Sharpness of Spike Initiation in Neurons Explained by Compartmentalization
A, Simplified electrical model of the axon initial segment (used for theoretical analysis but not for simulations). The initiation site is coupled to the soma through an axial resistance Ra. Sodium current f(Va) equals axial current (Va−Vs)/Ra. B, Sodium current (red) and lateral current (black) as a function of voltage at the initiation site when Na channels are placed at 20 µm away from the soma. The three lines correspond to somatic voltages of −60 mV, −55 mV and −50 mV. C, Same as B, with Na channels at 40 µm from the soma. D, Same as A at the critical point, with channels at 27 µm away from the soma. E, Predicted somatic spike threshold, defined as the bifurcation point, as a function of location of the initiation site (logarithmic scale) for the full formula (black) and its approximation (blue). The red curve shows the somatic voltage at which half of the sodium channels are activated in the numerical simulation of the ball-and-stick model. The dashed line is the predicted spike threshold at the critical point.