Nano-Ionic Current Dynamics in Microtubules: An Analytical Approach with Stability Analysis

The nano-ionic current along microtubules equation, which allows microtubules to act as nonlinear electrical transmission lines and allows ions to flow through the cylindrical shapes of the microtubules. The paper derives new solitary-wave solutions of the dynamical equations of ionic currents along microtubules with the aid of an new extended direct algebraic method (NEDAM) which is much relevant to nanotechnology. The NEDA method is a strong analytical tool that allows us to derive solutions, such as bright, dark, combined dark-bright solitons, the w-shaped soliton, kink, anti-kink, and singular solitons, based on various mathematical functions, including polynomial, rational, exponential, hyperbolic, and trigonometric functions. We produce 2D, 3D, density, and contour graphs to illustrate the soliton’s propagation under particular conditions, demonstrating an accurate representation of real instances. Furthermore, we examine the microtubule equation for modulation instability in the nano ionic currents. We discovered that the suggested approach provides precise and analytical answers and is accurate and efficient. Mathematica is used to verify all results, guaranteeing their precision and stability.