Spike initiating dynamics of the neuron with different adaptation mechanisms to extracellular electric fields

In this paper, we address how adaptation mediated by different biophysical mechanisms modulates neuronal spike initiating dynamics to extracellular electric fields. We incorporate two adaptation currents, i.e., voltage-sensitive potassium current (IM) and calcium-sensitive potassium current (IAHP), into a reduced two-compartment neuron model, and extensively investigate the modeling behavior to a range of electric fields. With phase plane analysis, it is shown whether neuron continues to spike depends on whether adaptation currents could be sufficiently activated to stabilize membrane potential at subthreshold voltages. With stability and bifurcation analysis, we find the steady-state spiking in the neuron with IM occurs through a Hopf bifurcation, whereas it is generated through a saddle-node on invariant circle (SNIC) bifurcation in the cases of IAHP or no adaptation. By identifying the biophysical basis for these dynamics, we observe that IM could alter the competitive outcomes between kinetically mismatched opposite currents to result in a Hopf bifurcation, while IAHP cannot alter these competitive outcomes. From this, we conclude that different modulations of spike initiating dynamics derive from the biophysical mechanism responsible for distinct adaptation currents. Our study suggests that the adaptation mediated by different mechanisms indeed has different effects on neuronal dynamics to electric field stimulus. It could contribute to uncover the underlying mechanism of how neuron encodes electric field signals.