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

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34 Surface tension in lipid bilayers (a) NL = 900, γ = −1 (b) NL = 1600, γ = −1 (c) NL = 900, γ = −2 (d) NL = 1600, γ = −2 Figure 3.7: Snapshots of the equilibrium configurations of compressed bilayers, i.e. with imposed negative surface tension, γ, for two, large, system sizes (number of lipids in the bilayer, NL). (a) NL = 900, and γ = −1. (b) NL = 1600, and γ = −1. (c) NL = 900, and γ = −2. (d) NL = 1600, and γ = −2. Two periodic images (in the x direction) of each bilayer are shown to better display the undulation modes. Note that in (b) the bilayer undulations are in both x and y directions, while in (c) and (d) they are only in the x direction. The lipid headgroups are depicted in black, and the lipid tails in gray, with the terminal tail beads (located in the bilayer center) in darker gray. The water is not shown.
3.4 Surface tension in lipid bilayers 35 Area compressibility From the dependence of the area per lipid on the surface tension, the bilayer area compressibility can be calculated. The bilayer area compressibility KA is defined as [77] Integrating equation 3.21 we have KA = A γ = KA ln A ∂γ . (3.21) ∂A Ao (3.22) where Ao is the area at the free energy minimum, i.e. at zero surface tension. Expanding equation 3.22 around Ao we obtain a linear dependence of γ on A γ ≈ KA (A − Ao). (3.23) Ao In simulation, the area compressibility can be calculated from the above equation, either by fixing the area of the bilayer and computing the corresponding surface tension, or by imposing the surface tension and calculating the area. In this study we use the latter method. If the area is taken as the dependent variable, then, from 3.23, we have A = Ao γ + Ao (3.24) KA To fit the area as function of γ using equation 3.24, we used two approaches. The first one consists in computing the area at different values of imposed surface tension, in the regime were the area dependence on surface tension is linear. We found the behavior of the average projected area per lipid to be linear in the applied surface tension for values of the tension in the range γ=[-0.5,1.5]. The second method consists in considering the spontaneous fluctuations at equilibrium, of both the area and the measured surface tension, in a tensionless bilayer, as computed in the histogram shown in figure 3.6(b). The results of both fitting methods are in very good agreement: in both cases we find KAR 2 c/kBT=20.8 from the slope of the fitted lines. Also, a value of 1.66 R 2 c is found as the intercept, which is the same value of the area at zero surface tension, Ao, as directly measured from the simulation at γ = 0. Using Rc=6.4633 ˚A and taking kBT as room temperature, i.e. kBT = 4.14 10 −21 J, we can convert the area compressibility into physical units, resulting in KA ≈ 210 mN/m. This value is comparable to the value of the compressibility equal to 300 mN/m found by Lindahl and Edholm [77] in atomistic MD simulations of lipid bilayers, and to the values measured by micropipette aspiration experiments which, for saturated phosphatidylcholine bilayers in the fluid phase, are also in the range 230-240 mN/m [78].
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 and 36: 3.3 Constant surface tension ensemb
Page 37 and 38: 3.4 Surface tension in lipid bilaye
Page 39: 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
Page 87 and 88: 6.2 Computational details 81 For re
Page 89 and 90: 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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