A Threshold Equation for Action Potential Initiation
All plots were generated using the single-compartment model described in the Materials and Methods. A, In vitro, the neuron is stimulated with short current pulses with increasing intensity (bottom) and the threshold is the minimal value of that intensity above which the neuron spikes (top). The voltage threshold is the value of the membrane potential at that critical point. B, The threshold can be defined similarly with current steps (bottom) or other types of parameterized stimulations, yielding different values for the voltage threshold. C, In vivo, spike “threshold” is defined as a measure of the voltage at the onset of the action potential (black dots). The plot shows a simulated trace of a conductance-based model with fluctuating conductances (see Materials and Methods) and threshold is measured with the first derivative method. D, Representation of the trace in (C) in phase space, showing dV/dt vs. V. The first derivative method consists in measuring the membrane potential V when the derivative crosses a predefined value (dashed line) shortly before an action potential. The trace is superimposed on the excitability curve dV/dt = (F(V)+I0)/C, which defines the dynamics of the model. I0 is the mean input current, so that trajectories in phase space fluctuate around this excitability curve.