As some background I've been building Electrophysiological models of neurons, and in the process stumbled upon a model, that in all respects is biologically plausible, but has a bizarre property I didn't think happened in nature. It spikes in response to hyper polarized currents.
My particular model has only one ion channel which is has similar properties to Hodgkin-Huxley's transient sodium channel. It has one activation gate and one inactivation gate. The reason I only use a single Ion Channel was I was exploring If I could create a minimal spiking neuron with just a single channel. The answer is yes, but has different properties then I expected.
Basically when I inject a hyper-polarizing current it spikes and depolarizing current causes it to stop spiking.
I know that Depolarization block can occur, my current isn't that High, in fact its no current produces no spikes. It has a normal rest potential around -55 mV and Fires upward to about +40 mV.
Also note that If I change the parameters around I get a more normal neuron that spikes in response to depolarizing currents. So the property must be somehow related to the ion channel kinetics.
The question is: Are there biological neurons that spike when hyper-polarizing currents are injected?