Electrotonically linear 1-D model: Neuronal morphology predicts somatic and dendritic tuft sensitivity to sub-threshold electric fields. A, Example morphological reconstruction of a L5 regular spiking pyramidal neuron with electric field induced somatic polarization of 0.14 mV*(mV/mm)⁻¹. The left circle indicates the largest segment diameter for this neuron’s segments, d_max. The right circle and inset illustrates a sample segment length, l; segment diameter, d; and angle with respect to the electric field, φ; used to construct the 1-D cylinder in B. B, 1-D cylinder model of transmembrane polarization. Schematic (left) represents construction of equivalent neuron with apical and basal combined cylinders and soma. Linear distribution of polarization along the equivalent neuron is plotted (right), with maximal polarization of +/− E_m √d_max at the distal ends of the neuron. Equations represent construction of apical and basal cylinders, using variables illustrated in A. C, For all reconstructed neurons, the 1-d model of B is applied to predict somatic polarization (x-axis), and correlated to experimentally recorded somatic transmembrane polarization (p < .05, r² = .55, n=30). D, The slope, m, of the best fit line in C is then used as a general membrane property constant (see Methods) that is multiplied by each individual neuron’s √d_max to predict terminal polarization. 1-D cylinder model predictions of terminal polarization, separated according to cortical cell type, yields a statistically significant difference between interneurons and L5/6 pyramidal neurons (p < .02) as well as between interneurons and L2/3 pyramidal neurons (p < .03).

Sub-threshold electric fields polarize cortical neuronal soma linearly. A, Example morphological reconstruction of a L5 pyramidal neuron (black), and L5 fast-spiking interneuron (red) B, Incrementing electric field steps of 5.8 mV/mm (bottom) linearly polarize cell soma (top). Reconstructions shown are from L5 regular spiking pyramidal neuron of A (top). C, Summary of the polarization per electric field for the neurons shown in A. The slope of the fitted line determines the sub-threshold field polarization sensitivity for each neuron. LV pyramidal neuron (black) = .27 mV*(mV/mm)⁻¹, LV fast-spiking interneuron (red) = −.02 mV*(mV/mm)⁻¹.