Mesoscopic models of lipid bilayers and bilayers with embedded ...

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30 Surface tension in lipid bilayers 3.4 Surface tension in lipid bilayers To investigate the system size dependence of the area per lipid on the surface tension, we consider bilayers formed by 100, 200, 400, 900, and 1600 lipids to which we impose different values of the surface tension using the above described hybrid DPD- MC scheme. The area per lipid, AL, is calculated in our simulations as the bilayer projected area divided by half the number of lipids that form the bilayer, considered that, on average, there is an equal number of lipids in each monolayer. Computational details The lipid model used for these simulations is a double-tail lipid with three headbeads and five hydrophobic beads in each of the tails, denoted as h3(t5)2, and shown in figure 3.4. Figure 3.4: Schematic representation of the model lipid h3(t5)2, used in the simulations presented in this section. The black particles represent the hydrophilic head-beads and the gray particles the hydrophobic tail-beads. The interaction parameters between the beads are the ones described in section 2.2 of Chapter 2. Two consecutive beads in the lipid are connected by harmonic springs (equation 2.13) with spring constant Kr = 100 and equilibrium distance ro = 0.7. To control the tail flexibility, a bond-bending potential (equation 2.16) between two consecutive bonds in the lipid tails was added with bending constant Kθ = 6 and equilibrium angle θo = 180 o . An additional bond-bending potential was applied between the vectors connecting the tails to the headgroup, with Kθ = 3 and θo = 90 o . The lipid h3(t5)2, with the chosen interaction parameters, self-assemble into a stable bilayer. First a self-assembled bilayer of 100 lipids and 2500 water particles, corresponding to a fully hydrated bilayer, was formed by using DPD steps only, then the bilayer was replicated in the x and y directions (plane of the bilayer) to form bilayers of different size: i.e. of NL=100, 200, 400, 900, and 1600 lipids. In each case, 25 water particles per lipid were considered, resulting in a maximum total number of beads of 60800, in the case of the bilayer formed by 1600 lipids. For each considered system the overall density was ρ = 3 and the reduced temperature T ∗ =1. To each
3.4 Surface tension in lipid bilayers 31 of these bilayers different values of the surface tension were then imposed by applying the hybrid MC-DPD scheme, with a probability of 70% of performing DPD steps (chosen at random with a maximum of 50), or to attempt a change of the box aspect ratio. The total number of MC-DPD cycles was 100,000 for each simulation and the instantaneous values of the area and surface tension were sampled every 50 cycles. Negative values of applied surface tension, γ, correspond to a compression of the bilayer; γ = 0, corresponds to a tensionless, unconstrained bilayer; and positive values to a stretched bilayer. For each of these values of surface tension and for each of the bilayer sizes considered, the bilayer configuration was the stable state throughout the simulation. Results and discussion The instantaneous value of the area per lipid for a bilayer of 400 lipids is shown in figure 3.5(a), as function of MC cycles and at three different values of imposed surface tension (one positive, one negative and one zero). All the systems start from the same value of the area per lipid and, after about 20,000 MC cycles, have converged to the average values: 〈AL〉 = 1.50 ± 0.03 for imposed γ = −2, 〈AL〉 = 1.66 ± 0.02 for imposed γ = 0, and 〈AL〉 = 1.83 ± 0.02 for imposed γ = 2. The fluctuations of the computed surface tension are very large, though decreasing in magnitude with increasing value of the imposed surface tension. For example, at imposed value of γ = −2, the calculated value of the surface tension was -2.0 ± 1.4, at imposed γ = 0, the calculated surface tension was 0.0 ± 1.3, and at imposed γ = 2, the calculated surface tension was 2.0 ± 1.1. Despite these large fluctuations, the average value of the surface tension is equal to the imposed one, as can be seen from the running averages plotted in figure 3.5(b). A further verification that the equilibrium area per lipid does correspond to the imposed surface tension, was obtained by making the histogram of the sampled values of the area at equilibrium, and by calculating the corresponding average surface tension in each bin. In figure 3.6 three of these histograms for the bilayer of 400 lipids are shown, relative to negative, zero and positive values of the imposed surface tension, respectively. Each of the histograms is computed after the area has reached its equilibrium value, hence the width of the distribution of the area per lipid corresponds to the spontaneous fluctuations at equilibrium. The average values of γ show a linear increase with increasing area. The larger the area, the more stretched is the membrane, corresponding to higher values of the surface tension, and in correspondence with the maximum in the area distribution the surface tension is equal to the imposed value. These trends are more pronounced for positive and zero imposed surface tension (graphs (b) and (c) in figure 3.6), while in the case of negative imposed surface tension (graph (a)) there are deviations from a linear dependence of the surface tension on the area. The dependence of the area per lipid on system size, NL, and on imposed surface tension, γ, is shown in figure 3.8.
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 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: 3.3 Constant surface tension ensemb
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 85 and 86: VI Interaction of small molecules w
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6.2 Computational details 81 For re
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6.3 Results and Discussion 83 withi
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6.3 Results and Discussion 85 ρ(z)
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6.3 Results and Discussion 87 ρ(z)
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6.3 Results and Discussion 89 S m 0
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6.3 Results and Discussion 91 π(z)
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6.3 Results and Discussion 93 the l
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96 Mesoscopic model for lipid bilay
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98 Mesoscopic model for lipid bilay
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100 Mesoscopic model for lipid bila
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References [1] Tanford, C. Science
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7.4 Conclusion 121 [68] Ono, S.; Ko
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7.4 Conclusion 123 [139] Lee, A. Bi
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Summary Biological membranes, as th
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agreement we find gives us confiden
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Samenvatting Biologische membranen,
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de lage temperatuur gel fase of Lβ
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ied dat het dichtst bij het hydrofo
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This thesis is based on the followi
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