A theory for cell microtubule wall in external field and pseudo-spin wave excitation

The cytoskeleton of eukaryotic cells contains networks of protein polymers called microtubules (MTs), which provide a wide range of microskeletal and micromuscular functionalities. Evidences from a number of directions suggest that they can also serve as a medium for intracellular signal processing. For the inherent symmetry structures and the electric properties of the microtubule (MT), we treat the MT wall as a one-dimension ferroelectric system and describe the nonlinear dynamics of the dimer electric dipoles with the double-well potential, and then map the physical problems onto the pseudo-spin system. By using the random phase approximation, the effect from the external electric field has been taken into account. We have developed an expression for the Hamiltonian in the pseudo-spin system and obtained the coupled motion equations for the disturbed pseudo-spin wave, and there appears to be a transverse collective excitation with an intrinsic frequency.