The effect of surface tension and pulling rate on the dynamic behavior of tether extrusion process using a mathematical model

Dynamic behavior of biological membranes is involved in many processes within the cells and organelles like transport in the Golgi apparatus, endoplasmic reticulum and mechanisms of shaping used by cytoskeleton. Among different dynamic procedures and shape transformations of membranes, formation of tubular structures called tether is well-known. Tethers are involved in many cellular processes such as inter, intracellular transport and cell-cell adhesion. Tubular networks are also observed in the Golgi apparatus, the smooth part of the Endoplasmic reticulum and the inner membrane of the Mitochondrion. Membrane tubes can be formed by in vitro experiments. Tethers are also extracted from synthetic vesicles using different techniques such as optical tweezer and hydrodynamic flow. In this paper, the dynamic behavior of a bilayer membrane in tether extension process is studied using a mathematical model based on the mechanical properties of the bilayer membrane. A fluid bilayer membrane is utilized in this model consisting of two monolayers sliding on each other. The bending and stretching energies in addition to dissipations due to the fluidity of each monolayer and the inter-monolayer drag are defined for the bilayer membrane. The dynamic behavior of the bilayer membranes in the tether extension process is studied. The tether is extruded by a constant pulling rate and the dynamic pulling force is measured. The effect of the pulling rate and the surface tension on the dynamic pulling force is investigated. These two parameters have a great effect on the dynamic pulling force and the steady state of the process.