Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration
A, The membrane potential is clamped at a given voltage , then a constant current I is injected (iEIF model). The steady-state threshold is defined as the maximum voltage that can be reached without triggering an action potential. B, Two excitability curves dV/dt = F(V,V0)/C are shown in the phase plane , for two different initial clamp values V0 (solid lines; V0 = −80 mV and −26 mV). The steady-state threshold is the voltage at the minimum of the excitability curve for the initial voltage V0. C, Steady-state threshold (red lines) of a cortical neuron model  for the original maximal Na conductance (solid line) and for a higher and lower Na conductance (resp. bottom and top dashed line). When the cell is slowly depolarized, it spikes when , i.e., the spike threshold is the intersection of the red and black dashed curves. If there is no intersection, the neuron cannot spike with slow depolarization. The top dashed line (low Na conductance) is interrupted because the threshold is infinite at high voltages (i.e., the cell is no longer excitable).