2012, Vol.15, No.4, pp.339-349
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 different "cargos"
such as vesicles and mitochondria to different sub-cellular
locations.
In this article we explain three models describing its nonlinear dynamics
and we call them u, z and -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 differential 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
-model, is a
bell-type soliton, which, we believe, has a profound biophysical meaning.
Key words:
microtubule, nonlinear models, nonlinear differential equations,
kink soliton
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