Allosteric propagation of curvature along filament

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.