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

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104 Mesoscopic model for lipid bilayers with embedded proteins In some cases, to facilitate the interpretation of the data obtained from the simulations, it was necessary to determine the degree of order/disorder of the lipid chains in the vicinity of the protein, and eventually to compare it with the one of the pure lipid bilayer, i.e. in the bulk, away from the protein-induced perturbation. Therefore, we have calculated the value of the lipid chain order parameter, S(r), which is defined as follows: S = 1 2 (3 cos2 φS − 1), (7.4) with cos φS = rij · ^n rij = zij , (7.5) rij where φS is the angle between the orientation of the vector rij = rj − ri (rij = |rij|) along two consecutive lipid chain beads, i, j, and the bilayer normal unit vector, ^n. S(r) has been independently calculated for each of the two monolayers of the bilayer, as well as averaged over all the bonds of the lipid chains at distance r from the surface of the protein. 7.3 Results and discussion In this section we present the results from the simulations of the lipid bilayer modelsystem with embedded proteins. We focus on the low protein-concentration regime, where the correlation between different proteins can be neglected, and hence consider bilayers with embedded a single protein. To investigate the dependence on mismatch and protein size on the lipid bilayer around an embedded protein we first studied the behavior of the system at a constant temperature, well above the pure lipid bilayer transition temperature. Since the bilayer hydrophobic thickness varies with temperature, a way to change the hydrophobic mismatch is by changing temperature. Hence, we studied the behavior of ξP and φ tilt in the temperature range above the melting temperature of the pure system, i.e. in the fluid phase, and for a number of lipid-protein model-systems. Finally, for few hydrophobic mismatch conditions and for few selected temperatures below the melting temperature, we investigated how the phase behavior of the pure lipid system in the gel-phase affects the localization and orientation of the proteins in this phase. The results discussed next refer to lipid bilayers of 900 lipids and 22500 water beads (i.e. 25 water beads per lipid), corresponding to a fully hydrated bilayer. We have made calculations for smaller systems, and we have found that a size corresponding to 900 lipid molecules was sufficient to avoid finite-size effects, at least for temperatures close or above the main-transition temperature. Before collecting the data used to estimate statistical quantities, we have first equilibrated each bilayer system for 20,000 DPD-MC cycles. In each cycle it was chosen (with a probability of
7.3 Results and discussion 105 70%) whether to perform a number of DPD steps or an attempt to change the box aspect ratio according to the imposed value of the surface tension, γ = 0. After equilibration, data were collected over 50,000 DPD-MC cycles, at γ = 0. The statistical averages were then made over configurations that were separated from one another by 50 DPD steps. On average, 10,000 independent configurations were considered for the statistical averages. 7.3.1 Protein-induced bilayer perturbation The results shown next refer to the reduced temperature T ∗ =0.7, well above the melting temperature of the system, i.e. in the fluid phase. The pure lipid bilayer hydrophobic thickness calculated at this reduced temperature is d o L =(23.6±0.2) ˚A. Figure 7.3 shows the calculated bilayer hydrophobic thickness profile, dL(r), as a function of the distance r from the protein surface. The data refer to different values of dP, resulting in different values of hydrophobic mismatch ∆d, ranging from ∆d=-8 ˚A to 28˚A, and to the three protein sizes, which correspond to NP =4, 7, and 43. Because the probability of finding a lipid molecule in the lipid-shell closest to the protein is much lower than in the other lipid-shells, the data collected at a distance r = ∆r from the protein surface have not been considered for the statistics. One can clearly see from the curves in figure 7.3 that the protein induces a perturbation of the lipid bilayer in its vicinity. The perturbation decays in a manner that depends on the hydrophobic mismatch and on protein size. If the protein hydrophobic length is smaller than the unperturbed bilayer hydrophobic thickness (dP < d o L ), i.e. negative mismatch, ∆d < 0 (open symbols), the lipids around the protein shrink to match the protein hydrophobic surface. By choosing the peptide hydrophobic length to approximately match the value of the hydrophobic thickness of the unperturbed lipid bilayer, i.e. ∆d ≈0 (crosses), one can clearly see from figure 7.3 that the perturbation induced by the protein on the surrounding lipids becomes negligible. Instead, when the chosen protein is such that dP > do L , i.e. ∆d > 0 (full symbols), to match the protein hydrophobic surface the lipids in the vicinity of the protein stretch and become more gel-like than the bulk lipids, far away from the protein. Figure 7.4 shows the thickness profiles for two values of mismatch ∆d=-10 ˚A, and ∆d=17 ˚A, and for the three considered protein sizes. The symbols indicate the data obtained directly from the simulations, while the continuum line is obtained by best- fitting with the function in equation 7.3, where do L and ξP are the fitting parameters (and where deff P is the input parameter). For convenience, we have drawn a horizon- tal dashed line to indicate the value of the pure lipid bilayer hydrophobic thickness, do L , calculated at the same reduced temperature considered for the simulations of the mixed systems. To help the interpretation of the data, the values of the protein hydrophobic length, dP, directly calculated from the simulations, and of deff P , the projected protein hydrophobic length onto the normal to the bilayer plane, are also plot-
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Mesoscopic models of lipid bilayers
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Promotiecommissie: Promotor: • pr
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ii CONTENTS 5.3 Double-tail lipid b
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2 Introduction 1.1 The cell membran
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4 Introduction between the beads, a
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6 Introduction whether the preferre
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8 Simulation method for coarse-grai
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10 Simulation method for coarse-gra
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III Surface tension in lipid bilaye
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3.2 Method of calculation of surfac
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3.2 Method of calculation of surfac
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3.3 Constant surface tension ensemb
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3.3 Constant surface tension ensemb
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3.4 Surface tension in lipid bilaye
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IV Structural characterization of l
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4.2 Structural quantities 39 been r
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4.3 Computational details 41 lipid
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4.4 Results and discussion 43 ρ(z)
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4.4 Results and discussion 45 one l
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4.4 Results and discussion 47 WH HT
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4.4 Results and discussion 49 Shill
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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
Page 91 and 92: 6.3 Results and Discussion 85 ρ(z)
Page 93 and 94: 6.3 Results and Discussion 87 ρ(z)
Page 95 and 96: 6.3 Results and Discussion 89 S m 0
Page 97 and 98: 6.3 Results and Discussion 91 π(z)
Page 99: 6.3 Results and Discussion 93 the l
Page 102 and 103: 96 Mesoscopic model for lipid bilay
Page 104 and 105: 98 Mesoscopic model for lipid bilay
Page 106 and 107: 100 Mesoscopic model for lipid bila
Page 125 and 126: References [1] Tanford, C. Science
Page 127 and 128: 7.4 Conclusion 121 [68] Ono, S.; Ko
Page 129 and 130: 7.4 Conclusion 123 [139] Lee, A. Bi
Page 131 and 132: Summary Biological membranes, as th
Page 133 and 134: agreement we find gives us confiden
Page 135 and 136: Samenvatting Biologische membranen,
Page 137 and 138: de lage temperatuur gel fase of Lβ
Page 139: ied dat het dichtst bij het hydrofo
Page 143: This thesis is based on the followi
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