Phase Response Curves to Measure Ion Channel Effects on Neurons

In this chapter, we explore how different common ionic currents change the shape of the PRC using several well-known conductance-based models. By also studying the simplest possible network – two pulse coupled neural oscillators – we can use the shape of the PRC to quantify the degree of synchrony in such a pair. We find a number of qualitative effects that include changing the sign of the PRC during certain phases and altering the skew of the PRC. Using bifurcation theory, we trace these effects back to the underlying dynamics that govern the onset of repetitive firing as the neuron is depolarized by a constant current. The key bifurcation involves the so-called Takens-Bogdanov bifurcation. We show that many of the shape changes of the PRC can be understood by examining the dynamics of the neuron near this bifurcation.