  We perform a theoretical study of the dynamics of the electric field
excitations in a microtubule by taking into consideration the realistic
cylindrical geometry, dipole-dipole interactions of the tubulin-based protein
heterodimers, the radial electric field produced by the solvent, and a possible
degeneracy of energy states of individual heterodimers. The consideration is
done in the frames of the classical pseudo-spin model. We derive the system of
nonlinear dynamical ordinary differential equations of motion for interacting
dipoles, and the continuum version of these equations. We obtain the solutions
of these equations in the form of snoidal waves, solitons, kinks, and localized
spikes. Our results will help to a better understanding of the functional
properties of microtubules including the motor protein dynamics and the
information transfer processes. Our considerations are based on classical
dynamics. Some speculations on the role of possible quantum effects are also
made.
