Nonlinear Dynamics of Microtubules as Electrical Conduits in Cellular and Neuronal Functions: Soliton Solutions and Modulation Instability

Microtubules are fundamental to the cellular cytoskeleton, participating in diverse functions like cell division and intracellular transport facilitated by motor proteins such as dynein and kinesin. Moreover, they have critical roles in advanced neuronal activities, including consciousness and memory. This study explores the specific conditions that allow microtubules to operate as nonlinear electrical conduits for ion flow along their structures. By modeling them as nonlinear resistive, inductive, and capacitive (RLC) transmission lines, we employ the generalized Riccati equation mapping method to derive solutions for these dynamics. This study also gives a comprehensive literature review for the modeled equation and emphasizes the uniqueness of this interdisciplinary approach. Comparative analyses of specific outcomes are presented, with graphical illustrations to clarify the physical implications. Modulation instability (MI) analysis has been incorporated to investigate the frequency behavior of \( w(a) \) under varying parameters. By applying nonlinear engineering principles sheds new light on microtubule functionality in neuronal and cellular contexts, laying a foundation for new developments in bioengineering and nanobioscience.