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

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38 Structural characterization of lipid bilayers 4.1 Introduction An important aspect in coarse-grained (CG) models for lipid bilayers is the level of chemical and molecular detail chosen to represent the components of the system. This choice is determined by the properties one wants to investigate, and on how these properties depend on the details of the model. In this Chapter we address these questions by studying the effect of modifications in the topology of the bilayer constituents (i.e. the model lipids) on the structural properties of the bilayer. Examples of lipid characteristics that can be varied in our CG model are the length of the acylchain, the size of the lipid headgroup, or the chain stiffness. Also, we will consider model lipids with one or two hydrophobic tails, the latter better resembling a real phospholipid. While for some aspects the lack of molecular detail implicit in a simplified representation can be seen as the limitation of CG models, on the other hand it allows to identify some general features that might be responsible for the structure and behavior of phospholipid bilayers. Of particular interest is the characterization of the pressure profile in lipid bilayers. It is well known, both from experiments and simulations [12, 79], that bilayers are very different than simple bulk hydrocarbon/water interfaces, in that they exhibit an internal structure. The lipids are oriented, with the headgroups sticking in the water phase, while the tails extend into the bilayer core, and segments of the lipid chains are located at different depths in the bilayer. This “ordering” of the lipids results in a characteristic, non-uniform, density distribution in the bilayer. This inhomogeneity in the internal structure is also reflected in the distribution of the lateral pressure across the bilayer. Structural properties of lipid bilayers, such as order parameters, density profiles, area per lipid, and bilayer thickness, have been extensively studied and determined for a wide range of phospholipids, temperatures and bilayer compositions, both experimentally and by simulations. On the other hand, an exhaustive characterization of the distribution of local pressures in lipid bilayers is still lacking. Since direct experimental measurements of the pressure profile in lipid bilayers are not yet available, although some attempts have been reported [80], theoretical models or computer simulation can be a valuable tool in the investigation of this quantity. Mean-field approaches have been applied to the calculation of pressure profiles. However, those approaches are often limited by the fact that they are lattice models, in which the headgroups of the lipids have to be constrained at the interface in order to obtain a bilayer structure. Also, in such models, it is difficult to incorporate details of the chemical structure of the lipids. By atomistic molecular dynamics (MD), many more details of the lipid chemistry and topology can be implemented, and their effect on the distribution of pressure can be studied. However, very long runs are needed for a sufficient statistical samplings, due to the large fluctuations related to this quantity. Also, to date, very few simulations on pressure profiles have
4.2 Structural quantities 39 been reported in literature. Lindahl and Edholm were the first to compute the pressure distribution in an atomistic MD simulation of a fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer [77]. Very recently Gullinsgrud and Schulten [81] reported an extensive MD study on the effect of changes in the lipid topology on the pressure profiles in lipid bilayers, by considering differences in the lipid headgroup (choline or ethanolamine) and chain unsaturation. The CG approach has also been used to study pressure profiles. Harries and Ben-Shaul in [82] presented a study on the comparison between mean-field calculations and Monte Carlo (MC) simulations of bilayers formed by flexible linear chains of bonded identical spheres interacting with 6-12 Lennard- Jones potentials. They found good agreement in the shape of the pressure profiles calculated with the two approaches. Pressure profiles in CG model bilayers were computed by Goetz and Lipowsky [21], Shillcock and Lipowsky [50], and Groot and Rabone [24]. In all the cited works, with the exception of [81], the effect of changes in the lipid topology on the shape of the pressure profiles has not been considered, and a systematic study is still lacking. Using the DPD-CG model and the constant surface tension ensemble introduced in the previous Chapters, we investigate the effect of lipid architecture on the bilayer structure and compare our results with atomistic MD and CG simulations. First we describe the structural quantities we use to characterize a bilayer. By systematically changing chain length and stiffness of the model lipids, we investigate how these quantities depend on the lipid architecture. We then characterize the shape of the pressure profile in these different lipid bilayers, and show that the distribution of the pressure across a bilayer can be affected by modifications at specific sites in the lipid architecture. Finally, we show that the lateral pressure profile in bilayers of CG lipids with two tails is very similar in shape to the one computed in atomistic MD simulations of phosphatidylicholine bilayers. 4.2 Structural quantities Orientational order parameter An important, and accurately determined property of lipid bilayers, is the orientational order parameter. This order parameter can be directly measured by deuterium substitution NMR spectroscopy [83], and is given by S = 1 2 3 cos φ − 1 2 (4.1) where φ is the angle between the orientation of the vector along a given C-H bond and the bilayer normal. In our coarse-grained model, however, the hydrogen atoms are not present, hence we use a different definition. The mathematical expression is
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 43: IV Structural characterization of l
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
Page 91 and 92: 6.3 Results and Discussion 85 ρ(z)
Page 93 and 94: 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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