Relaxation effects in cell microtubule under the influence of an external electric field: The mean field approximation.

The quantum relaxation processes in the microtubule dipole system under the action of an external electric field have been studied. The study is based on the Born-Markov equation. Tubulins dipole-dipole interaction and the internal dynamics of the dipole system that is determined by the quantum tunneling effect in the double potential well is taken into account. A system of differential equations defining the relaxation processes in a microtubule consisting of 676 tubulins is obtained. It was shown that the relaxation nature strongly depends on the magnitude of the dipole-dipole interaction, the internal dynamics of the dipole system, and the influence of the dissipative process. The decoherence time equal to 10-14 s - 10-9 s depending on the features of the relaxation process was determined. It has been proved that, the relaxation can have a twofold character, defining mixed or pure states.