A Solvable Model for Polymorphic Dynamics of Biofilaments

TL;DR

This paper introduces an analytically solvable toy model for the thermally driven polymorphic dynamics of biofilaments like microtubules, providing insights into their complex behavior across different length scales.

Contribution

The paper presents a simplified 4-block model that allows complete analytical analysis of biofilament polymorphic dynamics, bridging microscopic properties with macroscopic behavior.

Findings

Model explains length-dependent persistence length

Filaments mimic worm-like chain behavior at small and large scales

Reveals inner switching dynamics at intermediate scales

Abstract

We investigate an analytically tractable toy model for thermally induced polymorphic dynamics of cooperatively rearranging biofilaments - like microtubules. The proposed 4 -block model, which can be seen as a coarse-grained approximation of the full polymorphic tube model, permits a complete analytical treatment of all thermodynamic properties including correlation functions and angular fourier mode distributions. Due to its mathematical tractability the model straightforwardly leads to some physical insights in recently discussed phenomena like the "length dependent persistence length". We show that a polymorphic filament can disguise itself as a classical worm like chain on small and on large scales and yet display distinct anomalous tell-tale features indicating an inner switching dynamics on intermediate length scales.