Mesoscopic models of lipid bilayers and bilayers with embedded ...
Mesoscopic models of lipid bilayers and bilayers with embedded ... Mesoscopic models of lipid bilayers and bilayers with embedded ...
12 Simulation method for coarse-grained lipids a timestep at least three orders of magnitude larger than in atomistic molecular dynamics simulations, where a timestep of the order of few fs is typically used. In the next section we describe the coarse-grained model we use to represent lipid molecules and we show that these model lipids, simulated with DPD, spontaneously self-assemble into micelles and bilayers. 2.2 Coarse-grained model of lipids Within the mesoscopic approach, each molecule of the system (or groups of molecules) is coarse-grained by a set of beads. We consider three types of beads: a water-like bead (denoted as ’w’), which models the solvent, an hydrophilic bead (denoted as ’h’) which models a section of the lipid headgroup, and an hydrophobic bead (denoted as ’t’) which models a segment of the lipid hydrocarbon tail. A lipid is constructed by connecting head- and tail-beads with springs. The simplest lipid consists of a linear chain of one hydrophilic head-bead and one tail of hydrophobic beads. A more realistic model of a phospholipid can be constructed by connecting two hydrophobic tails to an headgroup consisting of one or more head-beads. In both single- and double-tail lipids the tail(s) can have different length. We denote a single-tail lipid with one head-bead and n tail beads as htn, and a double-tail lipid with m headbeads and n tail-beads as hm(tn)2 (see figure 2.1). Figure 2.1: Schematic drawing of the single- and double-tail model lipids described in the text and their nomenclature. The black particles represent the hydrophilic head-beads and the white particles the hydrophobic tail-beads. A mapping of coarse-grained lipids onto real phospholipids can be established through the factor Nm. We have chosen a mapping factor of Nm = 3, corresponding to three water molecules represented by one DPD-bead of volume of 90 ˚A 3 . In terms
2.2 Coarse-grained model of lipids 13 of methyl groups of an actual lipid molecule, this volume corresponds to three CH2 groups (or one CH2 plus one CH3 group). By also mapping the choline, phosphate, and glycerol groups of the phospholipid hydrophilic head on one DPD bead each, a real phospholipid, like, for example, dimyristoylphosphatidylcholine (DMPC), can be represented by a double-tail coarse-grained lipid with three hydrophilic headbeads and five hydrophobic beads in each tail (lipid h3(t5)2), as shown in figure 2.2. 13 12 11 H3 C H3 C 9 H 10 2 H C 2 H C 2 H C C 2 H C 2 H2 C H C 2 H2 C C H2 C C H2 H2 C H2 H2 H2 H2 H2 H2 H2 C C C C C C C C C C C C C H2 H2 H2 H2 H2 H2 O O C O O H2 C CH CH2 3 O 8 7 6 5 4 O − P O H O 2 C C N H2 + CH3 CH3 CH 3 2 1 Figure 2.2: The atomistic representation of DMPC and the corresponding coarse-grained model used in this work. Hydrophilic head-beads are indicated in gray and hydrophobic tailbeads in white. Model parameters Non-bonded interactions The non-bonded interactions between the beads are described by the conservative force of equation 2.2. The relative strength of the force between different bead types is represented by setting the repulsion parameter between two beads–either both hydrophilic or hydrophobic– to a smaller value than the one between two beads where one is hydrophilic and the other is hydrophobic. In particular, the interaction parameter between water-beads (aww) can be derived by fitting the calculated value of the compressibility of water at room temperature to the experimental one [24, 28], according to 1 kBT ∂p = ∂ρ sim Nm kBT ∂p ∂n exp (2.11) where Nm is the number of water molecules that are represented by one DPD bead, p is the pressure, and n and ρ are the water and DPD water-like bead densities, respectively. Groot and Warren [28] have shown that for densities ρ > 2, the equation of state of a DPD single-component system for different densities and different repulsion parameters follows a simple scaling relation. Since the higher the system density the larger the number of interactions for each particle, it is convenient to choose the
- Page 1: Mesoscopic models of lipid bilayers
- Page 4 and 5: Promotiecommissie: Promotor: • pr
- Page 6 and 7: ii CONTENTS 5.3 Double-tail lipid b
- Page 8 and 9: 2 Introduction 1.1 The cell membran
- Page 10 and 11: 4 Introduction between the beads, a
- Page 12 and 13: 6 Introduction whether the preferre
- Page 14 and 15: 8 Simulation method for coarse-grai
- Page 16 and 17: 10 Simulation method for coarse-gra
- Page 20 and 21: 14 Simulation method for coarse-gra
- Page 22 and 23: 16 Simulation method for coarse-gra
- Page 24 and 25: 18 Simulation method for coarse-gra
- Page 27 and 28: III Surface tension in lipid bilaye
- Page 29 and 30: 3.2 Method of calculation of surfac
- Page 31 and 32: 3.2 Method of calculation of surfac
- Page 33 and 34: 3.3 Constant surface tension ensemb
- Page 35 and 36: 3.3 Constant surface tension ensemb
- Page 37 and 38: 3.4 Surface tension in lipid bilaye
- Page 39 and 40: 3.4 Surface tension in lipid bilaye
- Page 41 and 42: 3.4 Surface tension in lipid bilaye
- Page 43 and 44: IV Structural characterization of l
- Page 45 and 46: 4.2 Structural quantities 39 been r
- Page 47 and 48: 4.3 Computational details 41 lipid
- Page 49 and 50: 4.4 Results and discussion 43 ρ(z)
- Page 51 and 52: 4.4 Results and discussion 45 one l
- Page 53 and 54: 4.4 Results and discussion 47 WH HT
- Page 55 and 56: 4.4 Results and discussion 49 Shill
- Page 57 and 58: 4.4 Results and discussion 51 chain
- Page 59 and 60: 4.4 Results and discussion 53 4.4.4
- Page 61: 4.4 Results and discussion 55 headg
- Page 64 and 65: 58 Phase behavior of coarse-grained
- Page 66 and 67: 60 Phase behavior of coarse-grained
2.2 Coarse-grained model <strong>of</strong> <strong>lipid</strong>s 13<br />
<strong>of</strong> methyl groups <strong>of</strong> an actual <strong>lipid</strong> molecule, this volume corresponds to three CH2<br />
groups (or one CH2 plus one CH3 group). By also mapping the choline, phosphate,<br />
<strong>and</strong> glycerol groups <strong>of</strong> the phospho<strong>lipid</strong> hydrophilic head on one DPD bead each, a<br />
real phospho<strong>lipid</strong>, like, for example, dimyristoylphosphatidylcholine (DMPC), can<br />
be represented by a double-tail coarse-grained <strong>lipid</strong> <strong>with</strong> three hydrophilic headbeads<br />
<strong>and</strong> five hydrophobic beads in each tail (<strong>lipid</strong> h3(t5)2), as shown in figure 2.2.<br />
13<br />
12<br />
11<br />
H3 C<br />
H3 C<br />
9<br />
H 10<br />
2 H<br />
C<br />
2 H<br />
C<br />
2 H<br />
C C 2 H<br />
C<br />
2<br />
H2 C H<br />
C 2<br />
H2 C C<br />
H2 C<br />
C<br />
H2<br />
H2 C<br />
H2<br />
H2 H2 H2 H2 H2 H2 C C C C C C<br />
C C C C C C C<br />
H2 H2 H2 H2 H2 H2<br />
O<br />
O<br />
C<br />
O<br />
O H2 C<br />
CH<br />
CH2 3<br />
O<br />
8<br />
7<br />
6<br />
5<br />
4<br />
O −<br />
P<br />
O<br />
H<br />
O 2<br />
C<br />
C N<br />
H2 +<br />
CH3 CH3 CH 3<br />
2 1<br />
Figure 2.2: The atomistic representation <strong>of</strong> DMPC <strong>and</strong> the corresponding coarse-grained<br />
model used in this work. Hydrophilic head-beads are indicated in gray <strong>and</strong> hydrophobic tailbeads<br />
in white.<br />
Model parameters<br />
Non-bonded interactions<br />
The non-bonded interactions between the beads are described by the conservative<br />
force <strong>of</strong> equation 2.2. The relative strength <strong>of</strong> the force between different bead types<br />
is represented by setting the repulsion parameter between two beads–either both hydrophilic<br />
or hydrophobic– to a smaller value than the one between two beads where<br />
one is hydrophilic <strong>and</strong> the other is hydrophobic.<br />
In particular, the interaction parameter between water-beads (aww) can be derived<br />
by fitting the calculated value <strong>of</strong> the compressibility <strong>of</strong> water at room temperature<br />
to the experimental one [24, 28], according to<br />
1<br />
kBT<br />
<br />
∂p<br />
=<br />
∂ρ sim<br />
Nm<br />
kBT<br />
<br />
∂p<br />
∂n exp<br />
(2.11)<br />
where Nm is the number <strong>of</strong> water molecules that are represented by one DPD bead, p<br />
is the pressure, <strong>and</strong> n <strong>and</strong> ρ are the water <strong>and</strong> DPD water-like bead densities, respectively.<br />
Groot <strong>and</strong> Warren [28] have shown that for densities ρ > 2, the equation <strong>of</strong><br />
state <strong>of</strong> a DPD single-component system for different densities <strong>and</strong> different repulsion<br />
parameters follows a simple scaling relation. Since the higher the system density<br />
the larger the number <strong>of</strong> interactions for each particle, it is convenient to choose the
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