Nonlinear Soliton Dynamics in Microtubules: Analytical Solutions and Biological Implications

ABSTRACT This study explores the nonlinear dynamics of microtubules by developing and analyzing a nonlinear equation of motion that accounts for their inherent dipolar characteristics. We systematically derive analytical soliton solutions using both the unified method and the unified Riccati equation expansion method. These approaches allow us to transform the nonlinear partial differential equation into a solvable ordinary differential equation, leading to the construction of exact kink and other soliton solutions through algebraic manipulation and parameter determination. Our findings demonstrate that kink soliton solutions can emerge and propagate stably along the microtubule structure. These solutions exhibit key features such as exponential localization and shape invariance. We show that the system's total energy is an integral of motion when the system is conservative. By deriving the full energy balance equation, we establish that the system becomes a driven‐dissipative one, where dynamic stability relies on the active balance between energy input and viscous loss. Furthermore, a detailed modulation instability analysis identifies the parameter regimes that permit stable soliton propagation and determines the thresholds for instability onset. These results offer novel insights into the mechanisms governing energy and information transfer along microtubules, with broader implications for understanding motor protein activity and microtubule depolymerization.