Nonlinear dynamics of microtubules —A longitudinal model
1 Institut za nuklearne nauke Vinča, Univerzitet u Beogradu - Poštanski fah 522, 11001 Beograd, Serbia
2 Fakultet tehničkih nauka, Univerzitet u Novom Sadu - 21000 Novi Sad, Serbia
Received: 28 January 2013
Accepted: 23 April 2013
In the present letter we describe a model of nonlinear dynamics of microtubules (MTs) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimer's dynamics within MT, is solved both analytically and numerically. It is shown that such a nonlinear model can lead to the existence of kink solitons moving along the MTs. The internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled the estimation of the total energy, kink velocity and kink width. To simplify the calculation of the total energy we stated and proved a useful auxiliary theorem.
PACS: 87.15.-v – Biomolecules: structure and physical properties / 31.15.xv – Molecular dynamics and other numerical methods / 05.45.Yv – Solitons
© EPLA, 2013