Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration
A, The steady-state threshold curve (red curve) is well approximated by a piecewise linear curve determined by Na channel properties (top dashed black curve), where Vi is the half-inactivation voltage and VT is the non-inactivated threshold. The slope of the linear asymptote is ka/ki (resp. activation and inactivation slope parameters). Na channel properties in this figure were taken from Kuba et al. (2009). The spike threshold is variable only when , and very variable when (additionally) . B, The non-inactivated threshold VT is determined by the maximum Na conductance gNa, relative to the leak conductance gL. As the ratio increases, the steady-state threshold curve shifts downward (red curves; r = 0.4; 2; 10) and threshold variability is reduced. C, Trajectory of the model in the phase plane (blue), superimposed on the steady-state threshold curve (red). Spikes are initiated when (dashed line: ), but the empirical measurement overestimates the threshold. The spike threshold is highly variable in this example (−50 to −10 mV). D, Trajectory of the model in the phase plane (blue), superimposed on the Na inactivation curve (black). The threshold is very variable when most Na channels are inactivated. E, Voltage trace (black curve) and spike threshold (red curve; ) in the inactivating exponential model driven by a fluctuating input (see Methods), where black dots represent empirical measurement of spike onsets (first derivative method, kth = 5 mV/ms). Note that the membrane potential can exceed threshold without triggering a spike because the threshold is soft (unlike in integrate-and-fire models).