Effects of cellular geometry on current flow during a propagated action potential.

An impulse propagating in a cell with nonuniform geometry sees an increased electrical load at regions of increasing diameter or at branch points with certain morphologies. We present here theoretical and experimental studies on the changes in membrane current and axial current associated with diameter changes. The theoretical studies were done with numerical solutions for cable equations that were generalized to include a varying diameter; the Hodgkin-Huxley equations were used to represent the membrane properties. The experimental studied were done using squid axons with the axial insertion of platinized platinum wires to create a localized region of increased electrical load. As an action potential approaches a region of increased electrical load, the action potential amplitude and rate of rise decrease, but there is a marked increase in the magnitude of the inward sodium current. The time integrals of the inward and outward currents are not constant along the fiber and indicate net inward charge movement at regions subjected to an increased electrical load. Changes in the waveform of the axial current at such a region help to explain the temperature dependence of propagation failure at regions of increasing electrical load.