Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis.

Recent observations indicate that it is possible to form tethers from large phospholipid vesicles. The process of tether formation is analyzed using a continuum mechanical approach to obtain the surface viscosity of the bilayer in terms of experimentally measurable parameters. The membrane is treated as a two-dimensional isotropic material which deforms a constant area. The constitutive equation relates the maximum surface shear resultant to the rate of deformation via the surface viscosity coefficient. The force which acts to increase the tether length is generated by fluid moving past the vesicle. The magnitude of the force is estimated from Stoke's drag equation. The analysis predicts that there is a critical force necessary to produce an increase in the tether length. A dimensionless tether growth parameter is defined, and its value is obtained as a function of the ratio of the applied force on the vesicle to the critical force. This relationship is independent of both the size of the vesicle and the radius of the tether. Knowing the force on the vesicle, the critical force, and the rate of tether growth, the surface viscosity can be calculated.