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Influence of Thermally Driven Surface Undulations on Tethers Formed from Bilayer Membranes

Department of Bioengineering, Rice University, Houston, Texas

Correspondence: Address reprint requests to Dr. Robert M. Raphael, Rice University, Dept. of Bioengineering, MS-142, PO Box 1892, Houston, TX 77251-1892.E-mail: rraphael{at}rice.edu.

Tether formation is a powerful method to study the mechanical properties of soft lipid bilayer membranes. The force required to maintain a tether at a given length depends upon both membrane elastic properties and tension. In this report, we develop a theoretical analysis that considers the contribution of thermally driven surface undulations and the corresponding entropically driven tensions on the conformation of tethers formed from unaspirated lipid vesicles. In this model, thermal undulations of the vesicle surface provide the excess area required for tether formation. Energy minimization demonstrates the dependence of equilibrium tether conformation on membrane tension and provides an analytical relationship between tether force and radius. If the contributions of nonlocal bending are not considered, an analytical relationship between tether force and length can also be obtained. The predictions of the model are compared to recently reported experimental data, and a value for the initial vesicle tension is obtained. Since most analyses of tether formation from cells and unaspirated vesicles neglect the contributions of nonlocal bending, the appropriateness of this assumption is analyzed. The effect of surface microvesiculations on the tether force-length relation is also considered.