Solitary wave dynamics as a mechanism for explaining the internal motion during microtubule growth

Microtubules, which play many diverse and important roles in biological systems, are usually made up of 13 nearly axial protofilaments formed from individual tubulin molecules. In this paper, a nonlinear dynamic model has been developed to elucidate the mechanism of the internal motion occurring during the assembly of microtubules. The results derived from the model indicate that such internal motion is associated with a solitary wave, or kink, excited by the energy released from the hydrolysis of GTP-->GDP in microtubular solutions. As the kink moves forward, the individual tubulin molecules involved in the kink undergo motions that can be likened to the dislocation of atoms within the crystal lattice. Thus, the dynamic instability of microtubules may be characterized by a series of dislocation motions of the tubulin molecules. An energy estimate shows that a kink in the system possesses about 0.36-0.44 eV, which is quite close to but smaller than the 0.49 eV of energy released from the hydrolysis of GTP. Therefore, the relevant energy derived from our model is fully consistent with experimental observations; this finding also suggests that the hydrolysis energy may be responsible for exciting the solitary wave, or kink, leading to tubulin dislocation in microtubules. Our model, and its intrinsic properties, i.e., dynamic nonlinearity, thermodynamic irreversibility, as well as an energy input from a sustained source, implies that the growth of microtubules is a typical dissipative process and that their structure in vivo is typical of dissipative structures.