A local friction model to develop microscopic transport parameters for membrane-soluble ions in bilayer membranes

Charged membrane-soluble ions in bilayer membranes move between opposing interfacial states on application of an electric field. The kinetics of this transition is modeled as discrete state electrophoresis using a Langevin formulation that focuses on local velocities at points along the spatial trajectory of the ion. These local velocities are used to establish both the decay time for the transition and the activation energy profile along the trajectory. The local velocities depend on local frictional coefficients. These coefficients are developed from the molecular structure along the trajectory by introducing a microscopic frictional force. This frictional force is produced by the lateral displacement of segments of the surrounding membrane molecules as the ion passes. The displaced molecular chains produce a non-linear resistive force that translates into a frictional force directly proportional to both ion radius and velocity.