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 L(ij) of the electrotonic distance between any two locations i and j on a neuron. If V(i) is the voltage at the origin and V(j) is the voltage at some other point, the electrotonic distance is L(ij) = ln(V(i)/V(j)). Voltage decays e-fold per unit of L for any two points on the neuron, regardless of its electrotonic architecture. L(ij) increases as the sinusoidal frequency of V(i) increases. If j lies on the direct path between i and k, then L(ik) = L(ij) + L(jk). 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 transforms furnish rapid insight into the electrotonic architecture of a neuron. We describe an efficient and accurate algorithm for computing the L(ij). Computation time scales linearly with anatomical complexity and independently of signal frequency. A graphical display facilitates comparisons between neuroanatomical and electrotonic space. We illustrate this new approach by generating electrotonic transforms of three classes of hippocampal neurons, vividly revealing general principles and interesting similarities and differences among the dendrites.