Efficient mapping from neuroanatomical to electrotonic space

Previous studies documented the importance of electrotonic structure in single-neuron computations. Here we elaborate a new approach to electrotonic theory and analysis. We begin with a more versatile measure Lij of the electrotonic distance between any two locations i and j on a neuron. If Vi is the voltage at the origin and Vj is the voltage at Some other point, the electrotonic distance is Lij=ln(Vi/Vj). Voltage decays e-fold per unit of L for any two points on the neuron, regardless of its electrotonic architecture. Lij increases as the sinusoidal frequency of Vi increases. If j lies on the direct path between i and k, then Lik=Lij+Ljk. This relation enables electrotonic transforms of the neuron—graphical mappings from neuroanatomical to electrotonic space. For each neuron, there exists an infinite number of such transforms, which can be done from any reference location on the neuron, as a function of voltage transfer to or from that location, and for any frequency of input signal. Sets of these trans...