Local and nonlocal curvature elasticity in bilayer membranes by tether formation from lecithin vesicles

Abstract

Bilayer membranes exhibit an elastic resistance to changes in curvature. This resistance depends both on the intrinsic stiffness of the constituent monolayers and on the curvature-induced expansion or compression of the monolayers relative to each other. The monolayers are constrained by hydrophobic forces to remain in contact, but they are capable of independent lateral redistribution to minimize the relative expansion or compression of each leaflet. Therefore, the magnitude of the expansion and compression of the monolayers relative to each other depends on the integral of the curvature over the entire membrane capsule. The coefficient characterizing the membrane stiffness resulting from relative expansion is the nonlocal bending modulus kr. Both the intrinsic (local) bending modulus (kc) and the nonlocal bending modulus (kr) can be measured by the formation of thin cylindrical membrane strands (tethers) from giant phospholipid vesicles. Previously, we reported measurements of kc based on measurements of tether radius as a function of force (Song and Waugh, 1991, J. Biomech. Engr. 112:233). Further analysis has revealed that the contribution from the nonlocal bending stiffness can be detected by measuring the change in the aspiration pressure required to establish equilibrium with increasing tether length. Using this approach, we obtain a mean value for the nonlocal bending modulus kr of approximately 4.1 x 10(-19)J. The range of values is broad (1.1-10.1 x 10(-19)J) and could reflect contributions other than simple mechanical equilibrium. Inclusion of the nonlocal bending stiffness in the calculation of kc results in a value for that modulus of approximately 1.20 +/- 0.17 x 10(-19)J, in close agreement with values obtained by other methods.

Membrane shape as a reporter for applied forces

“…Although the formation of membrane tethers is both well-known and well-studied in the membrane mechanics literature (34)(35)(36)(37), it nevertheless provides a convenient proofof-principle experiment where both the force, applied by the optical trap, and the membrane conformation are known simultaneously. Similarly, a direct analysis of membrane conformation has been performed by Baumgart and coworkers to measure the material properties and line tension in multiphase vesicles (38).…”

“…We can estimate the spatial resolution required to image structures of interest by examining the dependence of the force at tether formation on curvature. [The tether-force equation is the exact equilibrium force required to support a tether radius R in the absence of spontaneous curvature (35).] Given an applied force F, the approximate scale of membrane bending R is given by R ϳ 2k C /F ϭ 0.4 (1 pN/F) m. Because the typical protein-scale biological forces are several piconewtons, the The axisymmetric vesicle conformation is represented as a cubic spline.…”

Hydrodynamic narrowing of tubes extruded from cells

“…We follow the thermodynamic analysis of tether formation proposed by Waugh and coworkers (7,13,14), Evans and Yeung (15), and Derényi and coworkers (16) for lipidic bilayers and extended to cell membranes by Sheetz and coworkers (10, 12). As shown in Fig.…”

Shape behavior of lipid vesicles as the basis of some cellular processes

“…The importance of the nonlocal bending term for the shape behavior of phospholipid vesicles has been proven in tether-pulling experiments (Bo and Waugh, 1989;Waugh et al, 1992). In those experiments, which were designed to measure membrane elastic parameters, a thin cylindrical tether was pulled out of an aspirated vesicle.…”