Allosteric propagation of curvature along filament

Abstract Can a filament transmit the curvatures across the constituting modules and control them at one of its ends? Inspired by the observation of protofilament —a constituent biopolymer of microtubules— 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 transcritical type.