Is there a biological neuron that spikes in response to hyperpolarizing currents?

Question

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?

Answer 1

Short answer
Action potentials are always generated after a depolarization step.

Background
Action potentials are generated by prior depolarization of a neuron, typically by the action of an excitatory neurotransmitter. An action potential is per definition a sharp depolarization, followed by a somewhat slower re-polarization step. The most important step in an action potential is the activation of voltage-gated sodium channels (VGSCs). VGSCs open when the membrane potential exceeds a certain voltage upon depolarization (Liu et al. 2012), in turn initiating the depolarization step of the action potential. Hence, action potentials are always generated through depolarization.

The only ion channel I am aware of that may mediate a hyperpolarization-induced cation influx resembling that seen in VOSCs is the hyperpolarization-activated cyclic nucleotide-gated (HCN) class of channels. The associated current (I_h) is a non-specific cation flux (Na⁺, Ca²⁺). The HCN channel opens when the membrane potential hyperpolarizes. Thereby it generates a relatively small positive, depolarizing influx current. it is mainly involved in setting the frequency of pacemaker activity in, e.g., thalamic relay neurons that are involved in the oscillatory cortical activity characteristic of slow-wave sleep. However, I_h itself does not elicit spikes, it generates excitatory postsynaptic currents (EPSCs) associated with excitatory postsynaptic potentials (EPSPs), but not full blown spikes (McCormick & Pape, 1990).

Model evaluation and recommendations

1. Perhaps you identified EPSPs as action potentials? They are not.
2. Your resting membrane potential is very high (depolarized) - a more typical value is -70 mV.
3. VOSCs are opened at around -50 mV, hence your resting membrane potential is awfully close to action potential threshold. Any small perturbation leading to a bit cation influx will trigger action potentials. With a bit of stochastic leak currents included, a spontaneous spiking neuron is what you get. I_h (-like) activity may also set the stage for your out-of-the-ordinary observation.
4. Suggestion - lower your resting membrane potential to a more conservative value (-70 mV) and check the difference between EPSPs and action potentials. If you look at the following figure you can see that at your chosen resting membrane potential you are hovering between EPSP / actin potential threshold. A bi-stable situation results.

^{Action potential versus EPSP. Source: What when and how}

References
Liu et al. BMC Neurosci 2012;25:2-9
McCormick & Pape. J Physiol 1990;431:291-318

Answer 2

I was doing some more research and stumbled upon this paper here by Dr. Izhikevich that describe neurons as a system that can exhibit resonance. The author built a model that he calls the resonate and fire, which is a linear piece-wise model of a neuron.

The interesting thing, and why I bring it up, is it can respond to a "two inhibitory pulses, that if timed correctly will cause the neuron to fire. but neither inhibitory pulse alone can cause the neuron to fire.

Following some of the citations in the article (found here), apparently thalumus neurons can exhibit resonance and thus theoretically can fire in response to the right frequency of input. However it is important to note that they thalamic neurons are close to threshold, and are not receiving the double inhibitory input that Izhekivich talks about in his paper. The second paper uses a ZAP protocol.

A Zap protocol is injecting a Sine wave into a neuron and slowly change the frequency linearly in time.

$$I_{ZAP}(t) = \sin((\omega_0+\omega t) t) $$ where $\omega_0$ and $\omega_1$ are constants.