Computational dynamics method for evaluating the mobility of charged biomolecules passing through the electrical potential field within the ion selective channel on an excitable membrane

A mathematical method is introduced to characterize the electrokinetic behavior (electrophoresis) of a biomolecular particle which passes through a specific channel pore on an excitable biological membrane. The basic approach was first proposed by Booth (1950). The system was described by an equation of continuity and an equation of motion in which the driving force involves the diffusion effect, the hydrostatic pressure, and the electrostatic potential. By assuming linear relations between the velocity and the applied electrical field, solutions for the potential, pressure, and velocity were given by a series expansion of the charges on the particle. To examine the influence of ions surrounding the particle and forming an ionic cloud, the Debye–Huckel parameter was introduced. As the thickness of the double layer around the particle increased, the potential, velocity, pressure, and viscosity were changed significantly. The maximum influence was obtained when the radius of the particle became equal to the thickness of the double layer. Although this theory is valid for a charged, spherical, nonconducting particle only, the method is available for evaluating the kinetic behavior of a biomolecule that passes through a channel pore on a cellular membrane.This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003