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

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100 Mesoscopic model for lipid bilayers with embedded proteins built by connecting ntP hydrophobic beads into a chain, to which ends n h headgrouplike beads are attached. NP of these amphiphatic chains are linked together into a bundle. In each model protein, all the NP chains are linked to the neighboring ones by springs, to form a relatively rigid body. We have considered three typical modelprotein sizes, two of them referring to a “skinny” peptide-like molecule, and the third type to a “fat” protein. These model proteins consist of NP=4, 7, or 43 chains linked together in a bundle. The bundle of NP=7 chains is formed by a central chain surrounded by a single layer of six other chains. The NP=43 bundle is made of three layers arranged concentrically around a central chain, and containing each six, twelve, and twenty four amphiphatic chains, respectively. The number of beads at each hydrophilic end of the bead-chains forming the protein is set equal to three. Each protein hydrophobic bead, tP, corresponds to a section of a α- or β-helical membrane protein. The distance spanned by a bead corresponds approximately to that spanned by a helix turn. About the chosen protein sizes, NP=4, 7, and 43, and their relation to the ones of actual proteins, the hydrophobic section of single-spanning membrane proteins like Glycophorin [172], and the M13 major coat protein from phage [173] or α-helical synthetic peptides [164] may be modeled by a skinny NP=4 type. β-helix proteins like gramicidin A [165], may be modeled by a NP=7 type. The fat protein may be a model for larger proteins consisting of transmembrane α-helical peptides that associate in bundles, or β-barrel proteins [174]. Specific examples could be bacteriorhodopsin [175], lactose permease [176], the photosynthetic reaction center [177], cytochrome c oxidase [178], or aquaglycerolporin [179]. Because we were interested in mismatch dependent effects, we have chosen protein hydrophobic sections composed of chains with different number of hydrophobic beads: ntP =2, 4, 6, 8, 10, and 12. To have an idea of what these numbers correspond to in terms of protein hydrophobic length, one can consider that the equilibrium distance between the beads is req=0.7Rc; assuming a value of Rc=6.4633 ˚A, the resulting values for the protein hydrophobic lengths will be, dP=14 ˜ ˚A (4 beads), 18 ˚A (5 beads), 23 ˚A (6 beads), 32 ˚A (8 beads), 41 ˚A (10 beads), and 50 ˚A (12 beads). It is worth mentioning that these estimated protein hydrophobic lengths (which we denoted by dP, ˜ to distinguish from the lengths calculated from the simulations), are only meant to be indicative. Because of the soft interactions involved in DPD, the value of the protein hydrophobic length that results from the simulations (and which, in the following, is denoted by dP) might be subjected to a small deviation of the order of 1 ˚A with respect to the values given above. Figure 7.1(b) shows a cartoon of a model protein of size NP=43, while figure 7.1(c) shows a snapshot of a typical configuration of the assembled bilayer with the embedded protein, as results from the simulations. Model parameters The non-bonded interactions between the beads are represented by the soft-repulsive conservative force F C ij = aij(1 − rij/Rc)^rij. The values of the parameters referring
7.2 Computational details 101 to the lipid-lipid and lipid-water interactions have been chosen equal to the ones used for modeling the pure lipid bilayer system. The numerical values of the interaction parameters between different bead types are shown in Table 7.1. Regarding Table 7.1: Repulsion parameters aij for different bead-types. aij w h tL tP w 25 15 80 120 h 15 35 80 80 tL 80 80 25 25 tP 120 80 25 25 the protein-protein interactions, the parameters related to the repulsive interactions between the beads forming the hydrophilic part of the protein, as well as the ones between the hydrophobic beads, have been chosen with the same values as the interaction parameters between hydrophilic and hydrophobic beads of the lipid, respectively, i.e. ahh = 35 and atPtP = atLtL = 25. About the parameter related to the interaction between the protein hydrophobic beads and the water, we have chosen a value to ensure that the hydrophobic section of the protein was sufficiently shielded from the water environment. This was done by calculating the interaction energy between the protein outer hydrophobic chains and the water, for different values of the repulsion parameter awtP . The trend in the energy shows the onset of a plateau for awtP ≥ 120, which was hence the chosen value for the interaction parameter. Two consecutive beads in the lipid or in the protein are connected by harmonic springs (equation 2.13) with spring constant Kr=100 and equilibrium distance ro=0.7. To control the lipid flexibility, a harmonic bond-bending potential 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 lipid tails to the headgroup, with Kθ=3 and θo=90 o . Compared to the lipid hydrocarbon chains, the hydrophobic part of membrane proteins can be considered fairly rigid; therefore the value of the bending constant in the protein chains was set to Kθ=100, i.e. about an order of magnitude larger than the one used for the lipid chains. At this point it is important to mention that, although these parameters are chosen such that the system behavior is in reasonable agreement with the experimental system, a one to one link to all specific properties is not always possible to make. 7.2.2 Method of calculation of statistical quantities We have studied the physical properties of the system both in the absence and in the presence of the proteins. The pure lipid bilayer hydrophobic thickness, do L , was estimated by calculating, for each sampled configuration, the difference between the average position along the bilayer normal (z direction, considering the bilayer paral-
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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
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
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 108 and 109: 102 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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