Phagocytosis is one of endocytosis functions to capture vesicles or microorganism into a cell. The lipid binding mechanism between vesicles and membranes plays a crucial role in the cell engulf process, most literatures focused on the discussion of membrane equilibrium state or static problems without the consideration of fluid flow. In this talk, we present a mathematical model in the immersed boundary (IB) formulation which consists of fluid equations, fluid-structure interaction, and molecule concentration equations, to study the role of interfacial properties (surface tension and bending rigidity) in phagocytosis.
A two-layer structure is used for the membrane-bound receptor-ligand binding process, and interfacial forces are derived from Canham-Helfrich Hamiltonian. The membrane-bound molecules are treated as insoluble surfactants such that the molecules after binding are regarded as a product after chemical reaction. Mass conservation constraint and the law of mass action are imposed to obtain the corresponding governing equations of the membrane-bound molecules. A conventional IB method and a conservative numerical scheme with the consideration of reaction for the membrane molecules are proposed. In numerical experiments, we give an energy balance investigation to conform the numerical scheme, then we examine the engulf process by altering the surface energy reduction, the ratio of bending rigidity, vesicle size, and an adhesion energy assistance. The studies of convection-diffusion-reaction effect to engulf process are also presented.
This is a joint work with Y-H Tseng.