Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis (original) (raw)

1982, Biophysical Journal

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 at 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 Stokes'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. INTRODUCTION Biological membranes behave as two-dimensional materials. Strictly speaking, they can be considered as continuous only in the two dimensions of the surface, with a molecular character in the direction normal to the surface. The erythrocyte membrane has served as a model system for the study of such materials, and the continuum mechanical properties of erythrocyte membrane have been characterized. (See Evans and Skalak, 1980, for a thorough review.) The application of material science to other types of membrane has been slow, largely because of the existence of cytoplasmic structures in most cells which, at best, complicate the mechanical analysis and, at worst, dominate the behavior of the cell in deformation. The mechanical behavior of any membrane reflects the composite properties of the membrane constituents. Therefore, an alternative approach to the study of membrane mechanics is to study the properties of reconstituted membrane components to ascertain the contribution of each constituent. The phospholipid bilayer is a major constituent of virtually all biological membranes, and it is with the bilayer that the study of membrane components logically begins. Recently, it has been observed that large multilamellar phospholipid bilayer vesicles can become attached to glass surfaces and form tethers between the point of attachment and the body of the vesicle (E.