A Solvable Model for Polymorphic Dynamics of Biofilaments

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.