Theory and simulation of interactive membrane-macromolecule structures in biological systems
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This thesis focuses on one of the branches of soft matter: biological systems. More specifically, we study the morphological transformation of lipid bilayer membranes induced by interacting with macromolecules. Recent progress of the topic is reviewed, and there are two types of systems studied in the thesis; macromolecules can either passively or actively interact with membranes. In the first part, the Monte Carlo simulation is used to study the structural properties of the system consisting of a self-avoiding polymer chain confined between a fluid membrane and a flat hard surface. There are no attraction or repulsion between the polymer and the membrane, and the membrane is adhesive to the flat surface or is pressed against the surface due to a pressure difference. As the adhesion between the soft membrane and the surface increases, the polymer is subject to a strong confinement; the state containing a pancake-shaped polymer conformation eventually yields to a bud state through an abrupt, discontinuous structural transition. We explore the scaling behavior of the physical properties of the system as functions of the polymer's size, the membrane's surface tension, and the adhesion energy. As for the pressure difference case, we show that it has a discontinuous structural phase transition. Monte Carlo simulations reveal that the system undergoes a transition from a confined (bump) state to a strongly confined (flatten-out) state as the pressure increases. A scaling argument is also made to understand the physical mechanism behind the phase transition and the properties of each state. In the second part, to understand how the nanoparticle adhesion strength and the deformation capability induce different protruding membrane structures, a model based on grand canonical ensemble and its solution are presented. With free energy minimization, we demonstrate that multiple nanoparticles with certain range of the adhesion strength and the deformation capability are able to induce stably not only tubes and buds but also pearls, and the structure diagrams of these shapes were computed. The results suggest that the pearling structure results from a balance between the adhesion strength, the deformation capability and the reduced volume of the vesicle. We also find a structural transformation that a tubular structure changes abruptly into a pearling structure.