Allosteric propagation of curvature along filament

TL;DR

This paper models how a filament can transmit curvature along its length through allosteric coupling, allowing control of its shape via a simple, bifurcation-based dynamical system inspired by microtubule protofilaments.

Contribution

It introduces a novel allosteric model for filament curvature propagation, linking biopolymer behavior with dynamical systems theory.

Findings

Curvature can be propagated along the filament through allosteric coupling.

The model exhibits bifurcation behavior similar to trans-critical bifurcations.

Global shape control is achievable via local allosteric interactions.

Abstract

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.