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Nanomechanical Model of Microtubule Translocation in the Presence of Electric Fields

Taesung Kim ^*, Ming-Tse Kao , Ernest F. Hasselbrink ^* and Edgar Meyhöfer ^* 

^* Department of Mechanical Engineering and Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan 48109

Correspondence: Address reprint requests to Edgar Meyhöfer, University of Michigan Dept. of Mechanical Engineering, 2350 Hayward St., Ann Arbor, MI 48109. Tel.: 734-647-7856; Fax: 734-647-7856; E-mail:meyhofer{at}umich.edu.

Research efforts in recent years have been directed toward actively controlling the direction of translocation of microtubules on a kinesin-coated glass surface with E-fields (electric fields), opening up the possibility of engineering controllable nanodevices that integrate microtubules and motor proteins into their function. Here, we present a detailed, biophysical model that quantitatively describes our observations on the steering of microtubules by electric fields. A sudden application of an electric field parallel to the surface and normal to the translocation direction of a microtubule bends the leading end toward the anode, because Coulombic (electrophoretic) forces are dominant on negatively charged microtubules. Modeling this bending as a cantilever deflection with uniform loading requires accurate mechanical and electrical properties of microtubules, including their charge density, viscous drag, and flexural rigidity. We determined the charge density of microtubules from measurements of the electrophoretic mobility in a "zero flow" capillary electrophoresis column and estimate it to be 256 e^– per micron of length. Viscous drag forces on deflecting microtubules in electroosmotic flows were studied theoretically and experimentally by directly characterizing flows using a caged dye imaging method. The flexural rigidity of microtubules was measured by applying E-fields to microtubules with biotinylated segments that were bound to streptavidin-coated surfaces. From the calculated loading, and the Bernoulli-Euler curvature and moment equation, we find that the flexural rigidity of microtubules depends on their length, suggesting microtubules are anisotropic. Finally, our model accurately predicts the biophysical properties and behavior of microtubules directed by E-fields, which opens new avenues for the design of biomolecular nanotransport systems.