Microtubules are the major part of the cytoskeleton. They are involved in nuclear and cell division and serve as a network for motor proteins. The first model that describes nonlinear dynamics of microtubules was introduced in 1993. Three nonlinear models are described in this chapter. They are longitudinal U-model, representing an improved version of the first model, radial φ -model and new general model. Also, two mathematical procedures are explained. These are continuum and semi-discrete approximations. Continuum approximation yields to either kink-type or bell-type solitons, while semi-discrete one predicts localized modulated waves moving along microtubules. Some possible improvements and suggestions for future research are discussed.
Part of the book: Complexity in Biological and Physical Systems