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

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32 Surface tension in lipid bilayers A L 1.9 1.8 1.7 1.6 1.5 1.4 0e+00 2e+04 4e+04 6e+04 8e+04 1e+05 MC cycles (a) γ= 2 γ= 0 γ=−2 γ 2.0 0.0 −2.0 0e+00 2e+04 4e+04 6e+04 8e+04 1e+05 MC cycles Figure 3.5: (a) Instantaneous value of the area per lipid, AL, as function of MC cycles for three values of imposed surface tension γ. In figure (b) the corresponding running averages (of length 100) of the instantaneous value of the surface tension are plotted. The straight lines parallel to the graph abscissa correspond to the imposed values of the surface tension. The data refer to a bilayer of 400 h3(t5)2 lipids. The area per lipid increases with increasing value of the imposed surface tension, for all the system sizes. Furthermore, the area per lipid at positive or zero surface tension does not depend on the system size, while if the bilayer is compressed (negative values of γ), a size dependence of the area is found, and the (projected) area per lipid decreases with increasing system size. For clarity reasons, the projected area per lipid for NL = 900 and NL = 1600 at the lowest surface tension considered, γ = −2, are not shown in figure 3.8, but they were found to be about two times smaller than the value for NL = 400. The reason of these deviations becomes clear by looking at instantaneous snapshots of the two largest bilayers (900 and 1600 lipids) at negative values of the surface tension, as shown in figure 3.7. In large bilayer patches, like the ones shown in the figure, the lateral compression activates bending modes in the bilayer: the bilayer is not flat anymore, but shows out-of-plane undulations. The amplitude of these undulations increases with increasing system size and with decreasing surface tension. These bending modes are completely suppressed in small bilayer patches of 100 and 200 lipids, and partially suppressed in bilayer patches of 400 lipids. Considering that, in most atomistic-detailed molecular dynamics simulations of bilayer membranes, the typical number of lipids considered is usually smaller than 200, care must be used when choosing boundary conditions that compress the bilayer. On the other hand, our results suggest that, for stretched or tensionless bilayer, small bilayer patches can be considered with no finite-size effects. This result partly contradicts the findings of Marrink and Mark [60] discussed in the Introduction to this Chapter. These authors found a system size dependence not only (b)
3.4 Surface tension in lipid bilayers 33 γ 1.0 0.0 −1.0 −2.0 −3.0 P(A L ) −4.0 =1.50 −5.0 1.42 1.44 1.46 1.48 1.50 AL 1.52 1.54 1.56 (a) γ = −2 γ 3.0 2.0 1.0 0.0 −1.0 P(A L ) −2.0 =1.66 −3.0 1.60 1.62 1.64 1.66 AL 1.68 1.70 1.72 (b) γ = 0 γ 5.0 4.0 3.0 2.0 1.0 P(A L ) 0.0 =1.83 −1.0 1.76 1.78 1.80 1.82 1.84 AL 1.86 1.88 1.90 (c) γ = 2 Figure 3.6: Histograms of the area per lipid AL and corresponding average value of the calculated surface tension γ (filled circles) in each bin. The three plots refer to a bilayer of 400 h3(t5)2 lipids with different values of the imposed surface tension: (a) γ = −2, (b) γ = 0, and (c) γ = 2. The values on the graph ordinate refer to γ only, while the height of the bins in the histogram is proportional to P(AL), i.e. to the probability distribution of the area per lipid. The basis line of each of the histograms corresponds to the imposed value of γ. The average values of the area per lipid, 〈AL〉, are also reported in the graphs. The error on these values is ±0.02. at negative values of the surface tension, but also for stretched bilayers, and only tensionless bilayers were found to display no finite-size effects. It must be pointed out that the more complex and long range (electrostatic) interactions used in atomistic MD, and not represented in our mesoscopic model, might have an influence on the calculation of the surface tension and on its dependence on system size. A L 2.1 1.9 1.7 1.5 N L =100 N L =200 N L =400 N L =900 N L =1600 1.3 −3 −2 −1 0 1 2 3 4 γ Figure 3.8: Average values of the area per lipid at equilibrium, AL, as function of applied surface tension γ, for bilayer patches of different sizes, i.e. number of lipids NL. The lines connecting the symbols are only a guide to the eye.
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: 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
Page 87 and 88: 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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