Possible link between guanosine $5^{|\mathrm{I}\mathrm{H}}$ triphosphate hydrolysis and solitary waves in microtubules

The cytoskeleton of eucaryotic cells is composed of several classes of protein polymers among which microtubules (MTs) are the most prominent. Microtubules are important in a variety of cellular activities but the physical reasons underlying their behavior are largely unknown. Inside the cell they usually exist in an unstable dynamic state characterized by a continuous addition and dissociation of the molecules of tubulin. The addition of each tubulin is accompanied by the hydrolysis of guanosine $5^{|\mathrm{I}\mathrm{H}}$ triphosphate bound to the Β monomer of the molecule. Experiments show that an amount of energy comparable to 6.25×${10}^{\mathrm{-}21}$ J is freed in this reaction. A few researchers have put forward a hypothesis that this energy can travel along MTs as a kinklike solitary wave. In this paper two models are analyzed whose special solutions are traveling kinks that arise as a result of coupling between dielectric and elastic degrees of freedom of tubulin. By means of these models a collision of the kink wave with an impurity in the microtubule is studied. The impurity may represent a protein attached to the microtubule or a structural discontinuity in the arrangement of the tubulin molecules. We conjecture that the collisions of the quanta of energy propagating in the form of kinks with such defects may explain some features of the microtubule behavior.