In our investigation, the decoherence and dissipation processes in microtubule cause by the pseudo-spin-boson interaction have been considered. The spin-boson model corresponds to a two-level system interacting with a large reservoir of bosons. This model well studied in the context of decoherence and dissipation in quantum systems. Microtubule is modeled as a macroobject presenting a system of bound tubulins, forming a skewed hexagonal lattice which has rotational helical symmetry. There are two different conformations of tubulin dimers. These conformations are supposed to be conditioned by the fact that the electron located in the hydrophobic pocket (in the area of the dimer center) can occupy one of the two possible positions in tubulin. Thus, tubulins can be in two different polarization states whose dipole moments interact with each other. In our study, the quantum dynamics of this system is investigated. Pseudo-spin formalism is used to describe the system. Thus, electric dipoles are represented as two-level pseudo spin systems in which one of the two tubulin polarization states corresponds to each of pseudo-spin ones. The mobile electron that determines changes in tubulin conformations is in a double potential well, one local minimum of which is determined in $\alpha$ tubulin and correlates with the pseudo-spin-down orientation while the other is determined in $\beta$ tubulin and correlates with the pseudo-spin-up orientation. 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 $1.86\cdot 10^{-13}~s$. 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 our investigation 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.
References
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[2] S.Eh. Shirmovsky, D.V. Shulga, Microtubules lattice equal-frequency maps: The dynamics of relief changes in dependence on elastic properties, tubulins’ dipole-dipole interaction and viscosity, Physica A 534 (2019) 122165.
[3] S.Eh. Shirmovsky, D.V. Shulga, Quantum relaxation effects in Microtubules, Physica A 582 (2021) 126254.