  In the present paper we describe a model of nonlinear dynamics of
microtubules (MT) 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 nonlinear model can lead to existence of
kink solitons moving along the MTs. Internal electrical field strength is
calculated using two procedures and a perfect agreement between the results is
demonstrated. This enabled estimation of total energy, kink velocity and kink
width. To simplify the calculation of the total energy we proved a useful
theorem.
