Concentration Fluctuations and Phase Separations in Lipid Bilayers

In this thesis, we proposed a model for lipid bilayers, and discussed the mechanism of thefinite-sized domain formation together with the effects of coupling of the two monolayers.A lipid monolayer consisting of saturated lipid, hybrid lipid and cholesterol was considered.We proposed a phenomenological Ginzburg-Landau model in which the couplingof the lipid composition and chain orientational vector field is considered. This couplingarises from the liquid crystalline nature of the hybrid lipid which adjusts its orientationalorder in the tails to reduce the line tension. As a result, finite-sized domains can beformed. The minimization of the free energy with respect to the vector field yields aneffective free energy which is analogous to that of 3D microemulsions (above the transitiontemperature) and modulated structures (below the transition temperature).Then we considered the model for lipid bilayers comprised of two modulated monolayerswhich are coupled via interleaflet interactions. The structure and the dynamics ofthe coupled modulated bilayer are investigated theoretically.We first studied concentration fluctuations in bilayers occurring above the transitiontemperature. We have calculated the static structure factors, and obtained the bilayerphase diagrams close to the critical temperature. In both monolayers, fluctuations areinduced due to the coupling, and the spectrum of the induced fluctuations is determinedby the cross correlation of the structure factor. When the two monolayers having differentpreferred wavenumbers are coupled, the peak height at smaller wavenumber becomes larger, whereas that at a larger wavenumber remains the same. We studied the dynamics of concentration fluctuations by using the coupled time dependent Ginzburg-Landauequations, and calculated the intermediate structure factors of the bilayer. In general,concentration fluctuations exhibit a double-exponential decay. Due to the coupling, thetime for the cross over of the two concentration fluctuations appears when the characteristiclength scale of each monolayer is different.Then we discussed the phase separation of the coupled modulated bilayers. Withinthe mean field approximation, we constructed phase diagrams of the bilayer when the twomonolayers have the same wavenumber of the modulations. The phase behavior of thebilayers is described by the combinations of the stripe and the hexagonal morphologies.Due to the coupling effect, one of the monolayers induces micro-phase separation in theother monolayer. As the coupling strength increases, the asymmetric phases tend todisappear. By performing numerical simulations, we obtained various phase separatedpatterns when the two monolayers have different modulations. The obtained patternsare approximately classified into “independent”, “intermediate” and “coincident” cases.The degree of the overlap between the two monolayers is characterized by the inter-leafletcorrelation of the local compositions. We showed that the initial growth rates of the mostunstable mode are essentially identical to the decay rates of the concentration fluctuations.We showed that the formation of the intermediate structures is related to the stability ofthe concentration fluctuations occurring above the transition temperature.Using the mechanism of finite-sized domain formation proposed above, we shall alsodiscuss its relation to the biologically relevant context of lipid rafts.首都大学東京, 2011-03-25, 博士（理学