A primary model of decoherence in neuronal microtubules based on the interaction Hamiltonian between microtubules and plasmon in neurons

Microtubules (MTs) are part of the cellular cytoskeleton and they play a role in many activities, such as cell division and maintenance of cell shape. In recent years, MTs have been thought to be involved in storing and processing information. Several models have been developed to describe the information-processing ability of MTs. In these models, MTs are considered as a device that can transmit quantum information. However, MTs are affected by the “wet and warm” cellular environment, thus it is essential to calculate the decoherence time. Many researchers have attempted to calculate this parameter but the values that have been obtained vary markedly. Previous studies considered the cellular environment as a distant ion; however, this treatment is somewhat simplified. In this study, we develop a model to determine the decoherence time in neuronal MTs while considering the interaction effects of the neuronal fluid environment. The neuronal environment is considered as a plasmon reservoir. The coupling between MTs and neuronal environment occurs due to the interaction between dipoles and plasmon. The interaction Hamiltonian is derived by using the second quantization method, and the coupling coefficient is calculated. Finally, the decoherence time scale is estimated according to the interaction Hamiltonian. In this paper, the time scale of decoherence in MTs is approximately 1 fs-100 fs. This model may be used as a reference in other decoherence processes in biological tissues.