Topological Edge States in Helical Soft-Matter Lattices: Microtubules as a Natural Platform

We show that the structural seam of the 13-protofilament microtubule acts as a Jackiw–Rebbi domain wall in an effective Su–Schrieffer–Heeger (SSH) model, binding a topologically protected mid-gap state. The tight binding parameters are treated as effective excitonic couplings (tryptophan-based Frenkel excitons) anchored to the α–β tubulin heterodimer geometry. Assuming beyond-dipole contributions invert the point-dipole ordering (t₂ > t₁, to be verified by DFT/DFTB), the model predicts a topological gap of ~20 meV, substantial decoherence suppression (Γ_eff/Γ₀ ~ 10⁻³), and a dipole-active absorption feature near 160 cm⁻¹ (~5 THz) that disappears upon depolymerization. The accompanying code repository is available at https://github.com/lucasgpinheiro-rgb/microtubule-topology.