THE MORPHOELECTROTONIC TRANSFORM - A GRAPHICAL APPROACH TO DENDRITIC FUNCTION

Electrotonic structure of dendrites plays a critical role in neuronal computation and plasticity, In this article we develop two novel measu res of electrotonic structure that describe intraneuronal signaling in dendrites of arbitrary geometry. The log-attenuation L(ij) measures t he efficacy, and the propagation delay P-ij the speed, of signal trans fer between any two points i and j. These measures are additive, in th e sense that if j lies between i and k, the total distance L(ik) is ju st the sum of the partial distances: L(ik) = L(ij) + L(jk), and simila rly P-ik = P-ij + P-jk. This property serves as the basis for the morp hoelectrotonic transform (MET), a graphical mapping from morphological into electrotonic space. In a MET, either P-ij or L(ij) replace anato mical distance as the fundamental unit and so provide direct functiona l measures of intraneuronal signaling. The analysis holds for arbitrar y transient signals, even those generated by nonlinear conductance cha nges underlying both synaptic and action potentials. Depending on inpu t location and the measure of interest, a single neuron admits many ME Ts, each emphasizing different functional consequences of the dendriti c electrotonic structure. Using a single layer 5 cortical pyramidal ne uron, we illustrate a collection of METs that lead to a deeper underst anding of the electrical behavior of its dendritic tree. We then compa re this cortical cell to representative neurons from other brain regio ns (cortical layer 2/3 pyramidal, region CA1 hippocampal pyramidal, an d cerebellar Purkinje). Finally, we apply the MET to electrical signal ing in dendritic spines, and extend this analysis to calcium signaling within spines. Our results demonstrate that the MET provides a powerf ul tool for obtaining a rapid and intuitive grasp of the functional pr operties of dendritic trees.