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Wolff Jean, Ternary Mixtures of Lipids and Cholesterol: a Theoretical Model (2013)

Supervision: Fabrice Thalmann and Carlos Marques

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We propose a new theoretical model for describing the formation and the phase coexistence in ternary mixtures of phospholipids and cholesterol. This model com- bines the properties of the liquid-gel phase transition, described with an internal order pa- rameter, with some non ideal mixing behavior accounting for the influence of cholesterol, and inspired by Flory’s description of polymer melts. Our thermodynamical approach successfully accounts for the coexistence of binary phospholipid mixtures such as DOPC- DPPC. The order parameter, originally introduced by Doniach, describes in a simplified manner the thermodynamics of the alkyl chains in a lipid bilayer, by analogy with the Ising model under magnetic field. We not only obtain ternary diagrams resembling to experi- mental diagrams, but also discuss the evolution of these phase equilibria with temperature. This approach is then generalized to other lipid components, namely PSM, POPC and DiphytanoylPC. Our approach, made of a combination of discrete geometry calculations and numerical resolutions of the analytical equations for determining the properties of the Gibbs diagram is novel, and applies to a wide class of thermodynamic models with order parameters. A Landau-Ginzburg extension of the above model allows us to study inhomo- geneous systems. A first important application consists in determining the line tension τ and the profile of an interface separating macrodomains of ordered and disordered liquid phase. We extend Cahn’s wetting theory to the case of a circular inclusion of finite radius R in a “lipid sea”, at coexistence and off-coexistence. We finally discuss the effects of the proximity of a critical point, and the consequences relative to mutual interactions between impurities induced by the wetting process.