A Model Cellular System Encapsulating Two Aqueous Phase Systems In A Computational Model

Being widespread in nature, in our daily life and industry, the soft matter playsan important role in our lives. As two important consists of soft matter, biomembraneand polymers are investigated in this thesis.Novel soft matter systems, which consist of lipid vesicles and two species ofwater-soluble polymers such as dextran and polyethylene glycol (PEG), have a richphase structure. Related experiments have been carried out by biophysicists withdifferent methods. However, few studies have been reported on the theoretical studyof this composite system. In this thesis, the computational model which combines theself-consistent field theory (SCFT) for polymers and Helfrich elastic theory for thefluid membrane is extended to study the morphological change of a model cellularsystem encapsulating two aqueous phase systems. An auxiliary filed is also introducedin our computational model to distinguish the interior of the vesicle from the exterior.Taking the interaction between polymers and polymers, polymers and vesicles,polymers and solvent molecules into account, the new shape equation of themembrane is re-derived. The concentration distribution of the polymers thatencapsulated in the vesicle and the vesicle shapes were obtained based on the SCFTand Helfrich elastic theory.In the third chapter, we focused on the effect of the penetration, the compositionand adsorption strength of the polymers on the phase morphology of polymer andvesicle system. Compared with the phase diagram of simple vesicle system, it wasclear to see that oblate region has significant increase. The main difference betweenthe two systems was the limitation of vesicle to the geometric space of polymer chainscaused the decrease of entropy, which eventually induced the vesicle shape change.During the interaction of the membrane and polymer chain segments, the polymerchains not only put a entropy pressure on the vesicle surface but also changed thesurface tension of the vesicles. While the changes of entropy pressure and the surfacetension were closely related with interaction parameter as well as the polymerconcentration around the inner surface of vesicles.According to the equation of shape, we can also know that many parameters ofthe polymer and vesicle composite system play a role in the phase morphology, suchas the bending rigidity modules and surface tension of the vesicle. This is a complex process in the interaction among the homopolymer, the homopolymer and thevesicle membrane. Furthermore, our theory can be extended to more complicatedsystems, such as the multi-components homopolymers or copolymer chains thatencapsulated in the vesicle membrane. This study will provide a theoretical guidancefor the experimental studies of phase morphology of the polymer and the vesiclecomposite system.Additionally, we carried out the theoretical study of the polymerization anddepolymerization dynamics of actin monomers into actin filaments, which has attractlarge amounts of attention in biophysics recent years. In this study, the masterequation method was utilized to study the self-assembly dynamics of actin filamentscoupled with adenosine triphosphate (ATP) hydrolysis, and a detailed derivedtheoretical analysis model was established. Also, we simulate ensembles of filamentsand determine the overall growth rate and length diffusivity of the filament as afunction of the free ATP-actin monomer concentrations. The results showed that thecritical concentration and the maximum diffusion coefficient not only agrees wellwith the results of the experiments, but perfectly consistent with the results of theBrownian dynamics simulation in the previous reports. It is, therefore, expected thatthe dependence of length diffusivity on ATP-actin monomer concentrations is utilizedto analyze the surprising experiments on the length fluctuations of individual actinfilaments.