Ionic wave propagation along actin filaments.

We investigate the conditions enabling actin filaments to act as electrical transmission lines for ion flows along their lengths. We propose a model in which each actin monomer is an electric element with a capacitive, inductive, and resistive property due to the molecular structure of the actin filament and viscosity of the solution. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived for the propagation of ionic waves. We solve this equation in two different regimes. In the first, the maximum propagation velocity wave is found in terms of Jacobi elliptic functions. In the general case, we analyze the equation in terms of Fisher-Kolmogoroff modes with both localized and extended wave characteristics. We propose a new signaling mechanism in the cell, especially in neurons.