Quantum relaxation effects in Microtubules

Abstract

The paper investigates quantum dynamics of a system of microtubule tubulins electric dipole moments. Electric dipoles represent two-level pseudo-spin systems, with one of the two polarized tubulin states corresponding to each of a pseudo-spin one. The pseudo-spin system behavior with time has been analyzed on basis of the Born–Markov formalism. The decoherence and dissipation processes caused by pseudo-spin–boson interaction have been considered. The problem of a possible signal propagation mechanism in the microtubule dipole–dipole system, which can be exclusively quantum in nature, has been discussed. It has been determined that the decoherence time depends considerably on dissipative processes in microtubules. Thus, the decoherence time in case of weak dissipation or absence of it equals 10−11–10−10 s. The decoherence time in the presence of dissipation process has been found to be 1.86⋅10−13 s. The temperature dependence of decoherence process has been considered. It has been stated that temperature values are the major factor influencing the dissipation-less decoherence time. The results obtained in the paper make it possible to describe the microtubule as a system in which quantum relaxation processes are important and comparable in time with those occurring in bio systems.