Elastic, dipole-dipole interaction and viscosity impact on vibrational properties of anisotropic hexagonal microtubule lattice

Modeling of the entangled states transfer processes in microtubule tryptophan system

The paper simulates the process of the migration of a single energy excitation along a chain of tryptophans in cell microtubules connected by dipole-dipole interaction. The paper shows that the excited states propagation rate falls within the range of nerve impulse velocity. It was shown that such a process also causes a transfer of quantum entanglement between tryptophans, so that microtubules can be considered as signaling system, the basis for transmitting information via the quantum channel. The conditions under which the migration of entangled states in the microtubule is possible are obtained. In a certain sense, it allows us to argue that the signal function of tryptophans works as an analogue of a quantum repeater that transmits entangled states over microtubule by relaying through intermediate tryptophans. Thus, the paper shows that the tryptophan system can be considered as an environment that supports the existence of entangled states during the time comparable with the time of the processes in biosystems.

Dynamics of exciton polaron in microtubule

In this paper, we study the dynamical properties of the exciton-polaron in the microtubule. The study was carried out using a unitary transformation and an approximate diagonalization technique. Analytically, the modeling of exciton-polaron dynamics in microtubules is presented. From this model, the ground state energy, mobility, and entropy of the exciton-polaron are derived as a function of microtubule's parameters. Numerical results show that, depending on the three vibrational modes (protofilament, helix, antihelix) in MTs, exciton-polaron energy is anisotropic and is more present on the protofilament than the helix and absent on the antihelix. Taking into account the variation of the protofilament vibrations by fixing the helix vibrations, exciton-polaron moves between the 1st and 2nd protofilaments. It is seen that the variation of the two vibrations induces mobility of the quasiparticle between the 1st and 15th protofilament. This result points out the importance of helix vibrations on the dynamics of quasiparticles. It is observed that the mobility of the exciton polaron and the entropy of the system are strongly influenced by the vibrations through the protofilament and helix. The effects of the one through the antihelix is negligible. The entropy of the system is similar to that of mobility. Confirming that the quasiparticles move in the protofilament faster than in the helix.