
of event is very rare in the present simulation model.
Correlation times and order parameter profiles
2H-NMR provides two distinct kinds of information on membranes: orientational order and fluidity (Bloom et al., 1991). No simple relationship between the two quantities is known
for a lipid bilayer (Seelig, 1977). Fluidity here refers to the rate of
motion and not to the ordering of the molecular system, as exemplified
by the so-called glass-type materials that are disordered but rigid. From a simulation trajectory both properties can be evaluated.
The order parameter of the carbon-deuterium bond,
SCD, is defined by
SCD = 
1/2 (3 cos2 
(t) 1)
, where
(t) is the angle between the carbon-deuterium bond vector
and the bilayer normal; "" means "time average." Fig.
10 A presents experimental
and simulation-derived order parameters for the sn-2 chains of the
control system. With one exception (the C2 atom) the order parameters
in the control simulation are close to experiment. For C2 experiment
suggests the presence of two long-living conformations: the relatively
long convergence times for this carbon may contribute to the difference
with experiment for C2 seen here and in previous simulations (Tieleman
and Berendsen, 1996).
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2SCD) in Fig. 10 B. The
figure also shows experimental data obtained using NMR quadrupole
splitting experiments on fully deuterated multilamellar dispersions of
DMPC doped with GS at a molar ratio of 1:5.5 at 305 K (Zidovetzki et
al., 1988). The results show again that the free lipids are more
ordered than in the control simulation. The bound lipid order
parameters are close to the experimental values of Zidovetzki et al.
(1988). Clearly, the lipids interacting with GS are more disordered.
The narrowing of the width distribution for the headgroup O, N, and P
atom distributions in the GS simulation (Fig. 7) suggests that peptide
might be ordering the phospholipid headgroups. To verify this the order
parameters of the CH bonds of the two methylene groups between the
phosphate and ammonium groups in the lipid heads were computed. The
results (not shown) indicate that bound lipid headgroups have a similar
order to the control, whereas the free lipids are significantly more ordered.
NMR relaxation parameters probe angular correlation functions of the
relaxing nucleus. These correlation functions and their Fourier
transforms, the spectral densities, can be obtained directly from MD
trajectories. For an 13C nucleus in a DMPC tail
the geometrical quantities of interest are spherical polar coordinates
(with respect to a laboratory frame) of the C-H internuclear vectors.
The T1 values were computed from this
using the equations given in Levy et al. (1981) and Brüschweiler
et al. (1992). The required correlation functions reached plateau
values in a few hundreds of picoseconds (data not shown).
If the anisotropy of the motion is neglected and the motion assumed to
fall into the extreme narrowing limit of the NMR resonance (
o2 
c2 
1;
o is the resonance frequency) then
T1 and c are
the quadrupole spin-lattice relaxation time and the rotational
correlation time of the lipids, respectively, assuming that
T1 is independent of the vesicle
tumbling rate, the following equation may be written (Brown et al.,
1979):
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) denotes the static
quadrupole constant (170 kHz for carbon-deuterium bonds). Using this
equation the T1 values were
used to compute c assuming (1 SCD)2 ~ 1.
The calculated c are plotted in Fig.
11 A together with
experimental values obtained from quadrupole spin-lattice relaxation times, T1, of deuterium-labeled DPPC
bilayer, at 51°C (Brown et al., 1979). The experiment and simulation
are in approximate agreement. Fig. 11 A also shows that the
fluidity of the bound lipids is increased. The origin of the increased
fluidity is a priori unknown. However, one possibility lies in the
dihedral transitions. These are plotted in Fig. 11 B for the
bound, free, and control lipid tails. The differences between the total
numbers of transitions are small, although a slightly higher number of
transitions is observed for the bound lipids, consistent with the
increased fluidity.
|
Electrostatic potential
The electrostatic potential difference from the center of the membrane may play a role in ion permeability (Brockman, 1994). Phloretin and gramicidin A are known to affect this potential difference (Cseh and Benz, 1999; Shapovalov et al., 1999). The potential profile was calculated by integrating the charge density as
follows:
|
(z) denotes the electrostatic potential and
(z) the charge density. The total and component
electrostatic membrane dipole potentials for GS-DMPC and control
systems are shown in Fig. 12. In the
present study, values closer to experiment were obtained if the
dielectric constant, 
was considered equal to 20, where 0 is the
vacuum permittivity. The same approach was used in Tieleman and
Berendsen (1996) while other studies have considered = 0 (for example, Essemann and Berkowitz, 1999).
|
0.6 V are
obtained, with the membrane interior positive compared to the exterior.
Experimentally, this quantity is rather difficult to obtain (Brockman,
1994). Measurements on PC/water interfaces have obtained somewhat lower
values, between 0.2 V (Gawrisch et al., 1992) and 0.4 V (Pickar and
Benz, 1978).
As discussed above, there is a change in the headgroup orientation in
the GS layer. Fig. 12 shows that this change is reflected in the
headgroup contribution to the dipole potential, which differs significantly from the control. The contribution of GS itself to the
total membrane dipole potential is small. The total dipole potential
computed from the DMPC-GS simulation remains symmetric and close to
that of the control, due in part to compensation of the effects of
asymmetry in the contributions of lipids and water. Indeed, it has been
suggested that reorientation of the water can play a significant role
in balancing the dipole potential (Essemann and Berkowitz, 1999).
Water
Finally, we examine the water molecule distributions in the two simulations. These are given in Fig. 13, A and B. The number of water molecules outside the membrane is different because the two systems contain different total numbers of water molecules, having been initially constructed with the same size. The distributions in the control and GS/DMPC simulations are similar. However, a small but significant asymmetric feature is observed within the GS/DMPC system, illustrated in Fig. 13C in which the difference between the time-averaged number of water molecules in opposite monolayers is plotted (positive z is the GS layer). The positive difference indicates that more water molecules penetrate into the non-GS layer. From a total of 1666 water molecules in the system, only four penetrated to within 3 Å of the center at any moment during the trajectory, these making only transient visits. None of these actually cross the membrane.
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CONCLUSIONS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
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The approach taken in the present work on peptide/membrane interaction was to perform a control simulation of a hydrated model phospholipid bilayer and to investigate perturbative effects of a peptide on it in a second simulation. It is encouraging that the variety of properties of the control (hydrated DMPC) simulation examined are in overall agreement with experiment (area per lipid, lipid tail order parameters, quadrupole spin-lattice relaxation times), giving confidence in the simulation methodology and in the description it affords of the qualitative changes induced by GS.
The simple C2-symmetric cyclic GS decapeptide has significantly limited
conformational flexibility, and its experimentally observed
antiparallel -sheet conformation with two Type II' -turns is
rigidly retained over the 3-ns length of the present simulation. This
conformation leads to an amphipathic "sidedness" in the side-chain orientations and, after an excursion during the initial equilibration, GS returns to its initial orientation and position at the polar interface and remains there. The main-chain dihedrals are close to
those of NMR experiment on GS in DMSO. Of particular interest is the
observation that sequence-symmetric main-chain and side-chain dihedral
angle pairs gradually converge to within ~5° and ~10°, respectively, on the time scale examined.
The effects of gramicidin S on the membrane structure and dynamics are
smaller than have been seen in some peptide/membrane simulations. For
example, in the work on the melittin-DMPC system significant local
thinning of the bilayer was seen (Berneche et al., 1998); this may be
related to the significantly larger size of melittin (26 residues). GS
has little effect on the electrostatic potential difference between the
center and outside of the membrane and there is no noticeable effect on
the water permeability over the accessible time scale. There is,
therefore, no clear indication from the present simulation as to how GS
affects membrane permeability. This is not surprising, as the GS/lipid
ratio here is significantly lower than would be required for
permeability effects to be clearly detectable experimentally. Moreover,
as only a single GS molecule is included in the system, the present
simulations do not allow mechanisms involving peptide-peptide
associations to be probed.
However, lipid perturbation by a single GS molecule is clearly an
essential first step toward understanding permeability effects. For
example, pore formation has been suggested to occur due to the
bilayer-disturbing mechanisms of amphipathic peptides (Bechinger, 1999). Here, a significant reduction in the solvent-accessible area per
lipid is seen in both the non-GS-containing and GS-containing layers of
the GS/DMPC system. This may be relevant for explaining electron
paramagnetic resonance data that indicate that GS decreases the amount
of an amphiphilic spin label (Tempo) incorporated into the hydrophobic
regions of phospholipid vesicles (Hubbel and McConnell, 1968). It was
speculated that GS might tend to freeze the otherwise fluid hydrophobic
regions and therefore to decrease the volume available to the
amphipathic label, consistent with the present findings. However, as
discussed in the Results section, the result for the area per lipid in
the peptide-containing layer depends on whether the peptide
cross-sectional area is included.
In the present work GS has a small but significant effect on membrane
thickness here, but no clear effect on membrane curvature, which is
also of interest in light of the suggestion that localized increases in
membrane monolayer curvature stress may be part of the mechanism
through which GS exhibits its antimicrobial and hemolytic activities
(Prenner et al., 1997).
The "bound" lipids are more disordered (in agreement with NMR
experiment) and more fluid, an effect that has been observed for almost
all the lipid-protein interactions studied so far by NMR and computer
simulation techniques, an exception being the MD studies on gramicidin
A in DMPC (Woolf and Roux, 1996; Chiu et al., 1999). The lipids in the
GS/DMPC system not interacting with GS are ordered relative to the
control lipids. The possibility that this is a simulation artefact
cannot be ruled out, as long-range collective effects may be sensitive
to system size, simulation length, force field, and pressure effects.
However, this intriguing indirect effect certainly merits further investigation.
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FOOTNOTES |
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Received for publication 10 December 1999 and in final form 13 July 2000.
Address reprint requests to Dr. Jeremy C. Smith, Lehrstuhl für Biocomputing, IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany. Tel.: 49-6221-54-88-57; Fax: 49-6221-54-88-68; E-mail: biocomputing{at}iwr.uni-heidelberg.de.
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REFERENCES |
|---|
|
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
CONCLUSIONS
REFERENCES
|
|---|
the ordering of water and its relation to the hydration force.
Langmuir.
9:3122-3131
phase dipalmitoylphosphatidylcholine bilayers.
Biophys. J.
70:1419-1431
)
torsion angles during the, NVE, and NPT dynamics.
) and control (
). To obtain
these the systems were divided into 1 Å bins and the time-averaged
numbers of atoms calculated. The size of the symbols corresponds to the
highest fluctuation of the values.
); "free"
lipids from the layer without GS (
); control simulation (
);
"bound" lipids (
) (Douliez et al., 1995
(0) is taken as zero at z = 0.
