Direct correction of non-space-clamped currents via Cole's theorem

The currents measured during voltage clamp of a non-isopotential neuron reflect axial as well as membrane conductances. One wishes to remove the former in the hope that the latter will reveal quantitative information on the nature of the voltage gated channels at the clamp site. We here show that Cole's theorem can be used to directly remove the axial component from simulated voltage clamp recordings. It is direct in the sense that it requires neither simulation nor fitting. As it comes down to squaring the clamp current and then differentiating with respect to clamp voltage it may indeed be implemented in real time. When applied to synthetic potassium currents in straight fibers we find that our method accurately and robustly recovers both non-uniform conductances and non-uniform channel kinetics. We indicate the degree to which such accuracy is diminished for cells that taper and/or branch.