  Can a filament transmit the curvatures across the constituting modules and
control them at one of its end? Inspired by the observation of protofilament -
constituent biopolymer of microtubule - this question is addressed by a
constructive approach. In our model a simple allosteric element in each module
couples with the neighboring modules at its interfaces, which gives rise to a
single degree of freedom to control the global shape of the filament. The model
can be analyzed in analogy with discrete-time dynamical systems having a
bifurcation of trans-critical type.
