Nonlinear Dynamics of Microtubules

Abstract

Microtubule (MT) is a major cytoskeletal protein. Beside its mechanical role in cells it serves as a “road network” for motor proteins (kinesin and dynein) dragging di˙erent “cargos” such as vesicles and mitochondria to di˙erent sub-cellular locations. In this article we explain three models describing its nonlinear dynamics and we call them u, z and Á-model. Each of them assumes one degree of freedom per dimer. The u-model assumes an angular degree of freedom, while the used coordinate u is a projection of the top of the dimer on the direction of a protofilament (PF). As for the remaining two models, a radial and a longitudinal coordinates are used to describe displacements of the dimers. All the models bring about nonlinear di˙erential equations (NLDE). The solutions of these equations are kink solitons that we understand as signals for the protein to start moving along PF. In addition, one of the solutions of a discrete NLDE, describing the Á-model, is a bell-type soliton, which, we believe, has a profound biophysical meaning.