Influence of next-nearest neighbor interactions on the dynamics of discrete energy transport within neuronal microtubules

Abstract

In this study, we investigate the influence of next-nearest neighbor interactions or homodimer coupling on the dynamics of quantum breathers in neuronal microtubules (nMTs) using both analytical and numerical methods. From the classical model describing the dynamics of the microtubule using a Hamiltonian, we formulated its quantum equivalent through Bose operators. By employing Ehrenfest’s theorem and Glauber’s method of coherent states, we showed that nMT dynamics can be described by the discrete nonlinear Schrödinger equation (DNLSE). The analysis of modulational instability (MI) allowed us to define localization zones for breathers, revealing the impact of the second coupling term and well width on system’s behavior. We conducted numerical simulations to examine three scenarios based on homodimer and heterodimer coupling values in relation to breather propagation. We found that homodimer coupling enhances the temporal distribution of energy and extends breather localization towards the central site. Additionally, we observed that energy within nMTs is quantized with a linear profile, influenced by homodimer coupling. The interaction between two breathers indicated that this coupling also affects energy exchanges, impacting the collective dynamics of microtubules and potentially stabilizing or destabilizing configurations, thereby influencing neuronal responses. These findings enhance the understanding of energy transfer in biological systems such as the nervous system, which is responsible for coordinating actions and rapid communication within the body. This system, also known as the neuronal system, utilizes synapses to transmit signals. In this process, neurons release chemical neurotransmitters that can influence the activity of receiving cells.