249
8 Molecular Dynamics Simulations of Lipid Bilayers with Incorporated Peptides
the bilayers on the basis of the experimental data (taking into account parameters
for the area per lipid and bilayer thickness) [33, 74]. Initial structures were solvated
with SPC water model (4764 molecules for DMPC and 4784 for DPPC), energetically minimized and simulated for over 20 ns until the membrane parameters were
close to the experimental values. A cylindrical hole has been created in the center
of a bilayer by removing four lipids whose atoms were within 0.23 nm of the central axis of a cylinder. The peptide was then inserted into the cavity. The resulting
system (peptide, 124 PC molecules, 4 chlorine ions and water) consisted from more
than 16,000 atoms for LC and more than 20,000 for gel state of the membrane. The
system has been energetically minimized and equilibrated during 0.5 ns while the
peptide atoms were fixed. Then MD took place for at least 40 ns at temperatures
T = 288 and 310 K (bellow and over phase transition) for DMPC and 296/346 K for
DPPC bilayer. The temperature of phase transition is 297 K for DMPC and 314 K
for DPPC. MD was performed with constant pressure of 1 bar (semi-isotropic barostat), constant temperatures and with the time step of 2 fs. The LINCS algorithm
has been used to constrain covalent bond lengths. The used conditions were similar
to that reported by Berger et al. [75]. For results confirmation we extended seven
simulations to 100 ns.
Trajectories were analyzed from the last 5 ns of the simulations by subroutines
(programs) available from Gromacs package. Ramachandran plot were calculated
by Procheck software [76].
8.3 Properties of Pure Membranes
Interactions of the peptides with lipid bilayers have been studied in a gel and in a
liquid-crystalline state. At the end of the simulation the hydrophobic core of pure
lipid bilayers in a gel state is 3.61 nm thick for DPPC and 3.26 nm for DMPC.
The area per lipid is 0.4733 nm
2
per lipid for DPPC and 0.4676 nm
2
per lipid for
DMPC membrane, respectively. Values determined by experimental methods are
0.479 nm
2
/lipid for DPPC and 0.472 nm
2
for DMPC [74, 77]. Membranes with
similar difference in parameters have been used in MD simulations by Tu et al. [78]
or Tieleman et al. [79].
For the membrane in a gel state most of dihedral angles should be in trans
conformation [80]. Almost for whole chains it is over 90 %, only on beginnings
and ends it goes lower, but it is still more than 80 %. Also deuterium order parameters (S CD ) shows highly ordered system. The order parameters are defined
as
2
,
3/2 cos ( ) 1/2
CD z
z
S
Θ
=
-
, where Θ z is the angle between normal to the membrane and axis of that molecule. The axis is defined as a vector from C n − 1 to C n + 1
and angle brackets represents averaging in time. Maximal and minimal values are 1
(parallel to the membrane normal) and − 1/2 (perpendicular to the membrane) [81].
Order parameters depend on the structural state of lipid membrane—in a gel state
it reaches up to value 0.4, but in LC state it is only up to 0.3. Experimental values
for gel state reaches maximum 0.35 till 0.4 at 3
rd
till 4
th
C
α
atom and goes down to
8 Molecular Dynamics Simulations of Lipid Bilayers with Incorporated Peptides
the bilayers on the basis of the experimental data (taking into account parameters
for the area per lipid and bilayer thickness) [33, 74]. Initial structures were solvated
with SPC water model (4764 molecules for DMPC and 4784 for DPPC), energetically minimized and simulated for over 20 ns until the membrane parameters were
close to the experimental values. A cylindrical hole has been created in the center
of a bilayer by removing four lipids whose atoms were within 0.23 nm of the central axis of a cylinder. The peptide was then inserted into the cavity. The resulting
system (peptide, 124 PC molecules, 4 chlorine ions and water) consisted from more
than 16,000 atoms for LC and more than 20,000 for gel state of the membrane. The
system has been energetically minimized and equilibrated during 0.5 ns while the
peptide atoms were fixed. Then MD took place for at least 40 ns at temperatures
T = 288 and 310 K (bellow and over phase transition) for DMPC and 296/346 K for
DPPC bilayer. The temperature of phase transition is 297 K for DMPC and 314 K
for DPPC. MD was performed with constant pressure of 1 bar (semi-isotropic barostat), constant temperatures and with the time step of 2 fs. The LINCS algorithm
has been used to constrain covalent bond lengths. The used conditions were similar
to that reported by Berger et al. [75]. For results confirmation we extended seven
simulations to 100 ns.
Trajectories were analyzed from the last 5 ns of the simulations by subroutines
(programs) available from Gromacs package. Ramachandran plot were calculated
by Procheck software [76].
8.3 Properties of Pure Membranes
Interactions of the peptides with lipid bilayers have been studied in a gel and in a
liquid-crystalline state. At the end of the simulation the hydrophobic core of pure
lipid bilayers in a gel state is 3.61 nm thick for DPPC and 3.26 nm for DMPC.
The area per lipid is 0.4733 nm
2
per lipid for DPPC and 0.4676 nm
2
per lipid for
DMPC membrane, respectively. Values determined by experimental methods are
0.479 nm
2
/lipid for DPPC and 0.472 nm
2
for DMPC [74, 77]. Membranes with
similar difference in parameters have been used in MD simulations by Tu et al. [78]
or Tieleman et al. [79].
For the membrane in a gel state most of dihedral angles should be in trans
conformation [80]. Almost for whole chains it is over 90 %, only on beginnings
and ends it goes lower, but it is still more than 80 %. Also deuterium order parameters (S CD ) shows highly ordered system. The order parameters are defined
as
2
,
3/2 cos ( ) 1/2
CD z
z
S
Θ
=
-
, where Θ z is the angle between normal to the membrane and axis of that molecule. The axis is defined as a vector from C n − 1 to C n + 1
and angle brackets represents averaging in time. Maximal and minimal values are 1
(parallel to the membrane normal) and − 1/2 (perpendicular to the membrane) [81].
Order parameters depend on the structural state of lipid membrane—in a gel state
it reaches up to value 0.4, but in LC state it is only up to 0.3. Experimental values
for gel state reaches maximum 0.35 till 0.4 at 3
rd
till 4
th
C
α
atom and goes down to