Postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents: A simulation study

Postinhibitory excitation is a transient overshoot of a neuron’s baseline firing rate following an inhibitory stimulus and can be observed in vivo in human motoneurons. However, the biophysical origin of this phenomenon is still unknown and both reflex pathways and intrinsic motoneuron properties have been proposed. We hypothesized that postinhibitory excitation in motoneurons can be facilitated by hyperpolarization-activated inward currents (h-currents). Using an electrical circuit model, we investigated how h-currents can modulate the postinhibitory response of motoneurons. Further, we analyzed the spike trains of human motor units from the tibialis anterior muscle during reciprocal inhibition. The simulations revealed that the activation of h-currents by an inhibitory postsynaptic potential can cause a short-term increase in a motoneuron’s firing probability. This result suggests that the neuron can be excited by an inhibitory stimulus. In detail, the modulation of the firing probability depends on the time delay between the inhibitory stimulus and the previous action potential. Further, the postinhibitory excitation’s strength correlates with the inhibitory stimulus’s amplitude and is negatively correlated with the baseline firing rate as well as the level of input noise. Hallmarks of h-current activity, as identified from the modeling study, were found in 50% of the human motor units that showed postinhibitory excitation. This study suggests that h-currents can facilitate postinhibitory excitation and act as a modulatory system to increase motoneuron excitability after a strong inhibition.

In the model, we injected an inhibitory postsynaptic current (IPSC) to induce an IPSP.Thereby, the duration of this current kernel was fixed to 20 ms.The IPSP caused by this current has a duration of ~50 ms, due to the integrative behavior of the motoneuron membrane.The exact duration of the IPSP depends on the timing of the current injection.The change in membrane potential in response to a particular current injection depends on the momentary value of the membrane potential and active conductances.This can be seen in Figure 5.The black trace corresponds to an undisturbed reference interspike interval, i.e., only a constant depolarizing current is applied.The inhibitory current (IPSC) was applied for 20 ms in the blue and the green trace.Even after the release of the current, the membrane potential does not directly "jump" back but gradually increases until it matches the black trace.We illustrated this behavior in the figure below.In red we marked the duration of the injected current (IPSC); in yellow we marked the duration of the IPSP.
The time course for the rising phase of the AHP you drew in red in the Figure, is impossible with the chosen inputs.The black trace corresponds to the model response for a purely excitatory (constant) input.Therefore, the increase in membrane potential will be similar to the black trace when the IPSP is over.
In Figure 3, we only showed the IPSC, because it is the input for the simulations and is constant for each simulation.However, we agree that it is common to plot the IPSP, especially in experimental (invitro) studies.Hence, Figure 3   In addition, we clarified the descriptions in the manuscript (new text is underlined):

Discussion/Limitations:
Reciprocal inhibition indirectly stimulates the motoneurons through the afferent nerve.The magnitude of the IPSP in the motoneuron inhibitory input to the motoneuron caused by interneurons is unknown.To compare the simulations and experimental data, the amplitude of the injected current was chosen such that the inhibition amplitudes and latencies determined from the PSF-cusum are in the same range as for the experimental study.In this way, we assume that the injected current produces an IPSP comparable to the in-vivo conditions.Nevertheless, a quantitative comparison of the postinhibitory excitation amplitudes of in-silico and in-vivo motoneurons is beyond the scope of this study.

Methods/Simulation of reciprocal inhibition:
The inhibitory postsynaptic current was applied for 20 ms, as this, for the chosen amplitudes, achieved the minimum firing rate at a time comparable to the experiment.The current-induced IPSP usually last longer than 20 ms (Fig 3a, b).
might cause confusion to some readers.Therefore, we added a schematic IPSP profile to the figure.Now, the figure shows both the relation between injected current and resulting IPSP and the relation between IPSP and the firing behavior.

Fig 3 .
Fig 3. Peristimulus analysis for simulated motoneurons.(a): Peristimulus frequencygram (PSF) for a simulated neuron with h-current.(b): PSF for a simulated neuron without h-current.In (a) and (b), the injected inhibitory synaptic current (IPSC) and the schematic trajectory of the induced inhibitory postsynaptic potential (IPSP) are depicted in gray and blue color, respectively.The actual time course of the membrane potential depends on the membrane potential value and the size of other inputs at IPSC application time.(c): PSF cumulative summation (PSF-cusum) for a simulated neuron with hcurrent.(d): PSF-cusum for a simulated neuron without h-current.Solid horizontal lines show prestimulus mean values and dashed lines mark the significance threshold for reflex responses.Arrows show the distance between two manually determined turning points in PSF-cusum, i.e., inhibition and excitation amplitude.