Allosteric propagation of curvature along filament

Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL 10 rue Vauquelin, 75005, Paris, France and Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Cité 10 rue Alice Domon et Léonie Duquet, 75013, Paris, France

Received: 12 June 2024
Accepted: 13 September 2024

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.